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# -*- coding: utf-8 -*-
"""
:mod:`orion.algo.robo.rbayes -- TODO
============================================
.. module:: robo
:platform: Unix
:synopsis: TODO
TODO: Write long description
"""
import george
import numpy
from robo.acquisition_functions.ei import EI
from robo.acquisition_functions.lcb import LCB
from robo.acquisition_functions.log_ei import LogEI
from robo.acquisition_functions.marginalization import MarginalizationGPMCMC
from robo.acquisition_functions.pi import PI
from robo.initial_design import init_latin_hypercube_sampling
from robo.maximizers.differential_evolution import DifferentialEvolution
from robo.maximizers.random_sampling import RandomSampling
from robo.maximizers.scipy_optimizer import SciPyOptimizer
from robo.models.gaussian_process import GaussianProcess
from robo.models.gaussian_process_mcmc import GaussianProcessMCMC
from robo.models.random_forest import RandomForest
from robo.models.wrapper_bohamiann import WrapperBohamiann
from robo.priors.default_priors import DefaultPrior
from robo.solver.bayesian_optimization import BayesianOptimization
from orion.algo.base import BaseAlgorithm
from orion.algo.space import Space
def build_bounds(space):
"""
Build bounds of optimization space
:param space:
"""
lower = numpy.zeros(len(space.keys()))
upper = numpy.zeros(len(space.keys()))
for i, (_name, dim) in enumerate(space.items()):
lower[i], upper[i] = dim.interval()
if dim.prior_name == 'reciprocal':
lower[i] = numpy.log(lower[i])
upper[i] = numpy.log(upper[i])
return lower, upper
def build_optimizer(model, maximizer="random", acquisition_func="log_ei", maximizer_seed=1):
"""
General interface for Bayesian optimization for global black box
optimization problems.
Parameters
----------
maximizer: {"random", "scipy", "differential_evolution"}
The optimizer for the acquisition function.
acquisition_func: {"ei", "log_ei", "lcb", "pi"}
The acquisition function
maximizer_seed: int
Seed for random number generator of the acquisition function maximizer
Returns
-------
Optimizer
:param maximizer_seed:
:param acquisition_func:
:param maximizer:
:param model:
"""
if acquisition_func == "ei":
a = EI(model)
elif acquisition_func == "log_ei":
a = LogEI(model)
elif acquisition_func == "pi":
a = PI(model)
elif acquisition_func == "lcb":
a = LCB(model)
else:
raise ValueError("'{}' is not a valid acquisition function"
.format(acquisition_func))
if isinstance(model, GaussianProcessMCMC):
acquisition_func = MarginalizationGPMCMC(a)
else:
acquisition_func = a
maximizer_rng = | numpy.random.RandomState(maximizer_seed) | numpy.random.RandomState |
import numpy as np
# Simple feedforward neural network:
#
# x (input layer) -> hidden layers -> y (output layer) -> backpropagation -> ...
#
# Forward pass:
# a_i = sigmoid(w_i.a_{i-1} + b_i)
# => a = (a_1, ..., a_m)
#
# Backpropagation:
# - updates weights and biases by trying to find the minimum of the
# loss function (i.e. stochastic gradient descent)
#
# Note: use automatic differentiation instead of symbolic differentiation. (How???)
class FNN():
'''
How is this used:
1. Initialize the neural network
model = fnn(input_size, output_size, hidden_layer_size, activation_function)
model.initialize_weights_and_biases()
2. Set the loss funciton and optimizer and compile
3. Training
4. Prediction
'''
def __init__(self, input_size, output_size, hidden_layer_sizes, activation_function):
self.input_size = input_size
self.output_size = output_size
self.hidden_layer_sizes = hidden_layer_sizes
self.activation_function = activation_function
self.Ws = None
self.Bs = None
self.loss_function = None
self.optimizer = None
def initialize_weights_and_biases(self):
'''
Set the weights and biases to some random values
'''
Ws = []
Bs = []
# Mapping from input layer into the 1. hidden layer
W = np.random.normal(size=(self.hidden_layer_sizes[0], self.input_size))
B = np.random.normal(size=self.hidden_layer_sizes[0])
Ws.append(W)
Bs.append(B)
for i in range(1, len(self.hidden_layer_sizes)):
# Mapping from i-1. to i. hidden layer
W = np.random.normal(size=(self.hidden_layer_sizes[i], self.hidden_layer_sizes[i-1]))
B = np.random.normal(size=self.hidden_layer_sizes[i])
Ws.append(W)
Bs.append(B)
# Mapping from the last hidden layer into the output layer
W = np.random.normal(size=(self.output_size, self.hidden_layer_sizes[-1]))
B = np.random.normal(size=self.output_size)
Ws.append(W)
Bs.append(B)
self.Ws = Ws
self.Bs = Bs
def forward_propagation(self, x):
'''
Calculation from the input layer to the output layer using the currect
weights and biases.
'''
# Input layer:
a = x.copy()
# Hidden layers + output layer:
for i in range(len(self.hidden_layer_sizes) + 1):
# Error: ?????
Wi = self.Ws[i]
Bi = self.Bs[i]
a = self.activation_function(Wi.dot(a) + Bi) # == activation_function(matmul(Wi, a) + Bi)
return a
# # Should this particular loss function and gradient descent for it
# # be done in a separate class?
# def loss_function(self, y_true, y_pred):
# '''
# Mean squarred error (MSE) = (1/n) sum_{i=1}^n (y_true - y_pred)^2
# where n is the number of observartion.
# '''
# # sum over all of (y_pred - y_true)**2
# pass
# def gradient_descent(self):
# '''
# -grad(loss_function(Ws, Bs)) = -grad(C(Ws, Bs))
# = - dC/dw1 - dC/dw2 - ... - dC/dB1 - ...
# where each weight and bias of each layer are summed.
# '''
# # Can this be done more simply and quickly, using Numpy for example?
# gradient = []
# for W in Ws:
# for w in W:
# # Do the gradient with w
# for B in Bs:
# for b in B:
# # do the gradient with b
# return gradient
def backpropagation(self):
'''
Updates the weighs and biases
'''
pass
def compile(self):
pass
def training(self, epochs):
'''
forwar propagation + backpropagtion
'''
pass
# Some (common) loss function
class MeanAbsoluteError:
'''
The loss/cost function:
L = sum_{i=1}^n (y_pred_i - y_true_i)^2
and its
'''
def __init__(self):
pass
def loss_function(self, y_pred, y_true):
return np.sum((y_pred - y_true)**2)
def gradient_descent(self):
pass
# Some (common) activation function
def sigmoid(x):
return 1 / (1 + | np.exp(-x) | numpy.exp |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import dataclasses
from typing import List
import numpy as np
from scipy.misc import derivative
from scipy.interpolate import interp1d
from scipy.integrate import solve_ivp
from .ship_obj_3dof import ShipObj3dof
@dataclasses.dataclass
class Mmg3DofBasicParams:
"""Dataclass for setting basic parameters of MMG 3DOF.
Attributes:
L_pp (float):
Ship length between perpendiculars [m]
B (float):
Ship breadth [m]
d (float):
Ship draft [m]
x_G (float):
Longitudinal coordinate of center of gravity of ship [m]
D_p (float):
Propeller diameter [m]
m (float):
Ship mass [kg]
I_zG (float):
Moment of inertia of ship around center of gravity
A_R (float):
Profile area of movable part of mariner rudder [m^2]
η (float):
Ratio of propeller diameter to rudder span (=D_p/HR)
m_x (float):
Added masses of x axis direction [kg]
m_y (float):
Added masses of y axis direction [kg]
J_z (float):
Added moment of inertia
f_α (float):
Rudder lift gradient coefficient
ϵ (float):
Ratio of wake fraction at propeller and rudder positions
t_R (float):
Steering resistance deduction factor
a_H (float):
Rudder force increase factor
x_H (float):
Longitudinal coordinate of acting point of the additional lateral force component induced by steering
γ_R_minus (float):
Flow straightening coefficient if βR < 0
γ_R_plus (float):
Flow straightening coefficient if βR > 0
l_R (float):
Effective longitudinal coordinate of rudder position in formula of βR
κ (float):
An experimental constant for expressing uR
t_P (float):
Thrust deduction factor
w_P0 (float):
Wake coefficient at propeller position in straight moving
x_P (float):
Effective Longitudinal coordinate of propeller position in formula of βP
Note:
For more information, please see the following articles.
- <NAME>., <NAME>. (2015) Introduction of MMG standard method for ship maneuvering predictions.
J Mar Sci Technol 20, 37–52 https://doi.org/10.1007/s00773-014-0293-y
"""
L_pp: float
B: float
d: float
x_G: float
D_p: float
m: float
I_zG: float
A_R: float
η: float
m_x: float
m_y: float
J_z: float
f_α: float
ϵ: float
t_R: float
a_H: float
x_H: float
γ_R_minus: float
γ_R_plus: float
l_R: float
κ: float
t_P: float
w_P0: float
x_P: float
@dataclasses.dataclass
class Mmg3DofManeuveringParams:
"""Dataclass for setting maneuvering parameters of MMG 3ODF.
Attributes:
k_0 (float): One of manuevering parameters of coefficients representing K_T
k_1 (float): One of manuevering parameters of coefficients representing K_T
k_2 (float): One of manuevering parameters of coefficients representing K_T
R_0_dash (float): One of manuevering parameters of Ship resistance coefficient in straight moving
X_vv_dash (float): One of manuevering parameters of MMG 3DOF
X_vr_dash (float): One of manuevering parameters of MMG 3DOF
X_rr_dash (float): One of manuevering parameters of MMG 3DOF
X_vvvv_dash (float): One of manuevering parameters of MMG 3DOF
Y_v_dash (float): One of manuevering parameters of MMG 3DOF
Y_r_dash (float): One of manuevering parameters of MMG 3DOF
Y_vvv_dash (float): One of manuevering parameters of MMG 3DOF
Y_vvr_dash (float): One of manuevering parameters of MMG 3DOF
Y_vrr_dash (float): One of manuevering parameters of MMG 3DOF
Y_rrr_dash (float): One of manuevering parameters of MMG 3DOF
N_v_dash (float): One of manuevering parameters of MMG 3DOF
N_r_dash (float): One of manuevering parameters of MMG 3DOF
N_vvv_dash (float): One of manuevering parameters of MMG 3DOF
N_vvr_dash (float): One of manuevering parameters of MMG 3DOF
N_vrr_dash (float): One of manuevering parameters of MMG 3DOF
N_rrr_dash (float): One of manuevering parameters of MMG 3DOF
Note:
For more information, please see the following articles.
- <NAME>., <NAME>. (2015) Introduction of MMG standard method for ship maneuvering predictions.
J Mar Sci Technol 20, 37–52 https://doi.org/10.1007/s00773-014-0293-y
"""
k_0: float
k_1: float
k_2: float
R_0_dash: float
X_vv_dash: float
X_vr_dash: float
X_rr_dash: float
X_vvvv_dash: float
Y_v_dash: float
Y_r_dash: float
Y_vvv_dash: float
Y_vvr_dash: float
Y_vrr_dash: float
Y_rrr_dash: float
N_v_dash: float
N_r_dash: float
N_vvv_dash: float
N_vvr_dash: float
N_vrr_dash: float
N_rrr_dash: float
def simulate_mmg_3dof(
basic_params: Mmg3DofBasicParams,
maneuvering_params: Mmg3DofManeuveringParams,
time_list: List[float],
δ_list: List[float],
npm_list: List[float],
u0: float = 0.0,
v0: float = 0.0,
r0: float = 0.0,
ρ: float = 1.025,
method: str = "RK45",
t_eval=None,
events=None,
vectorized=False,
**options
):
"""MMG 3DOF simulation
MMG 3DOF simulation by follwoing equation of motion.
.. math::
m (\\dot{u}-vr)&=-m_x\\dot{u}+m_yvr+X_H+X_P+X_R
m (\\dot{v}+ur)&=-m_y\\dot{v}+m_xur+Y_H+Y_R
I_{zG}\\dot{r}&=-J_Z\\dot{r}+N_H+N_R
Args:
basic_params (Mmg3DofBasicParams):
Basic paramters for MMG 3DOF simulation.
maneuvering_params (Mmg3DofManeuveringParams):
Maneuvering parameters for MMG 3DOF simulation.
time_list (list[float]):
time list of simulation.
δ_list (list[float]):
rudder angle list of simulation.
npm_list (List[float]):
npm list of simulation.
u0 (float, optional):
axial velocity [m/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
v0 (float, optional):
lateral velocity [m/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
r0 (float, optional):
rate of turn [rad/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
ρ (float, optional):
seawater density [kg/m^3]
Defaults to 1.025.
method (str, optional):
Integration method to use in
`scipy.integrate.solve_ivp()
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html>`_:
"RK45" (default):
Explicit Runge-Kutta method of order 5(4).
The error is controlled assuming accuracy of the fourth-order method,
but steps are taken using the fifth-order accurate formula (local extrapolation is done).
A quartic interpolation polynomial is used for the dense output.
Can be applied in the complex domain.
"RK23":
Explicit Runge-Kutta method of order 3(2).
The error is controlled assuming accuracy of the second-order method,
but steps are taken using the third-order accurate formula (local extrapolation is done).
A cubic Hermite polynomial is used for the dense output.
Can be applied in the complex domain.
"DOP853":
Explicit Runge-Kutta method of order 8.
Python implementation of the “DOP853” algorithm originally written in Fortran.
A 7-th order interpolation polynomial accurate to 7-th order is used for the dense output.
Can be applied in the complex domain.
"Radau":
Implicit Runge-Kutta method of the Radau IIA family of order 5.
The error is controlled with a third-order accurate embedded formula.
A cubic polynomial which satisfies the collocation conditions is used for the dense output.
"BDF":
Implicit multi-step variable-order (1 to 5) method
based on a backward differentiation formula for the derivative approximation.
A quasi-constant step scheme is used and accuracy is enhanced using the NDF modification.
Can be applied in the complex domain.
"LSODA":
Adams/BDF method with automatic stiffness detection and switching.
This is a wrapper of the Fortran solver from ODEPACK.
t_eval (array_like or None, optional):
Times at which to store the computed solution, must be sorted and lie within t_span.
If None (default), use points selected by the solver.
events (callable, or list of callables, optional):
Events to track. If None (default), no events will be tracked.
Each event occurs at the zeros of a continuous function of time and state.
Each function must have the signature event(t, y) and return a float.
The solver will find an accurate value of t at which event(t, y(t)) = 0 using a root-finding algorithm.
By default, all zeros will be found. The solver looks for a sign change over each step,
so if multiple zero crossings occur within one step, events may be missed.
Additionally each event function might have the following attributes:
terminal (bool, optional):
Whether to terminate integration if this event occurs. Implicitly False if not assigned.
direction (float, optional):
Direction of a zero crossing.
If direction is positive, event will only trigger when going from negative to positive,
and vice versa if direction is negative.
If 0, then either direction will trigger event. Implicitly 0 if not assigned.
You can assign attributes like `event.terminal = True` to any function in Python.
vectorized (bool, optional):
Whether `fun` is implemented in a vectorized fashion. Default is False.
options:
Options passed to a chosen solver.
All options available for already implemented solvers are listed in
`scipy.integrate.solve_ivp()
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html>`_:
Returns:
Bunch object with the following fields defined:
t (ndarray, shape (`n_points`,)):
Time points.
y (ndarray, shape (`n_points`,)):
Values of the solution at t.
sol (OdeSolution):
Found solution as OdeSolution instance from MMG 3DOF simulation.
t_events (list of ndarray or None):
Contains for each event type a list of arrays at which an event of that type event was detected.
None if events was None.
y_events (list of ndarray or None):
For each value of t_events, the corresponding value of the solution.
None if events was None.
nfev (int):
Number of evaluations of the right-hand side.
njev (int):
Number of evaluations of the jacobian.
nlu (int):
Number of LU decomposition.
status (int):
Reason for algorithm termination:
- -1: Integration step failed.
- 0: The solver successfully reached the end of `tspan`.
- 1: A termination event occurred.
message (string):
Human-readable description of the termination reason.
success (bool):
True if the solver reached the interval end or a termination event occurred (`status >= 0`).
Examples:
>>> duration = 200 # [s]
>>> sampling = 2000
>>> time_list = np.linspace(0.00, duration, sampling)
>>> δ_list = np.full(len(time_list), 35.0 * np.pi / 180.0)
>>> npm_list = np.full(len(time_list), 20.338)
>>> basic_params = Mmg3DofBasicParams(
>>> L_pp=7.00,
>>> B=1.27,
>>> d=0.46,
>>> x_G=0.25,
>>> D_p=0.216,
>>> m=3.27*1.025,
>>> I_zG=m*((0.25 * L_pp) ** 2),
>>> A_R=0.0539,
>>> η=D_p/0.345,
>>> m_x=0.022*(0.5 * ρ * (L_pp ** 2) * d),
>>> m_y=0.223*(0.5 * ρ * (L_pp ** 2) * d),
>>> J_z=0.011*(0.5 * ρ * (L_pp ** 4) * d),
>>> f_α=2.747,
>>> ϵ=1.09,
>>> t_R=0.387,
>>> a_H=0.312,
>>> x_H=-0.464*L_pp,
>>> γ_R_minus=0.395,
>>> γ_R_plus=0.640,
>>> l_R=-0.710,
>>> κ=0.50,
>>> t_P=0.220,
>>> w_P0=0.40,
>>> x_P=-0.650,
>>> )
>>> maneuvering_params = Mmg3DofManeuveringParams(
>>> k_0 = 0.2931,
>>> k_1 = -0.2753,
>>> k_2 = -0.1385,
>>> R_0_dash = 0.022,
>>> X_vv_dash = -0.040,
>>> X_vr_dash = 0.002,
>>> X_rr_dash = 0.011,
>>> X_vvvv_dash = 0.771,
>>> Y_v_dash = -0.315,
>>> Y_r_dash = 0.083,
>>> Y_vvv_dash = -1.607,
>>> Y_vvr_dash = 0.379,
>>> Y_vrr_dash = -0.391,
>>> Y_rrr_dash = 0.008,
>>> N_v_dash = -0.137,
>>> N_r_dash = -0.049,
>>> N_vvv_dash = -0.030,
>>> N_vvr_dash = -0.294,
>>> N_vrr_dash = 0.055,
>>> N_rrr_dash = -0.013,
>>> )
>>> sol = simulate_mmg_3dof(
>>> basic_params,
>>> maneuvering_params,
>>> time_list,
>>> δ_rad_list,
>>> npm_list,
>>> u0=2.29 * 0.512,
>>> )
>>> result = sol.sol(time_list)
Note:
For more information, please see the following articles.
- <NAME>., <NAME>. (2015) Introduction of MMG standard method for ship maneuvering predictions.
J Mar Sci Technol 20, 37–52 https://doi.org/10.1007/s00773-014-0293-y
"""
return simulate(
L_pp=basic_params.L_pp,
B=basic_params.B,
d=basic_params.d,
x_G=basic_params.x_G,
D_p=basic_params.D_p,
m=basic_params.m,
I_zG=basic_params.I_zG,
A_R=basic_params.A_R,
η=basic_params.η,
m_x=basic_params.m_x,
m_y=basic_params.m_y,
J_z=basic_params.J_z,
f_α=basic_params.f_α,
ϵ=basic_params.ϵ,
t_R=basic_params.t_R,
a_H=basic_params.a_H,
x_H=basic_params.x_H,
γ_R_minus=basic_params.γ_R_minus,
γ_R_plus=basic_params.γ_R_plus,
l_R=basic_params.l_R,
κ=basic_params.κ,
t_P=basic_params.t_P,
w_P0=basic_params.w_P0,
x_P=basic_params.x_P,
k_0=maneuvering_params.k_0,
k_1=maneuvering_params.k_1,
k_2=maneuvering_params.k_2,
R_0_dash=maneuvering_params.R_0_dash,
X_vv_dash=maneuvering_params.X_vv_dash,
X_vr_dash=maneuvering_params.X_vr_dash,
X_rr_dash=maneuvering_params.X_rr_dash,
X_vvvv_dash=maneuvering_params.X_vvvv_dash,
Y_v_dash=maneuvering_params.Y_v_dash,
Y_r_dash=maneuvering_params.Y_r_dash,
Y_vvv_dash=maneuvering_params.Y_vvv_dash,
Y_vvr_dash=maneuvering_params.Y_vvr_dash,
Y_vrr_dash=maneuvering_params.Y_vrr_dash,
Y_rrr_dash=maneuvering_params.Y_rrr_dash,
N_v_dash=maneuvering_params.N_v_dash,
N_r_dash=maneuvering_params.N_r_dash,
N_vvv_dash=maneuvering_params.N_vvv_dash,
N_vvr_dash=maneuvering_params.N_vvr_dash,
N_vrr_dash=maneuvering_params.N_vrr_dash,
N_rrr_dash=maneuvering_params.N_rrr_dash,
time_list=time_list,
δ_list=δ_list,
npm_list=npm_list,
u0=u0,
v0=v0,
r0=r0,
ρ=ρ,
method=method,
t_eval=t_eval,
events=events,
vectorized=vectorized,
**options
)
def simulate(
L_pp: float,
B: float,
d: float,
x_G: float,
D_p: float,
m: float,
I_zG: float,
A_R: float,
η: float,
m_x: float,
m_y: float,
J_z: float,
f_α: float,
ϵ: float,
t_R: float,
a_H: float,
x_H: float,
γ_R_minus: float,
γ_R_plus: float,
l_R: float,
κ: float,
t_P: float,
w_P0: float,
x_P: float,
k_0: float,
k_1: float,
k_2: float,
R_0_dash: float,
X_vv_dash: float,
X_vr_dash: float,
X_rr_dash: float,
X_vvvv_dash: float,
Y_v_dash: float,
Y_r_dash: float,
Y_vvv_dash: float,
Y_vvr_dash: float,
Y_vrr_dash: float,
Y_rrr_dash: float,
N_v_dash: float,
N_r_dash: float,
N_vvv_dash: float,
N_vvr_dash: float,
N_vrr_dash: float,
N_rrr_dash: float,
time_list: List[float],
δ_list: List[float],
npm_list: List[float],
u0: float = 0.0,
v0: float = 0.0,
r0: float = 0.0,
ρ: float = 1.025,
method: str = "RK45",
t_eval=None,
events=None,
vectorized=False,
**options
):
"""MMG 3DOF simulation
MMG 3DOF simulation by follwoing equation of motion.
.. math::
m (\\dot{u}-vr)&=-m_x\\dot{u}+m_yvr+X_H+X_P+X_R
m (\\dot{v}+ur)&=-m_y\\dot{v}+m_xur+Y_H+Y_R
I_{zG}\\dot{r}&=-J_Z\\dot{r}+N_H+N_R
Args:
L_pp (float):
Ship length between perpendiculars [m]
B (float):
Ship breadth [m]
d (float):
Ship draft [m]
x_G (float):
Longitudinal coordinate of center of gravity of ship
D_p (float):
Propeller diameter [m]
m (float):
Ship mass [kg]
I_zG (float):
Moment of inertia of ship around center of gravity
A_R (float):
Profile area of movable part of mariner rudder [m^2]
η (float):
Ratio of propeller diameter to rudder span (=D_p/HR)
m_x (float):
Added masses of x axis direction [kg]
m_y (float):
Added masses of y axis direction [kg]
J_z (float):
Added moment of inertia
f_α (float):
Rudder lift gradient coefficient
ϵ (float):
Ratio of wake fraction at propeller and rudder positions
t_R (float):
Steering resistance deduction factor
a_H (float):
Rudder force increase factor
x_H (float):
Longitudinal coordinate of acting point of the additional lateral force component induced by steering
γ_R_minus (float):
Flow straightening coefficient if βR < 0
γ_R_plus (float):
Flow straightening coefficient if βR > 0
l_R (float):
Effective longitudinal coordinate of rudder position in formula of βR
κ (float):
An experimental constant for expressing uR
t_P (float):
Thrust deduction factor
w_P0 (float):
Wake coefficient at propeller position in straight moving
x_P (float):
Effective Longitudinal coordinate of propeller position in formula of βP
k_0 (float):
One of manuevering parameters of coefficients representing K_T
k_1 (float):
One of manuevering parameters of coefficients representing K_T
k_2 (float):
One of manuevering parameters of coefficients representing K_T
R_0_dash (float):
One of manuevering parameters of MMG 3DOF
X_vv_dash (float):
One of manuevering parameters of MMG 3DOF
X_vr_dash (float):
One of manuevering parameters of MMG 3DOF
X_rr_dash (float):
One of manuevering parameters of MMG 3DOF
X_vvvv_dash (float):
One of manuevering parameters of MMG 3DOF
Y_v_dash (float):
One of manuevering parameters of MMG 3DOF
Y_r_dash (float):
One of manuevering parameters of MMG 3DOF
Y_vvv_dash (float):
One of manuevering parameters of MMG 3DOF
Y_vvr_dash (float):
One of manuevering parameters of MMG 3DOF
Y_vrr_dash (float):
One of manuevering parameters of MMG 3DOF
Y_rrr_dash (float):
One of manuevering parameters of MMG 3DOF
N_v_dash (float):
One of manuevering parameters of MMG 3DOF
N_r_dash (float):
One of manuevering parameters of MMG 3DOF
N_vvv_dash (float):
One of manuevering parameters of MMG 3DOF
N_vvr_dash (float):
One of manuevering parameters of MMG 3DOF
N_vrr_dash (float):
One of manuevering parameters of MMG 3DOF
N_rrr_dash (float):
One of manuevering parameters of MMG 3DOF
time_list (list[float]):
time list of simulation.
δ_list (list[float]):
rudder angle list of simulation.
npm_list (List[float]):
npm list of simulation.
u0 (float, optional):
axial velocity [m/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
v0 (float, optional):
lateral velocity [m/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
r0 (float, optional):
rate of turn [rad/s] in initial condition (`time_list[0]`).
Defaults to 0.0.
ρ (float, optional):
seawater density [kg/m^3]
Defaults to 1.025.
method (str, optional):
Integration method to use in
`scipy.integrate.solve_ivp()
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html>`_:
"RK45" (default):
Explicit Runge-Kutta method of order 5(4).
The error is controlled assuming accuracy of the fourth-order method,
but steps are taken using the fifth-order accurate formula (local extrapolation is done).
A quartic interpolation polynomial is used for the dense output.
Can be applied in the complex domain.
"RK23":
Explicit Runge-Kutta method of order 3(2).
The error is controlled assuming accuracy of the second-order method,
but steps are taken using the third-order accurate formula (local extrapolation is done).
A cubic Hermite polynomial is used for the dense output.
Can be applied in the complex domain.
"DOP853":
Explicit Runge-Kutta method of order 8.
Python implementation of the “DOP853” algorithm originally written in Fortran.
A 7-th order interpolation polynomial accurate to 7-th order is used for the dense output.
Can be applied in the complex domain.
"Radau":
Implicit Runge-Kutta method of the Radau IIA family of order 5.
The error is controlled with a third-order accurate embedded formula.
A cubic polynomial which satisfies the collocation conditions is used for the dense output.
"BDF":
Implicit multi-step variable-order (1 to 5) method
based on a backward differentiation formula for the derivative approximation.
A quasi-constant step scheme is used and accuracy is enhanced using the NDF modification.
Can be applied in the complex domain.
"LSODA":
Adams/BDF method with automatic stiffness detection and switching.
This is a wrapper of the Fortran solver from ODEPACK.
t_eval (array_like or None, optional):
Times at which to store the computed solution, must be sorted and lie within t_span.
If None (default), use points selected by the solver.
events (callable, or list of callables, optional):
Events to track. If None (default), no events will be tracked.
Each event occurs at the zeros of a continuous function of time and state.
Each function must have the signature event(t, y) and return a float.
The solver will find an accurate value of t at which event(t, y(t)) = 0 using a root-finding algorithm.
By default, all zeros will be found. The solver looks for a sign change over each step,
so if multiple zero crossings occur within one step, events may be missed.
Additionally each event function might have the following attributes:
terminal (bool, optional):
Whether to terminate integration if this event occurs. Implicitly False if not assigned.
direction (float, optional):
Direction of a zero crossing.
If direction is positive, event will only trigger when going from negative to positive,
and vice versa if direction is negative.
If 0, then either direction will trigger event. Implicitly 0 if not assigned.
You can assign attributes like `event.terminal = True` to any function in Python.
vectorized (bool, optional):
Whether `fun` is implemented in a vectorized fashion. Default is False.
options:
Options passed to a chosen solver.
All options available for already implemented solvers are listed in
`scipy.integrate.solve_ivp()
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html>`_:
Returns:
Bunch object with the following fields defined:
t (ndarray, shape (`n_points`,)):
Time points.
y (ndarray, shape (`n_points`,)):
Values of the solution at t.
sol (OdeSolution):
Found solution as OdeSolution instance from MMG 3DOF simulation.
t_events (list of ndarray or None):
Contains for each event type a list of arrays at which an event of that type event was detected.
None if events was None.
y_events (list of ndarray or None):
For each value of t_events, the corresponding value of the solution.
None if events was None.
nfev (int):
Number of evaluations of the right-hand side.
njev (int):
Number of evaluations of the jacobian.
nlu (int):
Number of LU decomposition.
status (int):
Reason for algorithm termination:
- -1: Integration step failed.
- 0: The solver successfully reached the end of `tspan`.
- 1: A termination event occurred.
message (string):
Human-readable description of the termination reason.
success (bool):
True if the solver reached the interval end or a termination event occurred (`status >= 0`).
Examples:
>>> duration = 200 # [s]
>>> sampling = 2000
>>> time_list = np.linspace(0.00, duration, sampling)
>>> δ_list = np.full(len(time_list), 35.0 * np.pi / 180.0)
>>> npm_list = np.full(len(time_list), 17.95)
>>> L_pp=7.00
>>> B=1.27
>>> d=0.46
>>> x_G=0.25
>>> D_p=0.216
>>> m=3.27*1.025
>>> I_zG=m*((0.25 * L_pp) ** 2)
>>> A_R=0.0539
>>> η=D_p/0.345
>>> m_x=0.022*(0.5 * ρ * (L_pp ** 2) * d)
>>> m_y=0.223*(0.5 * ρ * (L_pp ** 2) * d)
>>> J_z=0.011*(0.5 * ρ * (L_pp ** 4) * d)
>>> f_α=2.747
>>> ϵ=1.09
>>> t_R=0.387
>>> a_H=0.312
>>> x_H=-0.464*L_pp
>>> γ_R=0.395
>>> l_R=-0.710
>>> κ=0.50
>>> t_P=0.220
>>> w_P0=0.40
>>> x_P=-0.650
>>> k_0 = 0.2931
>>> k_1 = -0.2753
>>> k_2 = -0.1385
>>> R_0_dash = 0.022
>>> X_vv_dash = -0.040
>>> X_vr_dash = 0.002
>>> X_rr_dash = 0.011
>>> X_vvvv_dash = 0.771
>>> Y_v_dash = -0.315
>>> Y_r_dash = 0.083
>>> Y_vvv_dash = -1.607
>>> Y_vvr_dash = 0.379
>>> Y_vrr_dash = -0.391
>>> Y_rrr_dash = 0.008
>>> N_v_dash = -0.137
>>> N_r_dash = -0.049
>>> N_vvv_dash = -0.030
>>> N_vvr_dash = -0.294
>>> N_vrr_dash = 0.055
>>> N_rrr_dash = -0.013
>>> sol = simulate_mmg_3dof(
>>> L_pp=L_pp,
>>> B=B,
>>> d=d,
>>> x_G=x_G,
>>> D_p=D_p,
>>> m=m,
>>> I_zG=I_zG,
>>> A_R=A_R,
>>> η=η,
>>> m_x=m_x,
>>> m_y=m_y,
>>> J_z=J_z,
>>> f_α=f_α,
>>> ϵ=ϵ,
>>> t_R=t_R,
>>> a_H=a_H,
>>> x_H=x_H,
>>> γ_R=γ_R,
>>> l_R=l_R,
>>> κ=κ,
>>> t_P=t_P,
>>> w_P0=w_P0,
>>> x_P=x_P,
>>> k_0=k_0,
>>> k_1=k_1,
>>> k_2=k_2,
>>> X_0=X_0,
>>> X_ββ=X_ββ,
>>> X_βγ=X_βγ,
>>> X_γγ=X_γγ,
>>> X_vvvv_dash=X_vvvv_dash,
>>> Y_β=Y_β,
>>> Y_γ=Y_γ,
>>> Y_βββ=Y_βββ,
>>> Y_vvr_dash=Y_vvr_dash,
>>> Y_vrr_dash=Y_vrr_dash,
>>> Y_rrr_dash=Y_rrr_dash,
>>> N_β=N_β,
>>> N_γ=N_γ,
>>> N_vvv_dash=N_vvv_dash,
>>> N_vvr_dash=N_vvr_dash,
>>> N_vrr_dash=N_vrr_dash,
>>> N_rrr_dash=N_rrr_dash,
>>> time_list,
>>> δ_rad_list,
>>> npm_list,
>>> u0=2.29 * 0.512,
>>> )
>>> result = sol.sol(time_list)
Note:
For more information, please see the following articles.
- <NAME>., <NAME>. (2015) Introduction of MMG standard method for ship maneuvering predictions.
J Mar Sci Technol 20, 37–52 https://doi.org/10.1007/s00773-014-0293-y
"""
spl_δ = interp1d(time_list, δ_list, "cubic", fill_value="extrapolate")
spl_npm = interp1d(time_list, npm_list, "cubic", fill_value="extrapolate")
def mmg_3dof_eom_solve_ivp(t, X):
u, v, r, δ, npm = X
U = np.sqrt(u ** 2 + (v - r * x_G) ** 2)
β = 0.0 if U == 0.0 else np.arcsin(-(v - r * x_G) / U)
v_dash = 0.0 if U == 0.0 else v / U
r_dash = 0.0 if U == 0.0 else r * L_pp / U
# w_P = w_P0
w_P = w_P0 * np.exp(-4.0 * (β - x_P * r_dash) ** 2)
J = 0.0 if npm == 0.0 else (1 - w_P) * u / (npm * D_p)
K_T = k_0 + k_1 * J + k_2 * J ** 2
β_R = β - l_R * r_dash
γ_R = γ_R_minus if β_R < 0.0 else γ_R_plus
v_R = U * γ_R * β_R
u_R = (
np.sqrt(η * (κ * ϵ * 8.0 * k_0 * npm ** 2 * D_p ** 4 / np.pi) ** 2)
if J == 0.0
else u
* (1 - w_P)
* ϵ
* np.sqrt(
η * (1.0 + κ * (np.sqrt(1.0 + 8.0 * K_T / (np.pi * J ** 2)) - 1)) ** 2
+ (1 - η)
)
)
U_R = np.sqrt(u_R ** 2 + v_R ** 2)
α_R = δ - np.arctan2(v_R, u_R)
F_N = 0.5 * A_R * ρ * f_α * (U_R ** 2) * np.sin(α_R)
X_H = (
0.5
* ρ
* L_pp
* d
* (U ** 2)
* (
-R_0_dash
+ X_vv_dash * (v_dash ** 2)
+ X_vr_dash * v_dash * r_dash
+ X_rr_dash * (r_dash ** 2)
+ X_vvvv_dash * (v_dash ** 4)
)
)
X_R = -(1 - t_R) * F_N * np.sin(δ)
X_P = (1 - t_P) * ρ * K_T * npm ** 2 * D_p ** 4
Y_H = (
0.5
* ρ
* L_pp
* d
* (U ** 2)
* (
Y_v_dash * v_dash
+ Y_r_dash * r_dash
+ Y_vvv_dash * (v_dash ** 3)
+ Y_vvr_dash * (v_dash ** 2) * r_dash
+ Y_vrr_dash * v_dash * (r_dash ** 2)
+ Y_rrr_dash * (r_dash ** 3)
)
)
Y_R = -(1 + a_H) * F_N * np.cos(δ)
N_H = (
0.5
* ρ
* (L_pp ** 2)
* d
* (U ** 2)
* (
N_v_dash * v_dash
+ N_r_dash * r_dash
+ N_vvv_dash * (v_dash ** 3)
+ N_vvr_dash * (v_dash ** 2) * r_dash
+ N_vrr_dash * v_dash * (r_dash ** 2)
+ N_rrr_dash * (r_dash ** 3)
)
)
N_R = -(-0.5 + a_H * x_H) * F_N * np.cos(δ)
d_u = ((X_H + X_R + X_P) + (m + m_y) * v * r + x_G * m * (r ** 2)) / (m + m_x)
d_v = (
(x_G ** 2) * (m ** 2) * u * r
- (N_H + N_R) * x_G * m
+ ((Y_H + Y_R) - (m + m_x) * u * r) * (I_zG + J_z + (x_G ** 2) * m)
) / ((I_zG + J_z + (x_G ** 2) * m) * (m + m_y) - (x_G ** 2) * (m ** 2))
d_r = (N_H + N_R - x_G * m * (d_v + u * r)) / (I_zG + J_z + (x_G ** 2) * m)
d_δ = derivative(spl_δ, t)
d_npm = derivative(spl_npm, t)
return [d_u, d_v, d_r, d_δ, d_npm]
sol = solve_ivp(
mmg_3dof_eom_solve_ivp,
[time_list[0], time_list[-1]],
[u0, v0, r0, δ_list[0], npm_list[0]],
dense_output=True,
method=method,
t_eval=t_eval,
events=events,
vectorized=vectorized,
**options
)
return sol
def get_sub_values_from_simulation_result(
u_list: List[float],
v_list: List[float],
r_list: List[float],
δ_list: List[float],
npm_list: List[float],
basic_params: Mmg3DofBasicParams,
maneuvering_params: Mmg3DofManeuveringParams,
ρ: float = 1.025,
return_all_vals: bool = False,
):
"""Get sub values of MMG calculation from simulation result.
Args:
u_list (List[float]):
u list of MMG simulation result.
v_list (List[float]):
v list of MMG simulation result.
r_list (List[float]):
r list of MMG simulation result.
δ_list (List[float]):
δ list of MMG simulation result.
npm_list (List[float]):
npm list of MMG simulation result.
basic_params (Mmg3DofBasicParams):
u of MMG simulation result.
maneuvering_params (Mmg3DofManeuveringParams):
u of MMG simulation result.
ρ (float, optional):
seawater density [kg/m^3]
Defaults to 1.025.
return_all_vals (bool, optional):
Whether all sub values are returned or not.
Defaults to false.
Returns:
X_H_list (List[float]): List of X_H
X_R_list (List[float]): List of X_R
X_P_list (List[float]): List of X_P
Y_H_list (List[float]): List of Y_H
Y_R_list (List[float]): List of Y_R
N_H_list (List[float]): List of N_H
N_R_list (List[float]): List of N_R
U_list (List[float], optional): List of U if return_all_vals is True
β_list (List[float], optional): List of β if return_all_vals is True
v_dash_list (List[float], optional): List of v_dash if return_all_vals is True
r_dash_list (List[float], optional): List of r_dash if return_all_vals is True
w_P_list (List[float], optional): List of w_P if return_all_vals is True
J_list (List[float], optional): List of J if return_all_vals is True
K_T_list (List[float], optional): List of K_T if return_all_vals is True
v_R_list (List[float], optional): List of v_R if return_all_vals is True
u_R_list (List[float], optional): List of u_R if return_all_vals is True
U_R_list (List[float], optional): List of U_R if return_all_vals is True
α_R_list (List[float], optional): List of α_R if return_all_vals is True
F_N_list (List[float], optional): List of F_N if return_all_vals is True
"""
U_list = list(
map(
lambda u, v, r: np.sqrt(u ** 2 + (v - r * basic_params.x_G) ** 2),
u_list,
v_list,
r_list,
)
)
β_list = list(
map(
lambda U, v, r: 0.0
if U == 0.0
else np.arcsin(-(v - r * basic_params.x_G) / U),
U_list,
v_list,
r_list,
)
)
v_dash_list = list(map(lambda U, v: 0.0 if U == 0.0 else v / U, U_list, v_list))
r_dash_list = list(
map(lambda U, r: 0.0 if U == 0.0 else r * basic_params.L_pp / U, U_list, r_list)
)
β_P_list = list(
map(
lambda β, r_dash: β - basic_params.x_P * r_dash,
β_list,
r_dash_list,
)
)
# w_P_list = [basic_params.w_P0 for i in range(len(r_dash_list))]
w_P_list = list(
map(lambda β_P: basic_params.w_P0 * np.exp(-4.0 * β_P ** 2), β_P_list)
)
J_list = list(
map(
lambda w_P, u, npm: 0.0
if npm == 0.0
else (1 - w_P) * u / (npm * basic_params.D_p),
w_P_list,
u_list,
npm_list,
)
)
K_T_list = list(
map(
lambda J: maneuvering_params.k_0
+ maneuvering_params.k_1 * J
+ maneuvering_params.k_2 * J ** 2,
J_list,
)
)
β_R_list = list(
map(
lambda β, r_dash: β - basic_params.l_R * r_dash,
β_list,
r_dash_list,
)
)
γ_R_list = list(
map(
lambda β_R: basic_params.γ_R_minus if β_R < 0.0 else basic_params.γ_R_plus,
β_R_list,
)
)
v_R_list = list(
map(
lambda U, γ_R, β_R: U * γ_R * β_R,
U_list,
γ_R_list,
β_R_list,
)
)
u_R_list = list(
map(
lambda u, J, npm, K_T, w_P: np.sqrt(
basic_params.η
* (
basic_params.κ
* basic_params.ϵ
* 8.0
* maneuvering_params.k_0
* npm ** 2
* basic_params.D_p ** 4
/ np.pi
)
** 2
)
if J == 0.0
else u
* (1 - w_P)
* basic_params.ϵ
* np.sqrt(
basic_params.η
* (
1.0
+ basic_params.κ * (np.sqrt(1.0 + 8.0 * K_T / (np.pi * J ** 2)) - 1)
)
** 2
+ (1 - basic_params.η)
),
u_list,
J_list,
npm_list,
K_T_list,
w_P_list,
)
)
U_R_list = list(
map(lambda u_R, v_R: np.sqrt(u_R ** 2 + v_R ** 2), u_R_list, v_R_list)
)
α_R_list = list(
map(lambda δ, u_R, v_R: δ - np.arctan2(v_R, u_R), δ_list, u_R_list, v_R_list)
)
F_N_list = list(
map(
lambda U_R, α_R: 0.5
* basic_params.A_R
* ρ
* basic_params.f_α
* (U_R ** 2)
* | np.sin(α_R) | numpy.sin |
"""Tests of cleverhans.attacks_tf
"""
# pylint: disable=missing-docstring
from functools import partial
import unittest
import numpy as np
import tensorflow as tf
from cleverhans.devtools.checks import CleverHansTest
from cleverhans.attacks_tf import (
fgm,
pgd_attack,
UnrolledAdam,
UnrolledGradientDescent,
parallel_apply_transformations,
)
from cleverhans.devtools.mocks import random_feed_dict
from cleverhans.model import Model
class SimpleModel(Model):
"""
A very simple neural network
"""
def __init__(self, scope="simple", nb_classes=2, **kwargs):
del kwargs
Model.__init__(self, scope, nb_classes, locals())
def fprop(self, x, **kwargs):
del kwargs
with tf.variable_scope(self.scope, reuse=tf.AUTO_REUSE):
w1 = tf.constant([[1.5, 0.3], [-2, 0.3]], dtype=tf.as_dtype(x.dtype))
w2 = tf.constant([[-2.4, 1.2], [0.5, -2.3]], dtype=tf.as_dtype(x.dtype))
h1 = tf.nn.sigmoid(tf.matmul(x, w1))
res = tf.matmul(h1, w2)
return {self.O_LOGITS: res, self.O_PROBS: tf.nn.softmax(res)}
class TestAttackTF(CleverHansTest):
def setUp(self):
super(TestAttackTF, self).setUp()
self.sess = tf.Session()
self.model = SimpleModel()
def test_fgm_gradient_max(self):
input_dim = 2
nb_classes = 3
batch_size = 4
rng = np.random.RandomState([2017, 8, 23])
x = tf.placeholder(tf.float32, [batch_size, input_dim])
weights = tf.placeholder(tf.float32, [input_dim, nb_classes])
logits = tf.matmul(x, weights)
probs = tf.nn.softmax(logits)
adv_x = fgm(x, probs)
random_example = rng.randint(batch_size)
random_feature = rng.randint(input_dim)
output = tf.slice(adv_x, [random_example, random_feature], [1, 1])
(dx,) = tf.gradients(output, x)
# The following line catches GitHub issue #243
self.assertIsNotNone(dx)
dx = self.sess.run(dx, feed_dict=random_feed_dict(rng, [x, weights]))
ground_truth = np.zeros((batch_size, input_dim))
ground_truth[random_example, random_feature] = 1.0
self.assertClose(dx, ground_truth)
def helper_pgd_attack(
self,
unrolled_optimizer,
targeted,
nb_iters=20,
epsilon=0.5,
clip_min=-5.0,
clip_max=5.0,
assert_threshold=0.5,
):
def loss_fn(input_image, label, targeted):
res = self.model.fprop(input_image)
logits = res[self.model.O_LOGITS]
multiplier = 1.0 if targeted else -1.0
return multiplier * tf.nn.sparse_softmax_cross_entropy_with_logits(
labels=label, logits=logits
)
x_val_ph = tf.placeholder(tf.float32, shape=[100, 2])
x_val = np.random.randn(100, 2).astype(np.float32)
init_model_output = self.model.fprop(x_val_ph)
init_model_logits = init_model_output[self.model.O_LOGITS]
if targeted:
labels = np.random.random_integers(0, 1, size=(100,))
else:
labels = tf.stop_gradient(tf.argmax(init_model_logits, axis=1))
def _project_perturbation(
perturbation, epsilon, input_image, clip_min, clip_max
):
clipped_perturbation = tf.clip_by_value(perturbation, -epsilon, epsilon)
new_image = tf.clip_by_value(
input_image + clipped_perturbation, clip_min, clip_max
)
return new_image - input_image
x_adv = pgd_attack(
loss_fn=partial(loss_fn, targeted=targeted),
input_image=x_val_ph,
label=labels,
epsilon=epsilon,
num_steps=nb_iters,
optimizer=unrolled_optimizer,
project_perturbation=_project_perturbation,
clip_min=clip_min,
clip_max=clip_max,
)
final_model_output = self.model.fprop(x_adv)
final_model_logits = final_model_output[self.model.O_LOGITS]
if not targeted:
logits1, logits2 = self.sess.run(
[init_model_logits, final_model_logits], feed_dict={x_val_ph: x_val}
)
preds1 = np.argmax(logits1, axis=1)
preds2 = np.argmax(logits2, axis=1)
self.assertTrue(
np.mean(preds1 == preds2) < assert_threshold, np.mean(preds1 == preds2)
)
else:
logits_adv = self.sess.run(final_model_logits, feed_dict={x_val_ph: x_val})
preds_adv = | np.argmax(logits_adv, axis=1) | numpy.argmax |
# coding: utf-8
from __future__ import print_function
from __future__ import division
import torch
import torch.nn as nn
import torch.nn.functional as F
from libcity.model.abstract_model import AbstractModel
from math import sin, cos, sqrt, atan2, radians
import numpy as np
def identity_loss(y_true, y_pred):
return torch.mean(y_pred - 0 * y_true)
class CARA1(nn.Module):
def hard_sigmoid(self, x):
x = torch.tensor(x / 6 + 0.5)
x = F.threshold(-x, -1, -1)
x = F.threshold(-x, 0, 0)
return x
def __init__(self, output_dim, input_dim,
init='glorot_uniform', inner_init='orthogonal',
**kwargs):
super(CARA1, self).__init__()
self.output_dim = output_dim
self.init = init
self.inner_init = inner_init
self.activation = self.hard_sigmoid
self.inner_activation = nn.Tanh()
self.build(input_dim)
def add_weight(self, shape, initializer):
ts = torch.zeros(shape)
if initializer == 'glorot_uniform':
ts = nn.init.xavier_normal_(ts)
elif initializer == 'orthogonal':
ts = nn.init.orthogonal_(ts)
return nn.Parameter(ts)
def build(self, input_shape):
# self.input_spec = [InputSpec(shape=input_shape)]
self.input_dim = input_shape
self.W_z = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init)
self.U_z = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init)
self.b_z = self.add_weight((self.output_dim,),
initializer='zero')
self.W_r = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init)
self.U_r = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init)
self.b_r = self.add_weight((self.output_dim,),
initializer='zero')
self.W_h = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init)
self.U_h = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init)
self.b_h = self.add_weight((self.output_dim,),
initializer='zero')
self.A_h = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init)
self.A_u = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init)
self.b_a_h = self.add_weight((self.output_dim,),
initializer='zero')
self.b_a_u = self.add_weight((self.output_dim,),
initializer='zero')
self.W_t = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init)
self.U_t = self.add_weight((1, self.output_dim),
initializer=self.init)
self.b_t = self.add_weight((self.output_dim,),
initializer='zero')
self.W_g = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init)
self.U_g = self.add_weight((1, self.output_dim),
initializer=self.init)
self.b_g = self.add_weight((self.output_dim,),
initializer='zero')
def preprocess_input(self, x):
return x
def forward(self, x):
"""
X : batch * timeLen * dims(有拓展)
"""
tlen = x.shape[1]
output = torch.zeros((x.shape[0], self.output_dim))
for i in range(tlen):
output = self.step(x[:, i, :], output)
return output
def step(self, x, states):
"""
用于多批次同一时间
states为上一次多批次统一时间数据
"""
h_tm1 = states
# phi_t
u = x[:, self.output_dim: 2 * self.output_dim]
# delta_t
t = x[:, 2 * self.output_dim: (2 * self.output_dim) + 1]
# delta_g
g = x[:, (2 * self.output_dim) + 1:]
# phi_v
x = x[:, :self.output_dim]
t = self.inner_activation(torch.matmul(t, self.U_t))
g = self.inner_activation(torch.matmul(g, self.U_g))
# Time-based gate
t1 = self.inner_activation(torch.matmul(x, self.W_t) + t + self.b_t)
# Geo-based gate
g1 = self.inner_activation(torch.matmul(x, self.W_g) + g + self.b_g)
# Contextual Attention Gate
a = self.inner_activation(
torch.matmul(h_tm1, self.A_h) + torch.matmul(u, self.A_u) + self.b_a_h + self.b_a_u)
x_z = torch.matmul(x, self.W_z) + self.b_z
x_r = torch.matmul(x, self.W_r) + self.b_r
x_h = torch.matmul(x, self.W_h) + self.b_h
u_z_ = torch.matmul((1 - a) * u, self.W_z) + self.b_z
u_r_ = torch.matmul((1 - a) * u, self.W_r) + self.b_r
u_h_ = torch.matmul((1 - a) * u, self.W_h) + self.b_h
u_z = torch.matmul(a * u, self.W_z) + self.b_z
u_r = torch.matmul(a * u, self.W_r) + self.b_r
u_h = torch.matmul(a * u, self.W_h) + self.b_h
# update gate
z = self.inner_activation(x_z + torch.matmul(h_tm1, self.U_z) + u_z)
# reset gate
r = self.inner_activation(x_r + torch.matmul(h_tm1, self.U_r) + u_r)
# hidden state
hh = self.activation(x_h + torch.matmul(r * t1 * g1 * h_tm1, self.U_h) + u_h)
h = z * h_tm1 + (1 - z) * hh
h = (1 + u_z_ + u_r_ + u_h_) * h
return h
# return h
def bpr_triplet_loss(x):
positive_item_latent, negative_item_latent = x
reg = 0
loss = 1 - torch.log(torch.sigmoid(
torch.sum(positive_item_latent, dim=-1, keepdim=True) -
torch.sum(negative_item_latent, dim=-1, keepdim=True))) - reg
return loss
class Recommender(nn.Module):
def __init__(self, num_users, num_items, num_times, latent_dim, maxvenue=5):
super(Recommender, self).__init__()
self.maxVenue = maxvenue
self.latent_dim = latent_dim
# num * maxVenue * dim
self.U_Embedding = nn.Embedding(num_users, latent_dim)
self.V_Embedding = nn.Embedding(num_items, latent_dim)
self.T_Embedding = nn.Embedding(num_times, latent_dim)
torch.nn.init.uniform_(self.U_Embedding.weight)
torch.nn.init.uniform_(self.V_Embedding.weight)
torch.nn.init.uniform_(self.T_Embedding.weight)
self.rnn = nn.Sequential(
CARA1(latent_dim, latent_dim, input_shape=(self.maxVenue, (self.latent_dim * 2) + 2,), unroll=True))
# latent_dim * 2 + 2 = v_embedding + t_embedding + time_gap + distance
def forward(self, x):
# INPUT = [self.user_input, self.time_input, self.gap_time_input, self.pos_distance_input,
# self.neg_distance_input, self.checkins_input,
# self.neg_checkins_input]
# pass
# User latent factor
user_input = torch.tensor(x[0])
time_input = torch.tensor(x[1])
gap_time_input = torch.tensor(x[2], dtype=torch.float32)
pos_distance_input = torch.tensor(x[3], dtype=torch.float32)
neg_distance_input = torch.tensor(x[4], dtype=torch.float32)
checkins_input = torch.tensor(x[5])
neg_checkins_input = torch.tensor(x[6])
self.u_latent = self.U_Embedding(user_input)
self.t_latent = self.T_Embedding(time_input)
h, w = gap_time_input.shape
gap_time_input = gap_time_input.view(h, w, 1)
rnn_input = torch.cat([self.V_Embedding(checkins_input), self.T_Embedding(time_input), gap_time_input], -1)
neg_rnn_input = torch.cat([self.V_Embedding(neg_checkins_input), self.T_Embedding(time_input), gap_time_input],
-1)
h, w = pos_distance_input.shape
pos_distance_input = pos_distance_input.view(h, w, 1)
h, w = neg_distance_input.shape
neg_distance_input = neg_distance_input.view(h, w, 1)
rnn_input = torch.cat([rnn_input, pos_distance_input], -1)
neg_rnn_input = torch.cat([neg_rnn_input, neg_distance_input], -1)
self.checkins_emb = self.rnn(rnn_input)
self.neg_checkins_emb = self.rnn(neg_rnn_input)
pred = (self.checkins_emb * self.u_latent).sum(dim=1)
neg_pred = (self.neg_checkins_emb * self.u_latent).sum(dim=1)
return bpr_triplet_loss([pred, neg_pred])
def rank(self, uid, hist_venues, hist_times, hist_time_gap, hist_distances):
# hist_venues = hist_venues + [candidate_venue]
# hist_times = hist_times + [time]
# hist_time_gap = hist_time_gap + [time_gap]
# hist_distances = hist_distances + [distance]
# u_latent = self.U_Embedding(torch.tensor(uid))
# v_latent = self.V_Embedding(torch.tensor(hist_venues))
# t_latent = self.T_Embedding(torch.tensor(hist_times))
u_latent = self.U_Embedding.weight[uid]
v_latent = self.V_Embedding.weight[hist_venues.reshape(-1)].view(hist_venues.shape[0], hist_venues.shape[1], -1)
t_latent = self.T_Embedding.weight[hist_times.reshape(-1)].view(hist_times.shape[0], hist_times.shape[1], -1)
h, w = hist_time_gap.shape
hist_time_gap = hist_time_gap.reshape(h, w, 1)
h, w = hist_distances.shape
hist_distances = hist_distances.reshape(h, w, 1)
rnn_input = torch.cat([t_latent, torch.tensor(hist_time_gap, dtype=torch.float32)], dim=-1)
rnn_input = torch.cat([rnn_input, torch.tensor(hist_distances, dtype=torch.float32)], dim=-1)
rnn_input = torch.cat([v_latent, rnn_input], dim=-1)
dynamic_latent = self.rnn(rnn_input)
scores = torch.mul(dynamic_latent, u_latent).sum(1)
# scores = np.dot(dynamic_latent, u_latent)
return scores
class CARA(AbstractModel):
"""rnn model with long-term history attention"""
def __init__(self, config, data_feature):
super(CARA, self).__init__(config, data_feature)
self.loc_size = data_feature['loc_size']
self.tim_size = data_feature['tim_size']
self.uid_size = data_feature['uid_size']
self.poi_profile = data_feature['poi_profile']
self.id2locid = data_feature['id2locid']
self.id2loc = []
for i in range(self.loc_size - 1):
self.id2loc.append(self.id2locid[str(i)])
self.id2loc.append(self.loc_size)
self.id2loc = np.array(self.id2loc)
self.coor = self.poi_profile['coordinates'].apply(eval)
self.rec = Recommender(self.uid_size, self.loc_size, self.tim_size, 10)
def get_time_interval(self, x):
y = x[:, :-1]
y = np.concatenate([x[:, 0, None], y], axis=1)
return x - y
def get_time_interval2(self, x):
y = x[:-1]
y = np.concatenate([x[0, None], y], axis=0)
return x - y
def get_pos_distance(self, x):
x = np.array(x.tolist())
y = np.concatenate([x[:, 0, None, :], x[:, :-1, :]], axis=1)
r = 6373.0
rx = np.radians(x)
ry = np.radians(y)
d = x - y
a = np.sin(d[:, :, 0] / 2) ** 2 + np.cos(rx[:, :, 0]) * np.cos(ry[:, :, 0]) * np.sin(d[:, :, 1] / 2) ** 2
c = 2 * np.arctan2(np.sqrt(a), np.sqrt(1 - a))
return r * c
def get_pos_distance2(self, x):
x = np.array(x.tolist())
y = np.concatenate([x[0, None, :], x[:-1, :]], axis=0)
r = 6373.0
rx = np.radians(x)
ry = np.radians(y)
d = x - y
a = np.sin(d[:, 0] / 2) ** 2 + np.cos(rx[:, 0]) * np.cos(ry[:, 0]) * np.sin(d[:, 1] / 2) ** 2
c = 2 * np.arctan2(np.sqrt(a), np.sqrt(1-a))
return r * c
def get_distance(self, lat1, lng1, lat2, lng2):
r = 6373.0
lat1 = radians(lat1)
lon1 = radians(lng1)
lat2 = radians(lat2)
lon2 = radians(lng2)
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat / 2) ** 2 + cos(lat1) * cos(lat2) * sin(dlon / 2) ** 2
c = 2 * atan2(sqrt(a), sqrt(1 - a))
distance = int(r * c)
return distance
def get_neg_checkins(self, vis, x, y):
len1, len2 = x.shape
x_res = []
x_res_distance = y[:].copy()
for i in range(len1):
visits = x[i]
j = np.random.randint(self.loc_size - 1)
while j in vis[i]:
j = np.random.randint(self.loc_size - 1)
tmp = visits[:].copy()
tmp[-1] = j
x_res.append(tmp)
j1 = self.coor[self.id2loc[visits[-1]]]
j = self.coor[self.id2loc[j]]
x_res_distance[i, -1] = self.get_distance(j1[0], j1[1], j[0], j[1])
return x_res, x_res_distance
def forward(self, batch):
hloc = np.array(batch['current_loc'])[:, :5]
target = np.array(batch['target'])
h = target.shape
target = target.reshape((*h, 1))
hloc = np.concatenate([hloc, target], axis=1)
hloc1 = self.id2loc[hloc]
tloc = | np.array(batch['current_tim']) | numpy.array |
import numpy as np
import matplotlib.pyplot as plt
from cvxopt import matrix
from cvxopt import solvers
from utils import *
## Define kernel RBF
def rbfKernel(x,y,k_params=0.5):
x = np.expand_dims(x,axis=1)
y = np.expand_dims(y,axis=1)
val = np.exp(-(np.linalg.norm(x-y)**2)/k_params**2)
val = np.array(val)
val = np.reshape(val,(1,1))
return val
def polyKernel(x,y,k_params=2):
x = np.expand_dims(x,axis=1)
y = np.expand_dims(y,axis=1)
val = (np.matmul(x.T, y) + 1) ** k_params
return val
def linKernel(x,y):
x = np.expand_dims(x,axis=1)
y = np.expand_dims(y,axis=1)
val = (np.matmul(x.T, y))
return val
class SVM(object):
def __init__(self, C_reg=0.5, thresh=1e-5, kernel='poly', k_params=3):
super(SVM,self).__init__()
self.C_reg = C_reg
self.thresh = thresh
self.alpha = None
self.intercept = None
self.sv = None
self.sv_l = None
self.kernel = kernel
self.k_params = k_params
def fit(self, X_train,y_train, print_options=False):
P = np.zeros((X_train.shape[0],X_train.shape[0]))
for i in range(X_train.shape[0]):
for j in range(X_train.shape[0]):
if self.kernel=='rbf':
P[i,j] = 1*y_train[i]*y_train[j]*rbfKernel(X_train[i],X_train[j],k_params=self.k_params)
if self.kernel=='poly':
P[i,j] = 1*y_train[i]*y_train[j]*polyKernel(X_train[i],X_train[j],k_params=self.k_params)
if self.kernel=='lin':
P[i,j] = 1*y_train[i]*y_train[j]*linKernel(X_train[i],X_train[j])
q = -1*np.ones((X_train.shape[0],1))
G = np.vstack((-1*np.eye(X_train.shape[0]),np.eye(X_train.shape[0])))
h = np.vstack(( | np.zeros((X_train.shape[0],1)) | numpy.zeros |
import numpy as np
import pandas as pd
ots = pd.read_csv("data/ot.csv",sep=',')
ots=ots.sort_values('Pedido')
xlsx_file = "data/layout.xlsx"
layout = pd.read_excel(xlsx_file, sheet_name="layout")
adyacencia=pd.read_excel(xlsx_file, sheet_name="adyacencia")
cant_ordenes=len(ots['Pedido'].unique())
pasillos=layout['pasillo'].unique()
tiempo_pickeo=20
velocidad=20
lista=[]
for x in range(cant_ordenes):
obj=list(ots.loc[ots["Pedido"]==x+1]["Cod.Prod"])
lista.append(obj)
ordenes= | np.array(lista) | numpy.array |
import numpy as np
import cv2
from PIL import Image
import torch.utils.data as D
from tqdm import tqdm
from torchvision import transforms
from PIL import ImageFile
ImageFile.LOAD_TRUNCATED_IMAGES = True
trans = transforms.Compose([
transforms.Resize((256,256)),
transforms.ToTensor()
])
def get_img(root):
img_ = []
mask_ = []
for idx in tqdm(range(1, 1001)):
img = Image.open(f'{root}/{idx}.jpg')
i1 = img.crop((0,0,256,256))
i2 = img.crop((235,235,491,491))
i3 = img.crop((235,0,491,256))
i4 = img.crop((0,235,256,491))
mask = Image.open(f'{root}/{idx}_gt.png')
m1 = mask.crop((0,0,256,256))
m2 = mask.crop((235,235,491,491))
m3 = mask.crop((235,0,491,256))
m4 = mask.crop((0,235,256,491))
# img_.append(img)
img_.append(i1)
img_.append(i2)
img_.append(i3)
img_.append(i4)
# mask_.append(mask)
mask_.append(m1)
mask_.append(m2)
mask_.append(m3)
mask_.append(m4)
img_ = img_[:3600]
mask_ = mask_[:3600]
return img_, mask_
def gamma_transform(img, gamma):
gamma_table = [np.power(x / 255.0, gamma) * 255.0 for x in range(256)]
gamma_table = np.round(np.array(gamma_table)).astype(np.uint8)
return cv2.LUT(img, gamma_table)
def random_gamma_transform(img, gamma_vari):
log_gamma_vari = np.log(gamma_vari)
alpha = | np.random.uniform(-log_gamma_vari, log_gamma_vari) | numpy.random.uniform |
"""Implementations of Feature the model scattering objects.
Provides some basic implementations of scattering objects
that are frequently used.
Classes
--------
Scatterer
Abstract base class for scatterers
PointParticle
Generates point particles
Ellipse
Generetes 2-d elliptical particles
Sphere
Generates 3-d spheres
Ellipsoid
Generates 3-d ellipsoids
"""
from typing import Callable, Tuple
import numpy as np
from . import backend as D
from .features import Feature, MERGE_STRATEGY_APPEND
from .image import Image
from . import image
from .types import PropertyLike, ArrayLike
import warnings
class Scatterer(Feature):
"""Base abstract class for scatterers.
A scatterer is defined by a 3-dimensional volume of voxels.
To each voxel corresponds an occupancy factor, i.e., how much
of that voxel does the scatterer occupy. However, this number is not
necessarily limited to the [0, 1] range. It can be any number, and its
interpretation is left to the optical device that images the scatterer.
This abstract class implements the `_process_properties` method to convert
the position to voxel units, as well as the `_process_and_get` method to
upsample the calculation and crop empty slices.
Parameters
----------
position : array_like of length 2 or 3
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
value : float
A default value of the characteristic of the particle. Used by
optics unless a more direct property is set (eg. `refractive_index`
for `Brightfield` and `intensity` for `Fluorescence`).
position_unit : "meter" or "pixel"
The unit of the provided position property.
Other Parameters
----------------
upsample_axes : tuple of ints
Sets the axes along which the calculation is upsampled (default is
None, which implies all axes are upsampled).
crop_zeros : bool
Whether to remove slices in which all elements are zero.
"""
__list_merge_strategy__ = MERGE_STRATEGY_APPEND
__distributed__ = False
def __init__(
self,
position: PropertyLike[ArrayLike[float]] = (32, 32),
z: PropertyLike[float] = 0.0,
value: PropertyLike[float] = 1.0,
position_unit: PropertyLike[str] = "pixel",
upsample: PropertyLike[int] = 1,
**kwargs
):
self._processed_properties = False
super().__init__(
position=position,
z=z,
value=value,
position_unit=position_unit,
upsample=upsample,
**kwargs
)
def _process_properties(self, properties: dict) -> dict:
# Rescales the position property
self._processed_properties = True
if "position" in properties:
if properties["position_unit"] == "meter":
properties["position"] = (
np.array(properties["position"])
/ np.array(properties["voxel_size"])[: len(properties["position"])]
/ properties.get("upscale", 1)
)
properties["z"] = (
np.array(properties["z"])
/ np.array(properties["voxel_size"])[: len(properties["position"])]
/ properties.get("upscale", 1)
)
return properties
def _process_and_get(
self, *args, voxel_size, upsample, upsample_axes=None, crop_empty=True, **kwargs
):
# Post processes the created object to handle upsampling,
# as well as cropping empty slices.
if not self._processed_properties:
warnings.warn(
"Overridden _process_properties method does not call super. "
+ "This is likely to result in errors if used with "
+ "Optics.upscale != 1."
)
# Calculates upsampled voxel_size
if upsample_axes is None:
upsample_axes = range(3)
voxel_size = np.array(voxel_size)
for axis in upsample_axes:
voxel_size[axis] /= upsample
# calls parent _process_and_get
new_image = super()._process_and_get(
*args, voxel_size=voxel_size, upsample=upsample, **kwargs
)
new_image = new_image[0]
if new_image.size == 0:
warnings.warn(
"Scatterer created that is smaller than a pixel. "
+ "This may yield inconsistent results."
+ " Consider using upsample on the scatterer,"
+ " or upscale on the optics.",
Warning,
)
# Downsamples the image along the axes it was upsampled
if upsample != 1 and upsample_axes:
# Pad image to ensure it is divisible by upsample
increase = np.array(new_image.shape)
for axis in upsample_axes:
increase[axis] = upsample - (new_image.shape[axis] % upsample)
pad_width = [(0, inc) for inc in increase]
new_image = np.pad(new_image, pad_width, mode="constant")
# Finds reshape size for downsampling
new_shape = []
for axis in range(new_image.ndim):
if axis in upsample_axes:
new_shape += [new_image.shape[axis] // upsample, upsample]
else:
new_shape += [new_image.shape[axis]]
# Downsamples
new_image = np.reshape(new_image, new_shape).mean(
axis=tuple(np.array(upsample_axes, dtype=np.int32) * 2 + 1)
)
# Crops empty slices
if crop_empty:
new_image = new_image[~np.all(new_image == 0, axis=(1, 2))]
new_image = new_image[:, ~np.all(new_image == 0, axis=(0, 2))]
new_image = new_image[:, :, ~np.all(new_image == 0, axis=(0, 1))]
return [Image(new_image)]
class PointParticle(Scatterer):
"""Generates a point particle
A point particle is approximated by the size of a pixel. For subpixel
positioning, the position is interpolated linearly.
Parameters
----------
position : array_like of length 2 or 3
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
value : float
A default value of the characteristic of the particle. Used by
optics unless a more direct property is set: (eg. `refractive_index`
for `Brightfield` and `intensity` for `Fluorescence`).
"""
def __init__(self, **kwargs):
kwargs.pop("upsample", False)
kwargs.pop("upsample_axes", False)
super().__init__(upsample=1, upsample_axes=(), **kwargs)
def get(self, image, **kwargs):
return np.ones((1, 1, 1))
class Ellipse(Scatterer):
"""Generates an elliptical disk scatterer
Parameters
----------
radius : float or array_like [float (, float)]
Radius of the ellipse in meters. If only one value,
assume circular.
rotation : float
Orientation angle of the ellipse in the camera plane in radians.
position : array_like[float, float (, float)]
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
value : float
A default value of the characteristic of the particle. Used by
optics unless a more direct property is set: (eg. `refractive_index`
for `Brightfield` and `intensity` for `Fluorescence`).
upsample : int
Upsamples the calculations of the pixel occupancy fraction.
"""
def __init__(
self,
radius: PropertyLike[float] = 1e-6,
rotation: PropertyLike[float] = 0,
**kwargs
):
super().__init__(
radius=radius, rotation=rotation, upsample_axes=(0, 1), **kwargs
)
def _process_properties(self, properties: dict) -> dict:
"""Preprocess the input to the method .get()
Ensures that the radius is an array of length 2. If the radius
is a single value, the particle is made circular
"""
properties = super()._process_properties(properties)
# Ensure radius is of length 2
radius = np.array(properties["radius"])
if radius.ndim == 0:
radius = np.array((properties["radius"], properties["radius"]))
elif radius.size == 1:
radius = np.array((*radius,) * 2)
else:
radius = radius[:2]
properties["radius"] = radius
return properties
def get(self, *ignore, radius, rotation, voxel_size, **kwargs):
# Create a grid to calculate on
rad = radius[:2] / voxel_size[:2]
ceil = int(np.max(np.ceil(rad)))
X, Y = np.meshgrid(np.arange(-ceil, ceil), np.arange(-ceil, ceil))
# Rotate the grid
if rotation != 0:
Xt = X * np.cos(-rotation) + Y * np.sin(-rotation)
Yt = -X * np.sin(-rotation) + Y * np.cos(-rotation)
X = Xt
Y = Yt
# Evaluate ellipse
mask = ((X * X) / (rad[0] * rad[0]) + (Y * Y) / (rad[1] * rad[1]) < 1) * 1.0
mask = np.expand_dims(mask, axis=-1)
return mask
class Sphere(Scatterer):
"""Generates a spherical scatterer
Parameters
----------
radius : float
Radius of the sphere in meters.
position : array_like[float, float (, float)]
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
value : float
A default value of the characteristic of the particle. Used by
optics unless a more direct property is set: (eg. `refractive_index`
for `Brightfield` and `intensity` for `Fluorescence`).
upsample : int
Upsamples the calculations of the pixel occupancy fraction.
"""
def __init__(self, radius: PropertyLike[float] = 1e-6, **kwargs):
super().__init__(radius=radius, **kwargs)
def get(self, image, radius, voxel_size, **kwargs):
# Create a grid to calculate on
rad = radius / voxel_size
rad_ceil = np.ceil(rad)
x = np.arange(-rad_ceil[0], rad_ceil[0])
y = np.arange(-rad_ceil[1], rad_ceil[1])
z = np.arange(-rad_ceil[2], rad_ceil[2])
X, Y, Z = np.meshgrid((x / rad[0]) ** 2, (y / rad[1]) ** 2, (z / rad[2]) ** 2)
mask = (X + Y + Z <= 1) * 1.0
return mask
class Ellipsoid(Scatterer):
"""Generates an ellipsoidal scatterer
Parameters
----------
radius : float or array_like[float (, float, float)]
Radius of the ellipsoid in meters. If only one value,
assume spherical.
rotation : float
Rotation of the ellipsoid in about the x, y and z axis.
position : array_like[float, float (, float)]
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
value : float
A default value of the characteristic of the particle. Used by
optics unless a more direct property is set: (eg. `refractive_index`
for `Brightfield` and `intensity` for `Fluorescence`).
upsample : int
Upsamples the calculations of the pixel occupancy fraction.
"""
def __init__(
self,
radius: PropertyLike[float] = 1e-6,
rotation: PropertyLike[float] = 0,
**kwargs
):
super().__init__(radius=radius, rotation=rotation, **kwargs)
def _process_properties(self, propertydict):
"""Preprocess the input to the method .get()
Ensures that the radius and the rotation properties both are arrays of
length 3.
If the radius is a single value, the particle is made a sphere
If the radius are two values, the smallest value is appended as the
third value
The rotation vector is padded with zeros until it is of length 3
"""
propertydict = super()._process_properties(propertydict)
# Ensure radius has three values
radius = np.array(propertydict["radius"])
if radius.ndim == 0:
radius = np.array([radius])
if radius.size == 1:
# If only one value, assume sphere
radius = (*radius,) * 3
elif radius.size == 2:
# If two values, duplicate the minor axis
radius = (*radius, np.min(radius[-1]))
elif radius.size == 3:
# If three values, convert to tuple for consistency
radius = (*radius,)
propertydict["radius"] = radius
# Ensure rotation has three values
rotation = np.array(propertydict["rotation"])
if rotation.ndim == 0:
rotation = np.array([rotation])
if rotation.size == 1:
# If only one value, pad with two zeros
rotation = (*rotation, 0, 0)
elif rotation.size == 2:
# If two values, pad with one zero
rotation = (*rotation, 0)
elif rotation.size == 3:
# If three values, convert to tuple for consistency
rotation = (*rotation,)
propertydict["rotation"] = rotation
return propertydict
def get(self, image, radius, rotation, voxel_size, **kwargs):
radius_in_pixels = radius / voxel_size
max_rad = np.max(radius) / voxel_size
rad_ceil = np.ceil(max_rad)
# Create grid to calculate on
x = np.arange(-rad_ceil[0], rad_ceil[0])
y = np.arange(-rad_ceil[1], rad_ceil[1])
z = np.arange(-rad_ceil[2], rad_ceil[2])
X, Y, Z = np.meshgrid(x, y, z)
# Rotate the grid
cos = np.cos(rotation)
sin = np.sin(rotation)
XR = (
(cos[0] * cos[1] * X)
+ (cos[0] * sin[1] * sin[2] - sin[0] * cos[2]) * Y
+ (cos[0] * sin[1] * cos[2] + sin[0] * sin[2]) * Z
)
YR = (
(sin[0] * cos[1] * X)
+ (sin[0] * sin[1] * sin[2] + cos[0] * cos[2]) * Y
+ (sin[0] * sin[1] * cos[2] - cos[0] * sin[2]) * Z
)
ZR = (-sin[1] * X) + cos[1] * sin[2] * Y + cos[1] * cos[2] * Z
mask = (
(XR / radius_in_pixels[0]) ** 2
+ (YR / radius_in_pixels[1]) ** 2
+ (ZR / radius_in_pixels[2]) ** 2
< 1
) * 1.0
return mask
class MieScatterer(Scatterer):
"""Base implementation of a Mie particle.
New Mie-theory scatterers can be implemented by extending this class, and
passing a function that calculates the coefficients of the harmonics up to
order `L`. To beprecise, the feature expects a wrapper function that takes
the current values of the properties, as well as a inner function that
takes an integer as the only parameter, and calculates the coefficients up
to that integer. The return format is expected to be a tuple with two
values, corresponding to `an` and `bn`. See
`deeptrack.backend.mie_coefficients` for an example.
Parameters
----------
coefficients : Callable[int] -> Tuple[ndarray, ndarray]
Function that returns the harmonics coefficients.
offset_z : "auto" or float
Distance from the particle in the z direction the field is evaluated.
If "auto", this is calculated from the pixel size and
`collection_angle`
collection_angle : "auto" or float
The maximum collection angle in radians. If "auto", this
is calculated from the objective NA (which is true if the objective is
the limiting
aperature).
polarization_angle : float
Angle of the polarization of the incoming light relative to the x-axis.
L : int or str
The number of terms used to evaluate the mie theory. If `"auto"`,
it determines the number of terms automatically.
position : array_like[float, float (, float)]
The position of the particle. Third index is optional,
and represents the position in the direction normal to the
camera plane.
z : float
The position in the direction normal to the
camera plane. Used if `position` is of length 2.
"""
def __init__(
self,
coefficients: Callable[..., Callable[[int], Tuple[ArrayLike, ArrayLike]]],
offset_z: PropertyLike[str] = "auto",
polarization_angle: PropertyLike[float] = 0,
collection_angle: PropertyLike[str] = "auto",
L: PropertyLike[str] = "auto",
**kwargs
):
kwargs.pop("is_field", None)
kwargs.pop("crop_empty", None)
super().__init__(
is_field=True,
crop_empty=False,
L=L,
offset_z=offset_z,
polarization_angle=polarization_angle,
collection_angle=collection_angle,
coefficients=coefficients,
**kwargs
)
def _process_properties(self, properties):
properties = super()._process_properties(properties)
if properties["L"] == "auto":
try:
v = 2 * np.pi * np.max(properties["radius"]) / properties["wavelength"]
properties["L"] = int(np.ceil(v + 4 * (v ** (1 / 3)) + 2))
except (ValueError, TypeError):
pass
if properties["collection_angle"] == "auto":
properties["collection_angle"] = np.arcsin(
properties["NA"] / properties["refractive_index_medium"]
)
if properties["offset_z"] == "auto":
properties["offset_z"] = (
32
* min(properties["voxel_size"][:2])
/ np.sin(properties["collection_angle"])
* properties["upscale"]
)
return properties
def get(
self,
inp,
position,
upscaled_output_region,
voxel_size,
padding,
wavelength,
refractive_index_medium,
L,
offset_z,
collection_angle,
polarization_angle,
coefficients,
upscale=1,
**kwargs
):
xSize = (
padding[2]
+ upscaled_output_region[2]
- upscaled_output_region[0]
+ padding[0]
)
ySize = (
padding[3]
+ upscaled_output_region[3]
- upscaled_output_region[1]
+ padding[1]
)
arr = image.pad_image_to_fft(np.zeros((xSize, ySize)))
# Evluation grid
x = np.arange(-padding[0], arr.shape[0] - padding[0]) - (position[0]) * upscale
y = np.arange(-padding[1], arr.shape[1] - padding[1]) - (position[1]) * upscale
X, Y = np.meshgrid(x * voxel_size[0], y * voxel_size[1], indexing="ij")
R2 = | np.sqrt(X ** 2 + Y ** 2) | numpy.sqrt |
""" Test functions for UMFPACK wrappers
"""
from __future__ import division, print_function, absolute_import
import random
import unittest
import warnings
from numpy.testing import assert_array_almost_equal, run_module_suite, dec
from scipy import rand, matrix, diag, eye
from scipy.sparse import csc_matrix, linalg, spdiags, SparseEfficiencyWarning
import numpy as np
import scikits.umfpack as um
_is_32bit_platform = np.intp(0).itemsize < 8
# Force int64 index dtype even when indices fit into int32.
def _to_int64(x):
y = csc_matrix(x).copy()
y.indptr = y.indptr.astype(np.int64)
y.indices = y.indices.astype(np.int64)
return y
class _DeprecationAccept(unittest.TestCase):
def setUp(self):
self.mgr = warnings.catch_warnings()
self.mgr.__enter__()
warnings.simplefilter('ignore', SparseEfficiencyWarning)
def tearDown(self):
self.mgr.__exit__()
class TestScipySolvers(_DeprecationAccept):
"""Tests inverting a sparse linear system"""
def test_solve_complex_umfpack(self):
# Solve with UMFPACK: double precision complex
linalg.use_solver(useUmfpack=True)
a = self.a.astype('D')
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a*x, b)
@dec.skipif(_is_32bit_platform)
def test_solve_complex_long_umfpack(self):
# Solve with UMFPACK: double precision complex, long indices
linalg.use_solver(useUmfpack=True)
a = _to_int64(self.a.astype('D'))
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a*x, b)
def test_solve_umfpack(self):
# Solve with UMFPACK: double precision
linalg.use_solver(useUmfpack=True)
a = self.a.astype('d')
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a*x, b)
@dec.skipif(_is_32bit_platform)
def test_solve_long_umfpack(self):
# Solve with UMFPACK: double precision
linalg.use_solver(useUmfpack=True)
a = _to_int64(self.a.astype('d'))
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a*x, b)
def test_solve_sparse_rhs(self):
# Solve with UMFPACK: double precision, sparse rhs
linalg.use_solver(useUmfpack=True)
a = self.a.astype('d')
b = csc_matrix(self.b).T
x = linalg.spsolve(a, b)
assert_array_almost_equal(a*x, self.b)
def test_factorized_umfpack(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
linalg.use_solver(useUmfpack=True)
a = self.a.astype('d')
solve = linalg.factorized(a)
x1 = solve(self.b)
assert_array_almost_equal(a*x1, self.b)
x2 = solve(self.b2)
| assert_array_almost_equal(a*x2, self.b2) | numpy.testing.assert_array_almost_equal |
import numpy as np
import torch
import torch.nn as nn
import warnings
from typing import Iterable
from datetime import datetime, timedelta
import ptan
import ptan.ignite as ptan_ignite
from ignite.engine import Engine
from ignite.metrics import RunningAverage
from ignite.contrib.handlers import tensorboard_logger as tb_logger
@torch.no_grad()
def calc_values_of_states(states, net, device="cpu"):
mean_vals = []
for batch in | np.array_split(states, 64) | numpy.array_split |
import numpy as np
import pandas as pds
import argparse
import warnings
np.random.seed(12349)
# cost functions available
def cost_function_misclassification_rate(labels):
# labels = labels.astype(int)
class_prob_arr = np.bincount(labels) / len(labels)
return 1 - np.max(class_prob_arr)
def cost_function_entropy(labels):
# labels = labels.astype(int)
class_prob_arr = np.bincount(labels) / len(labels)
class_prob_arr = class_prob_arr[class_prob_arr != 0]
return np.sum(class_prob_arr * np.log2(1./class_prob_arr))
def cost_function_gini_index(labels):
# labels = labels.astype(int)
class_prob_arr = np.bincount(labels) / len(labels)
return 1 - np.sum( | np.square(class_prob_arr) | numpy.square |
import numpy as np
import galsim
import batoid
from test_helpers import timer, init_gpu
@timer
def test_zernikeGQ():
if __name__ == '__main__':
nx=1024
rings=10
tol=1e-4
else:
nx=128
rings=5
tol=1e-3
telescope = batoid.Optic.fromYaml("LSST_r.yaml")
telescope.clearObscuration()
telescope['LSST.M1'].obscuration = batoid.ObscNegation(
batoid.ObscCircle(4.18)
)
zSquare = batoid.analysis.zernike(
telescope, 0.0, 0.0, 625e-9,
nx=nx, jmax=28, reference='chief'
)
zGQ = batoid.analysis.zernikeGQ(
telescope, 0.0, 0.0, 625e-9,
rings=rings, jmax=28, reference='chief'
)
np.testing.assert_allclose(
zSquare, zGQ, rtol=0, atol=tol
)
# Repeat with annular Zernikes
telescope['LSST.M1'].obscuration = batoid.ObscNegation(
batoid.ObscAnnulus(0.61*4.18, 4.18)
)
zSquare = batoid.analysis.zernike(
telescope, 0.0, 0.0, 625e-9,
nx=nx, jmax=28, reference='chief', eps=0.61
)
zGQ = batoid.analysis.zernikeGQ(
telescope, 0.0, 0.0, 625e-9,
rings=rings, jmax=28, reference='chief', eps=0.61
)
np.testing.assert_allclose(
zSquare, zGQ, rtol=0, atol=tol
)
# Try off-axis
zSquare = batoid.analysis.zernike(
telescope, np.deg2rad(0.2), np.deg2rad(0.1), 625e-9,
nx=nx, jmax=28, reference='chief', eps=0.61
)
zGQ = batoid.analysis.zernikeGQ(
telescope, np.deg2rad(0.2), np.deg2rad(0.1), 625e-9,
rings=rings, jmax=28, reference='chief', eps=0.61
)
np.testing.assert_allclose(
zSquare, zGQ, rtol=0, atol=tol
)
# Try reference == mean
# Try off-axis
zSquare = batoid.analysis.zernike(
telescope, np.deg2rad(0.2), np.deg2rad(0.1), 625e-9,
nx=nx, jmax=28, reference='mean', eps=0.61
)
zGQ = batoid.analysis.zernikeGQ(
telescope, np.deg2rad(0.2), np.deg2rad(0.1), 625e-9,
rings=rings, jmax=28, reference='mean', eps=0.61
)
# Z1-3 less reliable, but mostly uninteresting anyway...
np.testing.assert_allclose(
zSquare[4:], zGQ[4:], rtol=0, atol=tol
)
@timer
def test_huygensPSF():
telescope = batoid.Optic.fromYaml("LSST_r.yaml")
# Test that we can infer dy from dx properly
psf1 = batoid.analysis.huygensPSF(
telescope,
np.deg2rad(0.1), np.deg2rad(0.1),
620e-9,
nx=64,
nxOut=32,
dx=10e-6,
)
psf2 = batoid.analysis.huygensPSF(
telescope,
np.deg2rad(0.1), np.deg2rad(0.1),
620e-9,
nx=64,
nxOut=32,
dx=10e-6,
dy=10e-6
)
assert np.array_equal(psf1.primitiveVectors, psf2.primitiveVectors)
np.testing.assert_allclose(psf1.array, psf2.array, rtol=1e-14, atol=1e-15)
# Test vector vs scalar dx,dy
psf1 = batoid.analysis.huygensPSF(
telescope,
np.deg2rad(0.1), np.deg2rad(0.1),
620e-9,
nx=64,
nxOut=32,
dx=[10e-6, 0],
dy=[0, 11e-6]
)
psf2 = batoid.analysis.huygensPSF(
telescope,
| np.deg2rad(0.1) | numpy.deg2rad |
import numpy as np
import pkg_resources
from seekr import kmer_counts
class TestBasicCounter:
def _create_basic_counter_with_data(self, **kwargs):
infasta = 'tests/data/example.fa'
infasta = pkg_resources.resource_filename('seekr', infasta)
counter = kmer_counts.BasicCounter(infasta=infasta,
silent=True,
log2=kmer_counts.Log2.post,
**kwargs)
return counter
def test_counter_init(self):
counter = self._create_basic_counter_with_data()
assert len(counter.seqs) == 5
assert counter.seqs[0] == 'AAAAAA'
def test_occurrences_k1(self):
counter = self._create_basic_counter_with_data(k=1)
row = np.zeros(4)
expected = row.copy()
expected[0] = 1000
row = counter.occurrences(row, counter.seqs[0])
assert | np.allclose(row, expected) | numpy.allclose |
# -*- coding: utf-8 -*-
# Copyright © 2018 PyHelp Project Contributors
# https://github.com/cgq-qgc/pyhelp
#
# This file is part of PyHelp.
# Licensed under the terms of the GNU General Public License.
# ---- Standard Library Imports
import os
import os.path as osp
from multiprocessing import Pool
import multiprocessing as mp
import time
import csv
import calendar
# ---- Third Party imports
import numpy as np
# ---- Local Libraries Imports
from pyhelp import HELP3O
DEL_TEMPFILES = True
# ---- Run HELP
def run_help_singlecell(item):
"""Run HELP for a single cell."""
cellname, outparam = item
HELP3O.run_simulation(*outparam)
results = read_monthly_help_output(outparam[5])
if DEL_TEMPFILES:
os.remove(outparam[5])
return (cellname, results)
def run_help_allcells(cellparams, ncore=None):
"""Run HELP in batch for multiple cells."""
output = {}
ncore = max(mp.cpu_count() if ncore is None else ncore, 1)
tstart = time.perf_counter()
calcul_progress = 0
N = len(cellparams)
pool = Pool(ncore)
for cell in pool.imap_unordered(run_help_singlecell, cellparams.items()):
output[cell[0]] = cell[1]
calcul_progress += 1
progress_pct = calcul_progress/N*100
tpassed = time.perf_counter() - tstart
tremain = (100-progress_pct)*tpassed/progress_pct/60
print(('\rHELP simulation in progress: %3.1f%% (%0.1f min remaining)'
" ") % (progress_pct, tremain), end='')
calcul_time = (time.perf_counter() - tstart)
print('\nTask completed in %0.2f sec' % calcul_time)
return output
# ---- Read HELP output
def read_monthly_help_output(filename):
"""
Read the monthly output from .OUT HELP file and return the data as
numpy arrays stored in a dictionary. Support the output format that was
modified from HELP 3.07 (see PR#2).
"""
with open(filename, 'r') as csvfile:
csvread = list(csv.reader(csvfile))
arr_years = []
vstack_precip = []
vstack_runoff = []
vstack_evapo = []
vstack_subrun1 = []
vstack_subrun2 = []
vstack_percol = []
vstack_rechg = []
year = None
i = 0
while True:
if i+1 >= len(csvread):
break
if len(csvread[i]) == 0:
i += 1
continue
line = csvread[i][0]
if 'MONTHLY TOTALS' in line:
year = int(line.split()[-1])
arr_years.append(year)
subrun1 = None
subrun2 = np.zeros(12).astype('float32')
percol = None
while True:
i += 1
if len(csvread[i]) == 0:
continue
line = csvread[i][0]
if '**********' in line:
break
elif 'PRECIPITATION' in line:
precip = np.array(line.split()[-12:]).astype('float32')
elif 'RUNOFF' in line:
runoff = np.array(line.split()[-12:]).astype('float32')
elif 'EVAPOTRANSPIRATION' in line:
evapo = np.array(line.split()[-12:]).astype('float32')
elif 'LAT. DRAINAGE' in line:
if subrun1 is None:
subrun1 = np.array(
line.split()[-12:]).astype('float32')
else:
subrun2 += np.array(
line.split()[-12:]).astype('float32')
elif 'PERCOLATION' in line:
if percol is None:
percol = np.array(line.split()[-12:]).astype('float32')
rechg = np.array(line.split()[-12:]).astype('float32')
vstack_precip.append(precip)
vstack_runoff.append(runoff)
vstack_evapo.append(np.array(evapo).astype('float32'))
vstack_rechg.append(np.array(rechg).astype('float32'))
vstack_percol.append(np.array(percol).astype('float32'))
if subrun1 is None:
vstack_subrun1.append(np.zeros(12).astype('float32'))
else:
vstack_subrun1.append(subrun1)
vstack_subrun2.append(subrun2)
elif 'FINAL WATER STORAGE' in line:
break
i += 1
data = {'years': np.array(arr_years).astype('uint16'),
'precip': np.vstack(vstack_precip),
'runoff': np.vstack(vstack_runoff),
'evapo': np.vstack(vstack_evapo),
'subrun1': np.vstack(vstack_subrun1),
'subrun2': np.vstack(vstack_subrun2),
'perco': np.vstack(vstack_percol),
'rechg': | np.vstack(vstack_rechg) | numpy.vstack |
from six import with_metaclass
from abc import ABCMeta, abstractmethod
from collections import defaultdict
import numpy
try:
from collections.abc import Set, Mapping
except ImportError:
from collections import Set, Mapping
class AccumulatorABC(with_metaclass(ABCMeta)):
'''
ABC for an accumulator. Derived must implement:
identity: returns a new object of same type as self,
such that self + self.identity() == self
add(other): adds an object of same type as self to self
Concrete implementations are provided for __add__, __radd__, __iadd__
'''
@abstractmethod
def identity(self):
pass
@abstractmethod
def add(self, other):
pass
def __add__(self, other):
ret = self.identity()
ret.add(self)
ret.add(other)
return ret
def __radd__(self, other):
ret = self.identity()
ret.add(other)
ret.add(self)
return ret
def __iadd__(self, other):
self.add(other)
return self
class value_accumulator(AccumulatorABC):
'''
Holds a value of arbitrary type, with identity
as constructed by default_factory
'''
def __init__(self, default_factory, initial=None):
self.value = default_factory() if initial is None else initial
self.default_factory = default_factory
def __repr__(self):
if type(self.default_factory) is type:
defrepr = self.default_factory.__name__
else:
defrepr = repr(self.default_factory)
return "value_accumulator(%s, %r)" % (defrepr, self.value)
def identity(self):
return value_accumulator(self.default_factory)
def add(self, other):
if isinstance(other, value_accumulator):
self.value = self.value + other.value
else:
self.value = self.value + other
class set_accumulator(set, AccumulatorABC):
'''
A set with accumulator semantics
'''
def identity(self):
return set_accumulator()
def add(self, other):
if isinstance(other, Set):
set.update(self, other)
else:
set.add(self, other)
class dict_accumulator(dict, AccumulatorABC):
'''
Like a dict but also has accumulator semantics
It is assumed that the contents of the dict have accumulator semantics
'''
def identity(self):
ret = dict_accumulator()
for key, value in self.items():
ret[key] = value.identity()
return ret
def add(self, other):
if isinstance(other, Mapping):
for key, value in other.items():
if key not in self:
if isinstance(value, AccumulatorABC):
self[key] = value.identity()
else:
raise ValueError
self[key] += value
else:
raise ValueError
class defaultdict_accumulator(defaultdict, AccumulatorABC):
'''
Like a defaultdict but also has accumulator semantics
It is assumed that the contents of the dict have accumulator semantics
'''
def identity(self):
return defaultdict_accumulator(self.default_factory)
def add(self, other):
for key, value in other.items():
self[key] += value
class column_accumulator(AccumulatorABC):
def __init__(self, value):
if not isinstance(value, numpy.ndarray):
raise ValueError("column_accumulator only works with numpy arrays")
self._empty = | numpy.zeros(dtype=value.dtype, shape=(0,) + value.shape[1:]) | numpy.zeros |
import logging
import numpy as np
from . import timer
def inv_logtransform(plog):
""" Transform the power spectrum for the log field to the power spectrum of delta.
Inputs
------
plog - power spectrum of log field computed at points on a Fourier grid
Outputs
-------
p - power spectrum of the delta field
"""
xi_log = np.fft.ifftn(plog)
xi = np.exp(xi_log) - 1
p = np.fft.fftn(xi).real.astype('float')
return p
def logtransform(p, return_corrected=False):
""" Transform the power spectrum of delta to the power spectrum of the log field.
Inputs
------
p - power spectrum computed at points on a Fourier grid
Outputs
-------
plog - power spectrum of the log field
p_corrected - corrected input power spectrum to match.
"""
if return_corrected:
p_corrected = p.copy()
xi = np.fft.ifftn(p.astype('complex'))
if not np.min(xi.real) > -1:
logging.critical("simbox fatal error with log transform! P(k) amp is too high maybe...")
raise ValueError
logxi = np.log(1 + xi)
plog = np.fft.fftn(logxi).real.astype('float')
plog.flat[0] = 0
# Set negative modes to 0
plog[plog<0] = 0
if return_corrected:
# Do the inverse transform to compute the corrected input power spectrum
p_corrected = inv_logtransform(plog)
return plog, p_corrected
return plog
def gofft(grid):
""" Forward FFT """
with timer.Timer("FFT shape %s time"%str(grid.shape)):
n = np.prod(grid.shape)
dk = 1./n*np.fft.fftn(grid)
return dk
def gofftinv(grid):
""" inverse FFT """
with timer.Timer("inv FFT shape %s time"%str(grid.shape)):
n = np.prod(grid.shape)
d = n*np.fft.ifftn(grid)
return d
class SimBox:
""" """
def __init__(self, pk_model, shape, length, lognorm=False, apply_window=False):
""" Generate Gaussian and lognormal simulations in a box.
Inputs
------
pk_model
shape
length
lognorm
"""
self.shape = shape
self.length = length
self.step = | np.array(self.length) | numpy.array |
""" Routines related to flexure, air2vac, etc. """
import inspect
import numpy as np
import copy
from matplotlib import pyplot as plt
from matplotlib import gridspec
from scipy import interpolate
from astropy import units
from astropy.coordinates import solar_system, ICRS
from astropy.coordinates import UnitSphericalRepresentation, CartesianRepresentation
from astropy.time import Time
from linetools.spectra import xspectrum1d
from pypeit import msgs
from pypeit.core import arc
from pypeit.core import qa
from pypeit import utils
from pypeit import debugger
def load_sky_spectrum(sky_file):
"""
Load a sky spectrum into an XSpectrum1D object
Args:
sky_file: str
Returns:
sky_spec: XSpectrum1D
spectrum
"""
sky_spec = xspectrum1d.XSpectrum1D.from_file(sky_file)
return sky_spec
def flex_shift(obj_skyspec, arx_skyspec, mxshft=20):
""" Calculate shift between object sky spectrum and archive sky spectrum
Parameters
----------
obj_skyspec
arx_skyspec
Returns
-------
flex_dict: dict
Contains flexure info
"""
flex_dict = {}
# Determine the brightest emission lines
msgs.warn("If we use Paranal, cut down on wavelength early on")
arx_amp, arx_amp_cont, arx_cent, arx_wid, _, arx_w, arx_yprep, nsig = arc.detect_lines(arx_skyspec.flux.value)
obj_amp, obj_amp_cont, obj_cent, obj_wid, _, obj_w, obj_yprep, nsig_obj= arc.detect_lines(obj_skyspec.flux.value)
# Keep only 5 brightest amplitude lines (xxx_keep is array of
# indices within arx_w of the 5 brightest)
arx_keep = np.argsort(arx_amp[arx_w])[-5:]
obj_keep = np.argsort(obj_amp[obj_w])[-5:]
# Calculate wavelength (Angstrom per pixel)
arx_disp = np.append(arx_skyspec.wavelength.value[1]-arx_skyspec.wavelength.value[0],
arx_skyspec.wavelength.value[1:]-arx_skyspec.wavelength.value[:-1])
#arx_disp = (np.amax(arx_sky.wavelength.value)-np.amin(arx_sky.wavelength.value))/arx_sky.wavelength.size
obj_disp = np.append(obj_skyspec.wavelength.value[1]-obj_skyspec.wavelength.value[0],
obj_skyspec.wavelength.value[1:]-obj_skyspec.wavelength.value[:-1])
#obj_disp = (np.amax(obj_sky.wavelength.value)-np.amin(obj_sky.wavelength.value))/obj_sky.wavelength.size
# Calculate resolution (lambda/delta lambda_FWHM)..maybe don't need
# this? can just use sigmas
arx_idx = (arx_cent+0.5).astype(np.int)[arx_w][arx_keep] # The +0.5 is for rounding
arx_res = arx_skyspec.wavelength.value[arx_idx]/\
(arx_disp[arx_idx]*(2*np.sqrt(2*np.log(2)))*arx_wid[arx_w][arx_keep])
obj_idx = (obj_cent+0.5).astype(np.int)[obj_w][obj_keep] # The +0.5 is for rounding
obj_res = obj_skyspec.wavelength.value[obj_idx]/ \
(obj_disp[obj_idx]*(2*np.sqrt(2*np.log(2)))*obj_wid[obj_w][obj_keep])
#obj_res = (obj_sky.wavelength.value[0]+(obj_disp*obj_cent[obj_w][obj_keep]))/(
# obj_disp*(2*np.sqrt(2*np.log(2)))*obj_wid[obj_w][obj_keep])
if not np.all( | np.isfinite(obj_res) | numpy.isfinite |
from __future__ import division
import glob
import numpy as NP
from functools import reduce
import numpy.ma as MA
import progressbar as PGB
import h5py
import healpy as HP
import warnings
import copy
import astropy.cosmology as CP
from astropy.time import Time, TimeDelta
from astropy.io import fits
from astropy import units as U
from astropy import constants as FCNST
from scipy import interpolate
from astroutils import DSP_modules as DSP
from astroutils import constants as CNST
from astroutils import nonmathops as NMO
from astroutils import mathops as OPS
from astroutils import lookup_operations as LKP
import prisim
from prisim import interferometry as RI
from prisim import primary_beams as PB
from prisim import delay_spectrum as DS
try:
from pyuvdata import UVBeam
except ImportError:
uvbeam_module_found = False
else:
uvbeam_module_found = True
prisim_path = prisim.__path__[0]+'/'
cosmoPlanck15 = CP.Planck15 # Planck 2015 cosmology
cosmo100 = cosmoPlanck15.clone(name='Modified Planck 2015 cosmology with h=1.0', H0=100.0) # Modified Planck 2015 cosmology with h=1.0, H= 100 km/s/Mpc
################################################################################
def write_PRISim_bispectrum_phase_to_npz(infile_prefix, outfile_prefix,
triads=None, bltriplet=None,
hdf5file_prefix=None, infmt='npz',
datakey='noisy', blltol=0.1):
"""
----------------------------------------------------------------------------
Write closure phases computed in a PRISim simulation to a NPZ file with
appropriate format for further analysis.
Inputs:
infile_prefix
[string] HDF5 file or NPZ file created by a PRISim simulation or
its replication respectively. If infmt is specified as 'hdf5',
then hdf5file_prefix will be ignored and all the observing
info will be read from here. If infmt is specified as 'npz',
then hdf5file_prefix needs to be specified in order to read the
observing parameters.
triads [list or numpy array or None] Antenna triads given as a list of
3-element lists or a ntriads x 3 array. Each element in the
inner list is an antenna label. They will be converted to
strings internally. If set to None, then all triads determined
by bltriplet will be used. If specified, then inputs in blltol
and bltriplet will be ignored.
bltriplet [numpy array or None] 3x3 numpy array containing the 3 baseline
vectors. The first axis denotes the three baselines, the second
axis denotes the East, North, Up coordinates of the baseline
vector. Units are in m. Will be used only if triads is set to
None.
outfile_prefix
[string] Prefix of the NPZ file. It will be appended by
'_noiseless', '_noisy', and '_noise' and further by extension
'.npz'
infmt [string] Format of the input file containing visibilities.
Accepted values are 'npz' (default), and 'hdf5'. If infmt is
specified as 'npz', then hdf5file_prefix also needs to be
specified for reading the observing parameters
datakey [string] Specifies which -- 'noiseless', 'noisy' (default), or
'noise' -- visibilities are to be written to the output. If set
to None, and infmt is 'hdf5', then all three sets of
visibilities are written. The datakey string will also be added
as a suffix in the output file.
blltol [scalar] Baseline length tolerance (in m) for matching baseline
vectors in triads. It must be a scalar. Default = 0.1 m. Will
be used only if triads is set to None and bltriplet is to be
used.
----------------------------------------------------------------------------
"""
if not isinstance(infile_prefix, str):
raise TypeError('Input infile_prefix must be a string')
if not isinstance(outfile_prefix, str):
raise TypeError('Input outfile_prefix must be a string')
if (triads is None) and (bltriplet is None):
raise ValueError('One of triads or bltriplet must be set')
if triads is None:
if not isinstance(bltriplet, NP.ndarray):
raise TypeError('Input bltriplet must be a numpy array')
if not isinstance(blltol, (int,float)):
raise TypeError('Input blltol must be a scalar')
if bltriplet.ndim != 2:
raise ValueError('Input bltriplet must be a 2D numpy array')
if bltriplet.shape[0] != 3:
raise ValueError('Input bltriplet must contain three baseline vectors')
if bltriplet.shape[1] != 3:
raise ValueError('Input bltriplet must contain baseline vectors along three corrdinates in the ENU frame')
else:
if not isinstance(triads, (list, NP.ndarray)):
raise TypeError('Input triads must be a list or numpy array')
triads = NP.asarray(triads).astype(str)
if not isinstance(infmt, str):
raise TypeError('Input infmt must be a string')
if infmt.lower() not in ['npz', 'hdf5']:
raise ValueError('Input file format must be npz or hdf5')
if infmt.lower() == 'npz':
if not isinstance(hdf5file_prefix, str):
raise TypeError('If infmt is npz, then hdf5file_prefix needs to be specified for observing parameters information')
if datakey is None:
datakey = ['noisy']
if isinstance(datakey, str):
datakey = [datakey]
elif not isinstance(datakey, list):
raise TypeError('Input datakey must be a list')
for dkey in datakey:
if dkey.lower() not in ['noiseless', 'noisy', 'noise']:
raise ValueError('Invalid input found in datakey')
if infmt.lower() == 'hdf5':
fullfnames_with_extension = glob.glob(infile_prefix + '*' + infmt.lower())
fullfnames_without_extension = [fname.split('.hdf5')[0] for fname in fullfnames_with_extension]
else:
fullfnames_without_extension = [infile_prefix]
if len(fullfnames_without_extension) == 0:
raise IOError('No input files found with pattern {0}'.format(infile_prefix))
try:
if infmt.lower() == 'hdf5':
simvis = RI.InterferometerArray(None, None, None, init_file=fullfnames_without_extension[0])
else:
simvis = RI.InterferometerArray(None, None, None, init_file=hdf5file_prefix)
except:
raise IOError('Input PRISim file does not contain a valid PRISim output')
latitude = simvis.latitude
longitude = simvis.longitude
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
last = simvis.lst / 15.0 / 24.0 # from degrees to fraction of day
last = last.reshape(-1,1)
daydata = NP.asarray(simvis.timestamp[0]).ravel()
if infmt.lower() == 'npz':
simvisinfo = NP.load(fullfnames_without_extension[0]+'.'+infmt.lower())
skyvis = simvisinfo['noiseless'][0,...]
vis = simvisinfo['noisy']
noise = simvisinfo['noise']
n_realize = vis.shape[0]
else:
n_realize = len(fullfnames_without_extension)
cpdata = {}
outfile = {}
for fileind in range(n_realize):
if infmt.lower() == 'npz':
simvis.vis_freq = vis[fileind,...]
simvis.vis_noise_freq = noise[fileind,...]
else:
simvis = RI.InterferometerArray(None, None, None, init_file=fullfnames_without_extension[fileind])
if fileind == 0:
if triads is None:
triads, bltriplets = simvis.getThreePointCombinations(unique=False)
# triads = NP.asarray(prisim_BSP_info['antenna_triplets']).reshape(-1,3)
# bltriplets = NP.asarray(prisim_BSP_info['baseline_triplets'])
triads = NP.asarray(triads).reshape(-1,3)
bltriplets = NP.asarray(bltriplets)
blinds = []
matchinfo = LKP.find_NN(bltriplet, bltriplets.reshape(-1,3), distance_ULIM=blltol)
revind = []
for blnum in NP.arange(bltriplet.shape[0]):
if len(matchinfo[0][blnum]) == 0:
revind += [blnum]
if len(revind) > 0:
flip_factor = NP.ones(3, dtype=NP.float)
flip_factor[NP.array(revind)] = -1
rev_bltriplet = bltriplet * flip_factor.reshape(-1,1)
matchinfo = LKP.find_NN(rev_bltriplet, bltriplets.reshape(-1,3), distance_ULIM=blltol)
for blnum in NP.arange(bltriplet.shape[0]):
if len(matchinfo[0][blnum]) == 0:
raise ValueError('Some baselines in the triplet are not found in the model triads')
triadinds = []
for blnum in NP.arange(bltriplet.shape[0]):
triadind, blind = NP.unravel_index(NP.asarray(matchinfo[0][blnum]), (bltriplets.shape[0], bltriplets.shape[1]))
triadinds += [triadind]
triadind_intersection = NP.intersect1d(triadinds[0], NP.intersect1d(triadinds[1], triadinds[2]))
if triadind_intersection.size == 0:
raise ValueError('Specified triad not found in the PRISim model. Try other permutations of the baseline vectors and/or reverse individual baseline vectors in the triad before giving up.')
triads = triads[triadind_intersection,:]
selected_bltriplets = bltriplets[triadind_intersection,:,:].reshape(-1,3,3)
prisim_BSP_info = simvis.getClosurePhase(antenna_triplets=triads.tolist(),
delay_filter_info=None,
specsmooth_info=None,
spectral_window_info=None,
unique=False)
if fileind == 0:
triads = NP.asarray(prisim_BSP_info['antenna_triplets']).reshape(-1,3) # Re-establish the triads returned after the first iteration (to accunt for any order flips)
for outkey in datakey:
if fileind == 0:
outfile[outkey] = outfile_prefix + '_{0}.npz'.format(outkey)
if outkey == 'noiseless':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_skyvis'][triadind_intersection,:,:][NP.newaxis,...]
cpdata[outkey] = prisim_BSP_info['closure_phase_skyvis'][NP.newaxis,...]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_skyvis'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_skyvis'][NP.newaxis,...]), axis=0)
if outkey == 'noisy':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_vis'][triadind_intersection,:,:][NP.newaxis,...]
cpdata[outkey] = prisim_BSP_info['closure_phase_vis'][NP.newaxis,...]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_vis'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_vis'][NP.newaxis,...]), axis=0)
if outkey == 'noise':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_noise'][triadind_intersection,:,:]
cpdata[outkey] = prisim_BSP_info['closure_phase_noise'][NP.newaxis,:,:]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_noise'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_noise'][NP.newaxis,...]), axis=0)
for outkey in datakey:
cpdata[outkey] = NP.rollaxis(cpdata[outkey], 3, start=0)
flagsdata = NP.zeros(cpdata[outkey].shape, dtype=NP.bool)
NP.savez_compressed(outfile[outkey], closures=cpdata[outkey],
flags=flagsdata, triads=triads,
last=last+NP.zeros((1,n_realize)),
days=daydata+NP.arange(n_realize))
################################################################################
def loadnpz(npzfile, longitude=0.0, latitude=0.0, lst_format='fracday'):
"""
----------------------------------------------------------------------------
Read an input NPZ file containing closure phase data output from CASA and
return a dictionary
Inputs:
npzfile [string] Input NPZ file including full path containing closure
phase data. It must have the following files/keys inside:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA units
which is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is (nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard deviation
of closure phases across days. Shape is
(nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard deviation
of closure phases across triads. Shape is
(nlst,ndays,nchan)
latitude [scalar int or float] Latitude of site (in degrees).
Default=0.0 deg.
longitude [scalar int or float] Longitude of site (in degrees).
Default=0.0 deg.
lst_format [string] Specifies the format/units in which the 'last' key
is to be interpreted. If set to 'hourangle', the LST is in
units of hour angle. If set to 'fracday', the fractional
portion of the 'last' value is the LST in units of days.
Output:
cpinfo [dictionary] Contains one top level keys, namely, 'raw'
Under key 'raw' which holds a dictionary, the subkeys
include 'cphase' (nlst,ndays,ntriads,nchan),
'triads' (ntriads,3), 'lst' (nlst,ndays), and 'flags'
(nlst,ndays,ntriads,nchan), and some other optional keys
----------------------------------------------------------------------------
"""
npzdata = NP.load(npzfile)
cpdata = npzdata['closures']
triadsdata = npzdata['triads']
flagsdata = npzdata['flags']
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
daydata = Time(npzdata['days'].astype(NP.float64), scale='utc', format='jd', location=location)
# lstdata = Time(npzdata['last'].astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=('+21.4278d', '-30.7224d')).sidereal_time('apparent') # Subtract 6713 based on CASA convention to obtain MJD
if lst_format.lower() == 'hourangle':
lstHA = npzdata['last']
lstday = daydata.reshape(1,-1) + TimeDelta(NP.zeros(lstHA.shape[0]).reshape(-1,1)*U.s)
elif lst_format.lower() == 'fracday':
lstfrac, lstint = NP.modf(npzdata['last'])
lstday = Time(lstint.astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=location) # Subtract 6713 based on CASA convention to obtain MJD
lstHA = lstfrac * 24.0 # in hours
else:
raise ValueError('Input lst_format invalid')
cp = cpdata.astype(NP.float64)
flags = flagsdata.astype(NP.bool)
cpinfo = {}
datapool = ['raw']
for dpool in datapool:
cpinfo[dpool] = {}
if dpool == 'raw':
qtys = ['cphase', 'triads', 'flags', 'lst', 'lst-day', 'days', 'dayavg', 'std_triads', 'std_lst']
for qty in qtys:
if qty == 'cphase':
cpinfo[dpool][qty] = NP.copy(cp)
elif qty == 'triads':
cpinfo[dpool][qty] = NP.copy(triadsdata)
elif qty == 'flags':
cpinfo[dpool][qty] = NP.copy(flags)
elif qty == 'lst':
cpinfo[dpool][qty] = NP.copy(lstHA)
elif qty == 'lst-day':
cpinfo[dpool][qty] = NP.copy(lstday.jd)
elif qty == 'days':
cpinfo[dpool][qty] = NP.copy(daydata.jd)
elif qty == 'dayavg':
if 'averaged_closures' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_dayavg)
elif qty == 'std_triads':
if 'std_dev_triad' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_std_triads)
elif qty == 'std_lst':
if 'std_dev_lst' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_std_lst)
return cpinfo
################################################################################
def npz2hdf5(npzfile, hdf5file, longitude=0.0, latitude=0.0,
lst_format='fracday'):
"""
----------------------------------------------------------------------------
Read an input NPZ file containing closure phase data output from CASA and
save it to HDF5 format
Inputs:
npzfile [string] Input NPZ file including full path containing closure
phase data. It must have the following files/keys inside:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA units
ehich is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is (nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard deviation
of closure phases across days. Shape is
(nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard deviation
of closure phases across triads. Shape is
(nlst,ndays,nchan)
hdf5file [string] Output HDF5 file including full path.
latitude [scalar int or float] Latitude of site (in degrees).
Default=0.0 deg.
longitude [scalar int or float] Longitude of site (in degrees).
Default=0.0 deg.
lst_format [string] Specifies the format/units in which the 'last' key
is to be interpreted. If set to 'hourangle', the LST is in
units of hour angle. If set to 'fracday', the fractional
portion of the 'last' value is the LST in units of days.
----------------------------------------------------------------------------
"""
npzdata = NP.load(npzfile)
cpdata = npzdata['closures']
triadsdata = npzdata['triads']
flagsdata = npzdata['flags']
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
daydata = Time(npzdata['days'].astype(NP.float64), scale='utc', format='jd', location=location)
# lstdata = Time(npzdata['last'].astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=('+21.4278d', '-30.7224d')).sidereal_time('apparent') # Subtract 6713 based on CASA convention to obtain MJD
if lst_format.lower() == 'hourangle':
lstHA = npzdata['last']
lstday = daydata.reshape(1,-1) + TimeDelta(NP.zeros(lstHA.shape[0]).reshape(-1,1)*U.s)
elif lst_format.lower() == 'fracday':
lstfrac, lstint = NP.modf(npzdata['last'])
lstday = Time(lstint.astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=location) # Subtract 6713 based on CASA convention to obtain MJD
lstHA = lstfrac * 24.0 # in hours
else:
raise ValueError('Input lst_format invalid')
cp = cpdata.astype(NP.float64)
flags = flagsdata.astype(NP.bool)
if 'averaged_closures' in npzdata:
day_avg_cpdata = npzdata['averaged_closures']
cp_dayavg = day_avg_cpdata.astype(NP.float64)
if 'std_dev_triad' in npzdata:
std_triads_cpdata = npzdata['std_dev_triad']
cp_std_triads = std_triads_cpdata.astype(NP.float64)
if 'std_dev_lst' in npzdata:
std_lst_cpdata = npzdata['std_dev_lst']
cp_std_lst = std_lst_cpdata.astype(NP.float64)
with h5py.File(hdf5file, 'w') as fobj:
datapool = ['raw']
for dpool in datapool:
if dpool == 'raw':
qtys = ['cphase', 'triads', 'flags', 'lst', 'lst-day', 'days', 'dayavg', 'std_triads', 'std_lst']
for qty in qtys:
data = None
if qty == 'cphase':
data = NP.copy(cp)
elif qty == 'triads':
data = NP.copy(triadsdata)
elif qty == 'flags':
data = NP.copy(flags)
elif qty == 'lst':
data = NP.copy(lstHA)
elif qty == 'lst-day':
data = NP.copy(lstday.jd)
elif qty == 'days':
data = NP.copy(daydata.jd)
elif qty == 'dayavg':
if 'averaged_closures' in npzdata:
data = NP.copy(cp_dayavg)
elif qty == 'std_triads':
if 'std_dev_triad' in npzdata:
data = NP.copy(cp_std_triads)
elif qty == 'std_lst':
if 'std_dev_lst' in npzdata:
data = NP.copy(cp_std_lst)
if data is not None:
dset = fobj.create_dataset('{0}/{1}'.format(dpool, qty), data=data, compression='gzip', compression_opts=9)
################################################################################
def save_CPhase_cross_power_spectrum(xcpdps, outfile):
"""
----------------------------------------------------------------------------
Save cross-power spectrum information in a dictionary to a HDF5 file
Inputs:
xcpdps [dictionary] This dictionary is essentially an output of the
member function compute_power_spectrum() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains one or more of the following keys named
'whole', 'submodel', 'residual', and 'errinfo' each of which is
a dictionary. 'whole' contains power spectrum info about the
input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure
phase) from the 'whole' model. 'residual' contains power
spectrum info about the closure phases obtained as a difference
between 'whole' and 'submodel'. It contains the following keys
and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
outfile [string] Full path to the external HDF5 file where the cross-
power spectrum information provided in xcpdps will be saved
----------------------------------------------------------------------------
"""
if not isinstance(xcpdps, dict):
raise TypeError('Input xcpdps must be a dictionary')
with h5py.File(outfile, 'w') as fileobj:
hdrgrp = fileobj.create_group('header')
hdrkeys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in hdrkeys:
dset = hdrgrp.create_dataset(key, data=xcpdps[key])
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'kprll', 'lags', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in xcpdps:
smplgrp = fileobj.create_group(smplng)
for key in sampling_keys:
dset = smplgrp.create_dataset(key, data=xcpdps[smplng][key])
for dpool in dpool_keys:
if dpool in xcpdps[smplng]:
dpoolgrp = smplgrp.create_group(dpool)
keys = ['diagoffsets', 'diagweights', 'axesmap', 'nsamples_incoh', 'nsamples_coh']
for key in keys:
if key in xcpdps[smplng][dpool]:
if isinstance(xcpdps[smplng][dpool][key], dict):
subgrp = dpoolgrp.create_group(key)
for subkey in xcpdps[smplng][dpool][key]:
dset = subgrp.create_dataset(str(subkey), data=xcpdps[smplng][dpool][key][subkey])
else:
dset = dpoolgrp.create_dataset(key, data=xcpdps[smplng][dpool][key])
for stat in ['mean', 'median']:
if stat in xcpdps[smplng][dpool]:
if isinstance(xcpdps[smplng][dpool][stat], list):
for ii in range(len(xcpdps[smplng][dpool][stat])):
dset = dpoolgrp.create_dataset(stat+'/diagcomb_{0}'.format(ii), data=xcpdps[smplng][dpool][stat][ii].si.value)
dset.attrs['units'] = str(xcpdps[smplng][dpool][stat][ii].si.unit)
else:
dset = dpoolgrp.create_dataset(stat, data=xcpdps[smplng][dpool][stat].si.value)
dset.attrs['units'] = str(xcpdps[smplng][dpool][stat].si.unit)
################################################################################
def read_CPhase_cross_power_spectrum(infile):
"""
----------------------------------------------------------------------------
Read information about cross power spectrum from an external HDF5 file into
a dictionary. This is the counterpart to save_CPhase_corss_power_spectrum()
Input:
infile [string] Full path to the external HDF5 file that contains info
about cross-power spectrum.
Output:
xcpdps [dictionary] This dictionary has structure the same as output
of the member function compute_power_spectrum() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains one or more of the following keys named
'whole', 'submodel', 'residual', and 'errinfo' each of which is
a dictionary. 'whole' contains power spectrum info about the
input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure
phase) from the 'whole' model. 'residual' contains power
spectrum info about the closure phases obtained as a difference
between 'whole' and 'submodel'. It contains the following keys
and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
outfile [string] Full path to the external HDF5 file where the cross-
power spectrum information provided in xcpdps will be saved
----------------------------------------------------------------------------
"""
if not isinstance(infile, str):
raise TypeError('Input infile must be a string')
xcpdps = {}
with h5py.File(infile, 'r') as fileobj:
hdrgrp = fileobj['header']
hdrkeys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in hdrkeys:
xcpdps[key] = hdrgrp[key].value
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'kprll', 'lags', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in fileobj:
smplgrp = fileobj[smplng]
xcpdps[smplng] = {}
for key in sampling_keys:
xcpdps[smplng][key] = smplgrp[key].value
for dpool in dpool_keys:
if dpool in smplgrp:
xcpdps[smplng][dpool] = {}
dpoolgrp = smplgrp[dpool]
keys = ['diagoffsets', 'diagweights', 'axesmap', 'nsamples_incoh', 'nsamples_coh']
for key in keys:
if key in dpoolgrp:
if isinstance(dpoolgrp[key], h5py.Group):
xcpdps[smplng][dpool][key] = {}
for subkey in dpoolgrp[key]:
xcpdps[smplng][dpool][key][int(subkey)] = dpoolgrp[key][subkey].value
elif isinstance(dpoolgrp[key], h5py.Dataset):
xcpdps[smplng][dpool][key] = dpoolgrp[key].value
else:
raise TypeError('Invalid h5py data type encountered')
for stat in ['mean', 'median']:
if stat in dpoolgrp:
if isinstance(dpoolgrp[stat], h5py.Dataset):
valunits = dpoolgrp[stat].attrs['units']
xcpdps[smplng][dpool][stat] = dpoolgrp[stat].value * U.Unit(valunits)
elif isinstance(dpoolgrp[stat], h5py.Group):
xcpdps[smplng][dpool][stat] = []
for diagcomb_ind in range(len(dpoolgrp[stat].keys())):
if 'diagcomb_{0}'.format(diagcomb_ind) in dpoolgrp[stat]:
valunits = dpoolgrp[stat]['diagcomb_{0}'.format(diagcomb_ind)].attrs['units']
xcpdps[smplng][dpool][stat] += [dpoolgrp[stat]['diagcomb_{0}'.format(diagcomb_ind)].value * U.Unit(valunits)]
return xcpdps
################################################################################
def incoherent_cross_power_spectrum_average(xcpdps, excpdps=None, diagoffsets=None):
"""
----------------------------------------------------------------------------
Perform incoherent averaging of cross power spectrum along specified axes
Inputs:
xcpdps [dictionary or list of dictionaries] If provided as a list of
dictionaries, each dictionary consists of cross power spectral
information coming possible from different sources, and they
will be averaged be averaged incoherently. If a single
dictionary is provided instead of a list of dictionaries, the
said averaging does not take place. Each dictionary is
essentially an output of the member function
compute_power_spectrum() of class ClosurePhaseDelaySpectrum. It
has the following key-value structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and
'residual' each of which is a dictionary. 'whole' contains power
spectrum info about the input closure phases. 'submodel'
contains power spectrum info about the model that will have been
subtracted (as closure phase) from the 'whole' model. 'residual'
contains power spectrum info about the closure phases obtained
as a difference between 'whole' and 'submodel'. It contains the
following keys and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
excpdps [dictionary or list of dictionaries] If provided as a list of
dictionaries, each dictionary consists of cross power spectral
information of subsample differences coming possible from
different sources, and they will be averaged be averaged
incoherently. This is optional. If not set (default=None), no
incoherent averaging happens. If a single dictionary is provided
instead of a list of dictionaries, the said averaging does not
take place. Each dictionary is essentially an output of the
member function compute_power_spectrum_uncertainty() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndaycomb,) array), 'day_ind' ((ndaycomb,)
array), 'dday' ((ndaycomb,) array), 'oversampled' and
'resampled' corresponding to whether resample was set to False
or True in call to member function FT(). Values under keys
'triads_ind' and 'lst_ind' are numpy array corresponding to
triad and time indices used in selecting the data. Values under
keys 'oversampled' and 'resampled' each contain a dictionary
with the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz) of
the frequency subbands of the subband delay spectra. It
is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform.
It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains a key named 'errinfo' which is a dictionary.
It contains information about power spectrum uncertainties
obtained from subsample differences. It contains the following
keys and values:
'mean' [numpy array] Delay power spectrum uncertainties
incoherently estimated over the axes specified in
xinfo['axes'] using the 'mean' key in input cpds or
attribute cPhaseDS['errinfo']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided but avgcov is
False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum uncertainties
incoherently averaged over the axes specified in incohax
using the 'median' key in input cpds or attribute
cPhaseDS['errinfo']['dspec']. It has shape that depends
on the combination of input parameters. See examples
below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance
matrices. If collapse_axes is provided but avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal offsets
for those axes. If 'avgcov' was set, those entries will
be removed from 'diagoffsets' since all the leading
diagonal elements have been collapsed (averaged) further.
Value under each key is a numpy array where each element
in the array corresponds to the index of that leading
diagonal. This should match the size of the output along
that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
diagoffsets [NoneType or dictionary or list of dictionaries] This info is
used for incoherent averaging along specified diagonals along
specified axes. This incoherent averaging is performed after
incoherently averaging multiple cross-power spectra (if any).
If set to None, this incoherent averaging is not performed.
Many combinations of axes and diagonals can be specified as
individual dictionaries in a list. If only one dictionary is
specified, then it assumed that only one combination of axes
and diagonals is requested. If a list of dictionaries is given,
each dictionary in the list specifies a different combination
for incoherent averaging. Each dictionary should have the
following key-value pairs. The key is the axis number (allowed
values are 1, 2, 3) that denote the axis type (1=LST, 2=Days,
3=Triads to be averaged), and the value under they keys is a
list or numpy array of diagonals to be averaged incoherently.
These axes-diagonal combinations apply to both the inputs
xcpdps and excpdps, except axis=2 does not apply to excpdps
(since it is made of subsample differences already) and will be
skipped.
Outputs:
A tuple consisting of two dictionaries. The first dictionary contains the
incoherent averaging of xcpdps as specified by the inputs, while the second
consists of incoherent of excpdps as specified by the inputs. The structure
of these dictionaries are practically the same as the dictionary inputs
xcpdps and excpdps respectively. The only differences in dictionary
structure are:
* Under key ['oversampled'/'resampled']['whole'/'submodel'/'residual'
/'effinfo']['mean'/'median'] is a list of numpy arrays, where each
array in the list corresponds to the dictionary in the list in input
diagoffsets that defines the axes-diagonal combination.
----------------------------------------------------------------------------
"""
if isinstance(xcpdps, dict):
xcpdps = [xcpdps]
if not isinstance(xcpdps, list):
raise TypeError('Invalid data type provided for input xcpdps')
if excpdps is not None:
if isinstance(excpdps, dict):
excpdps = [excpdps]
if not isinstance(excpdps, list):
raise TypeError('Invalid data type provided for input excpdps')
if len(xcpdps) != len(excpdps):
raise ValueError('Inputs xcpdps and excpdps found to have unequal number of values')
out_xcpdps = {'triads': xcpdps[0]['triads'], 'triads_ind': xcpdps[0]['triads_ind'], 'lst': xcpdps[0]['lst'], 'lst_ind': xcpdps[0]['lst_ind'], 'dlst': xcpdps[0]['dlst'], 'days': xcpdps[0]['days'], 'day_ind': xcpdps[0]['day_ind'], 'dday': xcpdps[0]['dday']}
out_excpdps = None
if excpdps is not None:
out_excpdps = {'triads': excpdps[0]['triads'], 'triads_ind': excpdps[0]['triads_ind'], 'lst': excpdps[0]['lst'], 'lst_ind': excpdps[0]['lst_ind'], 'dlst': excpdps[0]['dlst'], 'days': excpdps[0]['days'], 'day_ind': excpdps[0]['day_ind'], 'dday': excpdps[0]['dday']}
for smplng in ['oversampled', 'resampled']:
if smplng in xcpdps[0]:
out_xcpdps[smplng] = {'z': xcpdps[0][smplng]['z'], 'kprll': xcpdps[0][smplng]['kprll'], 'lags': xcpdps[0][smplng]['lags'], 'freq_center': xcpdps[0][smplng]['freq_center'], 'bw_eff': xcpdps[0][smplng]['bw_eff'], 'shape': xcpdps[0][smplng]['shape'], 'freq_wts': xcpdps[0][smplng]['freq_wts'], 'lag_corr_length': xcpdps[0][smplng]['lag_corr_length']}
if excpdps is not None:
out_excpdps[smplng] = {'z': excpdps[0][smplng]['z'], 'kprll': excpdps[0][smplng]['kprll'], 'lags': excpdps[0][smplng]['lags'], 'freq_center': excpdps[0][smplng]['freq_center'], 'bw_eff': excpdps[0][smplng]['bw_eff'], 'shape': excpdps[0][smplng]['shape'], 'freq_wts': excpdps[0][smplng]['freq_wts'], 'lag_corr_length': excpdps[0][smplng]['lag_corr_length']}
for dpool in ['whole', 'submodel', 'residual']:
if dpool in xcpdps[0][smplng]:
out_xcpdps[smplng][dpool] = {'diagoffsets': xcpdps[0][smplng][dpool]['diagoffsets'], 'axesmap': xcpdps[0][smplng][dpool]['axesmap']}
for stat in ['mean', 'median']:
if stat in xcpdps[0][smplng][dpool]:
out_xcpdps[smplng][dpool][stat] = {}
arr = []
diagweights = []
for i in range(len(xcpdps)):
arr += [xcpdps[i][smplng][dpool][stat].si.value]
arr_units = xcpdps[i][smplng][dpool][stat].si.unit
if isinstance(xcpdps[i][smplng][dpool]['diagweights'], dict):
diagwts = 1.0
diagwts_shape = NP.ones(xcpdps[i][smplng][dpool][stat].ndim, dtype=NP.int)
for ax in xcpdps[i][smplng][dpool]['diagweights']:
tmp_shape = NP.copy(diagwts_shape)
tmp_shape[xcpdps[i][smplng][dpool]['axesmap'][ax]] = xcpdps[i][smplng][dpool]['diagweights'][ax].size
diagwts = diagwts * xcpdps[i][smplng][dpool]['diagweights'][ax].reshape(tuple(tmp_shape))
elif isinstance(xcpdps[i][smplng][dpool]['diagweights'], NP.ndarray):
diagwts = NP.copy(xcpdps[i][smplng][dpool]['diagweights'])
else:
raise TypeError('Diagonal weights in input must be a dictionary or a numpy array')
diagweights += [diagwts]
diagweights = NP.asarray(diagweights)
arr = NP.asarray(arr)
arr = NP.nansum(arr * diagweights, axis=0) / NP.nansum(diagweights, axis=0) * arr_units
diagweights = NP.nansum(diagweights, axis=0)
out_xcpdps[smplng][dpool][stat] = arr
out_xcpdps[smplng][dpool]['diagweights'] = diagweights
for dpool in ['errinfo']:
if dpool in excpdps[0][smplng]:
out_excpdps[smplng][dpool] = {'diagoffsets': excpdps[0][smplng][dpool]['diagoffsets'], 'axesmap': excpdps[0][smplng][dpool]['axesmap']}
for stat in ['mean', 'median']:
if stat in excpdps[0][smplng][dpool]:
out_excpdps[smplng][dpool][stat] = {}
arr = []
diagweights = []
for i in range(len(excpdps)):
arr += [excpdps[i][smplng][dpool][stat].si.value]
arr_units = excpdps[i][smplng][dpool][stat].si.unit
if isinstance(excpdps[i][smplng][dpool]['diagweights'], dict):
diagwts = 1.0
diagwts_shape = NP.ones(excpdps[i][smplng][dpool][stat].ndim, dtype=NP.int)
for ax in excpdps[i][smplng][dpool]['diagweights']:
tmp_shape = NP.copy(diagwts_shape)
tmp_shape[excpdps[i][smplng][dpool]['axesmap'][ax]] = excpdps[i][smplng][dpool]['diagweights'][ax].size
diagwts = diagwts * excpdps[i][smplng][dpool]['diagweights'][ax].reshape(tuple(tmp_shape))
elif isinstance(excpdps[i][smplng][dpool]['diagweights'], NP.ndarray):
diagwts = NP.copy(excpdps[i][smplng][dpool]['diagweights'])
else:
raise TypeError('Diagonal weights in input must be a dictionary or a numpy array')
diagweights += [diagwts]
diagweights = NP.asarray(diagweights)
arr = NP.asarray(arr)
arr = NP.nansum(arr * diagweights, axis=0) / NP.nansum(diagweights, axis=0) * arr_units
diagweights = NP.nansum(diagweights, axis=0)
out_excpdps[smplng][dpool][stat] = arr
out_excpdps[smplng][dpool]['diagweights'] = diagweights
if diagoffsets is not None:
if isinstance(diagoffsets, dict):
diagoffsets = [diagoffsets]
if not isinstance(diagoffsets, list):
raise TypeError('Input diagoffsets must be a list of dictionaries')
for ind in range(len(diagoffsets)):
for ax in diagoffsets[ind]:
if not isinstance(diagoffsets[ind][ax], (list, NP.ndarray)):
raise TypeError('Values in input dictionary diagoffsets must be a list or numpy array')
diagoffsets[ind][ax] = NP.asarray(diagoffsets[ind][ax])
for smplng in ['oversampled', 'resampled']:
if smplng in out_xcpdps:
for dpool in ['whole', 'submodel', 'residual']:
if dpool in out_xcpdps[smplng]:
masks = []
for ind in range(len(diagoffsets)):
mask_ones = NP.ones(out_xcpdps[smplng][dpool]['diagweights'].shape, dtype=NP.bool)
mask_agg = None
for ax in diagoffsets[ind]:
mltdim_slice = [slice(None)] * mask_ones.ndim
mltdim_slice[out_xcpdps[smplng][dpool]['axesmap'][ax].squeeze()] = NP.where(NP.isin(out_xcpdps[smplng][dpool]['diagoffsets'][ax], diagoffsets[ind][ax]))[0]
mask_tmp = NP.copy(mask_ones)
mask_tmp[tuple(mltdim_slice)] = False
if mask_agg is None:
mask_agg = NP.copy(mask_tmp)
else:
mask_agg = NP.logical_or(mask_agg, mask_tmp)
masks += [NP.copy(mask_agg)]
diagwts = NP.copy(out_xcpdps[smplng][dpool]['diagweights'])
out_xcpdps[smplng][dpool]['diagweights'] = []
for stat in ['mean', 'median']:
if stat in out_xcpdps[smplng][dpool]:
arr = NP.copy(out_xcpdps[smplng][dpool][stat].si.value)
arr_units = out_xcpdps[smplng][dpool][stat].si.unit
out_xcpdps[smplng][dpool][stat] = []
for ind in range(len(diagoffsets)):
masked_diagwts = MA.array(diagwts, mask=masks[ind])
axes_to_avg = tuple([out_xcpdps[smplng][dpool]['axesmap'][ax][0] for ax in diagoffsets[ind]])
out_xcpdps[smplng][dpool][stat] += [MA.sum(arr * masked_diagwts, axis=axes_to_avg, keepdims=True) / MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True) * arr_units]
if len(out_xcpdps[smplng][dpool]['diagweights']) < len(diagoffsets):
out_xcpdps[smplng][dpool]['diagweights'] += [MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True)]
if excpdps is not None:
for smplng in ['oversampled', 'resampled']:
if smplng in out_excpdps:
for dpool in ['errinfo']:
if dpool in out_excpdps[smplng]:
masks = []
for ind in range(len(diagoffsets)):
mask_ones = NP.ones(out_excpdps[smplng][dpool]['diagweights'].shape, dtype=NP.bool)
mask_agg = None
for ax in diagoffsets[ind]:
if ax != 2:
mltdim_slice = [slice(None)] * mask_ones.ndim
mltdim_slice[out_excpdps[smplng][dpool]['axesmap'][ax].squeeze()] = NP.where(NP.isin(out_excpdps[smplng][dpool]['diagoffsets'][ax], diagoffsets[ind][ax]))[0]
mask_tmp = NP.copy(mask_ones)
mask_tmp[tuple(mltdim_slice)] = False
if mask_agg is None:
mask_agg = NP.copy(mask_tmp)
else:
mask_agg = NP.logical_or(mask_agg, mask_tmp)
masks += [NP.copy(mask_agg)]
diagwts = NP.copy(out_excpdps[smplng][dpool]['diagweights'])
out_excpdps[smplng][dpool]['diagweights'] = []
for stat in ['mean', 'median']:
if stat in out_excpdps[smplng][dpool]:
arr = NP.copy(out_excpdps[smplng][dpool][stat].si.value)
arr_units = out_excpdps[smplng][dpool][stat].si.unit
out_excpdps[smplng][dpool][stat] = []
for ind in range(len(diagoffsets)):
masked_diagwts = MA.array(diagwts, mask=masks[ind])
axes_to_avg = tuple([out_excpdps[smplng][dpool]['axesmap'][ax][0] for ax in diagoffsets[ind] if ax!=2])
out_excpdps[smplng][dpool][stat] += [MA.sum(arr * masked_diagwts, axis=axes_to_avg, keepdims=True) / MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True) * arr_units]
if len(out_excpdps[smplng][dpool]['diagweights']) < len(diagoffsets):
out_excpdps[smplng][dpool]['diagweights'] += [MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True)]
return (out_xcpdps, out_excpdps)
################################################################################
def incoherent_kbin_averaging(xcpdps, kbins=None, num_kbins=None, kbintype='log'):
"""
----------------------------------------------------------------------------
Averages the power spectrum incoherently by binning in bins of k. Returns
the power spectrum in units of both standard power spectrum and \Delta^2
Inputs:
xcpdps [dictionary] A dictionary that contains the incoherent averaged
power spectrum along LST and/or triads axes. This dictionary is
essentially the one(s) returned as the output of the function
incoherent_cross_power_spectrum_average()
kbins [NoneType, list or numpy array] Bins in k. If set to None
(default), it will be determined automatically based on the
inputs in num_kbins, and kbintype. If num_kbins is None and
kbintype='linear', the negative and positive values of k are
folded into a one-sided power spectrum. In this case, the
bins will approximately have the same resolution as the k-values
in the input power spectrum for all the spectral windows.
num_kbins [NoneType or integer] Number of k-bins. Used only if kbins is
set to None. If kbintype is set to 'linear', the negative and
positive values of k are folded into a one-sided power spectrum.
In this case, the bins will approximately have the same
resolution as the k-values in the input power spectrum for all
the spectral windows.
kbintype [string] Specifies the type of binning, used only if kbins is
set to None. Accepted values are 'linear' and 'log' for linear
and logarithmic bins respectively.
Outputs:
Dictionary containing the power spectrum information. At the top level, it
contains keys specifying the sampling to be 'oversampled' or 'resampled'.
Under each of these keys is another dictionary containing the following
keys:
'z' [numpy array] Redshifts corresponding to the band centers in
'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,).
'freq_center'
[numpy array] contains the center frequencies (in Hz) of the
frequency subbands of the subband delay spectra. It is of size
n_win. It is roughly equivalent to redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform. It is
of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz) of the
subbands being delay transformed. It is of size n_win. It is
roughly equivalent to width in redshift or along line-of-sight
'shape' [string] shape of the frequency window function applied. Usual
values are 'rect' (rectangular), 'bhw' (Blackman-Harris),
'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was raised.
The value is be a positive scalar with default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in pixels) of
the subband delay spectra. It is proportional to inverse of
effective bandwidth. It is of size n_win. The unit size of a
pixel is determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is effectively inverse
of the effective bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and 'residual'
or one key named 'errinfo' each of which is a dictionary. 'whole'
contains power spectrum info about the input closure phases. 'submodel'
contains power spectrum info about the model that will have been
subtracted (as closure phase) from the 'whole' model. 'residual'
contains power spectrum info about the closure phases obtained as a
difference between 'whole' and 'submodel'. 'errinfo' contains power
spectrum information about the subsample differences. There is also
another dictionary under key 'kbininfo' that contains information about
k-bins. These dictionaries contain the following keys and values:
'whole'/'submodel'/'residual'/'errinfo'
[dictionary] It contains the following keys and values:
'mean' [dictionary] Delay power spectrum information under the
'mean' statistic incoherently obtained by averaging the
input power spectrum in bins of k. It contains output power
spectrum expressed as two quantities each of which is a
dictionary with the following key-value pairs:
'PS' [list of numpy arrays] Standard power spectrum in
units of 'K2 Mpc3'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'Del2' [list of numpy arrays] power spectrum in Delta^2
units of 'K2'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'median'
[dictionary] Delay power spectrum information under the
'median' statistic incoherently obtained by averaging the
input power spectrum in bins of k. It contains output power
spectrum expressed as two quantities each of which is a
dictionary with the following key-value pairs:
'PS' [list of numpy arrays] Standard power spectrum in
units of 'K2 Mpc3'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'Del2' [list of numpy arrays] power spectrum in Delta^2
units of 'K2'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'kbininfo'
[dictionary] Contains the k-bin information. It contains the
following key-value pairs:
'counts'
[list] List of numpy arrays where each numpy array in the stores
the counts in the determined k-bins. Each numpy array in the
list corresponds to a spectral window (redshift subband). The
shape of each numpy array is (nkbins,)
'kbin_edges'
[list] List of numpy arrays where each numpy array contains the
k-bin edges. Each array in the list corresponds to a spectral
window (redshift subband). The shape of each array is
(nkbins+1,).
'kbinnum'
[list] List of numpy arrays containing the bin number under
which the k value falls. Each array in the list corresponds to
a spectral window (redshift subband). The shape of each array
is (nlags,).
'ri'
[list] List of numpy arrays containing the reverse indices for
each k-bin. Each array in the list corresponds to a spectral
window (redshift subband). The shape of each array is
(nlags+nkbins+1,).
'whole'/'submodel'/'residual' or 'errinfo' [dictionary] k-bin info
estimated for the different datapools under different stats
and PS definitions. It has the keys 'mean' and 'median' for the
mean and median statistic respectively. Each of them contain a
dictionary with the following key-value pairs:
'PS' [list] List of numpy arrays where each numpy array
contains a standard power spectrum typically in units of
'K2 Mpc3'. Its shape is the same as input power spectrum
except the k-axis which now has nkbins number of
elements.
'Del2' [list] List of numpy arrays where each numpy array
contains a Delta^2 power spectrum typically in units of
'K2'. Its shape is the same as input power spectrum
except the k-axis which now has nkbins number of
elements.
----------------------------------------------------------------------------
"""
if not isinstance(xcpdps, dict):
raise TypeError('Input xcpdps must be a dictionary')
if kbins is not None:
if not isinstance(kbins, (list,NP.ndarray)):
raise TypeError('Input kbins must be a list or numpy array')
else:
if not isinstance(kbintype, str):
raise TypeError('Input kbintype must be a string')
if kbintype.lower() not in ['linear', 'log']:
raise ValueError('Input kbintype must be set to "linear" or "log"')
if kbintype.lower() == 'log':
if num_kbins is None:
num_kbins = 10
psinfo = {}
keys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in keys:
psinfo[key] = xcpdps[key]
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in xcpdps:
psinfo[smplng] = {}
for key in sampling_keys:
psinfo[smplng][key] = xcpdps[smplng][key]
kprll = xcpdps[smplng]['kprll']
lags = xcpdps[smplng]['lags']
eps = 1e-10
if kbins is None:
dkprll = NP.max(NP.mean(NP.diff(kprll, axis=-1), axis=-1))
if kbintype.lower() == 'linear':
bins_kprll = NP.linspace(eps, NP.abs(kprll).max()+eps, num=kprll.shape[1]/2+1, endpoint=True)
else:
bins_kprll = NP.geomspace(eps, NP.abs(kprll).max()+eps, num=num_kbins+1, endpoint=True)
bins_kprll = NP.insert(bins_kprll, 0, -eps)
else:
bins_kprll = NP.asarray(kbins)
num_kbins = bins_kprll.size - 1
psinfo[smplng]['kbininfo'] = {'counts': [], 'kbin_edges': [], 'kbinnum': [], 'ri': []}
for spw in range(kprll.shape[0]):
counts, kbin_edges, kbinnum, ri = OPS.binned_statistic(NP.abs(kprll[spw,:]), statistic='count', bins=bins_kprll)
counts = counts.astype(NP.int)
psinfo[smplng]['kbininfo']['counts'] += [NP.copy(counts)]
psinfo[smplng]['kbininfo']['kbin_edges'] += [kbin_edges / U.Mpc]
psinfo[smplng]['kbininfo']['kbinnum'] += [NP.copy(kbinnum)]
psinfo[smplng]['kbininfo']['ri'] += [NP.copy(ri)]
for dpool in dpool_keys:
if dpool in xcpdps[smplng]:
psinfo[smplng][dpool] = {}
psinfo[smplng]['kbininfo'][dpool] = {}
keys = ['diagoffsets', 'diagweights', 'axesmap']
for key in keys:
psinfo[smplng][dpool][key] = xcpdps[smplng][dpool][key]
for stat in ['mean', 'median']:
if stat in xcpdps[smplng][dpool]:
psinfo[smplng][dpool][stat] = {'PS': [], 'Del2': []}
psinfo[smplng]['kbininfo'][dpool][stat] = []
for combi in range(len(xcpdps[smplng][dpool][stat])):
outshape = NP.asarray(xcpdps[smplng][dpool][stat][combi].shape)
outshape[-1] = num_kbins
tmp_dps = NP.full(tuple(outshape), NP.nan, dtype=NP.complex) * U.Unit(xcpdps[smplng][dpool][stat][combi].unit)
tmp_Del2 = NP.full(tuple(outshape), NP.nan, dtype=NP.complex) * U.Unit(xcpdps[smplng][dpool][stat][combi].unit / U.Mpc**3)
tmp_kprll = NP.full(tuple(outshape), NP.nan, dtype=NP.float) / U.Mpc
for spw in range(kprll.shape[0]):
counts = NP.copy(psinfo[smplng]['kbininfo']['counts'][spw])
ri = NP.copy(psinfo[smplng]['kbininfo']['ri'][spw])
print('Processing datapool={0}, stat={1}, LST-Day-Triad combination={2:0d}, spw={3:0d}...'.format(dpool, stat, combi, spw))
progress = PGB.ProgressBar(widgets=[PGB.Percentage(), PGB.Bar(marker='-', left=' |', right='| '), PGB.Counter(), '/{0:0d} k-bins '.format(num_kbins), PGB.ETA()], maxval=num_kbins).start()
for binnum in range(num_kbins):
if counts[binnum] > 0:
ind_kbin = ri[ri[binnum]:ri[binnum+1]]
tmp_dps[spw,...,binnum] = NP.nanmean(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1), axis=-1)
k_shape = NP.ones(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1).ndim, dtype=NP.int)
k_shape[-1] = -1
tmp_Del2[spw,...,binnum] = NP.nanmean(NP.abs(kprll[spw,ind_kbin].reshape(tuple(k_shape))/U.Mpc)**3 * NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1), axis=-1) / (2*NP.pi**2)
tmp_kprll[spw,...,binnum] = NP.nansum(NP.abs(kprll[spw,ind_kbin].reshape(tuple(k_shape))/U.Mpc) * NP.abs(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1)), axis=-1) / NP.nansum(NP.abs(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1)), axis=-1)
progress.update(binnum+1)
progress.finish()
psinfo[smplng][dpool][stat]['PS'] += [copy.deepcopy(tmp_dps)]
psinfo[smplng][dpool][stat]['Del2'] += [copy.deepcopy(tmp_Del2)]
psinfo[smplng]['kbininfo'][dpool][stat] += [copy.deepcopy(tmp_kprll)]
return psinfo
################################################################################
class ClosurePhase(object):
"""
----------------------------------------------------------------------------
Class to hold and operate on Closure Phase information.
It has the following attributes and member functions.
Attributes:
extfile [string] Full path to external file containing information
of ClosurePhase instance. The file is in HDF5 format
cpinfo [dictionary] Contains the following top level keys,
namely, 'raw', 'processed', and 'errinfo'
Under key 'raw' which holds a dictionary, the subkeys
include 'cphase' (nlst,ndays,ntriads,nchan),
'triads' (ntriads,3), 'lst' (nlst,ndays), and 'flags'
(nlst,ndays,ntriads,nchan).
Under the 'processed' key are more subkeys, namely,
'native', 'prelim', and optionally 'submodel' and 'residual'
each holding a dictionary.
Under 'native' dictionary, the subsubkeys for further
dictionaries are 'cphase' (masked array:
(nlst,ndays,ntriads,nchan)), 'eicp' (complex masked
array: (nlst,ndays,ntriads,nchan)), and 'wts' (masked
array: (nlst,ndays,ntriads,nchan)).
Under 'prelim' dictionary, the subsubkeys for further
dictionaries are 'tbins' (numpy array of tbin centers
after smoothing), 'dtbins' (numpy array of tbin
intervals), 'wts' (masked array:
(ntbins,ndays,ntriads,nchan)), 'eicp' and 'cphase'.
The dictionaries under 'eicp' are indexed by keys
'mean' (complex masked array:
(ntbins,ndays,ntriads,nchan)), and 'median' (complex
masked array: (ntbins,ndays,ntriads,nchan)).
The dictionaries under 'cphase' are indexed by keys
'mean' (masked array: (ntbins,ndays,ntriads,nchan)),
'median' (masked array: (ntbins,ndays,ntriads,nchan)),
'rms' (masked array: (ntbins,ndays,ntriads,nchan)), and
'mad' (masked array: (ntbins,ndays,ntriads,nchan)). The
last one denotes Median Absolute Deviation.
Under 'submodel' dictionary, the subsubkeys for further
dictionaries are 'cphase' (masked array:
(nlst,ndays,ntriads,nchan)), and 'eicp' (complex masked
array: (nlst,ndays,ntriads,nchan)).
Under 'residual' dictionary, the subsubkeys for further
dictionaries are 'cphase' and 'eicp'. These are
dictionaries too. The dictionaries under 'eicp' are
indexed by keys 'mean' (complex masked array:
(ntbins,ndays,ntriads,nchan)), and 'median' (complex
masked array: (ntbins,ndays,ntriads,nchan)).
The dictionaries under 'cphase' are indexed by keys
'mean' (masked array: (ntbins,ndays,ntriads,nchan)),
and 'median' (masked array:
(ntbins,ndays,ntriads,nchan)).
Under key 'errinfo', it contains the following keys and
values:
'list_of_pair_of_pairs'
List of pair of pairs for which differences of
complex exponentials have been computed, where the
elements are bins of days. The number of elements
in the list is ncomb. And each element is a smaller
(4-element) list of pair of pairs
'eicp_diff'
Difference of complex exponentials between pairs
of day bins. This will be used in evaluating noise
properties in power spectrum. It is a dictionary
with two keys '0' and '1' where each contains the
difference from a pair of subsamples. Each of these
keys contains a numpy array of shape
(nlstbins,ncomb,2,ntriads,nchan)
'wts' Weights in difference of complex exponentials
obtained by sum of squares of weights that are
associated with the pair that was used in the
differencing. It is a dictionary with two keys '0'
and '1' where each contains the weights associated
It is of shape (nlstbins,ncomb,2,ntriads,nchan)
Member functions:
__init__() Initialize an instance of class ClosurePhase
expicp() Compute and return complex exponential of the closure phase
as a masked array
smooth_in_tbins()
Smooth the complex exponentials of closure phases in LST
bins. Both mean and median smoothing is produced.
subtract() Subtract complex exponential of the bispectrum phase
from the current instance and updates the cpinfo attribute
subsample_differencing()
Create subsamples and differences between subsamples to
evaluate noise properties from the data set.
save() Save contents of attribute cpinfo in external HDF5 file
----------------------------------------------------------------------------
"""
def __init__(self, infile, freqs, infmt='npz'):
"""
------------------------------------------------------------------------
Initialize an instance of class ClosurePhase
Inputs:
infile [string] Input file including full path. It could be a NPZ
with raw data, or a HDF5 file that could contain raw or
processed data. The input file format is specified in the
input infmt. If it is a NPZ file, it must contain the
following keys/files:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA
units which is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is
(nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard
deviation of closure phases across days. Shape
is (nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard
deviation of closure phases across triads.
Shape is (nlst,ndays,nchan)
freqs [numpy array] Frequencies (in Hz) in the input. Size is
nchan.
infmt [string] Input file format. Accepted values are 'npz'
(default) and 'hdf5'.
------------------------------------------------------------------------
"""
if not isinstance(infile, str):
raise TypeError('Input infile must be a string')
if not isinstance(freqs, NP.ndarray):
raise TypeError('Input freqs must be a numpy array')
freqs = freqs.ravel()
if not isinstance(infmt, str):
raise TypeError('Input infmt must be a string')
if infmt.lower() not in ['npz', 'hdf5']:
raise ValueError('Input infmt must be "npz" or "hdf5"')
if infmt.lower() == 'npz':
infilesplit = infile.split('.npz')
infile_noext = infilesplit[0]
self.cpinfo = loadnpz(infile)
# npz2hdf5(infile, infile_noext+'.hdf5')
self.extfile = infile_noext + '.hdf5'
else:
# if not isinstance(infile, h5py.File):
# raise TypeError('Input infile is not a valid HDF5 file')
self.extfile = infile
self.cpinfo = NMO.load_dict_from_hdf5(self.extfile)
if freqs.size != self.cpinfo['raw']['cphase'].shape[-1]:
raise ValueError('Input frequencies do not match with dimensions of the closure phase data')
self.f = freqs
self.df = freqs[1] - freqs[0]
force_expicp = False
if 'processed' not in self.cpinfo:
force_expicp = True
else:
if 'native' not in self.cpinfo['processed']:
force_expicp = True
self.expicp(force_action=force_expicp)
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['errinfo'] = {}
############################################################################
def expicp(self, force_action=False):
"""
------------------------------------------------------------------------
Compute the complex exponential of the closure phase as a masked array
Inputs:
force_action [boolean] If set to False (default), the complex
exponential is computed only if it has not been done so
already. Otherwise the computation is forced.
------------------------------------------------------------------------
"""
if 'processed' not in self.cpinfo:
self.cpinfo['processed'] = {}
force_action = True
if 'native' not in self.cpinfo['processed']:
self.cpinfo['processed']['native'] = {}
force_action = True
if 'cphase' not in self.cpinfo['processed']['native']:
self.cpinfo['processed']['native']['cphase'] = MA.array(self.cpinfo['raw']['cphase'].astype(NP.float64), mask=self.cpinfo['raw']['flags'])
force_action = True
if not force_action:
if 'eicp' not in self.cpinfo['processed']['native']:
self.cpinfo['processed']['native']['eicp'] = NP.exp(1j * self.cpinfo['processed']['native']['cphase'])
self.cpinfo['processed']['native']['wts'] = MA.array(NP.logical_not(self.cpinfo['raw']['flags']).astype(NP.float), mask=self.cpinfo['raw']['flags'])
else:
self.cpinfo['processed']['native']['eicp'] = NP.exp(1j * self.cpinfo['processed']['native']['cphase'])
self.cpinfo['processed']['native']['wts'] = MA.array(NP.logical_not(self.cpinfo['raw']['flags']).astype(NP.float), mask=self.cpinfo['raw']['flags'])
############################################################################
def smooth_in_tbins(self, daybinsize=None, ndaybins=None, lstbinsize=None):
"""
------------------------------------------------------------------------
Smooth the complex exponentials of closure phases in time bins. Both
mean and median smoothing is produced.
Inputs:
daybinsize [Nonetype or scalar] Day bin size (in days) over which mean
and median are estimated across different days for a fixed
LST bin. If set to None, it will look for value in input
ndaybins. If both are None, no smoothing is performed. Only
one of daybinsize or ndaybins must be set to non-None value.
ndaybins [NoneType or integer] Number of bins along day axis. Only
if daybinsize is set to None. It produces bins that roughly
consist of equal number of days in each bin regardless of
how much the days in each bin are separated from each other.
If both are None, no smoothing is performed. Only one of
daybinsize or ndaybins must be set to non-None value.
lstbinsize [NoneType or scalar] LST bin size (in seconds) over which
mean and median are estimated across the LST. If set to
None, no smoothing is performed
------------------------------------------------------------------------
"""
if (ndaybins is not None) and (daybinsize is not None):
raise ValueError('Only one of daybinsize or ndaybins should be set')
if (daybinsize is not None) or (ndaybins is not None):
if daybinsize is not None:
if not isinstance(daybinsize, (int,float)):
raise TypeError('Input daybinsize must be a scalar')
dres = NP.diff(self.cpinfo['raw']['days']).min() # in days
dextent = self.cpinfo['raw']['days'].max() - self.cpinfo['raw']['days'].min() + dres # in days
if daybinsize > dres:
daybinsize = NP.clip(daybinsize, dres, dextent)
eps = 1e-10
daybins = NP.arange(self.cpinfo['raw']['days'].min(), self.cpinfo['raw']['days'].max() + dres + eps, daybinsize)
ndaybins = daybins.size
daybins = NP.concatenate((daybins, [daybins[-1]+daybinsize+eps]))
if ndaybins > 1:
daybinintervals = daybins[1:] - daybins[:-1]
daybincenters = daybins[:-1] + 0.5 * daybinintervals
else:
daybinintervals = NP.asarray(daybinsize).reshape(-1)
daybincenters = daybins[0] + 0.5 * daybinintervals
counts, daybin_edges, daybinnum, ri = OPS.binned_statistic(self.cpinfo['raw']['days'], statistic='count', bins=daybins)
counts = counts.astype(NP.int)
# if 'prelim' not in self.cpinfo['processed']:
# self.cpinfo['processed']['prelim'] = {}
# self.cpinfo['processed']['prelim']['eicp'] = {}
# self.cpinfo['processed']['prelim']['cphase'] = {}
# self.cpinfo['processed']['prelim']['daybins'] = daybincenters
# self.cpinfo['processed']['prelim']['diff_dbins'] = daybinintervals
wts_daybins = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
eicp_dmean = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
eicp_dmedian = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
cp_drms = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
cp_dmad = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
for binnum in xrange(counts.size):
ind_daybin = ri[ri[binnum]:ri[binnum+1]]
wts_daybins[:,binnum,:,:] = NP.sum(self.cpinfo['processed']['native']['wts'][:,ind_daybin,:,:].data, axis=1)
eicp_dmean[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.mean(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:], axis=1)))
eicp_dmedian[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].real, axis=1) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].imag, axis=1)))
cp_drms[:,binnum,:,:] = MA.std(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:], axis=1).data
cp_dmad[:,binnum,:,:] = MA.median(NP.abs(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:] - NP.angle(eicp_dmedian[:,binnum,:,:][:,NP.newaxis,:,:])), axis=1).data
# mask = wts_daybins <= 0.0
# self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_daybins, mask=mask)
# self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_dmean, mask=mask)
# self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_dmedian, mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_dmean), mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_dmedian), mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_drms, mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_dmad, mask=mask)
else:
if not isinstance(ndaybins, int):
raise TypeError('Input ndaybins must be an integer')
if ndaybins <= 0:
raise ValueError('Input ndaybins must be positive')
days_split = NP.array_split(self.cpinfo['raw']['days'], ndaybins)
daybincenters = NP.asarray([NP.mean(days) for days in days_split])
daybinintervals = NP.asarray([days.max()-days.min() for days in days_split])
counts = NP.asarray([days.size for days in days_split])
wts_split = NP.array_split(self.cpinfo['processed']['native']['wts'].data, ndaybins, axis=1)
# mask_split = NP.array_split(self.cpinfo['processed']['native']['wts'].mask, ndaybins, axis=1)
wts_daybins = NP.asarray([NP.sum(wtsitem, axis=1) for wtsitem in wts_split]) # ndaybins x nlst x ntriads x nchan
wts_daybins = NP.moveaxis(wts_daybins, 0, 1) # nlst x ndaybins x ntriads x nchan
mask_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].mask, ndaybins, axis=1)
eicp_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].data, ndaybins, axis=1)
eicp_dmean = MA.array([MA.mean(MA.array(eicp_split[i], mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmean = NP.exp(1j * NP.angle(eicp_dmean))
eicp_dmean = NP.moveaxis(eicp_dmean, 0, 1) # nlst x ndaybins x ntriads x nchan
eicp_dmedian = MA.array([MA.median(MA.array(eicp_split[i].real, mask=mask_split[i]), axis=1) + 1j * MA.median(MA.array(eicp_split[i].imag, mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmedian = NP.exp(1j * NP.angle(eicp_dmedian))
eicp_dmedian = NP.moveaxis(eicp_dmedian, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_split = NP.array_split(self.cpinfo['processed']['native']['cphase'].data, ndaybins, axis=1)
cp_drms = NP.array([MA.std(MA.array(cp_split[i], mask=mask_split[i]), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_drms = NP.moveaxis(cp_drms, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_dmad = NP.array([MA.median(NP.abs(cp_split[i] - NP.angle(eicp_dmedian[:,[i],:,:])), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_dmad = NP.moveaxis(cp_dmad, 0, 1) # nlst x ndaybins x ntriads x nchan
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['processed']['prelim']['eicp'] = {}
self.cpinfo['processed']['prelim']['cphase'] = {}
self.cpinfo['processed']['prelim']['daybins'] = daybincenters
self.cpinfo['processed']['prelim']['diff_dbins'] = daybinintervals
mask = wts_daybins <= 0.0
self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_daybins, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_dmean, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_dmedian, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_dmean), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_dmedian), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_drms, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_dmad, mask=mask)
rawlst = NP.degrees(NP.unwrap(NP.radians(self.cpinfo['raw']['lst'] * 15.0), discont=NP.pi, axis=0)) / 15.0 # in hours but unwrapped to have no discontinuities
if NP.any(rawlst > 24.0):
rawlst -= 24.0
if rawlst.shape[0] > 1: # LST bin only if there are multiple LST
if lstbinsize is not None:
if not isinstance(lstbinsize, (int,float)):
raise TypeError('Input lstbinsize must be a scalar')
lstbinsize = lstbinsize / 3.6e3 # in hours
tres = NP.diff(rawlst[:,0]).min() # in hours
textent = rawlst[:,0].max() - rawlst[:,0].min() + tres # in hours
eps = 1e-10
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
no_change_in_lstbins = False
if lstbinsize > tres:
lstbinsize = NP.clip(lstbinsize, tres, textent)
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + tres + eps, lstbinsize)
nlstbins = lstbins.size
lstbins = NP.concatenate((lstbins, [lstbins[-1]+lstbinsize+eps]))
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
lstbincenters = lstbins[0] + 0.5 * lstbinintervals
self.cpinfo['processed']['prelim']['lstbins'] = lstbincenters
self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
no_change_in_lstbins = False
else:
# Perform no binning and keep the current LST resolution, data and weights
warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
lstbinsize = tres
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
nlstbins = lstbins.size - 1
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
self.cpinfo['processed']['prelim']['lstbins'] = lstbins[:-1]
# Ensure that the LST bins are inside the min/max envelope to
# error-free interpolation later
self.cpinfo['processed']['prelim']['lstbins'][0] += eps
self.cpinfo['processed']['prelim']['lstbins'][-1] -= eps
no_change_in_lstbins = True
counts, lstbin_edges, lstbinnum, ri = OPS.binned_statistic(rawlst[:,0], statistic='count', bins=lstbins)
counts = counts.astype(NP.int)
if 'wts' not in self.cpinfo['processed']['prelim']:
outshape = (counts.size, self.cpinfo['processed']['native']['eicp'].shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
else:
outshape = (counts.size, self.cpinfo['processed']['prelim']['wts'].shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
wts_lstbins = NP.zeros(outshape)
eicp_tmean = NP.zeros(outshape, dtype=NP.complex128)
eicp_tmedian = NP.zeros(outshape, dtype=NP.complex128)
cp_trms = NP.zeros(outshape)
cp_tmad = NP.zeros(outshape)
for binnum in xrange(counts.size):
if no_change_in_lstbins:
ind_lstbin = [binnum]
else:
ind_lstbin = ri[ri[binnum]:ri[binnum+1]]
if 'wts' not in self.cpinfo['processed']['prelim']:
indict = self.cpinfo['processed']['native']
else:
indict = self.cpinfo['processed']['prelim']
wts_lstbins[binnum,:,:,:] = NP.sum(indict['wts'][ind_lstbin,:,:,:].data, axis=0)
if 'wts' not in self.cpinfo['processed']['prelim']:
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(indict['eicp'][ind_lstbin,:,:,:], axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(indict['eicp'][ind_lstbin,:,:,:].real, axis=0) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][ind_lstbin,:,:,:].imag, axis=0)))
cp_trms[binnum,:,:,:] = MA.std(indict['cphase'][ind_lstbin,:,:,:], axis=0).data
cp_tmad[binnum,:,:,:] = MA.median(NP.abs(indict['cphase'][ind_lstbin,:,:,:] - NP.angle(eicp_tmedian[binnum,:,:,:][NP.newaxis,:,:,:])), axis=0).data
else:
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(NP.exp(1j*indict['cphase']['mean'][ind_lstbin,:,:,:]), axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(NP.cos(indict['cphase']['median'][ind_lstbin,:,:,:]), axis=0) + 1j * MA.median(NP.sin(indict['cphase']['median'][ind_lstbin,:,:,:]), axis=0)))
cp_trms[binnum,:,:,:] = MA.std(indict['cphase']['mean'][ind_lstbin,:,:,:], axis=0).data
cp_tmad[binnum,:,:,:] = MA.median(NP.abs(indict['cphase']['median'][ind_lstbin,:,:,:] - NP.angle(eicp_tmedian[binnum,:,:,:][NP.newaxis,:,:,:])), axis=0).data
mask = wts_lstbins <= 0.0
self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_lstbins, mask=mask)
if 'eicp' not in self.cpinfo['processed']['prelim']:
self.cpinfo['processed']['prelim']['eicp'] = {}
if 'cphase' not in self.cpinfo['processed']['prelim']:
self.cpinfo['processed']['prelim']['cphase'] = {}
self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_tmean, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_tmedian, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_tmean), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_tmedian), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_trms, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_tmad, mask=mask)
# else:
# # Perform no binning and keep the current LST resolution, data and weights
# warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
# lstbinsize = tres
# lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
# nlstbins = lstbins.size - 1
# if nlstbins > 1:
# lstbinintervals = lstbins[1:] - lstbins[:-1]
# lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
# else:
# lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
# lstbincenters = lstbins[0] + 0.5 * lstbinintervals
# if 'prelim' not in self.cpinfo['processed']:
# self.cpinfo['processed']['prelim'] = {}
# self.cpinfo['processed']['prelim']['lstbins'] = lstbincenters
# self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
if (rawlst.shape[0] <= 1) or (lstbinsize is None):
nlstbins = rawlst.shape[0]
lstbins = NP.mean(rawlst, axis=1)
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['processed']['prelim']['lstbins'] = lstbins
if lstbinsize is not None:
self.cpinfo['processed']['prelim']['dlstbins'] = NP.asarray(lstbinsize).reshape(-1)
else:
self.cpinfo['processed']['prelim']['dlstbins'] = NP.zeros(1)
############################################################################
def subtract(self, cphase):
"""
------------------------------------------------------------------------
Subtract complex exponential of the bispectrum phase from the current
instance and updates the cpinfo attribute
Inputs:
cphase [masked array] Bispectrum phase array as a maked array. It
must be of same size as freqs along the axis specified in
input axis.
Action: Updates 'submodel' and 'residual' keys under attribute
cpinfo under key 'processed'
------------------------------------------------------------------------
"""
if not isinstance(cphase, NP.ndarray):
raise TypeError('Input cphase must be a numpy array')
if not isinstance(cphase, MA.MaskedArray):
cphase = MA.array(cphase, mask=NP.isnan(cphase))
if not OPS.is_broadcastable(cphase.shape, self.cpinfo['processed']['prelim']['cphase']['median'].shape):
raise ValueError('Input cphase has shape incompatible with that in instance attribute')
else:
minshape = tuple(NP.ones(self.cpinfo['processed']['prelim']['cphase']['median'].ndim - cphase.ndim, dtype=NP.int)) + cphase.shape
cphase = cphase.reshape(minshape)
# cphase = NP.broadcast_to(cphase, minshape)
eicp = NP.exp(1j*cphase)
self.cpinfo['processed']['submodel'] = {}
self.cpinfo['processed']['submodel']['cphase'] = cphase
self.cpinfo['processed']['submodel']['eicp'] = eicp
self.cpinfo['processed']['residual'] = {'eicp': {}, 'cphase': {}}
for key in ['mean', 'median']:
eicpdiff = self.cpinfo['processed']['prelim']['eicp'][key] - eicp
eicpratio = self.cpinfo['processed']['prelim']['eicp'][key] / eicp
self.cpinfo['processed']['residual']['eicp'][key] = eicpdiff
self.cpinfo['processed']['residual']['cphase'][key] = MA.array(NP.angle(eicpratio.data), mask=self.cpinfo['processed']['residual']['eicp'][key].mask)
############################################################################
def subsample_differencing(self, daybinsize=None, ndaybins=4, lstbinsize=None):
"""
------------------------------------------------------------------------
Create subsamples and differences between subsamples to evaluate noise
properties from the data set.
Inputs:
daybinsize [Nonetype or scalar] Day bin size (in days) over which mean
and median are estimated across different days for a fixed
LST bin. If set to None, it will look for value in input
ndaybins. If both are None, no smoothing is performed. Only
one of daybinsize or ndaybins must be set to non-None value.
Must yield greater than or equal to 4 bins
ndaybins [NoneType or integer] Number of bins along day axis. Only
if daybinsize is set to None. It produces bins that roughly
consist of equal number of days in each bin regardless of
how much the days in each bin are separated from each other.
If both are None, no smoothing is performed. Only one of
daybinsize or ndaybins must be set to non-None value. If set,
it must be set to greater than or equal to 4
lstbinsize [NoneType or scalar] LST bin size (in seconds) over which
mean and median are estimated across the LST. If set to
None, no smoothing is performed
------------------------------------------------------------------------
"""
if (ndaybins is not None) and (daybinsize is not None):
raise ValueError('Only one of daybinsize or ndaybins should be set')
if (daybinsize is not None) or (ndaybins is not None):
if daybinsize is not None:
if not isinstance(daybinsize, (int,float)):
raise TypeError('Input daybinsize must be a scalar')
dres = NP.diff(self.cpinfo['raw']['days']).min() # in days
dextent = self.cpinfo['raw']['days'].max() - self.cpinfo['raw']['days'].min() + dres # in days
if daybinsize > dres:
daybinsize = NP.clip(daybinsize, dres, dextent)
eps = 1e-10
daybins = NP.arange(self.cpinfo['raw']['days'].min(), self.cpinfo['raw']['days'].max() + dres + eps, daybinsize)
ndaybins = daybins.size
daybins = NP.concatenate((daybins, [daybins[-1]+daybinsize+eps]))
if ndaybins >= 4:
daybinintervals = daybins[1:] - daybins[:-1]
daybincenters = daybins[:-1] + 0.5 * daybinintervals
else:
raise ValueError('Could not find at least 4 bins along repeating days. Adjust binning interval.')
counts, daybin_edges, daybinnum, ri = OPS.binned_statistic(self.cpinfo['raw']['days'], statistic='count', bins=daybins)
counts = counts.astype(NP.int)
wts_daybins = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
eicp_dmean = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
eicp_dmedian = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
cp_drms = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
cp_dmad = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
for binnum in xrange(counts.size):
ind_daybin = ri[ri[binnum]:ri[binnum+1]]
wts_daybins[:,binnum,:,:] = NP.sum(self.cpinfo['processed']['native']['wts'][:,ind_daybin,:,:].data, axis=1)
eicp_dmean[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.mean(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:], axis=1)))
eicp_dmedian[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].real, axis=1) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].imag, axis=1)))
cp_drms[:,binnum,:,:] = MA.std(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:], axis=1).data
cp_dmad[:,binnum,:,:] = MA.median(NP.abs(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:] - NP.angle(eicp_dmedian[:,binnum,:,:][:,NP.newaxis,:,:])), axis=1).data
else:
if not isinstance(ndaybins, int):
raise TypeError('Input ndaybins must be an integer')
if ndaybins < 4:
raise ValueError('Input ndaybins must be greater than or equal to 4')
days_split = NP.array_split(self.cpinfo['raw']['days'], ndaybins)
daybincenters = NP.asarray([NP.mean(days) for days in days_split])
daybinintervals = NP.asarray([days.max()-days.min() for days in days_split])
counts = NP.asarray([days.size for days in days_split])
wts_split = NP.array_split(self.cpinfo['processed']['native']['wts'].data, ndaybins, axis=1)
# mask_split = NP.array_split(self.cpinfo['processed']['native']['wts'].mask, ndaybins, axis=1)
wts_daybins = NP.asarray([NP.sum(wtsitem, axis=1) for wtsitem in wts_split]) # ndaybins x nlst x ntriads x nchan
wts_daybins = NP.moveaxis(wts_daybins, 0, 1) # nlst x ndaybins x ntriads x nchan
mask_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].mask, ndaybins, axis=1)
eicp_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].data, ndaybins, axis=1)
eicp_dmean = MA.array([MA.mean(MA.array(eicp_split[i], mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmean = NP.exp(1j * NP.angle(eicp_dmean))
eicp_dmean = NP.moveaxis(eicp_dmean, 0, 1) # nlst x ndaybins x ntriads x nchan
eicp_dmedian = MA.array([MA.median(MA.array(eicp_split[i].real, mask=mask_split[i]), axis=1) + 1j * MA.median(MA.array(eicp_split[i].imag, mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmedian = NP.exp(1j * NP.angle(eicp_dmedian))
eicp_dmedian = NP.moveaxis(eicp_dmedian, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_split = NP.array_split(self.cpinfo['processed']['native']['cphase'].data, ndaybins, axis=1)
cp_drms = NP.array([MA.std(MA.array(cp_split[i], mask=mask_split[i]), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_drms = NP.moveaxis(cp_drms, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_dmad = NP.array([MA.median(NP.abs(cp_split[i] - NP.angle(eicp_dmedian[:,[i],:,:])), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_dmad = NP.moveaxis(cp_dmad, 0, 1) # nlst x ndaybins x ntriads x nchan
mask = wts_daybins <= 0.0
wts_daybins = MA.array(wts_daybins, mask=mask)
cp_dmean = MA.array(NP.angle(eicp_dmean), mask=mask)
cp_dmedian = MA.array(NP.angle(eicp_dmedian), mask=mask)
self.cpinfo['errinfo']['daybins'] = daybincenters
self.cpinfo['errinfo']['diff_dbins'] = daybinintervals
self.cpinfo['errinfo']['wts'] = {'{0}'.format(ind): None for ind in range(2)}
self.cpinfo['errinfo']['eicp_diff'] = {'{0}'.format(ind): {} for ind in range(2)}
rawlst = NP.degrees(NP.unwrap(NP.radians(self.cpinfo['raw']['lst'] * 15.0), discont=NP.pi, axis=0)) / 15.0 # in hours but unwrapped to have no discontinuities
if NP.any(rawlst > 24.0):
rawlst -= 24.0
if rawlst.shape[0] > 1: # LST bin only if there are multiple LST
if lstbinsize is not None:
if not isinstance(lstbinsize, (int,float)):
raise TypeError('Input lstbinsize must be a scalar')
lstbinsize = lstbinsize / 3.6e3 # in hours
tres = NP.diff(rawlst[:,0]).min() # in hours
textent = rawlst[:,0].max() - rawlst[:,0].min() + tres # in hours
eps = 1e-10
no_change_in_lstbins = False
if lstbinsize > tres:
lstbinsize = NP.clip(lstbinsize, tres, textent)
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + tres + eps, lstbinsize)
nlstbins = lstbins.size
lstbins = NP.concatenate((lstbins, [lstbins[-1]+lstbinsize+eps]))
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
lstbincenters = lstbins[0] + 0.5 * lstbinintervals
self.cpinfo['errinfo']['lstbins'] = lstbincenters
self.cpinfo['errinfo']['dlstbins'] = lstbinintervals
no_change_in_lstbins = False
else:
# Perform no binning and keep the current LST resolution
warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
lstbinsize = tres
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
nlstbins = lstbins.size - 1
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
self.cpinfo['errinfo']['dlstbins'] = lstbinintervals
self.cpinfo['errinfo']['lstbins'] = lstbins[:-1]
# Ensure that the LST bins are inside the min/max envelope to
# error-free interpolation later
self.cpinfo['errinfo']['lstbins'][0] += eps
self.cpinfo['errinfo']['lstbins'][-1] -= eps
no_change_in_lstbins = True
counts, lstbin_edges, lstbinnum, ri = OPS.binned_statistic(rawlst[:,0], statistic='count', bins=lstbins)
counts = counts.astype(NP.int)
outshape = (counts.size, wts_daybins.shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
wts_lstbins = NP.zeros(outshape)
eicp_tmean = NP.zeros(outshape, dtype=NP.complex128)
eicp_tmedian = NP.zeros(outshape, dtype=NP.complex128)
cp_trms = NP.zeros(outshape)
cp_tmad = NP.zeros(outshape)
for binnum in xrange(counts.size):
if no_change_in_lstbins:
ind_lstbin = [binnum]
else:
ind_lstbin = ri[ri[binnum]:ri[binnum+1]]
wts_lstbins[binnum,:,:,:] = NP.sum(wts_daybins[ind_lstbin,:,:,:].data, axis=0)
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(NP.exp(1j*cp_dmean[ind_lstbin,:,:,:]), axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(NP.cos(cp_dmedian[ind_lstbin,:,:,:]), axis=0) + 1j * MA.median(NP.sin(cp_dmedian[ind_lstbin,:,:,:]), axis=0)))
mask = wts_lstbins <= 0.0
wts_lstbins = MA.array(wts_lstbins, mask=mask)
eicp_tmean = MA.array(eicp_tmean, mask=mask)
eicp_tmedian = MA.array(eicp_tmedian, mask=mask)
else:
wts_lstbins = MA.copy(wts_daybins)
mask = wts_lstbins.mask
eicp_tmean = MA.array(NP.exp(1j*NP.angle(NP.exp(1j*cp_dmean))), mask=mask)
eicp_tmedian = MA.array(NP.exp(1j*NP.angle(NP.cos(cp_dmedian) + 1j * NP.sin(cp_dmedian))), mask=mask)
if (rawlst.shape[0] <= 1) or (lstbinsize is None):
nlstbins = rawlst.shape[0]
lstbins = NP.mean(rawlst, axis=1)
self.cpinfo['errinfo']['lstbins'] = lstbins
if lstbinsize is not None:
self.cpinfo['errinfo']['dlstbins'] = NP.asarray(lstbinsize).reshape(-1)
else:
self.cpinfo['errinfo']['dlstbins'] = NP.zeros(1)
ncomb = NP.sum(NP.asarray([(ndaybins-i-1)*(ndaybins-i-2)*(ndaybins-i-3)/2 for i in range(ndaybins-3)])).astype(int)
diff_outshape = (nlstbins, ncomb, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
for diffind in range(2):
self.cpinfo['errinfo']['eicp_diff']['{0}'.format(diffind)]['mean'] = MA.empty(diff_outshape, dtype=NP.complex)
self.cpinfo['errinfo']['eicp_diff']['{0}'.format(diffind)]['median'] = MA.empty(diff_outshape, dtype=NP.complex)
self.cpinfo['errinfo']['wts']['{0}'.format(diffind)] = MA.empty(diff_outshape, dtype=NP.float)
ind = -1
self.cpinfo['errinfo']['list_of_pair_of_pairs'] = []
list_of_pair_of_pairs = []
for i in range(ndaybins-1):
for j in range(i+1,ndaybins):
for k in range(ndaybins-1):
if (k != i) and (k != j):
for m in range(k+1,ndaybins):
if (m != i) and (m != j):
pair_of_pairs = [set([i,j]), set([k,m])]
if (pair_of_pairs not in list_of_pair_of_pairs) and (pair_of_pairs[::-1] not in list_of_pair_of_pairs):
ind += 1
list_of_pair_of_pairs += [copy.deepcopy(pair_of_pairs)]
self.cpinfo['errinfo']['list_of_pair_of_pairs'] += [[i,j,k,m]]
for stat in ['mean', 'median']:
if stat == 'mean':
self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmean[:,j,:,:].data - eicp_tmean[:,i,:,:].data), mask=NP.logical_or(eicp_tmean[:,j,:,:].mask, eicp_tmean[:,i,:,:].mask))
self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmean[:,m,:,:].data - eicp_tmean[:,k,:,:].data), mask=NP.logical_or(eicp_tmean[:,m,:,:].mask, eicp_tmean[:,k,:,:].mask))
self.cpinfo['errinfo']['wts']['0'][:,ind,:,:] = MA.array(NP.sqrt(wts_lstbins[:,j,:,:].data**2 + wts_lstbins[:,i,:,:].data**2), mask=NP.logical_or(wts_lstbins[:,j,:,:].mask, wts_lstbins[:,i,:,:].mask))
self.cpinfo['errinfo']['wts']['1'][:,ind,:,:] = MA.array(NP.sqrt(wts_lstbins[:,m,:,:].data**2 + wts_lstbins[:,k,:,:].data**2), mask=NP.logical_or(wts_lstbins[:,m,:,:].mask, wts_lstbins[:,k,:,:].mask))
# self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = 0.5 * (eicp_tmean[:,j,:,:] - eicp_tmean[:,i,:,:])
# self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = 0.5 * (eicp_tmean[:,m,:,:] - eicp_tmean[:,k,:,:])
# self.cpinfo['errinfo']['wts']['0'][:,ind,:,:] = NP.sqrt(wts_lstbins[:,j,:,:]**2 + wts_lstbins[:,i,:,:]**2)
# self.cpinfo['errinfo']['wts']['1'][:,ind,:,:] = NP.sqrt(wts_lstbins[:,m,:,:]**2 + wts_lstbins[:,k,:,:]**2)
else:
self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmedian[:,j,:,:].data - eicp_tmedian[:,i,:,:].data), mask=NP.logical_or(eicp_tmedian[:,j,:,:].mask, eicp_tmedian[:,i,:,:].mask))
self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmedian[:,m,:,:].data - eicp_tmedian[:,k,:,:].data), mask=NP.logical_or(eicp_tmedian[:,m,:,:].mask, eicp_tmedian[:,k,:,:].mask))
# self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = 0.5 * (eicp_tmedian[:,j,:,:] - eicp_tmedian[:,i,:,:])
# self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = 0.5 * (eicp_tmedian[:,m,:,:] - eicp_tmedian[:,k,:,:])
mask0 = self.cpinfo['errinfo']['wts']['0'] <= 0.0
mask1 = self.cpinfo['errinfo']['wts']['1'] <= 0.0
self.cpinfo['errinfo']['eicp_diff']['0'][stat] = MA.array(self.cpinfo['errinfo']['eicp_diff']['0'][stat], mask=mask0)
self.cpinfo['errinfo']['eicp_diff']['1'][stat] = MA.array(self.cpinfo['errinfo']['eicp_diff']['1'][stat], mask=mask1)
self.cpinfo['errinfo']['wts']['0'] = MA.array(self.cpinfo['errinfo']['wts']['0'], mask=mask0)
self.cpinfo['errinfo']['wts']['1'] = MA.array(self.cpinfo['errinfo']['wts']['1'], mask=mask1)
############################################################################
def save(self, outfile=None):
"""
------------------------------------------------------------------------
Save contents of attribute cpinfo in external HDF5 file
Inputs:
outfile [NoneType or string] Output file (HDF5) to save contents to.
If set to None (default), it will be saved in the file
pointed to by the extfile attribute of class ClosurePhase
------------------------------------------------------------------------
"""
if outfile is None:
outfile = self.extfile
NMO.save_dict_to_hdf5(self.cpinfo, outfile, compressinfo={'compress_fmt': 'gzip', 'compress_opts': 9})
################################################################################
class ClosurePhaseDelaySpectrum(object):
"""
----------------------------------------------------------------------------
Class to hold and operate on Closure Phase information.
It has the following attributes and member functions.
Attributes:
cPhase [instance of class ClosurePhase] Instance of class
ClosurePhase
f [numpy array] Frequencies (in Hz) in closure phase spectra
df [float] Frequency resolution (in Hz) in closure phase
spectra
cPhaseDS [dictionary] Possibly oversampled Closure Phase Delay
Spectrum information.
cPhaseDS_resampled
[dictionary] Resampled Closure Phase Delay Spectrum
information.
Member functions:
__init__() Initialize instance of class ClosurePhaseDelaySpectrum
FT() Fourier transform of complex closure phase spectra mapping
from frequency axis to delay axis.
subset() Return triad and time indices to select a subset of
processed data
compute_power_spectrum()
Compute power spectrum of closure phase data. It is in units
of Mpc/h.
rescale_power_spectrum()
Rescale power spectrum to dimensional quantity by converting
the ratio given visibility amplitude information
average_rescaled_power_spectrum()
Average the rescaled power spectrum with physical units
along certain axes with inverse variance or regular
averaging
beam3Dvol() Compute three-dimensional volume of the antenna power
pattern along two transverse axes and one LOS axis.
----------------------------------------------------------------------------
"""
def __init__(self, cPhase):
"""
------------------------------------------------------------------------
Initialize instance of class ClosurePhaseDelaySpectrum
Inputs:
cPhase [class ClosurePhase] Instance of class ClosurePhase
------------------------------------------------------------------------
"""
if not isinstance(cPhase, ClosurePhase):
raise TypeError('Input cPhase must be an instance of class ClosurePhase')
self.cPhase = cPhase
self.f = self.cPhase.f
self.df = self.cPhase.df
self.cPhaseDS = None
self.cPhaseDS_resampled = None
############################################################################
def FT(self, bw_eff, freq_center=None, shape=None, fftpow=None, pad=None,
datapool='prelim', visscaleinfo=None, method='fft', resample=True,
apply_flags=True):
"""
------------------------------------------------------------------------
Fourier transform of complex closure phase spectra mapping from
frequency axis to delay axis.
Inputs:
bw_eff [scalar or numpy array] effective bandwidths (in Hz) on the
selected frequency windows for subband delay transform of
closure phases. If a scalar value is provided, the same
will be applied to all frequency windows
freq_center [scalar, list or numpy array] frequency centers (in Hz) of
the selected frequency windows for subband delay transform
of closure phases. The value can be a scalar, list or numpy
array. If a scalar is provided, the same will be applied to
all frequency windows. Default=None uses the center
frequency from the class attribute named channels
shape [string] frequency window shape for subband delay transform
of closure phases. Accepted values for the string are
'rect' or 'RECT' (for rectangular), 'bnw' and 'BNW' (for
Blackman-Nuttall), and 'bhw' or 'BHW' (for
Blackman-Harris). Default=None sets it to 'rect'
(rectangular window)
fftpow [scalar] the power to which the FFT of the window will be
raised. The value must be a positive scalar. Default = 1.0
pad [scalar] padding fraction relative to the number of
frequency channels for closure phases. Value must be a
non-negative scalar. For e.g., a pad of 1.0 pads the
frequency axis with zeros of the same width as the number
of channels. After the delay transform, the transformed
closure phases are downsampled by a factor of 1+pad. If a
negative value is specified, delay transform will be
performed with no padding. Default=None sets to padding
factor to 1.0
datapool [string] Specifies which data set is to be Fourier
transformed
visscaleinfo
[dictionary] Dictionary containing reference visibilities
based on which the closure phases will be scaled to units
of visibilities. It contains the following keys and values:
'vis' [numpy array or instance of class
InterferometerArray] Reference visibilities from the
baselines that form the triad. It can be an instance
of class RI.InterferometerArray or a numpy array.
If an instance of class InterferometerArray, the
baseline triplet must be set in key 'bltriplet'
and value in key 'lst' will be ignored. If the
value under this key 'vis' is set to a numpy array,
it must be of shape (nbl=3, nlst_vis, nchan). In
this case the value under key 'bltriplet' will be
ignored. The nearest LST will be looked up and
applied after smoothing along LST based on the
smoothing parameter 'smooth'
'bltriplet'
[Numpy array] Will be used in searching for matches
to these three baseline vectors if the value under
key 'vis' is set to an instance of class
InterferometerArray. However, if value under key
'vis' is a numpy array, this key 'bltriplet' will
be ignored.
'lst' [numpy array] Reference LST (in hours). It is of
shape (nlst_vis,). It will be used only if value
under key 'vis' is a numpy array, otherwise it will
be ignored and read from the instance of class
InterferometerArray passed under key 'vis'. If the
specified LST range does not cover the data LST
range, those LST will contain NaN in the delay
spectrum
'smoothinfo'
[dictionary] Dictionary specifying smoothing and/or
interpolation parameters. It has the following keys
and values:
'op_type' [string] Specifies the interpolating
operation. Must be specified (no
default). Accepted values are
'interp1d' (scipy.interpolate),
'median' (skimage.filters), 'tophat'
(astropy.convolution) and 'gaussian'
(astropy.convolution)
'interp_kind' [string (optional)] Specifies the
interpolation kind (if 'op_type' is
set to 'interp1d'). For accepted
values, see
scipy.interpolate.interp1d()
'window_size' [integer (optional)] Specifies the
size of the interpolating/smoothing
kernel. Only applies when 'op_type'
is set to 'median', 'tophat' or
'gaussian' The kernel is a tophat
function when 'op_type' is set to
'median' or 'tophat'. If refers to
FWHM when 'op_type' is set to
'gaussian'
resample [boolean] If set to True (default), resample the delay
spectrum axis to independent samples along delay axis. If
set to False, return the results as is even if they may be
be oversampled and not all samples may be independent
method [string] Specifies the Fourier transform method to be used.
Accepted values are 'fft' (default) for FFT and 'nufft' for
non-uniform FFT
apply_flags [boolean] If set to True (default), weights determined from
flags will be applied. If False, no weights from flagging
will be applied, and thus even flagged data will be included
Outputs:
A dictionary that contains the oversampled (if resample=False) or
resampled (if resample=True) delay spectrum information. It has the
following keys and values:
'freq_center' [numpy array] contains the center frequencies
(in Hz) of the frequency subbands of the subband
delay spectra. It is of size n_win. It is roughly
equivalent to redshift(s)
'freq_wts' [numpy array] Contains frequency weights applied
on each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff' [numpy array] contains the effective bandwidths
(in Hz) of the subbands being delay transformed. It
is of size n_win. It is roughly equivalent to width
in redshift or along line-of-sight
'shape' [string] shape of the window function applied.
Accepted values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow' [scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'npad' [scalar] Numbber of zero-padded channels before
performing the subband delay transform.
'lags' [numpy array] lags of the subband delay spectra
after padding in frequency during the transform. It
is of size nlags=nchan+npad if resample=True, where
npad is the number of frequency channels padded
specified under the key 'npad'. If resample=False,
nlags = number of delays after resampling only
independent delays. The lags roughly correspond to
k_parallel.
'lag_kernel' [numpy array] delay transform of the frequency
weights under the key 'freq_wts'. It is of size
n_win x nlst x ndays x ntriads x nlags.
nlags=nchan+npad if resample=True, where npad is the
number of frequency channels padded specified under
the key 'npad'. If resample=False, nlags = number of
delays after resampling only independent delays.
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is
proportional to inverse of effective bandwidth. It
is of size n_win. The unit size of a pixel is
determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is
effectively inverse of the effective bandwidth of
the subband specified in bw_eff
'whole' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'prelim' key of attribute cpinfo.
Contains the following keys and values:
'dspec' [dictionary] Contains the following keys and
values:
'twts' [numpy array] Weights from time-based
flags that went into time-averaging.
Shape=(nlst,ndays,ntriads,nchan)
'mean' [numpy array] Delay spectrum of closure
phases based on their mean across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'median'
[numpy array] Delay spectrum of closure
phases based on their median across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'submodel' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'submodel' key of attribute cpinfo.
Contains the following keys and values:
'dspec' [numpy array] Delay spectrum of closure phases
Shape=(nspw,nlst,ndays,ntriads,nlags)
'residual' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'residual' key of attribute cpinfo
after subtracting 'submodel' bispectrum phase from that
of 'prelim'. It contains the following keys and values:
'dspec' [dictionary] Contains the following keys and
values:
'twts' [numpy array] Weights from time-based
flags that went into time-averaging.
Shape=(nlst,ndays,ntriads,nchan)
'mean' [numpy array] Delay spectrum of closure
phases based on their mean across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'median'
[numpy array] Delay spectrum of closure
phases based on their median across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'errinfo' [dictionary] It has two keys 'dspec0' and 'dspec1' each
of which are dictionaries with the following keys and
values:
'twts' [numpy array] Weights for the subsample
difference. It is of shape (nlst, ndays,
ntriads, nchan)
'mean' [numpy array] Delay spectrum of the
subsample difference obtained by using the
mean statistic. It is of shape (nspw, nlst,
ndays, ntriads, nlags)
'median'
[numpy array] Delay spectrum of the subsample
difference obtained by using the median
statistic. It is of shape (nspw, nlst, ndays,
ntriads, nlags)
------------------------------------------------------------------------
"""
try:
bw_eff
except NameError:
raise NameError('Effective bandwidth must be specified')
else:
if not isinstance(bw_eff, (int, float, list, NP.ndarray)):
raise TypeError('Value of effective bandwidth must be a scalar, list or numpy array')
bw_eff = NP.asarray(bw_eff).reshape(-1)
if NP.any(bw_eff <= 0.0):
raise ValueError('All values in effective bandwidth must be strictly positive')
if freq_center is None:
freq_center = NP.asarray(self.f[self.f.size/2]).reshape(-1)
elif isinstance(freq_center, (int, float, list, NP.ndarray)):
freq_center = NP.asarray(freq_center).reshape(-1)
if NP.any((freq_center <= self.f.min()) | (freq_center >= self.f.max())):
raise ValueError('Value(s) of frequency center(s) must lie strictly inside the observing band')
else:
raise TypeError('Values(s) of frequency center must be scalar, list or numpy array')
if (bw_eff.size == 1) and (freq_center.size > 1):
bw_eff = NP.repeat(bw_eff, freq_center.size)
elif (bw_eff.size > 1) and (freq_center.size == 1):
freq_center = NP.repeat(freq_center, bw_eff.size)
elif bw_eff.size != freq_center.size:
raise ValueError('Effective bandwidth(s) and frequency center(s) must have same number of elements')
if shape is not None:
if not isinstance(shape, str):
raise TypeError('Window shape must be a string')
if shape not in ['rect', 'bhw', 'bnw', 'RECT', 'BHW', 'BNW']:
raise ValueError('Invalid value for window shape specified.')
else:
shape = 'rect'
if fftpow is None:
fftpow = 1.0
else:
if not isinstance(fftpow, (int, float)):
raise TypeError('Power to raise window FFT by must be a scalar value.')
if fftpow < 0.0:
raise ValueError('Power for raising FFT of window by must be positive.')
if pad is None:
pad = 1.0
else:
if not isinstance(pad, (int, float)):
raise TypeError('pad fraction must be a scalar value.')
if pad < 0.0:
pad = 0.0
if verbose:
print('\tPad fraction found to be negative. Resetting to 0.0 (no padding will be applied).')
if not isinstance(datapool, str):
raise TypeError('Input datapool must be a string')
if datapool.lower() not in ['prelim']:
raise ValueError('Specified datapool not supported')
if visscaleinfo is not None:
if not isinstance(visscaleinfo, dict):
raise TypeError('Input visscaleinfo must be a dictionary')
if 'vis' not in visscaleinfo:
raise KeyError('Input visscaleinfo does not contain key "vis"')
if not isinstance(visscaleinfo['vis'], RI.InterferometerArray):
if 'lst' not in visscaleinfo:
raise KeyError('Input visscaleinfo does not contain key "lst"')
lst_vis = visscaleinfo['lst'] * 15.0
if not isinstance(visscaleinfo['vis'], (NP.ndarray,MA.MaskedArray)):
raise TypeError('Input visibilities must be a numpy or a masked array')
if not isinstance(visscaleinfo['vis'], MA.MaskedArray):
visscaleinfo['vis'] = MA.array(visscaleinfo['vis'], mask=NP.isnan(visscaleinfo['vis']))
vistriad = MA.copy(visscaleinfo['vis'])
else:
if 'bltriplet' not in visscaleinfo:
raise KeyError('Input dictionary visscaleinfo does not contain key "bltriplet"')
blind, blrefind, dbl = LKP.find_1NN(visscaleinfo['vis'].baselines, visscaleinfo['bltriplet'], distance_ULIM=0.2, remove_oob=True)
if blrefind.size != 3:
blind_missing = NP.setdiff1d(NP.arange(3), blind, assume_unique=True)
blind_next, blrefind_next, dbl_next = LKP.find_1NN(visscaleinfo['vis'].baselines, -1*visscaleinfo['bltriplet'][blind_missing,:], distance_ULIM=0.2, remove_oob=True)
if blind_next.size + blind.size != 3:
raise ValueError('Exactly three baselines were not found in the reference baselines')
else:
blind = NP.append(blind, blind_missing[blind_next])
blrefind = NP.append(blrefind, blrefind_next)
else:
blind_missing = []
vistriad = NP.transpose(visscaleinfo['vis'].skyvis_freq[blrefind,:,:], (0,2,1))
if len(blind_missing) > 0:
vistriad[-blrefind_next.size:,:,:] = vistriad[-blrefind_next.size:,:,:].conj()
vistriad = MA.array(vistriad, mask=NP.isnan(vistriad))
lst_vis = visscaleinfo['vis'].lst
viswts = MA.array(NP.ones_like(vistriad.data), mask=vistriad.mask, dtype=NP.float)
lst_out = self.cPhase.cpinfo['processed']['prelim']['lstbins'] * 15.0
if lst_vis.size == 1: # Apply the visibility scaling from one reference LST to all LST
vis_ref = vistriad * NP.ones(lst_out.size).reshape(1,-1,1)
wts_ref = viswts * NP.ones(lst_out.size).reshape(1,-1,1)
else:
vis_ref, wts_ref = OPS.interpolate_masked_array_1D(vistriad, viswts, 1, visscaleinfo['smoothinfo'], inploc=lst_vis, outloc=lst_out)
if not isinstance(method, str):
raise TypeError('Input method must be a string')
if method.lower() not in ['fft', 'nufft']:
raise ValueError('Specified FFT method not supported')
if not isinstance(apply_flags, bool):
raise TypeError('Input apply_flags must be boolean')
flagwts = 1.0
visscale = 1.0
if datapool.lower() == 'prelim':
if method.lower() == 'fft':
freq_wts = NP.empty((bw_eff.size, self.f.size), dtype=NP.float_) # nspw x nchan
frac_width = DSP.window_N2width(n_window=None, shape=shape, fftpow=fftpow, area_normalize=False, power_normalize=True)
window_loss_factor = 1 / frac_width
n_window = NP.round(window_loss_factor * bw_eff / self.df).astype(NP.int)
ind_freq_center, ind_channels, dfrequency = LKP.find_1NN(self.f.reshape(-1,1), freq_center.reshape(-1,1), distance_ULIM=0.51*self.df, remove_oob=True)
sortind = NP.argsort(ind_channels)
ind_freq_center = ind_freq_center[sortind]
ind_channels = ind_channels[sortind]
dfrequency = dfrequency[sortind]
n_window = n_window[sortind]
for i,ind_chan in enumerate(ind_channels):
window = NP.sqrt(frac_width * n_window[i]) * DSP.window_fftpow(n_window[i], shape=shape, fftpow=fftpow, centering=True, peak=None, area_normalize=False, power_normalize=True)
window_chans = self.f[ind_chan] + self.df * (NP.arange(n_window[i]) - int(n_window[i]/2))
ind_window_chans, ind_chans, dfreq = LKP.find_1NN(self.f.reshape(-1,1), window_chans.reshape(-1,1), distance_ULIM=0.51*self.df, remove_oob=True)
sind = NP.argsort(ind_window_chans)
ind_window_chans = ind_window_chans[sind]
ind_chans = ind_chans[sind]
dfreq = dfreq[sind]
window = window[ind_window_chans]
window = NP.pad(window, ((ind_chans.min(), self.f.size-1-ind_chans.max())), mode='constant', constant_values=((0.0,0.0)))
freq_wts[i,:] = window
npad = int(self.f.size * pad)
lags = DSP.spectral_axis(self.f.size + npad, delx=self.df, use_real=False, shift=True)
result = {'freq_center': freq_center, 'shape': shape, 'freq_wts': freq_wts, 'bw_eff': bw_eff, 'fftpow': fftpow, 'npad': npad, 'lags': lags, 'lag_corr_length': self.f.size / NP.sum(freq_wts, axis=-1), 'whole': {'dspec': {'twts': self.cPhase.cpinfo['processed'][datapool]['wts']}}, 'residual': {'dspec': {'twts': self.cPhase.cpinfo['processed'][datapool]['wts']}}, 'errinfo': {'dspec0': {'twts': self.cPhase.cpinfo['errinfo']['wts']['0']}, 'dspec1': {'twts': self.cPhase.cpinfo['errinfo']['wts']['1']}}, 'submodel': {}}
if visscaleinfo is not None:
visscale = NP.nansum(NP.transpose(vis_ref[NP.newaxis,NP.newaxis,:,:,:], axes=(0,3,1,2,4)) * freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], axis=-1, keepdims=True) / NP.nansum(freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], axis=-1, keepdims=True) # nspw x nlst x (ndays=1) x (nbl=3) x (nchan=1)
visscale = NP.sqrt(1.0/NP.nansum(1/NP.abs(visscale)**2, axis=-2, keepdims=True)) # nspw x nlst x (ndays=1) x (ntriads=1) x (nchan=1)
for dpool in ['errinfo', 'prelim', 'submodel', 'residual']:
if dpool.lower() == 'errinfo':
for diffind in range(2):
if apply_flags:
flagwts = NP.copy(self.cPhase.cpinfo['errinfo']['wts']['{0}'.format(diffind)].data)
flagwts = flagwts[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
flagwts = 1.0 * flagwts / NP.mean(flagwts, axis=-1, keepdims=True) # (nspw=1) x nlst x ndays x ntriads x nchan
for stat in self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)]:
eicp = NP.copy(self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].data) # Minimum shape as stored
# eicp = NP.copy(self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].filled(0.0)) # Minimum shape as stored
eicp = NP.broadcast_to(eicp, self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].shape) # Broadcast to final shape
eicp = eicp[NP.newaxis,...] # nlst x ndayscomb x ntriads x nchan --> (nspw=1) x nlst x ndayscomb x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
result[dpool]['dspec{0}'.format(diffind)][stat] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
if dpool in self.cPhase.cpinfo['processed']:
if apply_flags:
flagwts = NP.copy(self.cPhase.cpinfo['processed'][datapool]['wts'].data)
flagwts = flagwts[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
flagwts = 1.0 * flagwts / NP.mean(flagwts, axis=-1, keepdims=True) # (nspw=1) x nlst x ndays x ntriads x nchan
if dpool == 'submodel':
eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'].data) # Minimum shape as stored
# eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'].filled(1.0)) # Minimum shape as stored
eicp = NP.broadcast_to(eicp, self.cPhase.cpinfo['processed'][datapool]['eicp']['mean'].shape) # Broadcast to final shape
eicp = eicp[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
result[dpool]['dspec'] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
for key in self.cPhase.cpinfo['processed'][dpool]['eicp']:
eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'][key].data)
# eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'][key].filled(1.0))
eicp = eicp[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
if dpool == 'prelim':
result['whole']['dspec'][key] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
result[dpool]['dspec'][key] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
result['lag_kernel'] = DSP.FT1D(NP.pad(flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
self.cPhaseDS = result
if resample:
result_resampled = copy.deepcopy(result)
downsample_factor = NP.min((self.f.size + npad) * self.df / bw_eff)
result_resampled['lags'] = DSP.downsampler(result_resampled['lags'], downsample_factor, axis=-1, method='interp', kind='linear')
result_resampled['lag_kernel'] = DSP.downsampler(result_resampled['lag_kernel'], downsample_factor, axis=-1, method='interp', kind='linear')
for dpool in ['errinfo', 'prelim', 'submodel', 'residual']:
if dpool.lower() == 'errinfo':
for diffind in self.cPhase.cpinfo[dpool]['eicp_diff']:
for key in self.cPhase.cpinfo[dpool]['eicp_diff'][diffind]:
result_resampled[dpool]['dspec'+diffind][key] = DSP.downsampler(result_resampled[dpool]['dspec'+diffind][key], downsample_factor, axis=-1, method='FFT')
if dpool in self.cPhase.cpinfo['processed']:
if dpool == 'submodel':
result_resampled[dpool]['dspec'] = DSP.downsampler(result_resampled[dpool]['dspec'], downsample_factor, axis=-1, method='FFT')
else:
for key in self.cPhase.cpinfo['processed'][datapool]['eicp']:
if dpool == 'prelim':
result_resampled['whole']['dspec'][key] = DSP.downsampler(result_resampled['whole']['dspec'][key], downsample_factor, axis=-1, method='FFT')
else:
result_resampled[dpool]['dspec'][key] = DSP.downsampler(result_resampled[dpool]['dspec'][key], downsample_factor, axis=-1, method='FFT')
self.cPhaseDS_resampled = result_resampled
return result_resampled
else:
return result
############################################################################
def subset(self, selection=None):
"""
------------------------------------------------------------------------
Return triad and time indices to select a subset of processed data
Inputs:
selection [NoneType or dictionary] Selection parameters based on which
triad, LST, and day indices will be returned. If set to None
(default), all triad, LST, and day indices will be returned.
Otherwise it must be a dictionary with the following keys
and values:
'triads' [NoneType or list of 3-element tuples] If set
to None (default), indices of all triads are
returned. Otherwise, the specific triads must
be specified such as [(1,2,3), (1,2,4), ...]
and their indices will be returned
'lst' [NoneType, list or numpy array] If set to None
(default), indices of all LST are returned.
Otherwise must be a list or numpy array
containing indices to LST.
'days' [NoneType, list or numpy array] If set to None
(default), indices of all days are returned.
Otherwise must be a list or numpy array
containing indices to days.
Outputs:
Tuple (triad_ind, lst_ind, day_ind, day_ind_eicpdiff) containing the
triad, LST, day, and day-pair (for subsample differences) indices,
each as a numpy array
------------------------------------------------------------------------
"""
if selection is None:
selsection = {}
else:
if not isinstance(selection, dict):
raise TypeError('Input selection must be a dictionary')
triads = map(tuple, self.cPhase.cpinfo['raw']['triads'])
if 'triads' not in selection:
selection['triads'] = triads
if selection['triads'] is None:
selection['triads'] = triads
triad_ind = [triads.index(triad) for triad in selection['triads']]
triad_ind = NP.asarray(triad_ind)
lst_ind = None
if 'lst' not in selection:
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])
else:
if selection['lst'] is None:
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])
elif isinstance(selection['lst'], (list,NP.ndarray)):
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = selection['lst']
if NP.any(NP.logical_or(lst_ind < 0, lst_ind >= self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])):
raise ValueError('Input processed lst indices out of bounds')
else:
raise TypeError('Wrong type for processed lst indices')
if lst_ind is None:
raise ValueError('LST index selection could not be performed')
day_ind = None
day_ind_eicpdiff = None
if 'days' not in selection:
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = NP.arange(len(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']))
else:
if selection['days'] is None:
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = NP.arange(len(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']))
elif isinstance(selection['days'], (list,NP.ndarray)):
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = selection['days']
if NP.any(NP.logical_or(day_ind < 0, day_ind >= self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])):
raise ValueError('Input processed day indices out of bounds')
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = [i for i,item in enumerate(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']) if len(set(item)-set(selection['days']))==0]
else:
raise TypeError('Wrong type for processed day indices')
if day_ind is None:
raise ValueError('Day index selection could not be performed')
return (triad_ind, lst_ind, day_ind, day_ind_eicpdiff)
############################################################################
def compute_power_spectrum(self, cpds=None, selection=None, autoinfo=None,
xinfo=None, cosmo=cosmo100, units='K', beamparms=None):
"""
------------------------------------------------------------------------
Compute power spectrum of closure phase data. It is in units of Mpc/h
Inputs:
cpds [dictionary] A dictionary that contains the 'oversampled' (if
resample=False) and/or 'resampled' (if resample=True) delay
spectrum information. If it is not specified the attributes
cPhaseDS['processed'] and cPhaseDS_resampled['processed'] are
used. Under each of these keys, it holds a dictionary that has
the following keys and values:
'freq_center' [numpy array] contains the center frequencies
(in Hz) of the frequency subbands of the subband
delay spectra. It is of size n_win. It is
roughly equivalent to redshift(s)
'freq_wts' [numpy array] Contains frequency weights applied
on each frequency sub-band during the subband
delay transform. It is of size n_win x nchan.
'bw_eff' [numpy array] contains the effective bandwidths
(in Hz) of the subbands being delay transformed.
It is of size n_win. It is roughly equivalent to
width in redshift or along line-of-sight
'shape' [string] shape of the window function applied.
Accepted values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow' [scalar] the power to which the FFT of the window
was raised. The value is be a positive scalar
with default = 1.0
'npad' [scalar] Numbber of zero-padded channels before
performing the subband delay transform.
'lags' [numpy array] lags of the subband delay spectra
after padding in frequency during the transform.
It is of size nlags. The lags roughly correspond
to k_parallel.
'lag_kernel' [numpy array] delay transform of the frequency
weights under the key 'freq_wts'. It is of size
n_bl x n_win x nlags x n_t.
'lag_corr_length'
[numpy array] It is the correlation timescale
(in pixels) of the subband delay spectra. It is
proportional to inverse of effective bandwidth.
It is of size n_win. The unit size of a pixel is
determined by the difference between adjacent
pixels in lags under key 'lags' which in turn is
effectively inverse of the effective bandwidth
of the subband specified in bw_eff
'processed' [dictionary] Contains the following keys and
values:
'dspec' [dictionary] Contains the following keys
and values:
'twts' [numpy array] Weights from
time-based flags that went into
time-averaging.
Shape=(ntriads,npol,nchan,nt)
'mean' [numpy array] Delay spectrum of
closure phases based on their
mean across time intervals.
Shape=(nspw,npol,nt,ntriads,nlags)
'median'
[numpy array] Delay spectrum of
closure phases based on their
median across time intervals.
Shape=(nspw,npol,nt,ntriads,nlags)
selection [NoneType or dictionary] Selection parameters based on which
triad, LST, and day indices will be returned. If set to None
(default), all triad, LST, and day indices will be returned.
Otherwise it must be a dictionary with the following keys
and values:
'triads' [NoneType or list of 3-element tuples] If set
to None (default), indices of all triads are
returned. Otherwise, the specific triads must
be specified such as [(1,2,3), (1,2,4), ...]
and their indices will be returned
'lst' [NoneType, list or numpy array] If set to None
(default), indices of all LST are returned.
Otherwise must be a list or numpy array
containing indices to LST.
'days' [NoneType, list or numpy array] If set to None
(default), indices of all days are returned.
Otherwise must be a list or numpy array
containing indices to days.
autoinfo
[NoneType or dictionary] Specifies parameters for processing
before power spectrum in auto or cross modes. If set to None,
a dictionary will be created with the default values as
described below. The dictionary must have the following keys
and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes that will
be averaged coherently before squaring (for auto) or
cross-multiplying (for cross) power spectrum. If set
to None (default), no axes are averaged coherently.
If set to int, list, tuple or numpy array, those axes
will be averaged coherently after applying the weights
specified under key 'wts' along those axes. 1=lst,
2=days, 3=triads.
'wts' [NoneType/list/numpy array] If not provided (equivalent
to setting it to None) or set to None (default), it is
set to a one element list which is a one element numpy
array of unity. Otherwise, it must be a list of same
number of elements as in key 'axes' and each of these
must be a numpy broadcast compatible array corresponding
to each of the axis specified in 'axes'
xinfo [NoneType or dictionary] Specifies parameters for processing
cross power spectrum. If set to None, a dictionary will be
created with the default values as described below. The
dictionary must have the following keys and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes over which
power spectrum will be computed incoherently by cross-
multiplication. If set to None (default), no cross-
power spectrum is computed. If set to int, list, tuple
or numpy array, cross-power over those axes will be
computed incoherently by cross-multiplication. The
cross-spectrum over these axes will be computed after
applying the pre- and post- cross-multiplication
weights specified in key 'wts'. 1=lst, 2=days,
3=triads.
'collapse_axes'
[list] The axes that will be collpased after the
cross-power matrix is produced by cross-multiplication.
If this key is not set, it will be initialized to an
empty list (default), in which case none of the axes
is collapsed and the full cross-power matrix will be
output. it must be a subset of values under key 'axes'.
This will reduce it from a square matrix along that axis
to collapsed values along each of the leading diagonals.
1=lst, 2=days, 3=triads.
'dlst' [scalar] LST interval (in mins) or difference between LST
pairs which will be determined and used for
cross-power spectrum. Will only apply if values under
'axes' contains the LST axis(=1).
'dlst_range'
[scalar, numpy array, or NoneType] Specifies the LST
difference(s) in minutes that are to be used in the
computation of cross-power spectra. If a scalar, only
the diagonal consisting of pairs with that LST
difference will be computed. If a numpy array, those
diagonals consisting of pairs with that LST difference
will be computed. If set to None (default), the main
diagonal (LST difference of 0) and the first off-main
diagonal (LST difference of 1 unit) corresponding to
pairs with 0 and 1 unit LST difference are computed.
Applies only if key 'axes' contains LST axis (=1).
'avgcov'
[boolean] It specifies if the collapse of square
covariance matrix is to be collapsed further to a single
number after applying 'postX' weights. If not set or
set to False (default), this late stage collapse will
not be performed. Otherwise, it will be averaged in a
weighted average sense where the 'postX' weights would
have already been applied during the collapsing
operation
'wts' [NoneType or Dictionary] If not set, a default
dictionary (see default values below) will be created.
It must have the follwoing keys and values:
'preX' [list of numpy arrays] It contains pre-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of weights. If
set to True, the delay spectrum will be
normalized by the sum of the weights.
'postX' [list of numpy arrays] It contains post-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of 'preX' weights.
If set to True, the delay spectrum will be
normalized by the sum of the weights.
'postXnorm'
[boolean] If False (default), no normalization
is done after the application of postX weights.
If set to True, the delay cross power spectrum
will be normalized by the sum of the weights.
cosmo [instance of cosmology class from astropy] An instance of class
FLRW or default_cosmology of astropy cosmology module. Default
uses Planck 2015 cosmology, with H0=100 h km/s/Mpc
units [string] Specifies the units of output power spectum. Accepted
values are 'Jy' and 'K' (default)) and the power spectrum will
be in corresponding squared units.
Output:
Dictionary with the keys 'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,) array),
'days' ((ndays,) array), 'day_ind' ((ndays,) array), 'dday'
((ndays,) array), 'oversampled' and 'resampled' corresponding to whether
resample was set to False or True in call to member function FT().
Values under keys 'triads_ind' and 'lst_ind' are numpy array
corresponding to triad and time indices used in selecting the data.
Values under keys 'oversampled' and 'resampled' each contain a
dictionary with the following keys and values:
'z' [numpy array] Redshifts corresponding to the band centers in
'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,).
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding to
'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz) of the
frequency subbands of the subband delay spectra. It is of size
n_win. It is roughly equivalent to redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform. It is
of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz) of the
subbands being delay transformed. It is of size n_win. It is
roughly equivalent to width in redshift or along line-of-sight
'shape' [string] shape of the frequency window function applied. Usual
values are 'rect' (rectangular), 'bhw' (Blackman-Harris),
'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was raised.
The value is be a positive scalar with default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in pixels) of
the subband delay spectra. It is proportional to inverse of
effective bandwidth. It is of size n_win. The unit size of a
pixel is determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is effectively inverse
of the effective bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and 'residual'
each of which is a dictionary. 'whole' contains power spectrum info
about the input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure phase) from
the 'whole' model. 'residual' contains power spectrum info about the
closure phases obtained as a difference between 'whole' and 'submodel'.
It contains the following keys and values:
'mean' [numpy array] Delay power spectrum incoherently estiamted over
the axes specified in xinfo['axes'] using the 'mean' key in input
cpds or attribute cPhaseDS['processed']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance matrices. If
collapse_axes is provided but avgcov is False, those axes will be
of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged over
the axes specified in incohax using the 'median' key in input
cpds or attribute cPhaseDS['processed']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance matrices. If
collapse_axes is provided bu avgcov is False, those axes will be
of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal offsets for
those axes. If 'avgcov' was set, those entries will be removed
from 'diagoffsets' since all the leading diagonal elements have
been collapsed (averaged) further. Value under each key is a
numpy array where each element in the array corresponds to the
index of that leading diagonal. This should match the size of
the output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in collapse_axes and
the value is a numpy array of weights corresponding to the
diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated but is
not collapsed, the number of dimensions in the output will have
changed. This parameter tracks where the original axis is now
placed. The keys are the original axes that are involved in
incoherent cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the power
spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the power
spectrum
Examples:
(1)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': None, 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False}}
Output delay power spectrum has shape (Nspw, Nlst, 1, Ntriads, Nlags)
(2)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False},
'dlst_range': None}
Output delay power spectrum has shape
(Nspw, 2, Nlst, 1, Ntriads, Ntriads, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)},
axesmap = {1: [1,2], 3: [4,5]}
(3)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [3],
'dlst_range': [0.0, 1.0, 2.0]}
Output delay power spectrum has shape
(Nspw, 3, Nlst, 1, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1,2], 3: [4]}
(4)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [1,3],
'dlst_range': [1.0, 2.0, 3.0, 4.0]}
Output delay power spectrum has shape
(Nspw, 4, Ndays, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1], 3: [3]}
(5)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': [3],
'dlst_range': None}
Output delay power spectrum has shape
(Nspw, 2, Nlst, Ndays, 1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)}, axesmap = {1: [1,2], 3: [4]}
(6)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': []}
Output delay power spectrum has shape
(Nspw, 1, Ndays, 1, Nlags)
diagoffsets = {}, axesmap = {1: [1], 3: [3]}
------------------------------------------------------------------------
"""
if not isinstance(units,str):
raise TypeError('Input parameter units must be a string')
if units.lower() == 'k':
if not isinstance(beamparms, dict):
raise TypeError('Input beamparms must be a dictionary')
if 'freqs' not in beamparms:
beamparms['freqs'] = self.f
beamparms_orig = copy.deepcopy(beamparms)
if autoinfo is None:
autoinfo = {'axes': None, 'wts': [NP.ones(1, dtpye=NP.float)]}
elif not isinstance(autoinfo, dict):
raise TypeError('Input autoinfo must be a dictionary')
if 'axes' not in autoinfo:
autoinfo['axes'] = None
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input autoinfo must be an integer, list, tuple or numpy array')
else:
autoinfo['axes'] = NP.asarray(autoinfo['axes']).reshape(-1)
if 'wts' not in autoinfo:
if autoinfo['axes'] is not None:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)] * len(autoinfo['axes'])
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['wts'], list):
raise TypeError('wts in input autoinfo must be a list of numpy arrays')
else:
if len(autoinfo['wts']) != len(autoinfo['axes']):
raise ValueError('Input list of wts must be same as length of autoinfo axes')
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
if xinfo is None:
xinfo = {'axes': None, 'wts': {'preX': [NP.ones(1, dtpye=NP.float)], 'postX': [NP.ones(1, dtpye=NP.float)], 'preXnorm': False, 'postXnorm': False}}
elif not isinstance(xinfo, dict):
raise TypeError('Input xinfo must be a dictionary')
if 'axes' not in xinfo:
xinfo['axes'] = None
else:
if not isinstance(xinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input xinfo must be an integer, list, tuple or numpy array')
else:
xinfo['axes'] = NP.asarray(xinfo['axes']).reshape(-1)
if 'wts' not in xinfo:
xinfo['wts'] = {}
for xkey in ['preX', 'postX']:
if xinfo['axes'] is not None:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)] * len(xinfo['axes'])
else:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
xinfo['wts']['preXnorm'] = False
xinfo['wts']['postXnorm'] = False
else:
if xinfo['axes'] is not None:
if not isinstance(xinfo['wts'], dict):
raise TypeError('wts in input xinfo must be a dictionary')
for xkey in ['preX', 'postX']:
if not isinstance(xinfo['wts'][xkey], list):
raise TypeError('{0} wts in input xinfo must be a list of numpy arrays'.format(xkey))
else:
if len(xinfo['wts'][xkey]) != len(xinfo['axes']):
raise ValueError('Input list of {0} wts must be same as length of xinfo axes'.format(xkey))
else:
for xkey in ['preX', 'postX']:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
if 'preXnorm' not in xinfo['wts']:
xinfo['wts']['preXnorm'] = False
if 'postXnorm' not in xinfo['wts']:
xinfo['wts']['postXnorm'] = False
if not isinstance(xinfo['wts']['preXnorm'], NP.bool):
raise TypeError('preXnorm in input xinfo must be a boolean')
if not isinstance(xinfo['wts']['postXnorm'], NP.bool):
raise TypeError('postXnorm in input xinfo must be a boolean')
if 'avgcov' not in xinfo:
xinfo['avgcov'] = False
if not isinstance(xinfo['avgcov'], NP.bool):
raise TypeError('avgcov under input xinfo must be boolean')
if 'collapse_axes' not in xinfo:
xinfo['collapse_axes'] = []
if not isinstance(xinfo['collapse_axes'], (int,list,tuple,NP.ndarray)):
raise TypeError('collapse_axes under input xinfo must be an integer, tuple, list or numpy array')
else:
xinfo['collapse_axes'] = NP.asarray(xinfo['collapse_axes']).reshape(-1)
if (autoinfo['axes'] is not None) and (xinfo['axes'] is not None):
if NP.intersect1d(autoinfo['axes'], xinfo['axes']).size > 0:
raise ValueError("Inputs autoinfo['axes'] and xinfo['axes'] must have no intersection")
cohax = autoinfo['axes']
if cohax is None:
cohax = []
incohax = xinfo['axes']
if incohax is None:
incohax = []
if selection is None:
selection = {'triads': None, 'lst': None, 'days': None}
else:
if not isinstance(selection, dict):
raise TypeError('Input selection must be a dictionary')
if cpds is None:
cpds = {}
sampling = ['oversampled', 'resampled']
for smplng in sampling:
if smplng == 'oversampled':
cpds[smplng] = copy.deepcopy(self.cPhaseDS)
else:
cpds[smplng] = copy.deepcopy(self.cPhaseDS_resampled)
triad_ind, lst_ind, day_ind, day_ind_eicpdiff = self.subset(selection=selection)
result = {'triads': self.cPhase.cpinfo['raw']['triads'][triad_ind], 'triads_ind': triad_ind, 'lst': self.cPhase.cpinfo['processed']['prelim']['lstbins'][lst_ind], 'lst_ind': lst_ind, 'dlst': self.cPhase.cpinfo['processed']['prelim']['dlstbins'][lst_ind], 'days': self.cPhase.cpinfo['processed']['prelim']['daybins'][day_ind], 'day_ind': day_ind, 'dday': self.cPhase.cpinfo['processed']['prelim']['diff_dbins'][day_ind]}
dlstbin = NP.mean(self.cPhase.cpinfo['processed']['prelim']['dlstbins'])
if 'dlst_range' in xinfo:
if xinfo['dlst_range'] is None:
dlst_range = None
lstshifts = NP.arange(2) # LST index offsets of 0 and 1 are only estimated
else:
dlst_range = NP.asarray(xinfo['dlst_range']).ravel() / 60.0 # Difference in LST between a pair of LST (in hours)
if dlst_range.size == 1:
dlst_range = NP.insert(dlst_range, 0, 0.0)
lstshifts = NP.arange(max([0, NP.ceil(1.0*dlst_range.min()/dlstbin).astype(NP.int)]), min([NP.ceil(1.0*dlst_range.max()/dlstbin).astype(NP.int), result['lst'].size]))
else:
dlst_range = None
lstshifts = NP.arange(2) # LST index offsets of 0 and 1 are only estimated
result['lstXoffsets'] = lstshifts * dlstbin # LST interval corresponding to diagonal offsets created by the LST covariance
for smplng in sampling:
result[smplng] = {}
wl = FCNST.c / (cpds[smplng]['freq_center'] * U.Hz)
z = CNST.rest_freq_HI / cpds[smplng]['freq_center'] - 1
dz = CNST.rest_freq_HI / cpds[smplng]['freq_center']**2 * cpds[smplng]['bw_eff']
dkprll_deta = DS.dkprll_deta(z, cosmo=cosmo)
kprll = dkprll_deta.reshape(-1,1) * cpds[smplng]['lags']
rz_los = cosmo.comoving_distance(z) # in Mpc/h
drz_los = FCNST.c * cpds[smplng]['bw_eff']*U.Hz * (1+z)**2 / (CNST.rest_freq_HI * U.Hz) / (cosmo.H0 * cosmo.efunc(z)) # in Mpc/h
if units == 'Jy':
jacobian1 = 1 / (cpds[smplng]['bw_eff'] * U.Hz)
jacobian2 = drz_los / (cpds[smplng]['bw_eff'] * U.Hz)
temperature_from_fluxdensity = 1.0
elif units == 'K':
beamparms = copy.deepcopy(beamparms_orig)
omega_bw = self.beam3Dvol(beamparms, freq_wts=cpds[smplng]['freq_wts'])
jacobian1 = 1 / (omega_bw * U.Hz) # The steradian is present but not explicitly assigned
jacobian2 = rz_los**2 * drz_los / (cpds[smplng]['bw_eff'] * U.Hz)
temperature_from_fluxdensity = wl**2 / (2*FCNST.k_B)
else:
raise ValueError('Input value for units invalid')
factor = jacobian1 * jacobian2 * temperature_from_fluxdensity**2
result[smplng]['z'] = z
result[smplng]['kprll'] = kprll
result[smplng]['lags'] = NP.copy(cpds[smplng]['lags'])
result[smplng]['freq_center'] = cpds[smplng]['freq_center']
result[smplng]['bw_eff'] = cpds[smplng]['bw_eff']
result[smplng]['shape'] = cpds[smplng]['shape']
result[smplng]['freq_wts'] = cpds[smplng]['freq_wts']
result[smplng]['lag_corr_length'] = cpds[smplng]['lag_corr_length']
for dpool in ['whole', 'submodel', 'residual']:
if dpool in cpds[smplng]:
result[smplng][dpool] = {}
inpshape = list(cpds[smplng]['whole']['dspec']['mean'].shape)
inpshape[1] = lst_ind.size
inpshape[2] = day_ind.size
inpshape[3] = triad_ind.size
if len(cohax) > 0:
nsamples_coh = NP.prod(NP.asarray(inpshape)[NP.asarray(cohax)])
else:
nsamples_coh = 1
if len(incohax) > 0:
nsamples = NP.prod(NP.asarray(inpshape)[NP.asarray(incohax)])
nsamples_incoh = nsamples * (nsamples - 1)
else:
nsamples_incoh = 1
twts_multidim_idx = NP.ix_(lst_ind,day_ind,triad_ind,NP.arange(1)) # shape=(nlst,ndays,ntriads,1)
dspec_multidim_idx = NP.ix_(NP.arange(wl.size),lst_ind,day_ind,triad_ind,NP.arange(inpshape[4])) # shape=(nspw,nlst,ndays,ntriads,nchan)
max_wt_in_chan = NP.max(NP.sum(cpds[smplng]['whole']['dspec']['twts'].data, axis=(0,1,2)))
select_chan = NP.argmax(NP.sum(cpds[smplng]['whole']['dspec']['twts'].data, axis=(0,1,2)))
twts = NP.copy(cpds[smplng]['whole']['dspec']['twts'].data[:,:,:,[select_chan]]) # shape=(nlst,ndays,ntriads,nlags=1)
if nsamples_coh > 1:
awts_shape = tuple(NP.ones(cpds[smplng]['whole']['dspec']['mean'].ndim, dtype=NP.int))
awts = NP.ones(awts_shape, dtype=NP.complex)
awts_shape = NP.asarray(awts_shape)
for caxind,caxis in enumerate(cohax):
curr_awts_shape = NP.copy(awts_shape)
curr_awts_shape[caxis] = -1
awts = awts * autoinfo['wts'][caxind].reshape(tuple(curr_awts_shape))
for stat in ['mean', 'median']:
if dpool == 'submodel':
dspec = NP.copy(cpds[smplng][dpool]['dspec'][dspec_multidim_idx])
else:
dspec = NP.copy(cpds[smplng][dpool]['dspec'][stat][dspec_multidim_idx])
if nsamples_coh > 1:
if stat == 'mean':
dspec = NP.sum(twts[twts_multidim_idx][NP.newaxis,...] * awts * dspec[dspec_multidim_idx], axis=cohax, keepdims=True) / NP.sum(twts[twts_multidim_idx][NP.newaxis,...] * awts, axis=cohax, keepdims=True)
else:
dspec = NP.median(dspec[dspec_multidim_idx], axis=cohax, keepdims=True)
if nsamples_incoh > 1:
expandax_map = {}
wts_shape = tuple(NP.ones(dspec.ndim, dtype=NP.int))
preXwts = NP.ones(wts_shape, dtype=NP.complex)
wts_shape = NP.asarray(wts_shape)
for incaxind,incaxis in enumerate(xinfo['axes']):
curr_wts_shape = NP.copy(wts_shape)
curr_wts_shape[incaxis] = -1
preXwts = preXwts * xinfo['wts']['preX'][incaxind].reshape(tuple(curr_wts_shape))
dspec1 = NP.copy(dspec)
dspec2 = NP.copy(dspec)
preXwts1 = NP.copy(preXwts)
preXwts2 = NP.copy(preXwts)
for incax in NP.sort(incohax)[::-1]:
dspec1 = NP.expand_dims(dspec1, axis=incax)
preXwts1 = NP.expand_dims(preXwts1, axis=incax)
if incax == 1:
preXwts1_outshape = list(preXwts1.shape)
preXwts1_outshape[incax+1] = dspec1.shape[incax+1]
preXwts1_outshape = tuple(preXwts1_outshape)
preXwts1 = NP.broadcast_to(preXwts1, preXwts1_outshape).copy() # For some strange reason the NP.broadcast_to() creates a "read-only" immutable array which is changed to writeable by copy()
preXwts2_tmp = NP.expand_dims(preXwts2, axis=incax)
preXwts2_shape = NP.asarray(preXwts2_tmp.shape)
preXwts2_shape[incax] = lstshifts.size
preXwts2_shape[incax+1] = preXwts1_outshape[incax+1]
preXwts2_shape = tuple(preXwts2_shape)
preXwts2 = NP.broadcast_to(preXwts2_tmp, preXwts2_shape).copy() # For some strange reason the NP.broadcast_to() creates a "read-only" immutable array which is changed to writeable by copy()
dspec2_tmp = NP.expand_dims(dspec2, axis=incax)
dspec2_shape = NP.asarray(dspec2_tmp.shape)
dspec2_shape[incax] = lstshifts.size
# dspec2_shape = NP.insert(dspec2_shape, incax, lstshifts.size)
dspec2_shape = tuple(dspec2_shape)
dspec2 = NP.broadcast_to(dspec2_tmp, dspec2_shape).copy() # For some strange reason the NP.broadcast_to() creates a "read-only" immutable array which is changed to writeable by copy()
for lstshiftind, lstshift in enumerate(lstshifts):
dspec2[:,lstshiftind,...] = NP.roll(dspec2_tmp[:,0,...], lstshift, axis=incax)
dspec2[:,lstshiftind,:lstshift,...] = NP.nan
preXwts2[:,lstshiftind,...] = NP.roll(preXwts2_tmp[:,0,...], lstshift, axis=incax)
preXwts2[:,lstshiftind,:lstshift,...] = NP.nan
else:
dspec2 = NP.expand_dims(dspec2, axis=incax+1)
preXwts2 = NP.expand_dims(preXwts2, axis=incax+1)
expandax_map[incax] = incax + NP.arange(2)
for ekey in expandax_map:
if ekey > incax:
expandax_map[ekey] += 1
result[smplng][dpool][stat] = factor.reshape((-1,)+tuple(NP.ones(dspec1.ndim-1, dtype=NP.int))) * (dspec1*U.Unit('Jy Hz') * preXwts1) * (dspec2*U.Unit('Jy Hz') * preXwts2).conj()
if xinfo['wts']['preXnorm']:
result[smplng][dpool][stat] = result[smplng][dpool][stat] / NP.nansum(preXwts1 * preXwts2.conj(), axis=NP.union1d(NP.where(logical_or(NP.asarray(preXwts1.shape)>1, NP.asarray(preXwts2.shape)>1))), keepdims=True) # Normalize by summing the weights over the expanded axes
if (len(xinfo['collapse_axes']) > 0) or (xinfo['avgcov']):
# if any one of collapsing of incoherent axes or
# averaging of full covariance is requested
diagoffsets = {} # Stores the correlation index difference along each axis.
diagweights = {} # Stores the number of points summed in the trace along the offset diagonal
for colaxind, colax in enumerate(xinfo['collapse_axes']):
if colax == 1:
shp = NP.ones(dspec.ndim, dtype=NP.int)
shp[colax] = lst_ind.size
multdim_idx = tuple([NP.arange(axdim) for axdim in shp])
diagweights[colax] = NP.sum(NP.logical_not(NP.isnan(dspec[multdim_idx]))) - lstshifts
# diagweights[colax] = result[smplng][dpool][stat].shape[expandax_map[colax][-1]] - lstshifts
if stat == 'mean':
result[smplng][dpool][stat] = NP.nanmean(result[smplng][dpool][stat], axis=expandax_map[colax][-1])
else:
result[smplng][dpool][stat] = NP.nanmedian(result[smplng][dpool][stat], axis=expandax_map[colax][-1])
diagoffsets[colax] = lstshifts
else:
pspec_unit = result[smplng][dpool][stat].si.unit
result[smplng][dpool][stat], offsets, diagwts = OPS.array_trace(result[smplng][dpool][stat].si.value, offsets=None, axis1=expandax_map[colax][0], axis2=expandax_map[colax][1], outaxis='axis1')
diagwts_shape = NP.ones(result[smplng][dpool][stat].ndim, dtype=NP.int)
diagwts_shape[expandax_map[colax][0]] = diagwts.size
diagoffsets[colax] = offsets
diagweights[colax] = NP.copy(diagwts)
result[smplng][dpool][stat] = result[smplng][dpool][stat] * pspec_unit / diagwts.reshape(diagwts_shape)
for ekey in expandax_map:
if ekey > colax:
expandax_map[ekey] -= 1
expandax_map[colax] = NP.asarray(expandax_map[colax][0]).ravel()
wts_shape = tuple(NP.ones(result[smplng][dpool][stat].ndim, dtype=NP.int))
postXwts = NP.ones(wts_shape, dtype=NP.complex)
wts_shape = NP.asarray(wts_shape)
for colaxind, colax in enumerate(xinfo['collapse_axes']):
curr_wts_shape = NP.copy(wts_shape)
curr_wts_shape[expandax_map[colax]] = -1
postXwts = postXwts * xinfo['wts']['postX'][colaxind].reshape(tuple(curr_wts_shape))
result[smplng][dpool][stat] = result[smplng][dpool][stat] * postXwts
axes_to_sum = tuple(NP.asarray([expandax_map[colax] for colax in xinfo['collapse_axes']]).ravel()) # for post-X normalization and collapse of covariance matrix
if xinfo['wts']['postXnorm']:
result[smplng][dpool][stat] = result[smplng][dpool][stat] / NP.nansum(postXwts, axis=axes_to_sum, keepdims=True) # Normalize by summing the weights over the collapsed axes
if xinfo['avgcov']:
# collapse the axes further (postXwts have already
# been applied)
diagoffset_weights = 1.0
for colaxind in zip(*sorted(zip(NP.arange(xinfo['collapse_axes'].size), xinfo['collapse_axes']), reverse=True))[0]:
# It is important to sort the collapsable axes in
# reverse order before deleting elements below,
# otherwise the axes ordering may be get messed up
diagoffset_weights_shape = NP.ones(result[smplng][dpool][stat].ndim, dtype=NP.int)
diagoffset_weights_shape[expandax_map[xinfo['collapse_axes'][colaxind]][0]] = diagweights[xinfo['collapse_axes'][colaxind]].size
diagoffset_weights = diagoffset_weights * diagweights[xinfo['collapse_axes'][colaxind]].reshape(diagoffset_weights_shape)
del diagoffsets[xinfo['collapse_axes'][colaxind]]
result[smplng][dpool][stat] = NP.nansum(result[smplng][dpool][stat]*diagoffset_weights, axis=axes_to_sum, keepdims=True) / NP.nansum(diagoffset_weights, axis=axes_to_sum, keepdims=True)
else:
result[smplng][dpool][stat] = factor.reshape((-1,)+tuple(NP.ones(dspec.ndim-1, dtype=NP.int))) * NP.abs(dspec * U.Jy)**2
diagoffsets = {}
expandax_map = {}
if units == 'Jy':
result[smplng][dpool][stat] = result[smplng][dpool][stat].to('Jy2 Mpc')
elif units == 'K':
result[smplng][dpool][stat] = result[smplng][dpool][stat].to('K2 Mpc3')
else:
raise ValueError('Input value for units invalid')
result[smplng][dpool]['diagoffsets'] = diagoffsets
result[smplng][dpool]['diagweights'] = diagweights
result[smplng][dpool]['axesmap'] = expandax_map
result[smplng][dpool]['nsamples_incoh'] = nsamples_incoh
result[smplng][dpool]['nsamples_coh'] = nsamples_coh
return result
############################################################################
def compute_power_spectrum_uncertainty(self, cpds=None, selection=None,
autoinfo=None,xinfo=None,
cosmo=cosmo100, units='K',
beamparms=None):
"""
------------------------------------------------------------------------
Compute uncertainty in the power spectrum of closure phase data. It is
in units of Mpc/h
Inputs:
cpds [dictionary] A dictionary that contains the 'oversampled' (if
resample=False) and/or 'resampled' (if resample=True) delay
spectrum information on the key 'errinfo'. If it is not
specified the attributes cPhaseDS['errinfo'] and
cPhaseDS_resampled['errinfo'] are used. Under each of these
sampling keys, it holds a dictionary that has the following
keys and values:
'freq_center' [numpy array] contains the center frequencies
(in Hz) of the frequency subbands of the subband
delay spectra. It is of size n_win. It is
roughly equivalent to redshift(s)
'freq_wts' [numpy array] Contains frequency weights applied
on each frequency sub-band during the subband
delay transform. It is of size n_win x nchan.
'bw_eff' [numpy array] contains the effective bandwidths
(in Hz) of the subbands being delay transformed.
It is of size n_win. It is roughly equivalent to
width in redshift or along line-of-sight
'shape' [string] shape of the window function applied.
Accepted values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow' [scalar] the power to which the FFT of the window
was raised. The value is be a positive scalar
with default = 1.0
'npad' [scalar] Numbber of zero-padded channels before
performing the subband delay transform.
'lags' [numpy array] lags of the subband delay spectra
after padding in frequency during the transform.
It is of size nlags. The lags roughly correspond
to k_parallel.
'lag_kernel' [numpy array] delay transform of the frequency
weights under the key 'freq_wts'. It is of size
n_bl x n_win x nlags x n_t.
'lag_corr_length'
[numpy array] It is the correlation timescale
(in pixels) of the subband delay spectra. It is
proportional to inverse of effective bandwidth.
It is of size n_win. The unit size of a pixel is
determined by the difference between adjacent
pixels in lags under key 'lags' which in turn is
effectively inverse of the effective bandwidth
of the subband specified in bw_eff
'errinfo' [dictionary] It has two keys 'dspec0' and
'dspec1' each of which are dictionaries with
the following keys and values:
'twts' [numpy array] Weights for the subsample
difference. It is of shape (nlst, ndays,
ntriads, nchan)
'mean' [numpy array] Delay spectrum of the
subsample difference obtained by using
the mean statistic. It is of shape
(nspw, nlst, ndays, ntriads, nlags)
'median'
[numpy array] Delay spectrum of the
subsample difference obtained by using
the median statistic. It is of shape
(nspw, nlst, ndays, ntriads, nlags)
selection [NoneType or dictionary] Selection parameters based on which
triad, LST, and day indices will be returned. If set to None
(default), all triad, LST, and day indices will be returned.
Otherwise it must be a dictionary with the following keys
and values:
'triads' [NoneType or list of 3-element tuples] If set
to None (default), indices of all triads are
returned. Otherwise, the specific triads must
be specified such as [(1,2,3), (1,2,4), ...]
and their indices will be returned
'lst' [NoneType, list or numpy array] If set to None
(default), indices of all LST are returned.
Otherwise must be a list or numpy array
containing indices to LST.
'days' [NoneType, list or numpy array] If set to None
(default), indices of all days are returned.
Otherwise must be a list or numpy array
containing indices to days.
autoinfo
[NoneType or dictionary] Specifies parameters for processing
before power spectrum in auto or cross modes. If set to None,
a dictionary will be created with the default values as
described below. The dictionary must have the following keys
and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes that will
be averaged coherently before squaring (for auto) or
cross-multiplying (for cross) power spectrum. If set
to None (default), no axes are averaged coherently.
If set to int, list, tuple or numpy array, those axes
will be averaged coherently after applying the weights
specified under key 'wts' along those axes. 1=lst,
3=triads. Value of 2 for axes is not allowed since
that denotes repeated days and it is along this axis
that cross-power is computed regardless.
'wts' [NoneType/list/numpy array] If not provided (equivalent
to setting it to None) or set to None (default), it is
set to a one element list which is a one element numpy
array of unity. Otherwise, it must be a list of same
number of elements as in key 'axes' and each of these
must be a numpy broadcast compatible array corresponding
to each of the axis specified in 'axes'
xinfo [NoneType or dictionary] Specifies parameters for processing
cross power spectrum. If set to None, a dictionary will be
created with the default values as described below. The
dictionary must have the following keys and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes over which
power spectrum will be computed incoherently by cross-
multiplication. If set to None (default), no cross-
power spectrum is computed. If set to int, list, tuple
or numpy array, cross-power over those axes will be
computed incoherently by cross-multiplication. The
cross-spectrum over these axes will be computed after
applying the pre- and post- cross-multiplication
weights specified in key 'wts'. 1=lst, 3=triads. Value
of 2 for axes is not allowed since that denotes
repeated days and it is along this axis that
cross-power is computed regardless.
'collapse_axes'
[list] The axes that will be collpased after the
cross-power matrix is produced by cross-multiplication.
If this key is not set, it will be initialized to an
empty list (default), in which case none of the axes
is collapsed and the full cross-power matrix will be
output. it must be a subset of values under key 'axes'.
This will reduce it from a square matrix along that axis
to collapsed values along each of the leading diagonals.
1=lst, 3=triads.
'dlst' [scalar] LST interval (in mins) or difference between LST
pairs which will be determined and used for
cross-power spectrum. Will only apply if values under
'axes' contains the LST axis(=1).
'dlst_range'
[scalar, numpy array, or NoneType] Specifies the LST
difference(s) in minutes that are to be used in the
computation of cross-power spectra. If a scalar, only
the diagonal consisting of pairs with that LST
difference will be computed. If a numpy array, those
diagonals consisting of pairs with that LST difference
will be computed. If set to None (default), the main
diagonal (LST difference of 0) and the first off-main
diagonal (LST difference of 1 unit) corresponding to
pairs with 0 and 1 unit LST difference are computed.
Applies only if key 'axes' contains LST axis (=1).
'avgcov'
[boolean] It specifies if the collapse of square
covariance matrix is to be collapsed further to a single
number after applying 'postX' weights. If not set or
set to False (default), this late stage collapse will
not be performed. Otherwise, it will be averaged in a
weighted average sense where the 'postX' weights would
have already been applied during the collapsing
operation
'wts' [NoneType or Dictionary] If not set, a default
dictionary (see default values below) will be created.
It must have the follwoing keys and values:
'preX' [list of numpy arrays] It contains pre-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of weights. If
set to True, the delay spectrum will be
normalized by the sum of the weights.
'postX' [list of numpy arrays] It contains post-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of 'preX' weights.
If set to True, the delay spectrum will be
normalized by the sum of the weights.
'postXnorm'
[boolean] If False (default), no normalization
is done after the application of postX weights.
If set to True, the delay cross power spectrum
will be normalized by the sum of the weights.
cosmo [instance of cosmology class from astropy] An instance of class
FLRW or default_cosmology of astropy cosmology module. Default
uses Planck 2015 cosmology, with H0=100 h km/s/Mpc
units [string] Specifies the units of output power spectum. Accepted
values are 'Jy' and 'K' (default)) and the power spectrum will
be in corresponding squared units.
Output:
Dictionary with the keys 'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,) array),
'days' ((ndaycomb,) array), 'day_ind' ((ndaycomb,) array), 'dday'
((ndaycomb,) array), 'oversampled' and 'resampled' corresponding to
whether resample was set to False or True in call to member function
FT(). Values under keys 'triads_ind' and 'lst_ind' are numpy array
corresponding to triad and time indices used in selecting the data.
Values under keys 'oversampled' and 'resampled' each contain a
dictionary with the following keys and values:
'z' [numpy array] Redshifts corresponding to the band centers in
'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,).
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding to
'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz) of the
frequency subbands of the subband delay spectra. It is of size
n_win. It is roughly equivalent to redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform. It is
of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz) of the
subbands being delay transformed. It is of size n_win. It is
roughly equivalent to width in redshift or along line-of-sight
'shape' [string] shape of the frequency window function applied. Usual
values are 'rect' (rectangular), 'bhw' (Blackman-Harris),
'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was raised.
The value is be a positive scalar with default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in pixels) of
the subband delay spectra. It is proportional to inverse of
effective bandwidth. It is of size n_win. The unit size of a
pixel is determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is effectively inverse
of the effective bandwidth of the subband specified in bw_eff
It further contains a key named 'errinfo' which is a dictionary. It
contains information about power spectrum uncertainties obtained from
subsample differences. It contains the following keys and values:
'mean' [numpy array] Delay power spectrum uncertainties incoherently
estimated over the axes specified in xinfo['axes'] using the
'mean' key in input cpds or attribute
cPhaseDS['errinfo']['dspec']. It has shape that depends on the
combination of input parameters. See examples below. If both
collapse_axes and avgcov are not set, those axes will be
replaced with square covariance matrices. If collapse_axes is
provided but avgcov is False, those axes will be of shape
2*Naxis-1.
'median'
[numpy array] Delay power spectrum uncertainties incoherently
averaged over the axes specified in incohax using the 'median'
key in input cpds or attribute cPhaseDS['errinfo']['dspec'].
It has shape that depends on the combination of input
parameters. See examples below. If both collapse_axes and
avgcov are not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal offsets for
those axes. If 'avgcov' was set, those entries will be removed
from 'diagoffsets' since all the leading diagonal elements have
been collapsed (averaged) further. Value under each key is a
numpy array where each element in the array corresponds to the
index of that leading diagonal. This should match the size of
the output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in collapse_axes and
the value is a numpy array of weights corresponding to the
diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated but is
not collapsed, the number of dimensions in the output will have
changed. This parameter tracks where the original axis is now
placed. The keys are the original axes that are involved in
incoherent cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the power
spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the power
spectrum
Examples:
(1)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': None, 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False}}
This will not do anything because axes cannot include value 2 which
denote the 'days' axis and the uncertainties are obtained through
subsample differencing along days axis regardless.
Output delay power spectrum has shape (Nspw, Nlst, Ndaycomb, Ntriads,
Nlags)
(2)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False},
'dlst_range': None}
This will not do anything about coherent averaging along axis=2 because
axes cannot include value 2 which denote the 'days' axis and the
uncertainties are obtained through subsample differencing along days
axis regardless.
Output delay power spectrum has shape
(Nspw, 2, Nlst, Ndaycomb, Ntriads, Ntriads, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)},
axesmap = {1: [1,2], 3: [4,5]}
(3)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [3],
'dlst_range': [0.0, 1.0, 2.0]}
This will not do anything about coherent averaging along axis=2 because
axes cannot include value 2 which denote the 'days' axis and the
uncertainties are obtained through subsample differencing along days
axis regardless.
Output delay power spectrum has shape
(Nspw, 3, Nlst, 1, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1,2], 3: [4]}
(4)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [1,3],
'dlst_range': [1.0, 2.0, 3.0, 4.0]}
Output delay power spectrum has shape
(Nspw, 4, Ndaycomb, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1], 3: [3]}
(5)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': [3],
'dlst_range': None}
Output delay power spectrum has shape
(Nspw, 2, Nlst, Ndays, 1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)}, axesmap = {1: [1,2], 3: [4]}
(6)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': []}
Output delay power spectrum has shape
(Nspw, 1, Ndays, 1, Nlags)
diagoffsets = {}, axesmap = {1: [1], 3: [3]}
------------------------------------------------------------------------
"""
if not isinstance(units,str):
raise TypeError('Input parameter units must be a string')
if units.lower() == 'k':
if not isinstance(beamparms, dict):
raise TypeError('Input beamparms must be a dictionary')
if 'freqs' not in beamparms:
beamparms['freqs'] = self.f
beamparms_orig = copy.deepcopy(beamparms)
if autoinfo is None:
autoinfo = {'axes': None, 'wts': [NP.ones(1, dtpye=NP.float)]}
elif not isinstance(autoinfo, dict):
raise TypeError('Input autoinfo must be a dictionary')
if 'axes' not in autoinfo:
autoinfo['axes'] = None
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input autoinfo must be an integer, list, tuple or numpy array')
else:
autoinfo['axes'] = NP.asarray(autoinfo['axes']).reshape(-1)
if 'wts' not in autoinfo:
if autoinfo['axes'] is not None:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)] * len(autoinfo['axes'])
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['wts'], list):
raise TypeError('wts in input autoinfo must be a list of numpy arrays')
else:
if len(autoinfo['wts']) != len(autoinfo['axes']):
raise ValueError('Input list of wts must be same as length of autoinfo axes')
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
if xinfo is None:
xinfo = {'axes': None, 'wts': {'preX': [NP.ones(1, dtpye=NP.float)], 'postX': [NP.ones(1, dtpye=NP.float)], 'preXnorm': False, 'postXnorm': False}}
elif not isinstance(xinfo, dict):
raise TypeError('Input xinfo must be a dictionary')
if 'axes' not in xinfo:
xinfo['axes'] = None
else:
if not isinstance(xinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input xinfo must be an integer, list, tuple or numpy array')
else:
xinfo['axes'] = NP.asarray(xinfo['axes']).reshape(-1)
if 'wts' not in xinfo:
xinfo['wts'] = {}
for xkey in ['preX', 'postX']:
if xinfo['axes'] is not None:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)] * len(xinfo['axes'])
else:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
xinfo['wts']['preXnorm'] = False
xinfo['wts']['postXnorm'] = False
else:
if xinfo['axes'] is not None:
if not isinstance(xinfo['wts'], dict):
raise TypeError('wts in input xinfo must be a dictionary')
for xkey in ['preX', 'postX']:
if not isinstance(xinfo['wts'][xkey], list):
raise TypeError('{0} wts in input xinfo must be a list of numpy arrays'.format(xkey))
else:
if len(xinfo['wts'][xkey]) != len(xinfo['axes']):
raise ValueError('Input list of {0} wts must be same as length of xinfo axes'.format(xkey))
else:
for xkey in ['preX', 'postX']:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
if 'preXnorm' not in xinfo['wts']:
xinfo['wts']['preXnorm'] = False
if 'postXnorm' not in xinfo['wts']:
xinfo['wts']['postXnorm'] = False
if not isinstance(xinfo['wts']['preXnorm'], NP.bool):
raise TypeError('preXnorm in input xinfo must be a boolean')
if not isinstance(xinfo['wts']['postXnorm'], NP.bool):
raise TypeError('postXnorm in input xinfo must be a boolean')
if 'avgcov' not in xinfo:
xinfo['avgcov'] = False
if not isinstance(xinfo['avgcov'], NP.bool):
raise TypeError('avgcov under input xinfo must be boolean')
if 'collapse_axes' not in xinfo:
xinfo['collapse_axes'] = []
if not isinstance(xinfo['collapse_axes'], (int,list,tuple,NP.ndarray)):
raise TypeError('collapse_axes under input xinfo must be an integer, tuple, list or numpy array')
else:
xinfo['collapse_axes'] = NP.asarray(xinfo['collapse_axes']).reshape(-1)
if (autoinfo['axes'] is not None) and (xinfo['axes'] is not None):
if | NP.intersect1d(autoinfo['axes'], xinfo['axes']) | numpy.intersect1d |
import keras.layers as kl
from keras.models import Model
from keras import regularizers
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
class NNModel:
def __init__(self, input_shape):
self.input_shape = input_shape
def make_model(self):
input_data = kl.Input(shape=(1, self.input_shape))
lstm = kl.LSTM(5, input_shape=(1, self.input_shape), return_sequences=True, activity_regularizer=regularizers.l2(0.003),
recurrent_regularizer=regularizers.l2(0), dropout=0.2, recurrent_dropout=0.2)(input_data)
perc = kl.Dense(5, activation="sigmoid", activity_regularizer=regularizers.l2(0.005))(lstm)
lstm2 = kl.LSTM(2, activity_regularizer=regularizers.l2(0.01), recurrent_regularizer=regularizers.l2(0.001),
dropout=0.2, recurrent_dropout=0.2)(perc)
out = kl.Dense(1, activation="sigmoid", activity_regularizer=regularizers.l2(0.001))(lstm2)
model = Model(input_data, out)
self.model = model
def train_model(self, x, y, epochs, model_name, save_model=True):
self.model.compile(optimizer="adam", loss="mean_squared_error", metrics=["mse", "acc"])
# load data
train_x = np.reshape(np.array(x), (len(x), 1, self.input_shape))
train_y = np.array(y)
# train_stock = np.array(pd.read_csv("train_stock.csv"))
# train model
self.model.fit(train_x, train_y, epochs=epochs)
if save_model:
self.model.save(f"models/saved_models/{model_name}.h5", overwrite=True, include_optimizer=True)
def test_model(self, x, y):
test_x = np.reshape( | np.array(x) | numpy.array |
# Copyright 2022 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""eval"""
import os
import ast
import codecs
import argparse
import cv2
import numpy as np
from sklearn.metrics import roc_auc_score
from mindspore import context
from mindspore.train.serialization import load_checkpoint, load_param_into_net
from mindspore import ops
from src.dataset import createDataset
from src.stpm import STPM
parser = argparse.ArgumentParser(description='test')
parser.add_argument('--category', type=str, default='screw')
parser.add_argument('--device_id', type=int, default=0, help='Device id')
parser.add_argument('--data_url', type=str, default="/")
parser.add_argument('--save_sample', type=ast.literal_eval, default=False, help='Whether to save the infer image')
parser.add_argument('--save_sample_path', type=str, default="", help='The path to save infer image')
parser.add_argument('--ckpt_path', type=str, default='./', help="The path to save checkpoint")
parser.add_argument('--num_class', type=int, default=1000, help="The num of class")
parser.add_argument('--out_size', type=int, default=256, help="out size")
args = parser.parse_args()
class SaveImageTool:
def __init__(self, save_sample_path):
self.save_sample_path = save_sample_path
def cvt2heatmap(self, gray):
heatmap = cv2.applyColorMap(np.uint8(gray), cv2.COLORMAP_JET)
return heatmap
def heatmap_on_image(self, heatmap, image):
out = np.float32(heatmap) / 255 + np.float32(image) / 255
out = out / np.max(out)
return np.uint8(255 * out)
def min_max_norm(self, image):
a_min, a_max = image.min(), image.max()
return (image - a_min) / (a_max - a_min)
def save_anomaly_map(self, anomaly_map, a_maps, input_img, gt_img, file_name, category):
anomaly_map_norm = self.min_max_norm(anomaly_map)
anomaly_map_norm_hm = self.cvt2heatmap(anomaly_map_norm * 255)
# 64x64 map
am64 = self.min_max_norm(a_maps[0])
am64 = self.cvt2heatmap(am64 * 255)
# 32x32 map
am32 = self.min_max_norm(a_maps[1])
am32 = self.cvt2heatmap(am32 * 255)
# 16x16 map
am16 = self.min_max_norm(a_maps[2])
am16 = self.cvt2heatmap(am16 * 255)
# anomaly map on image
heatmap = self.cvt2heatmap(anomaly_map_norm * 255)
hm_on_img = self.heatmap_on_image(heatmap, input_img)
# save images
save_path = os.path.join(self.save_sample_path, f'{category}_{file_name}')
cv2.imwrite(os.path.join(save_path + '.jpg'), input_img)
cv2.imwrite(os.path.join(save_path + '_am64.jpg'), am64)
cv2.imwrite(os.path.join(save_path + '_am32.jpg'), am32)
cv2.imwrite(os.path.join(save_path + '_am16.jpg'), am16)
cv2.imwrite(os.path.join(save_path + '_amap.jpg'), anomaly_map_norm_hm)
cv2.imwrite(os.path.join(save_path + '_amap_on_img.jpg'), hm_on_img)
cv2.imwrite(os.path.join(save_path + '_gt.jpg'), gt_img)
def normalize(self, in_x):
n, c, _, _ = in_x.shape
if n != 1:
raise ValueError(f"Only currently support batch size=1 in saving infer image. But got {n}.")
if c != 3:
raise ValueError(f"Only currently support that the channel of the input image is 3. But got {c}.")
mean = [-0.485 / 0.229, -0.456 / 0.224, -0.406 / 0.255]
std = [1 / 0.229, 1 / 0.224, 1 / 0.255]
for i in range(c):
in_x[:, i, :, :] = (in_x[:, i, :, :] - mean[i]) / std[i]
return in_x
def cal_anomaly_map(fs_list, ft_list, out_size=224):
"""cal_anomaly_map"""
unsqueeze = ops.ExpandDims()
Sum = ops.ReduceSum(keep_dims=False)
Norm = ops.L2Normalize(axis=1)
amap_mode = 'mul'
if amap_mode == 'mul':
anomaly_map = np.ones([out_size, out_size])
else:
anomaly_map = np.zeros([out_size, out_size])
map_list = []
for i in range(len(ft_list)):
fs = fs_list[i]
ft = ft_list[i]
fs_norm = Norm(fs)
ft_norm = Norm(ft)
num = fs_norm * ft_norm
cos = Sum(num, 1)
a_map = 1 - cos
a_map = unsqueeze(a_map, 1)
a_map = a_map[0, 0, :, :].asnumpy()
a_map = cv2.resize(a_map, (out_size, out_size))
map_list.append(a_map)
if amap_mode == 'mul':
anomaly_map *= a_map
else:
anomaly_map += a_map
return anomaly_map, map_list
if __name__ == "__main__":
context.set_context(mode=context.GRAPH_MODE,
device_target='Ascend',
save_graphs=False,
device_id=args.device_id)
_, ds_test = createDataset(args.data_url, args.category, save_sample=args.save_sample, out_size=args.out_size)
net = STPM(args, is_train=False)
param = load_checkpoint(os.path.join(args.ckpt_path))
load_param_into_net(net, param)
net.set_train(False)
gt_list_px_lvl = []
pred_list_px_lvl = []
gt_list_img_lvl = []
pred_list_img_lvl = []
if args.save_sample:
if args.save_sample_path == "":
current_path = os.path.abspath(os.path.dirname(__file__))
args.save_sample_path = os.path.join(current_path, f'scripts/eval_{args.category}/sample')
print(f"The image generated by inference will be saved in this path: {args.save_sample_path}")
os.makedirs(args.save_sample_path, exist_ok=True)
for data in ds_test.create_dict_iterator():
gt = data['gt']
label = data['label']
x = data['img']
features_s, features_t = net(x)
amap, a_map_list = cal_anomaly_map(features_s, features_t, out_size=args.out_size)
gt_np = gt.asnumpy()[0, 0].astype(int)
gt_list_px_lvl.extend(gt_np.ravel())
pred_list_px_lvl.extend(amap.ravel())
gt_list_img_lvl.append(label.asnumpy()[0])
pred_list_img_lvl.append(amap.max())
if args.save_sample:
filename = data['filename']
filename = str(codecs.decode(filename.asnumpy().tostring()).strip(b'\x00'.decode()))
x = x.asnumpy()
img_tool = SaveImageTool(args.save_sample_path)
input_x = img_tool.normalize(x)
input_x = | np.transpose(input_x, (0, 2, 3, 1)) | numpy.transpose |
# -*- coding: utf-8 -*-
"""
Trains a model on the source dataset
Then evaluates it on three OOD datasets:
- OOD instances
- OOD backgrounds
- OOD instances and background
"""
from re import I
import torch
import numpy as np
import PIL
import random
import os
from src import dataset, helpers, custom_dataloaders
from torch.utils.data import DataLoader
import matplotlib.pyplot as plt
from torchvision.models import Inception3
from torchvision import transforms
import torchvision
from tqdm import tqdm
from torch.nn import functional as F
import torch.nn as nn
import torch.optim as optim
import numpy as np
import yaml
import argparse
import json
# Ignore warining
import warnings
warnings.filterwarnings("ignore")
# output dictionnary
output = {}
# Companion functions
def return_f1(precision, recall):
return 2 * (np.array(precision) * np.array(recall)) / (np.array(precision) + np.array(recall))
def plot_curves(precision, recall):
"""
add points to compute the p/r curves
"""
precisions_plot = [[0]]
recall_plot = [[recall[0]]]
precisions_plot.append(precision)
recall_plot.append(recall)
precisions_plot.append([precision[-1]])
recall_plot.append([0.5])
precisions_plot = sum(precisions_plot, [])
recall_plot = sum(recall_plot, [])
return precisions_plot, recall_plot
# Setting up the seed
seed = 42
torch.backends.cudnn.deterministic = True
random.seed(seed)
torch.manual_seed(seed)
torch.cuda.manual_seed(seed)
np.random.seed(seed)
# Load the configuration file
config = 'config.yml'
with open(config, 'rb') as f:
configuration = yaml.load(f, Loader=yaml.FullLoader)
# Retrieve the directories
models_dir = configuration.get("models_dir")
files_dir = configuration.get("files_dir")
figs_dir = configuration.get("figs_dir")
data_dir = configuration.get("dataset_dir")
# Retrieve the options for the model
pretrained : configuration.get('pretrained', True)
model_family = configuration.get('model', 'inception')
model_weight = configuration.get('model_weight')
image_size = configuration.get('image_size')
# label_name = configuration.get('label_name', 'labels.csv')
output_directory = configuration.get("output_directory", 'results')
# If the directory does not exist, create the temporary folder
# where the checkpoints will be stored.
weights_dir = 'weights'
checkpoints_dir = os.path.join(weights_dir, 'losses')
if not os.path.isdir(weights_dir):
os.mkdir(weights_dir)
if not os.path.isdir(checkpoints_dir):
os.mkdir(checkpoints_dir)
# Arguments
parser = argparse.ArgumentParser(description = 'Model training')
parser.add_argument('--device', default = 'cuda:0', help = "GPU device")
parser.add_argument('--n_epochs', default = 30, help = "Number of training epochs", type=int)
parser.add_argument('--batch_size', default = 64, help = "Batch size", type=int)
parser.add_argument('--print_every', default = 20, help = "Evaluate the model every print_every iterations.", type=int)
parser.add_argument('--name', default = 'model', help = "Name of the model.")
# Additional arguments with which we will edit the label files
parser.add_argument('--array_type', default = None, help = "Class of arrays to consider.")
parser.add_argument('--max_count', default = None, help = 'Maximal number of samples to sample from.', type = int)
parser.add_argument('--source_domain', default = None, help = "The source domain. The target domain will be deduced.")
parser.add_argument('--bootstrap', default = 50, help = "Number of bootstrap iterations to estimate the dimensionality", type = int)
parser.add_argument('--n_iter', default = 10, help = "Number of train/dimensionality estimation/test iterations", type = int)
args = parser.parse_args()
# Transforms
# If the model is resnet, then we crop the image to be 224 * 224
# If the model is custom, then the size should be specified by the user.
if model_family == 'inception':
transforms = torchvision.transforms.Compose([
torchvision.transforms.ToPILImage(),
torchvision.transforms.RandomHorizontalFlip(),
torchvision.transforms.RandomVerticalFlip(),
torchvision.transforms.RandomRotation((90,90)),
torchvision.transforms.RandomRotation((-90,-90)),
torchvision.transforms.ColorJitter(brightness=0.1, contrast=0.2, saturation=0, hue=0),
torchvision.transforms.ToTensor(),
torchvision.transforms.Normalize(mean=[0.5, 0.5, 0.5], std=[0.5, 0.5, 0.5]),
])
elif model_family == 'resnet':
transforms = torchvision.transforms.Compose([
torchvision.transforms.ToPILImage(),
torchvision.transforms.RandomHorizontalFlip(),
torchvision.transforms.RandomVerticalFlip(),
torchvision.transforms.RandomRotation((90,90)),
torchvision.transforms.RandomRotation((-90,-90)),
torchvision.transforms.ColorJitter(brightness=0.1, contrast=0.2, saturation=0, hue=0),
torchvision.transforms.ToTensor(),
# torchvision.transforms.CenterCrop(224),
torchvision.transforms.Normalize(mean=[0.5, 0.5, 0.5], std=[0.5, 0.5, 0.5]),
])
elif model_family == 'custom':
transforms = torchvision.transforms.Compose([
torchvision.transforms.ToPILImage(),
torchvision.transforms.RandomHorizontalFlip(),
torchvision.transforms.RandomVerticalFlip(),
torchvision.transforms.RandomRotation((90,90)),
torchvision.transforms.RandomRotation((-90,-90)),
torchvision.transforms.ColorJitter(brightness=0.1, contrast=0.2, saturation=0, hue=0),
torchvision.transforms.ToTensor(),
torchvision.transforms.CenterCrop(image_size),
torchvision.transforms.Normalize(mean=[0.5, 0.5, 0.5], std=[0.5, 0.5, 0.5]),
])
# Data
# Load the data
# Load the correct image size
if model_family == 'resnet':
dataset_dir = os.path.join(data_dir, 'PITW_224')
elif model_family == 'inception':
dataset_dir = os.path.join(data_dir, 'PITW_299')
training_path = os.path.join(dataset_dir, 'train')
annotations_train = os.path.join(training_path, "labels.csv")
validation_path = os.path.join(dataset_dir, 'validation')
annotations_validation = os.path.join(validation_path, 'labels.csv')
test_path = os.path.join(dataset_dir, 'test')
annotations_test = os.path.join(test_path, 'labels.csv')
ood_background = os.path.join(dataset_dir, "test_ood_background")
annotations_ood_background = os.path.join(ood_background, 'labels.csv')
ood_instances = os.path.join(dataset_dir, "test_ood_instances")
annotations_ood_instances = os.path.join(ood_instances, 'labels.csv')
# ood dataset : custom path
ood_dir = 'PITW_urban'
ood = os.path.join(ood_dir, "test")
annotations_ood = os.path.join(ood, 'labels.csv')
training_data = dataset.BDPVClassificationDataset(annotations_train, training_path, transform = transforms, max_count = args.max_count)
validation_data = dataset.BDPVClassificationDataset(annotations_validation, validation_path, transform = transforms, max_count = args.max_count)
test_data = dataset.BDPVClassificationDataset(annotations_test, test_path, transform = transforms, max_count = args.max_count)
ood_background_data = dataset.BDPVClassificationDataset(annotations_ood_background, ood_background, transform = transforms, max_count = args.max_count)
ood_instances_data = dataset.BDPVClassificationDataset(annotations_ood_instances, ood_instances, transform = transforms, max_count = args.max_count)
ood_data = dataset.BDPVClassificationDataset(annotations_ood, ood, transform = transforms, max_count = args.max_count)
# Initialize the data
train = DataLoader(training_data, batch_size = args.batch_size, shuffle = True)
val = DataLoader(validation_data, batch_size = args.batch_size, shuffle = True)
test = DataLoader(test_data, batch_size = args.batch_size, shuffle = True)
background_ood = DataLoader(ood_background_data, batch_size = args.batch_size, shuffle = True)
instances_ood = DataLoader(ood_instances_data, batch_size = args.batch_size, shuffle = True)
ood_dataset = DataLoader(ood_data, batch_size = args.batch_size, shuffle = True)
dataloader = {"train": train, 'val' : val, 'test' : test}
ood_dataloader = {'ood_background' : background_ood,
'ood_instances' : instances_ood,
'ood' : ood_dataset}
def train(dataloader):
"""
trains the model
"""
# Initialize the model
if model_family == 'inception':
# Load the model fine-tuned on NRW
model = Inception3(num_classes = 2, aux_logits = True, transform_input = False, init_weights = True) # Load the architecture
checkpoint = torch.load(model_weight, map_location = args.device) # Load the weights
model.load_state_dict(checkpoint['model_state_dict']) # Upload the weights in the model
model = model.to(args.device) # move the model to the device
elif model_family == 'resnet':
# Load the model and send it to the GPU
model = torchvision.models.resnet50(pretrained = True)
# Last layer should have an output shape of 2.
model.fc = nn.Sequential(
nn.Linear(2048, 2),
nn.ReLU(inplace=True))
model = model.to(args.device)
elif model_family == 'custom':
# Load the model and send it to the GPU
model = torch.load(model_weight)
model = model.to(args.device)
# Train
# Initialization of the model
# Layers to update
for param in model.parameters():
param.requires_grad = True
# Criterion
criterion = nn.BCELoss()
# Parameters to update and optimizer
params_to_update = []
for _, param in model.named_parameters():
if param.requires_grad == True:
params_to_update.append(param)
optimizer = optim.Adam(params_to_update, lr = 0.0001)
# Training
running_loss = 0
waiting = 0
steps = 0
early_stop = False
train_losses, test_losses = [], []
threshold = 0.5 # Threshold set by default. Will be fine tuned afterwards
for epoch in range(args.n_epochs):
for inputs, labels, _ in tqdm(dataloader["train"]):
steps += 1
labels = labels.to(torch.float32)
inputs, labels = inputs.to(args.device), labels.to(args.device)
optimizer.zero_grad()
if model_family == 'inception':
# Accomodate for the particular architecture of inception
outputs, aux_outputs = model(inputs)
outputs, aux_outputs = F.softmax(outputs, dim=1), F.softmax(aux_outputs, dim=1)
outputs, aux_outputs = outputs[:,1], aux_outputs[:,1]
loss = criterion(outputs, labels) + 0.4 * criterion(aux_outputs, labels)
else:
outputs = model(inputs)
outputs = F.softmax(outputs, dim=1)
outputs = outputs[:,1]
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()
running_loss += loss.item()
# Evaluate the model
if steps % args.print_every == 0:
test_loss = 0
model.eval()
with torch.no_grad():
true_positives, false_positives, true_negatives, false_negatives = 0, 0, 0, 0
total = 0
for inputs, labels, names in dataloader["val"]:
labels = labels.to(torch.float32)
inputs, labels = inputs.to(args.device), labels.to(args.device)
outputs = model.forward(inputs)
outputs = F.softmax(outputs, dim=1) # the model returns the unnormalized probs. Softmax it to get probs
outputs = outputs[:,1]
batch_loss = criterion(outputs, labels)
test_loss += batch_loss.item()
predicted = (outputs >= threshold).long() # return 0 or 1 if an array has been detected
# compute the accuracy of the classification
tp, fp, tn, fn = helpers.confusion(predicted, labels)
true_positives += tp
false_positives += fp
true_negatives += tn
false_negatives += fn
train_total = 100 * running_loss / len(dataloader["train"])
test_total = 100 * test_loss / len(dataloader["val"])
train_losses.append(train_total)
test_losses.append(test_total)
# Add to the SummaryWriter
# loss_writer.add_scalar("train", train_total, steps)
# loss_writer.add_scalar("test", test_total, steps)
# Compute the F1 score
precision = np.divide(true_positives, (true_positives + false_positives))
recall = np.divide(true_positives, (true_positives + false_negatives))
f1 = 2 * np.divide((precision * recall), (precision + recall))
print(
f"Epoch {epoch+1}/{args.n_epochs}..."
f"Step {steps}...."
f"Train loss : {train_total:.3f}......"
f"Val loss : {test_total:.3f}......"
f"F1 score : {f1:.3f}"
)
running_loss = 0
model.train()
# early stopping condition
# if the model fails to improve for five subsequent epochs on the
# validation set, we stop the training
if steps == args.print_every: # first time on the validation set
min_val_loss = test_total
best_model = args.name + '_' + str(steps) + '.pth'
# Save the model
torch.save(model, os.path.join(checkpoints_dir, best_model))
else:
if not test_total < min_val_loss:
waiting += 1
else: # save the model, erase the former best model
best_model = args.name + '_' + str(steps) + '.pth'
torch.save(model, os.path.join(checkpoints_dir, best_model))
waiting = 0 # Reset the number of epochs we have to wait.
min_val_loss = test_total # Uptdate the new minimum loss
if waiting == 8:
early_stop = True
print('Model failed to improve for 5 subsequent epochs on the validation dataset.')
break
if early_stop : # early stop if necessary.
print('Training interrupted.')
model.eval()
break
# Save the best checkpoint as the best model
if not os.path.isdir(models_dir):
os.mkdir(models_dir)
# Load the best model
model = torch.load(os.path.join(checkpoints_dir, best_model))
model = model.to(args.device)
# Save it
best_model_name = args.name + '.pth'
torch.save(model, os.path.join(models_dir, best_model_name))
# Fine tune the classification threshold
print('Model trained. Now computing the precision and recall curves on the test set.')
# Thresholds to be considered
results_models = {}
thresholds = np.linspace(0.01,.99, 99)
model.eval()
# Now we compute the precision/recall curve on the test set directly for
# comprison with the out domain labels
# Forward pass on the validation dataset and accumulate the probabilities
# in a single vector.
probabilities = []
all_labels = []
with torch.no_grad():
for data in tqdm(dataloader["test"]):
# i +=1
images, labels, _ = data
# move the images to the device
images = images.to(args.device)
labels = labels.detach().cpu().numpy()
all_labels.append(list(labels))
# calculate outputs by running images through the network and computing the prediction using the threshold
outputs = model(images)
probs = F.softmax(outputs, dim=1).detach().cpu().numpy() # the model returns the unnormalized probs. Softmax it to get probs
probabilities.append(list(probs[:,1]))
# Convert the probabilities and labels as an array
probabilities = sum(probabilities, [])
probabilities = | np.array(probabilities) | numpy.array |
# Copyright 2017 Regents of the University of California
#
# Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with # the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 'AS IS' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import os, sys, time, copy, collections, math, json
import numpy as np
import scipy as sp
import matplotlib
from matplotlib import pyplot as plt
import llops as yp
# Custom scale bar object
from matplotlib_scalebar.scalebar import ScaleBar
# Libwallerlab imports
from llops import display
from llops import Roi
class StopAndStareAcquisition():
# Initialization
def __init__(self, hardware_controller_list, system_metadata,
illumination_type='bf',
illumination_sequence=None,
frame_spacing_mm=1,
object_size_mm=(0.5, 0.5),
reuse_illumination_sequence=True,
max_exposure_time_s=2,
exposure_time_pad_s=0.0,
velocity_mm_s=None,
exposure_time_s=None,
debug=False,
trigger_mode='software',
motion_acceleration_mm_s_2=1e3,
flip_pathway=False,
acquisition_timeout_s=3,
illumination_na_pad=0.03,
illumination_color={'w': 127},
settle_time_s=0):
# Parse options
self.illumination_type = illumination_type
self.settle_time_s = settle_time_s
self.object_size_mm = object_size_mm
self.frame_spacing_mm = frame_spacing_mm
self.flip_pathway = flip_pathway
self.exposure_time_pad_s = exposure_time_pad_s
self.debug = debug
self.motion_acceleration_mm_s_2 = motion_acceleration_mm_s_2
self.velocity_mm_s = velocity_mm_s
self.max_exposure_time_s = max_exposure_time_s
self.illumination_na_pad = illumination_na_pad
self.illumination_color = illumination_color
self.acquisition_timeout_s = acquisition_timeout_s
# Define controller objects, which act as hardware interfaces.
# These should be in an ordered dictionary because the order which they
# are initialized matters when using a mix of hardware and software triggering.
self.hardware_controller_list = collections.OrderedDict()
# First add hardware triggered elements so they perform their set-up before we trigger software elements
for controller in hardware_controller_list:
if controller.trigger_mode is 'hardware':
self.hardware_controller_list[controller.type] = controller
controller.reset()
controller.seq_clear()
# Then, add software triggered elements
for controller in hardware_controller_list:
if controller.trigger_mode is 'software':
self.hardware_controller_list[controller.type] = controller
controller.reset()
controller.seq_clear()
# Check to be sure a sequence acquisition is not running
assert 'camera' in self.hardware_controller_list, 'Did not find camera controller!'
# Store metadata object
self.metadata = system_metadata
# Ensure we have all necessary metadata for basic acquisition
assert self.metadata.objective.na is not None, 'Missing objective.na in metadata.'
assert self.metadata.objective.mag is not None, 'Missing objective.mag in metadata.'
assert self.metadata.camera.pixel_size_um is not None, 'Missing pixel size in metadata.'
# Update effective pixel size (for scale bar)
self.metadata.system.eff_pixel_size_um = self.metadata.camera.pixel_size_um / (self.metadata.objective.mag * self.metadata.system.mag)
# Trigger Constants
self.TRIG_MODE_EVERY_PATTERN = 1
self.TRIG_MODE_ITERATION = -1
self.TRIG_MODE_START = -2
# Frame state time sequence, will default to a sequence of one exposure time per frame if left as None
self.time_sequence_s = None
self.exposure_time_s = None
self.hardware_sequence_timing = None
# Turn off fast sequencing for illumination by default since this is only avaolable with certain LED arrays
if 'illumination' in self.hardware_controller_list:
self.hardware_controller_list['illumination'].use_fast_sequence = False
# print(type(self.))
self.metadata.type = 'stop and stare'
assert 'illumination' in self.hardware_controller_list, 'Stop and Stare acquisition requires programmable light source'
assert 'position' in self.hardware_controller_list, 'Stop and Stare acquisition requires programmable positioning device'
# Generate motion pathway
self.hardware_controller_list['position'].state_sequence = self.genStopAndStarePathwayRaster(
self.object_size_mm, self.frame_spacing_mm)
# Generate illumination sequence
illuminaiton_pattern_sequence = [self.illumination_type] * \
len(self.hardware_controller_list['position'].state_sequence)
self.hardware_controller_list['illumination'].state_sequence = self.genMultiContrastSequence(
illuminaiton_pattern_sequence)
# Tell device not to use feedback
self.hardware_controller_list['illumination'].trigger_wait_flag = False
self.hardware_controller_list['illumination'].command('trs.0.500.0')
self.hardware_controller_list['illumination'].command('trs.1.500.0')
self.hardware_controller_list['position'].goToPosition((0,0))
self.hardware_controller_list['position'].command('ENCODER X 1')
self.hardware_controller_list['position'].command('ENCODER Y 1')
self.hardware_controller_list['position'].command('ENCW X 100')
self.hardware_controller_list['position'].command('ENCW Y 100')
def acquire(self, exposure_time_ms=50):
# Allocate memory for frames
if self.hardware_controller_list['camera'].isSequenceRunning():
self.hardware_controller_list['camera'].sequenceStop()
self.hardware_controller_list['camera'].setBufferSizeMb(
20 * len(self.hardware_controller_list['position'].state_sequence))
# Set camera exposure
self.hardware_controller_list['camera'].setExposure(exposure_time_ms / 1e3)
self.hardware_controller_list['camera'].setTriggerMode('hardware')
self.hardware_controller_list['camera'].runSequence()
self.hardware_controller_list['illumination'].bf()
# Snap one image to ensure all acquisitons are started
self.hardware_controller_list['camera'].snap()
# generate frame_list
t0 = time.time()
frames_acquired = 0
frame_list = []
for frame in yp.display.progressBar(self.hardware_controller_list['position'].state_sequence, name='Frames Acquired'):
pos = frame['states']
x = pos[0][0]['value']['x']
y = pos[0][0]['value']['y']
self.hardware_controller_list['position'].goToPosition((x, y), blocking=True)
time.sleep(self.settle_time_s)
frame_list.append(self.hardware_controller_list['camera'].snap())
frames_acquired += 1
# print('Acquired %d of %d frames' % (frames_acquired, len(self.hardware_controller_list['position'].state_sequence)))
t_acq_sns = time.time() - t0
print("Acquisition took %.4f seconds" % (t_acq_sns))
# Create dataset
from htdeblur.mddataset import MotionDeblurDataset
dataset = MotionDeblurDataset()
# Assign acquisition time
self.metadata.acquisition_time_s = t_acq_sns
# Apply simple geometric transformations
if self.metadata.camera.transpose:
frame_list = frame_list.transpose(0, 2, 1)
if self.metadata.camera.flip_x:
frame_list = np.flip(frame_list, 2)
if self.metadata.camera.flip_y:
frame_list = np.flip(frame_list, 1)
# Assign
dataset.frame_list = [frame for frame in frame_list]
# Set frame state list
self.n_frames = len(self.hardware_controller_list['position'].state_sequence)
frame_state_list = []
for frame_index in range(self.n_frames):
single_frame_state_list = {}
# Loop over hardware controllers and record their state sequences
for hardware_controller_name in self.hardware_controller_list:
hardware_controller = self.hardware_controller_list[hardware_controller_name]
if hardware_controller.state_sequence is not None:
single_frame_state_list[hardware_controller_name] = hardware_controller.state_sequence[frame_index]
# Record time_sequence_s
single_frame_state_list['time_sequence_s'] = [0]
# Add to list of all frames
frame_state_list.append(single_frame_state_list)
dataset.metadata = self.metadata
dataset.type = 'stop_and_stare'
dataset.frame_state_list = frame_state_list
return dataset
def genStopAndStarePathwayRaster(self, object_size_mm, frame_spacing_mm, major_axis=1, include_minor_axis=False):
# Determine major axis
if major_axis is None:
major_axis = np.argmax(np.asarray(object_size_mm))
if object_size_mm[0] == object_size_mm[1]:
major_axis = 1
# Detemine number of measurements
measurement_count = np.ceil(np.asarray(object_size_mm) / np.asarray(frame_spacing_mm)
).astype(np.int) # two components in x and y
# Determine slightly smaller frame spacing for optimal coverage of object
frame_spacing_mm = (object_size_mm[0] / measurement_count[0], object_size_mm[1] / measurement_count[1])
# Error checking
assert np.any(measurement_count > 1), "image_size must be smaller than object_size!"
print("Image size requires %d x %d images" % (measurement_count[0], measurement_count[1]))
# This variable will be populated by the loop below
raster_segments = np.zeros((measurement_count[0] * 2, 2))
# Generate raster points
raster_end_point_list = []
pathway = []
linear_segment_index = 0 # This variable keeps track of linear segments, for use with path planning
for row in np.arange(measurement_count[0]):
if row % 2 == 0:
for index, col in enumerate(range(measurement_count[1])):
# Add pathway to list
pathway.append({'x_start': frame_spacing_mm[1] * col,
'y_start': frame_spacing_mm[0] * row,
'x_end': frame_spacing_mm[1] * col,
'y_end': frame_spacing_mm[0] * row,
'linear_segment_index': linear_segment_index})
else:
for index, col in enumerate(reversed(range(measurement_count[1]))):
# Add pathway to list
frame_spacing_mm[0] * row
pathway.append({'x_start': frame_spacing_mm[1] * col,
'y_start': frame_spacing_mm[0] * row,
'x_end': frame_spacing_mm[1] * col,
'y_end': frame_spacing_mm[0] * row,
'linear_segment_index': linear_segment_index})
linear_segment_index += 1
# make the center the mean of the pathway
path_means = []
for path in pathway:
path_mean = ((path['y_start']), (path['x_start']))
path_means.append(path_mean)
# mean = np.sum(np.asarray(path_means), axis=1) / len(path_means)
mean = np.sum(np.asarray(path_means), axis=0) / len(path_means)
for path in pathway:
path['x_start'] -= mean[1]
path['x_end'] -= mean[1]
path['y_start'] -= mean[0]
path['y_end'] -= mean[0]
# return pathway
state_sequence = []
for path in pathway:
# Store common information about this frame
common_state_dict = {}
common_state_dict['frame_time'] = self.hardware_controller_list['camera'].getExposure()
common_state_dict['led_update_rate_us'] = None
common_state_dict['linear_segment_index'] = None
common_state_dict['frame_distance'] = 0
common_state_dict['exposure_distance'] = 0
common_state_dict['velocity'] = self.velocity_mm_s
common_state_dict['acceleration'] = self.motion_acceleration_mm_s_2
common_state_dict['n_blur_positions_exposure'] = 1
common_state_dict['position_delta_x_mm'] = 0
common_state_dict['position_delta_y_mm'] = 0
path_dict = {'value': {'time_index' : 0,
'x': path['x_start'],
'y': path['y_start']}}
state_sequence.append({'states' : [[path_dict]], 'common' : common_state_dict})
return(state_sequence)
def plotPathway(self):
sequence_list = self.hardware_controller_list['position'].state_sequence
point_list_start = []
point_list_end = []
for sequence in sequence_list:
start_pos = (sequence['states'][0][0]['value']['x'], sequence['states'][0][0]['value']['y'])
end_pos = (sequence['states'][-1][0]['value']['x'], sequence['states'][-1][0]['value']['y'])
point_list_start.append(start_pos)
point_list_end.append(end_pos)
point_list_start = np.asarray(point_list_start)
point_list_end = np.asarray(point_list_end)
plt.figure()
for index in range(len(point_list_start)):
plt.scatter(point_list_start[index, 0], point_list_start[index, 1], c='b')
plt.scatter(point_list_end[index, 0], point_list_end[index, 1], c='r')
plt.plot([point_list_start[index, 0], point_list_end[index, 0]],
[point_list_start[index, 1], point_list_end[index, 1]], c='y')
plt.xlabel('Position X (mm)')
plt.ylabel('Position Y (mm)')
plt.title('Pathway (b is start, y/o is end)')
plt.gca().invert_yaxis()
def genMultiContrastSequence(self, illumination_pattern_sequence, n_acquisitions=1,
darkfield_annulus_width_na=0.1):
led_list = np.arange(self.metadata.illumination.state_list.design.shape[0])
bf_mask = self.metadata.illumination.state_list.design[:, 0] ** 2 \
+ self.metadata.illumination.state_list.design[:, 1] ** 2 < (
self.metadata.objective.na + self.illumination_na_pad) ** 2
led_list_bf = led_list[bf_mask]
led_list_df = led_list[~bf_mask]
led_list_an = led_list[~bf_mask & (self.metadata.illumination.state_list.design[:, 0] ** 2
+ self.metadata.illumination.state_list.design[:, 1] ** 2 < (self.metadata.objective.na + darkfield_annulus_width_na) ** 2)]
illumination_sequence = []
self.pattern_type_list = []
pattern_dict = {'dpc.top': np.ndarray.tolist(led_list_bf[self.metadata.illumination.state_list.design[bf_mask, 1] > 0]),
'dpc.bottom': np.ndarray.tolist(led_list_bf[self.metadata.illumination.state_list.design[bf_mask, 1] < 0]),
'dpc.left': np.ndarray.tolist(led_list_bf[self.metadata.illumination.state_list.design[bf_mask, 0] > 0]),
'dpc.right': np.ndarray.tolist(led_list_bf[self.metadata.illumination.state_list.design[bf_mask, 0] < 0]),
'single': [0],
'bf': np.ndarray.tolist(led_list_bf),
'df': np.ndarray.tolist(led_list_df),
'an': np.ndarray.tolist(led_list_an),
'full': np.ndarray.tolist(led_list)
}
# DPC does not flicker patterns within frames
n_time_points_per_frame = 1
illumination_state_list = []
# Write image sequence to list
for acquisition_index in range(n_acquisitions):
# Loop over DPC patterns (frames)
for frame_index, pattern in enumerate(illumination_pattern_sequence):
single_frame_state_list_illumination = []
# Loop over time points (irrelevent for dpc)
for time_index in range(n_time_points_per_frame):
time_point_state_list = []
# Loop over DPC patterns (which are themselves frames)
for led_idx in pattern_dict[pattern]:
values_dict = {}
for color_name in self.illumination_color:
values_dict[color_name] = self.illumination_color[color_name]
led_dict = {
'index': int(led_idx),
'time_index': 0,
'value': values_dict
}
# Append this to list with elements for each interframe time point
time_point_state_list.append(led_dict)
# Append to frame_dict
single_frame_state_list_illumination.append(time_point_state_list)
# Define illumination sequence
illumination_state_list.append({'states' : single_frame_state_list_illumination, 'common' : {}})
# Define illumination list
self.state_list = self.metadata.illumination.state_list.design
return illumination_state_list
class MotionDeblurAcquisition():
# Initialization
def __init__(self, hardware_controller_list, system_metadata,
illumination_sequence=None,
motion_path_type='linear',
use_l1_distance_for_motion_calculations=True,
blur_vector_method='pseudo_random',
kernel_pulse_count=150,
saturation_factor=1.0,
frame_spacing_mm=1,
object_size_mm=(0.5, 0.5),
reuse_illumination_sequence=True,
max_exposure_time_s=2,
max_velocity_mm_s=40.0,
max_led_update_rate_us=0.01,
exposure_time_pad_s=0.0,
velocity_mm_s=None,
exposure_time_s=None,
debug=False,
motion_acceleration_mm_s_2=1e3,
extra_run_up_time_s=0,
flip_pathway=False,
segment_delay_s=0,
initial_auto_exposure=False,
acquisition_timeout_s=3,
illumination_sequence_count=1,
illumination_na_pad=0.03,
illumination_color={'w': 127},
only_store_first_and_last_position=True):
# Parse options
self.motion_path_type = motion_path_type
self.object_size_mm = object_size_mm
self.frame_spacing_mm = frame_spacing_mm
self.flip_pathway = flip_pathway
self.use_l1_distance_for_motion_calculations = use_l1_distance_for_motion_calculations
self.velocity_mm_s = velocity_mm_s
self.exposure_time_pad_s = exposure_time_pad_s
self.debug = debug
self.motion_acceleration_mm_s_2 = motion_acceleration_mm_s_2
self.max_led_update_rate_us = max_led_update_rate_us
self.max_exposure_time_s = max_exposure_time_s
self.max_velocity_mm_s = max_velocity_mm_s
self.illumination_na_pad = illumination_na_pad
self.saturation_factor = saturation_factor
self.reuse_illumination_sequence = reuse_illumination_sequence
self.blur_vector_method = blur_vector_method
self.kernel_pulse_count = kernel_pulse_count
self.illumination_color = illumination_color
self.extra_run_up_time_s = extra_run_up_time_s
self.initial_auto_exposure = initial_auto_exposure
self.acquisition_timeout_s = acquisition_timeout_s
self.segment_delay_s = segment_delay_s
self.only_store_first_and_last_position = only_store_first_and_last_position
self.illumination_sequence = illumination_sequence
self.illumination_sequence_count = illumination_sequence_count
# Define controller objects, which act as hardware interfaces.
# These should be in an ordered dictionary because the order which they
# are initialized matters when using a mix of hardware and software triggering.
self.hardware_controller_list = collections.OrderedDict()
# First add hardware triggered elements so they perform their set-up before we trigger software elements
for controller in hardware_controller_list:
if hasattr(controller, 'trigger_mode'):
if controller.trigger_mode is 'hardware':
self.hardware_controller_list[controller.type] = controller
controller.reset()
controller.seq_clear()
# Then, add software triggered elements
for controller in hardware_controller_list:
self.hardware_controller_list[controller.type] = controller
controller.reset()
controller.seq_clear()
# Check to be sure a sequence acquisition is not running
assert 'camera' in self.hardware_controller_list, 'Did not find camera controller!'
# Store metadata object
self.metadata = system_metadata
# Ensure we have all necessary metadata for basic acquisition
assert self.metadata.objective.na is not None, 'Missing objective.na in metadata.'
assert self.metadata.objective.mag is not None, 'Missing objective.mag in metadata.'
assert self.metadata.camera.pixel_size_um is not None, 'Missing pixel size in metadata.'
# Update effective pixel size (for scale bar)
self.metadata.system.eff_pixel_size_um = self.metadata.camera.pixel_size_um / (self.metadata.objective.mag * self.metadata.system.mag)
# Trigger Constants
self.TRIG_MODE_EVERY_PATTERN = 1
self.TRIG_MODE_ITERATION = -1
self.TRIG_MODE_START = -2
# Frame state time sequence, will default to a sequence of one exposure time per frame if left as None
self.time_sequence_s = None
self.exposure_time_s = None
self.hardware_sequence_timing = None
# Turn off fast sequencing for illumination by default since this is only avaolable with certain LED arrays
if 'illumination' in self.hardware_controller_list:
self.hardware_controller_list['illumination'].use_fast_sequence = False
# Set metadata type
self.metadata.type = 'motiondeblur'
assert 'illumination' in self.hardware_controller_list, 'Motion deblur object requires programmable light source'
assert 'position' in self.hardware_controller_list, 'Motion deblur object requires motion stage'
# Initialize state_sequence
self.state_sequence = []
# Generate position sequence
self.hardware_controller_list['position'].state_sequence, self.time_sequence_s = self.genMotionPathway(
pathway_type=self.motion_path_type, frame_spacing_mm=frame_spacing_mm)
# Generate illumination sequence
self.hardware_controller_list['illumination'].state_sequence = self.genMotionIlluminationSequenceRandom(illumination_sequence=illumination_sequence,
sequence_count=self.illumination_sequence_count)
# Set up subframe captures
self.subframe_capture_count = len(self.hardware_controller_list['illumination'].state_sequence[0])
self.force_preload_all_frames = True
self.hardware_controller_list['position'].continuous_states_between_frames = True
# Configure illuination to use fast sequence updating if specified in options
self.hardware_controller_list['illumination'].use_fast_sequence = True
# Set bit depth
self.illumination_sequence_bit_depth = 1
# Set extra options for position controller
self.hardware_controller_list['position'].extra_run_up_time_s = self.extra_run_up_time_s
# Calculate effective pixel size if it hasn't already been calculated
self.metadata.system.eff_pixel_size_um = self.metadata.camera.pixel_size_um / \
(self.metadata.objective.mag * self.metadata.system.mag)
def preAcquire(self):
''' This method sets up the camera for an acquisition '''
# Check that the length of motion, illuimination, pupil, and focal sequences are same (or None)
frame_counts = []
for hardware_controller_name in list(self.hardware_controller_list):
# Get controller object from dictionary
hardware_controller = self.hardware_controller_list[hardware_controller_name]
if hardware_controller.state_sequence is not None:
# Reset Controller
hardware_controller.reset()
# Get number of frames in sequence. If there is no sequence, remove this element from hw_controller_list
if hardware_controller.type is not 'camera':
if hardware_controller.state_sequence is not None:
frame_counts.append(len(hardware_controller.state_sequence))
else:
self.hardware_controller_list.pop(hardware_controller_name)
else:
# Remove this controller from the list
if hardware_controller_name is not 'camera':
del self.hardware_controller_list[hardware_controller_name]
# Turn on hardware triggering for initialization
self.hardware_controller_list['camera'].setTriggerMode('hardware')
# Set illumination parameters
if 'illumination' in self.hardware_controller_list:
# self.hardware_controller_list['illumination'].setColor(self.illumination_color)
self.hardware_controller_list['illumination'].setSequenceBitDepth(
self.illumination_sequence_bit_depth)
# Ensure all hardware elements have the same number of frames
if len(frame_counts) > 0:
if not np.sum(np.mean(np.asarray(frame_counts)) == np.asarray(frame_counts)) == len(frame_counts):
raise ValueError('Sequence lengths are not the same (or None).')
else:
self.n_frames = frame_counts[0]
else:
raise ValueError('No sequence provided!')
# Initialize frame_list
self.frame_list = np.zeros((self.n_frames,
self.hardware_controller_list['camera'].getImageHeight(), self.hardware_controller_list['camera'].getImageWidth()), dtype=np.uint16)
# Apply simple geometric transformations
if self.metadata.camera.transpose:
self.frame_list = self.frame_list.transpose(0, 2, 1)
if self.metadata.camera.flip_x:
self.frame_list = np.flip(self.frame_list, 2)
if self.metadata.camera.flip_y:
self.frame_list = np.flip(self.frame_list, 1)
# Generate frame_state_list
frame_state_list = []
if self.time_sequence_s is None:
self.time_sequence_s = []
for _ in range(self.n_frames):
self.time_sequence_s.append([0])
# Loop over frames
for frame_index in range(self.n_frames):
single_frame_state_list = {}
# Loop over hardware controllers and record their state sequences
for hardware_controller_name in self.hardware_controller_list:
hardware_controller = self.hardware_controller_list[hardware_controller_name]
if hardware_controller.state_sequence is not None:
single_frame_state_list[hardware_controller_name] = hardware_controller.state_sequence[frame_index]
# Record time_sequence_s
single_frame_state_list['time_sequence_s'] = self.time_sequence_s[frame_index]
# Add to list of all frames
frame_state_list.append(single_frame_state_list)
self.frame_state_list = frame_state_list
# Perform auto-exposure if user desires
if self.initial_auto_exposure:
# Illuminate with first pattern
if 'illumination' in self.hardware_controller_list:
self.hardware_controller_list['illumination'].sequenceReset()
self.hardware_controller_list['illumination'].time_sequence_s = [[0]]
self.hardware_controller_list['illumination'].preloadSequence(0)
self.hardware_controller_list['illumination'].sequenceStep()
# Small delay to ensure illumination gets updated
time.sleep(0.1)
# Run Auto-Exposure
self.hardware_controller_list['camera'].autoExposure()
# Set camera memory footprint
if (self.hardware_controller_list['camera'].getBufferTotalCapacity() < self.frame_list.shape[0]):
self.frame_size_mb = int(
np.ceil(float(self.frame_list.shape[0] / 1e6) * float(self.frame_list.shape[1]) * float(self.frame_list.shape[2]) * 2))
print('Allocating %dmb for frames' % self.frame_size_mb)
self.hardware_controller_list['camera'].setBufferSizeMb(self.frame_size_mb)
assert self.hardware_controller_list['camera'].getBufferTotalCapacity(
) >= self.frame_list.shape[0], 'Buffer size too small!'
# Store initial time (acquisition start)
t0 = time.time()
# Tell camera to start waiting for frames
self.hardware_controller_list['camera'].runSequence()
# Keep track of how many images we have acquired
self.total_frame_count = 0
def acquire(self,
dataset=None,
reset_devices=False):
'''
This is a generic acquisition class, where LEDs are updated according to the sequence variable.
'''
# Call preacquire. which initializes hardware and variables
self.preAcquire()
# Determine which frames can be preloaded before serial acquisition. If each frame is only one state, we assume that we can preload all frames. But, if the state of any hardware element changes within any frame, we will assume we can't preload the frames
frame_count = 0
linear_segment_list = []
for frame_state in self.hardware_controller_list['position'].state_sequence:
if frame_state['common']['linear_segment_index'] >= 0:
frame_count += 1
if frame_state['common']['linear_segment_index'] not in linear_segment_list:
linear_segment_list.append(frame_state['common']['linear_segment_index'])
print("Found %d segments and %d frames" % (len(linear_segment_list), frame_count))
t_start = time.time()
for linear_segment_index in linear_segment_list:
self.frames_to_acquire = []
# Determine which linear segments to run
for frame_index, frame_state in enumerate(self.hardware_controller_list['position'].state_sequence):
if frame_state['common']['linear_segment_index'] == linear_segment_index:
self.frames_to_acquire += [frame_index]
self.n_frames_to_acquire = len(self.frames_to_acquire)
x_start = self.hardware_controller_list['position'].state_sequence[self.frames_to_acquire[0]]['states'][0][0]['value']['x']
y_start = self.hardware_controller_list['position'].state_sequence[self.frames_to_acquire[0]]['states'][0][0]['value']['y']
x_end = self.hardware_controller_list['position'].state_sequence[self.frames_to_acquire[-1]]['states'][0][0]['value']['x']
y_end = self.hardware_controller_list['position'].state_sequence[self.frames_to_acquire[-1]]['states'][0][0]['value']['y']
print('Starting linear segment %d which has %d frames moving from (%.4f, %.4f)mm to (%.4f, %.4f)mm' %
(linear_segment_index, self.n_frames_to_acquire, x_start, y_start, x_end, y_end))
frame_has_multiple_states = []
for frame_index in self.frames_to_acquire:
number_of_states_in_current_frame = 0
for hardware_controller_name in self.hardware_controller_list:
if hardware_controller_name is not 'camera' and self.hardware_controller_list[hardware_controller_name].state_sequence is not None:
# Check if this frame can be preloaded (if it has more than one state, it can't be preloaded)
number_of_states_in_current_frame = max(number_of_states_in_current_frame, len(
self.hardware_controller_list[hardware_controller_name].state_sequence[frame_index]['states']))
# Check that the length of time_sequence_s matches the max number of state changes within this frame
if number_of_states_in_current_frame > 1:
frame_has_multiple_states.append(True)
assert self.time_sequence_s is not None, "time_sequence_s can not be None if any frame has multiple states!"
assert len(self.time_sequence_s[frame_index]) == number_of_states_in_current_frame, "time_sequence_s for frame %d is of wrong length!" % len(
self.time_sequence_s[frame_index]['states'])
else:
frame_has_multiple_states.append(False)
# Determine if the entire multi-frame sequence can be preloaded (this will be False if ther eis only one system state (e.g. LED pattern) within each frame)
all_frames_will_be_preloaded = (not any(frame_has_multiple_states)) or self.force_preload_all_frames
# Determine optimal exposure time for all frames
if self.exposure_time_s is not None:
self.hardware_controller_list['camera'].setExposure(self.exposure_time_s)
elif self.time_sequence_s is not None and max(self.time_sequence_s[0]) > 0:
frame_exposures = []
for frame_index in range(self.n_frames_to_acquire):
frame_exposures.append(max(self.time_sequence_s[frame_index]))
self.exposure_time_s = sum(frame_exposures) / (self.n_frames_to_acquire)
self.hardware_controller_list['camera'].setExposure(self.exposure_time_s)
else:
self.exposure_time_s = self.hardware_controller_list['camera'].getExposure()
# Check that exposure time is correct
assert abs(self.exposure_time_s - self.hardware_controller_list['camera'].getExposure(
)) < 1e-3, "Desired exposure time %.2f is not equal to device exposure %.2f. This is probably a MM issue" % (self.exposure_time_s, self.hardware_controller_list['camera'].getExposure())
# print('Using exposure time %.2fs (%d ms)' % (self.exposure_time_s, int(self.exposure_time_s * 1000)))
# Check that time_sequence_s for multiple frames exists if there are inter-frame state changes
if (not any(frame_has_multiple_states)) or self.time_sequence_s is None:
self.time_sequence_s = [self.exposure_time_s]
# Configure hardware triggering
trigger_output_settings = [0, 0]
trigger_input_settings = [0, 0]
for hardware_controller_name in self.hardware_controller_list:
hardware_controller = self.hardware_controller_list[hardware_controller_name]
if hasattr(hardware_controller, 'trigger_mode') and 'hardware' in hardware_controller.trigger_mode:
# Check that trigger pins are configured
assert hardware_controller.trigger_pin is not None, 'Trigger pin must be configured for hardware triggering!'
# Determine if we're performing preloadable acquisitions or not
if self.subframe_capture_count > 1:
if self.reuse_illumination_sequence:
if hardware_controller_name == 'camera':
if self.illumination_sequence_count == 1:
trigger_output_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_ITERATION
trigger_input_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_ITERATION
else:
trigger_output_settings[hardware_controller.trigger_pin] = len(self.hardware_controller_list['position'].state_sequence[0]['states']) // self.illumination_sequence_count
trigger_input_settings[hardware_controller.trigger_pin] = len(self.hardware_controller_list['position'].state_sequence[0]['states']) // self.illumination_sequence_count
elif hardware_controller_name == 'position':
trigger_output_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_START
trigger_input_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_START
else:
if hardware_controller_name == 'camera':
trigger_output_settings[hardware_controller.trigger_pin] = self.subframe_capture_count
trigger_input_settings[hardware_controller.trigger_pin] = self.subframe_capture_count
elif hardware_controller_name == 'position':
trigger_output_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_START
trigger_input_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_START
# Case where there is only one system state wihtin each frame (trigger each frame)
elif all_frames_will_be_preloaded:
trigger_output_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_EVERY_PATTERN
trigger_input_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_EVERY_PATTERN
# Case where we only want to trigger on first frame. This is probably not a good default.
else:
trigger_output_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_ITERATION
trigger_input_settings[hardware_controller.trigger_pin] = self.TRIG_MODE_ITERATION
# Check that this hardware controller is ready for a sequence, if it is sequencable.
if hardware_controller.state_sequence is not None:
# Reset controller sequence to initial state
hardware_controller.sequenceReset()
time.sleep(0.1)
# Wait until initialization is complete
initialization_wait_time = 0
for hardware_controller_name in self.hardware_controller_list:
while not self.hardware_controller_list[hardware_controller_name].isReadyForSequence():
time.sleep(0.05)
initialization_wait_time += 0.05
if initialization_wait_time > self.acquisition_timeout_s:
raise ValueError('Pre-acquisiton isReadyForSequence timeout for %s' % hardware_controller_name)
# Tell the hardware controller about the acquisition time sequence
if len(hardware_controller.state_sequence) == len(self.time_sequence_s):
hardware_controller.time_sequence_s = [self.time_sequence_s[i] for i in self.frames_to_acquire]
else:
hardware_controller.time_sequence_s = [
[self.hardware_controller_list['camera'].getExposure()]] * self.n_frames_to_acquire
# Set up triggering for hardware acquision
self.hardware_controller_list['illumination'].trigger_output_settings = trigger_output_settings
self.hardware_controller_list['illumination'].trigger_input_settings = trigger_input_settings
# Determine which sequences get preloaded
if all_frames_will_be_preloaded: # One system state per acquisition
frame_preload_sequence = [-1] # Preload all frames at once
else:
frame_preload_sequence = range(self.n_frames_to_acquire) # Preload each frame serially
# Loop over frames to capture (may only execute once if we're preloading all frames)
for preload_index in frame_preload_sequence:
# Loop over hardware controllers, preload, and determine necessary exposure time (if using inter-frame state changes)
for hardware_controller_name in self.hardware_controller_list:
# If we're using the motion stage, calculate the mechanical delay
if hardware_controller_name == 'position':
# Get velocity and acceleration from state sequence
if preload_index == -1:
index = 0
else:
index = preload_index
velocity = self.hardware_controller_list[hardware_controller_name].state_sequence[0]['common']['velocity']
acceleration = self.hardware_controller_list[hardware_controller_name].acceleration
jerk = self.hardware_controller_list[hardware_controller_name].jerk
# Calculate spin-up time and distance
# http://www.wolframalpha.com/input/?i=v+%3D+t+*+(a+%2B+0.5*j+*+t)+solve+for+t
# http://www.wolframalpha.com/input/?i=v+%3D+t+*+(a+%2B+(1%2F8)*j+*+t)+solve+for+t
# Good reference:
# http://www.et.byu.edu/~ered/ME537/Notes/Ch5.pdf
# Total period
if False:
# First period (acceleration of acceleration)
t_1 = acceleration / jerk
# x_1 = 1/6 * jerk * t_1 ** 3
x_1 = acceleration ** 2 / (6 * jerk) * t_1
# v_1 = 1/2 * jerk * t_1 ** 2
v_1 = acceleration ** 2 / (2 * jerk)
# Second period (linear region)
dv = velocity - 2 * v_1
assert dv > 0
t_2 = dv / acceleration
x_2 = v_1 * t_2 + 1/2 * acceleration * t_2 ** 2
v_2 = velocity - v_1
# Third period (decelleration of acceleration)
t_3 = acceleration / jerk
x_3 = (v_2 + acceleration ** 2 / (3 * jerk)) * t_3
v_3 = v_1
# Calculate spin-up distance and time
spin_up_time_s = t_1 + t_2 + t_3
spin_up_distance_mm = x_1 + x_2 + x_3
assert (v_1 + v_2 + v_3 - velocity) < 1e-1, "Calculated velocity is %.4f, desired is %.4f" % (v_1 + v_2 + v_3, velocity)
else:
spin_up_time_s = velocity / acceleration
spin_up_distance_mm = 1/2 * acceleration * spin_up_time_s ** 2
# Add extra spin_up time
spin_up_time_s += self.extra_run_up_time_s
spin_up_distance_mm += self.extra_run_up_time_s * velocity
# spin_up_distance_mm = 0
spin_up_time_s = max(spin_up_time_s, 0.0001)
self.hardware_controller_list['illumination'].setupTriggering(self.hardware_controller_list['position'].trigger_pin, int(
self.hardware_controller_list['position'].trigger_pulse_width_us), int(spin_up_time_s * 1e6)) # convert to seconds
# Tell motion stage to offset it's positions by these amounts
self.hardware_controller_list['position'].preload_run_up_distance_mm = spin_up_distance_mm
else:
# no delay for other components
self.hardware_controller_list[hardware_controller_name].trigger_start_delay_s = 0
if hardware_controller_name is not 'camera' and self.hardware_controller_list[hardware_controller_name].state_sequence is not None:
if hardware_controller_name is not 'illumination' or linear_segment_index == 0:
if hardware_controller_name == 'illumination' and self.reuse_illumination_sequence:
self.hardware_controller_list[hardware_controller_name].preloadSequence(0)
else:
state_sequence_used = [
self.hardware_controller_list[hardware_controller_name].state_sequence[i] for i in self.frames_to_acquire]
self.hardware_controller_list[hardware_controller_name].preloadSequence(
preload_index, state_sequence=state_sequence_used)
if preload_index < 0 or self.reuse_illumination_sequence:
frames_to_wait_for = self.n_frames_to_acquire # wait for all frames
else:
frames_to_wait_for = 1
# Set trigger frame time based on first pathway TODO: This is a hack
if 'position' in self.hardware_controller_list:
self.hardware_controller_list['illumination'].trigger_frame_time_s[self.hardware_controller_list['camera']
.trigger_pin] = self.hardware_controller_list['position'].state_sequence[0]['common']['frame_time'] * 1e6
# Tell stage to start moving
self.hardware_controller_list['position'].runSequence()
if linear_segment_index == 0:
t_start = time.time()
# Tell illumination to start moving
if self.reuse_illumination_sequence:
self.hardware_controller_list['illumination'].runSequence(
n_acquisitions=1 * self.n_frames_to_acquire)
else:
self.hardware_controller_list['illumination'].runSequence(n_acquisitions=1)
# Wait for frames to be captured
t_frame = time.time()
frame_count = 0
while frame_count < frames_to_wait_for:
if self.total_frame_count + frame_count == frames_to_wait_for:
break
else:
if self.total_frame_count + frame_count == self.hardware_controller_list['camera'].getBufferSizeFrames():
time.sleep(0.01)
if (time.time() - t_frame) > self.acquisition_timeout_s:
print(self.hardware_controller_list['illumination'].response())
raise ValueError('Acquisition timeout (Total frame count: %d, Buffer size: %d, preload index %d, frames to wait for: %d)' % (
self.total_frame_count, self.hardware_controller_list['camera'].getBufferSizeFrames(), preload_index, frames_to_wait_for))
else:
if ((self.total_frame_count + frame_count) % int((self.n_frames) / min(10, self.n_frames_to_acquire))) == 0:
print('Acquired %d of %d frames' % (
self.hardware_controller_list['camera'].getBufferSizeFrames(), self.n_frames_to_acquire))
frame_count = self.hardware_controller_list['camera'].getBufferSizeFrames(
) - self.total_frame_count
self.total_frame_count = self.hardware_controller_list['camera'].getBufferSizeFrames()
t_frame = time.time()
# Get sequence timing information
time.sleep(0.1)
print(self.hardware_controller_list['illumination'].response())
# Wait for hardware to stop
for hardware_controller_name in self.hardware_controller_list:
while not self.hardware_controller_list[hardware_controller_name].isReadyForSequence():
time.sleep(0.05)
self.sequence_timing_dict = {}
# Reset sequences
for hardware_controller_name in self.hardware_controller_list:
if hardware_controller_name is not 'camera':
self.hardware_controller_list[hardware_controller_name].sequenceReset()
# Let user know we're finished
print('Finished linear segment %d' % linear_segment_index)
time.sleep(self.segment_delay_s)
t_acq = time.time() - t_start
self.metadata.acquisition_time_s = t_acq
print("Acquisition took %.4f seconds" % (t_acq))
# Call post-acquire functions
dataset = self.postAcquire(dataset=dataset, reset_devices=reset_devices)
# Return
return dataset
def postAcquire(self, dataset=None, reset_devices=True):
"""Post-acquisition steps for resetting hardware and preparing dataset."""
# Stop acquisition
# self.hardware_controller_list['camera'].sequenceStop()
# Parse dataset
if dataset is None:
from htdeblur.mddataset import MotionDeblurDataset
dataset = MotionDeblurDataset()
# Read frames and timestamps from buffer
(self.frame_list, elapsed_frame_time_ms) = self.hardware_controller_list['camera'].readFramesFromBuffer()
# Apply simple geometric transformations
if self.metadata.camera.transpose:
self.frame_list = self.frame_list.transpose(0, 2, 1)
if self.metadata.camera.flip_x:
self.frame_list = np.flip(self.frame_list, 2)
if self.metadata.camera.flip_y:
self.frame_list = np.flip(self.frame_list, 1)
# Let user know we're finished
print('Read frames from buffer.')
# Store camera timing in a standardized timing dict
self.sequence_timing_dict = {}
self.sequence_timing_dict['sequence_timing'] = []
for frame_index, frame_time in enumerate(elapsed_frame_time_ms):
timing_dict = {'trigger_number' : 0, 'acquisition_number' : frame_index, 'camera_start_time_us' : frame_time * 1000}
self.sequence_timing_dict['sequence_timing'].append(timing_dict)
# Reset all hardware elements
if reset_devices:
for hardware_controller_name in self.hardware_controller_list:
self.hardware_controller_list[hardware_controller_name].reset()
if self.only_store_first_and_last_position:
for frame_state in self.frame_state_list[1:]:
frame_state['position']['states'] = [frame_state['position']['states'][0], frame_state['position']['states'][-1]]
# Remove repeated illumination patterns and time_sequence_s if we used the same illumination for each pulse
if self.reuse_illumination_sequence:
for frame_state in self.frame_state_list[1:]:
frame_state['time_sequence_s'] = 'see_frame_#1'
frame_state['illumination'] = 'see_frame_#1'
# Illuminate with brightfield to indicate we're Finished
self.hardware_controller_list['illumination'].bf()
self.hardware_controller_list['position'].goToPosition((0,0))
# Save results to an itoools.Dataset object
dataset.frame_list = self.frame_list
dataset.frame_state_list = self.frame_state_list
dataset.metadata = self.metadata
dataset.type = 'motion_deblur'
# Return
return dataset
def genMotionPathway(self, n_acquisitions=1, pathway_type='raster', frame_spacing_mm=1.):
'''
This function generates a few example motion pathways.
'''
if pathway_type is 'raster':
pathway = self.genMotionPathwayRaster(self.object_size_mm, self.frame_spacing_mm)
elif (pathway_type is 'linear') or (pathway_type is 'linear_x'):
# predefine linear y sequence
n_frames = int(math.ceil(self.object_size_mm[1] / self.frame_spacing_mm[1]))
pathway = []
for frame_index in range(n_frames):
pathway.append({'x_start': frame_index * self.frame_spacing_mm[1],
'x_end': (frame_index + 1) * self.frame_spacing_mm[1],
'y_start': 0, 'y_end': 0, 'linear_segment_index': 0})
elif pathway_type in ['linear_y']:
# predefine linear y sequence
n_frames = int(np.ceil(self.object_size_mm[0] / self.frame_spacing_mm[0]))
pathway = []
for frame_index in range(n_frames):
pathway.append({'y_start': -frame_index * self.frame_spacing_mm[0],
'y_end': -(frame_index + 1) * self.frame_spacing_mm[0],
'x_start': 0, 'x_end': 0, 'linear_segment_index': 0})
elif pathway_type is 'linear_diag':
# predefine linear y sequence
n_frames = int(np.ceil(self.object_size_mm[0] / self.frame_spacing_mm[0]))
pathway = []
for frame_index in range(n_frames):
pathway.append({'y_start': frame_index * self.frame_spacing_mm[0],
'y_end': (frame_index + 1) * self.frame_spacing_mm[0],
'x_start': frame_index * self.frame_spacing_mm[0],
'x_end': (frame_index + 1) * self.frame_spacing_mm[0],
'linear_segment_index': 0})
else:
raise ValueError('Pathway type %s is not implemented.' % pathway_type)
# make the center the mean of the pathway
path_xmin = 1e8
path_ymin = 1e8
path_xmax = -1e8
path_ymax = -1e8
for path in pathway:
path_mean = ((path['y_start']), (path['y_start']))
path_xmin = min(path_xmin, min([path['x_start'], path['x_end']]))
path_xmax = max(path_xmax, max([path['x_start'], path['x_end']]))
path_ymin = min(path_ymin, min([path['y_start'], path['y_end']]))
path_ymax = max(path_ymax, max([path['y_start'], path['y_end']]))
mean = ((path_ymax + path_ymin) / 2, (path_xmax + path_xmin) / 2)
for path in pathway:
path['x_start'] = path['x_start'] - mean[1]
path['x_end'] = path['x_end'] - mean[1]
path['y_start'] = path['y_start'] - mean[0]
path['y_end'] = path['y_end'] - mean[0]
# Flip pathway if user desired
if self.flip_pathway:
for path in pathway:
path['x_start'] *= -1
path['x_end'] *= -1
path['y_start'] *= -1
path['y_end'] *= -1
position_state_list = []
time_sequence_s = []
# Write image sequence to list
for acquisition_index in range(n_acquisitions):
# Loop over DPC patterns (frames)
for frame_index, position in enumerate(pathway):
# define distance in terms of l1 or l2 distance
distance_l2 = float(np.sqrt((position['x_end'] - position['x_start'])
** 2 + (position['y_end'] - position['y_start']) ** 2))
distance_l1 = float(abs(position['x_end'] - position['x_start']) +
abs(position['y_end'] - position['y_start']))
if self.use_l1_distance_for_motion_calculations:
position['frame_distance'] = int(round(distance_l1 * 1000)) / 1000 # round to nearest um
else:
position['frame_distance'] = int(round(distance_l2 * 1000)) / 1000 # round to nearest um
# Determine number of qunatifiable positions in pathway
position['n_blur_positions_frame'] = int(
math.floor(position['frame_distance'] / (self.metadata.system.eff_pixel_size_um / 1000)))
# Determine necessary velocity
if self.velocity_mm_s is not None:
position['velocity_mm_s'] = self.velocity_mm_s
else:
position['velocity_mm_s'] = self.max_velocity_mm_s # Use fastest speed possible
# Calculate time between frames
position['frame_time_s'] = position['frame_distance'] / position['velocity_mm_s'] # t = x / v
# Determine camera exposure time for this frame
position['exposure_time_s'] = int(math.floor((self.hardware_controller_list['camera'].calcExposureTimeFromBusyTime(
position['frame_time_s']) - self.exposure_time_pad_s) * 1000)) / 1000 # round to nearest ms
# Determine LED update rate
dx_pixel = position['frame_distance'] / position['n_blur_positions_frame']
dt_pixel_raw = dx_pixel / position['velocity_mm_s']
position['led_update_rate_us'] = math.ceil(dt_pixel_raw * 1e6) # Round up to integer us
# Determine new velocity (ps / update rate)
new_velocity_mm_s = (self.metadata.system.eff_pixel_size_um / 1e3) / (position['led_update_rate_us'] / 1e6)
if self.debug > 0:
print('Reducing velocity to %.4f mm/s from %.4f mm/s to match illumination update rate of %d us' % (new_velocity_mm_s, position['velocity_mm_s'], position['led_update_rate_us']))
position['velocity_mm_s'] = new_velocity_mm_s
# Update frame time based on velocity
position['frame_time_s'] = position['frame_distance'] / position['velocity_mm_s']
# Determine number of pixels in exposure time
position['n_blur_positions_exposure'] = math.floor(position['exposure_time_s'] / (position['led_update_rate_us'] / 1e6))
# Determine the distance traveled during the exposure time
position['exposure_distance'] = position['n_blur_positions_exposure'] * position['led_update_rate_us'] / 1e6 * position['velocity_mm_s']
# Store acceleration
position['acceleration_mm_s_2'] = self.motion_acceleration_mm_s_2
# Print information about this pattern
if self.debug > 0:
print('Segment %d, index %d will require %d blur positions per frame (%d during exposure), %.2fms exposure time (%.2fms total frame time), scan %.2fmm (%.2fmm with exposure), move at %.2fmm/s, and update speed %dus' %
(position['linear_segment_index'], frame_index, position['n_blur_positions_frame'],position['n_blur_positions_exposure'], 1000. * position['exposure_time_s'], 1000. * position['frame_time_s'], position['frame_distance'], position['exposure_distance'], position['velocity_mm_s'], position['led_update_rate_us']))
# Check that all blur parameters are valid
assert position['led_update_rate_us'] >= self.max_led_update_rate_us, "LED Array update rate (%dms) < max update rate (%dms)" % (
position['led_update_rate_us'], self.max_led_update_rate_us)
assert position['exposure_time_s'] <= self.max_exposure_time_s, "Exposure time (%.3fs) > max_exposure_time_s (%.3f)" % (
position['exposure_time_s'], self.max_exposure_time_s)
assert position['velocity_mm_s'] <= self.max_velocity_mm_s, "Velocity (%.3fs) > max_velocity_mm_s (%.3f)" % (
position['velocity_mm_s'], self.max_velocity_mm_s)
# List for this positions
single_frame_state_list_position = []
single_frame_time_sequence_s = []
# Determine movement direction
direction = np.asarray((position['y_end'] - position['y_start'],
position['x_end'] - position['x_start']))
direction /= np.linalg.norm(direction)
# Store common information about this frame
common_state_dict = {}
common_state_dict['frame_time'] = position['frame_time_s']
common_state_dict['led_update_rate_us'] = position['led_update_rate_us']
common_state_dict['linear_segment_index'] = position['linear_segment_index']
common_state_dict['frame_distance'] = position['frame_distance']
common_state_dict['exposure_distance'] = position['exposure_distance']
common_state_dict['velocity'] = position['velocity_mm_s']
common_state_dict['acceleration'] = position['acceleration_mm_s_2']
common_state_dict['n_blur_positions_exposure'] = position['n_blur_positions_exposure']
common_state_dict['position_delta_x_mm'] = direction[1] * position['velocity_mm_s'] * position['led_update_rate_us'] / 1e6
common_state_dict['position_delta_y_mm'] = direction[0] * position['velocity_mm_s'] * position['led_update_rate_us'] / 1e6
# Loop over time points (irrelevent for dpc)
for time_index in range(position['n_blur_positions_exposure']):
time_point_state_list = []
x = position['x_start'] + direction[1] * abs(common_state_dict['position_delta_x_mm']) * time_index
y = position['y_start'] + direction[0] * abs(common_state_dict['position_delta_x_mm']) * time_index
# Append this to list with elements for each interframe time point
time_point_state_list.append({'time_index': time_index,
'value': {'x': x, 'y': y}})
# Append to frame_dict
single_frame_state_list_position.append(time_point_state_list)
single_frame_time_sequence_s.append((time_index + 1) * position['led_update_rate_us'] / 1e6)
# Define illumination sequence
position_state_list.append({'states' : single_frame_state_list_position, 'common' : common_state_dict})
# Define time_sequence
time_sequence_s.append(single_frame_time_sequence_s)
# for state in position_state_list:
# print(state['states'][0][0]['value']['x'] - state['states'][-1][0]['value']['x'])
return (position_state_list, time_sequence_s)
def genMotionPathwayRaster(self, object_size_mm, frame_spacing_mm, major_axis=None, include_minor_axis=False):
# Hard-code major axis since the rest of the code doesn't respect it for now
_major_axis = 1
# Detemine number of measurements
measurement_count = np.ceil(np.asarray(object_size_mm) / np.asarray(frame_spacing_mm)).astype(np.int) # two components in x and y
# Error checking
assert np.any(measurement_count > 1), "image_size must be smaller than object_size!"
print("Image size requires %d x %d images" % (measurement_count[0], measurement_count[1]))
# If number of measurements along major axis is odd, center this row
offset = [0, 0]
offset[_major_axis] -= frame_spacing_mm[_major_axis] / 2
# Generate raster points
raster_end_point_list = []
pathway = []
linear_segment_index = 0 # This variable keeps track of linear segments, for use with path planning
for row in np.arange(measurement_count[0]):
if row % 2 == 0:
for index, col in enumerate(range(measurement_count[1])):
# Add pathway to list
pathway.append({'x_start': frame_spacing_mm[1] * col + offset[1],
'y_start': frame_spacing_mm[0] * row + offset[0],
'x_end': frame_spacing_mm[1] * (col + 1) + offset[1],
'y_end': frame_spacing_mm[0] * row + offset[0],
'linear_segment_index': linear_segment_index})
# Add minor stride
if row < (measurement_count[0] - 1) and include_minor_axis:
pathway.append({'x_start': frame_spacing_mm[1] * (measurement_count[1] - 1) + offset[1],
'y_start': frame_spacing_mm[0] * row + offset[0],
'x_end': frame_spacing_mm[1] * (measurement_count[1] - 1) + offset[1],
'y_end': frame_spacing_mm[0] * (row + 1) + offset[0],
'linear_segment_index': -1 * (linear_segment_index + 1)})
else:
for index, col in enumerate(reversed(range(measurement_count[1]))):
# Add pathway to list
pathway.append({'x_start': frame_spacing_mm[1] * col - offset[1],
'y_start': frame_spacing_mm[0] * row - offset[0],
'x_end': frame_spacing_mm[1] * (col - 1) - offset[1],
'y_end': frame_spacing_mm[0] * row - offset[0],
'linear_segment_index': linear_segment_index})
# Add minor stride
if row < (measurement_count[0] - 1) and include_minor_axis:
pathway.append({'x_start': - offset[1],
'y_start': frame_spacing_mm[0] * row - offset[0],
'x_end': 0 - offset[1],
'y_end': frame_spacing_mm[0] * (row + 1) - offset[0],
'linear_segment_index': -1 * (linear_segment_index + 1)})
linear_segment_index += 1
print('Generated motion pathway with %d linear segments' % (linear_segment_index))
return pathway
def plotPathway(self):
sequence_list = self.hardware_controller_list['position'].state_sequence
point_list_start = []
point_list_end = []
for sequence in sequence_list:
start_pos = (sequence['states'][0][0]['value']['x'], sequence['states'][0][0]['value']['y'])
end_pos = (sequence['states'][-1][0]['value']['x'], sequence['states'][-1][0]['value']['y'])
point_list_start.append(start_pos)
point_list_end.append(end_pos)
point_list_start = np.asarray(point_list_start)
point_list_end = np.asarray(point_list_end)
plt.figure()
for index in range(len(point_list_start)):
plt.scatter(point_list_start[index, 0], point_list_start[index, 1], c='b')
plt.scatter(point_list_end[index, 0], point_list_end[index, 1], c='r')
plt.plot([point_list_start[index, 0], point_list_end[index, 0]],
[point_list_start[index, 1], point_list_end[index, 1]], c='y')
plt.xlabel('Position X (mm)')
plt.ylabel('Position Y (mm)')
plt.title('Pathway (b is start, y/o is end)')
plt.gca().invert_yaxis()
def genMotionIlluminationSequenceRandom(self, sequence_count=1,
illumination_sequence=None):
led_list = np.arange(self.metadata.illumination.state_list.design.shape[0])
bf_mask = self.metadata.illumination.state_list.design[:, 0] ** 2 \
+ self.metadata.illumination.state_list.design[:, 1] ** 2 < (
self.metadata.objective.na + self.illumination_na_pad) ** 2
illumination_state_list = []
linear_segments_processed = {}
# Loop over DPC patterns (frames)
for frame_index, frame_position_dict in enumerate(self.hardware_controller_list['position'].state_sequence):
frame_position_list = frame_position_dict['states']
# Get number of positions in blur kernel from this frame. Divide into subsequences
pattern_count = len(frame_position_list) // sequence_count
# Determine the number of non-zero illumination positions
pattern_count_used = int(round(pattern_count * self.saturation_factor))
# Place patterns at the END of the full sequence
pattern_count_start = 0
# Get linear segment index
current_segment_index = frame_position_dict['common']['linear_segment_index']
if not self.reuse_illumination_sequence or frame_index == 0:
blur_vector_full = []
# Generate several blur vectors
for _ in range(sequence_count):
# Use provided illumination seqence if given
if illumination_sequence:
blur_vector = illumination_sequence
else:
blur_vector = np.zeros(pattern_count)
# Generate blur vector
blur_vector = np.zeros(pattern_count)
if self.blur_vector_method == 'strobe':
blur_vector = np.zeros(pattern_count)
blur_vector[pattern_count_start + pattern_count_used // 2] = 1
elif self.blur_vector_method == 'center':
blur_vector = | np.zeros(pattern_count) | numpy.zeros |
#!/usr/bin/env python
from argparse import ArgumentParser
import rospy
# For importing cv2 packages we need to remove ros python paths
import sys
sys.path.remove('/opt/ros/kinetic/lib/python2.7/dist-packages')
import cv2
sys.path.append('/opt/ros/kinetic/lib/python2.7/dist-packages')
from sensor_msgs.msg import Image, PointCloud2
from cv_bridge import CvBridge, CvBridgeError
import numpy as np
from math import cos, sin, radians, sqrt
from itertools import combinations
import time
# ganav imports
from mmseg.apis import inference_segmentor, init_segmentor, show_result_pyplot
from mmseg.core.evaluation import get_palette
import torch
import mmcv
from shutil import copyfile
import os
import datetime
import matplotlib.pyplot as plt
from PIL import Image as im
# path extrapolation imports
from geometry_msgs.msg import Pose2D, Twist, PoseStamped
from nav_msgs.msg import Path,Odometry
class TerrainSeg():
def __init__(self):
rospy.init_node('TerrainSeg')
self.bridge = CvBridge()
# Subscribe to the camera image and depth topics and set the appropriate callbacks
self.depth_sub = rospy.Subscriber("/camera/color/image_raw", Image, self.img_callback)
# rospy.Subscriber("/jackal_velocity_controller/cmd_vel", Twist, self.vel_callback)
rospy.Subscriber("/odometry/filtered", Odometry, self.odom_callback)
parser = ArgumentParser()
# parser.add_argument('img', help='Image file')
parser.add_argument('config', help='Config file')
parser.add_argument('checkpoint', help='Checkpoint file')
parser.add_argument('-p', default=".", type=str)
parser.add_argument('-s', default="./vis.png", type=str)
parser.add_argument('-d', action='store_true')
parser.add_argument('--device', default='cuda:0', help='Device used for inference')
parser.add_argument('--palette', default='rugd_group', help='Color palette used for segmentation map')
args = parser.parse_args()
self.pal = get_palette(args.palette)
print(self.pal)
self.model = init_segmentor(args.config, args.checkpoint, device=args.device)
self.outVid = cv2.VideoWriter('subset5_pspnet.avi',cv2.VideoWriter_fourcc(*'DIVX'), 15, (688, 550))
self.numRed = 0
print(" Finished Initializing ")
def img_callback(self, data):
# print("Inside callback")
t1 = time.time()
try:
self.img = self.bridge.imgmsg_to_cv2(data, "bgr8")
except CvBridgeError as e:
print (e)
dim = (688, 550)
self.resized_img = cv2.resize(self.img, dim, interpolation = cv2.INTER_AREA)
result = inference_segmentor(self.model, self.resized_img)
exists = 4 in result[0]
self.numRed = self.numRed + exists
print(self.numRed)
# Result is a 1x1 list of a numpy array. i.e., result[0] contains a 688x550 array with numbers pointing to a color pallette
# The color pallette is stored in pal
# This function converts result into Mat format
self.pred_img = self.model.show_result(self.resized_img, result, self.pal, show=False)
# self.pred_img = self.resized_img
if self.x_d >= 0:
x_t =[]
y_t =[]
#time step vecotor (for how long the trajectory will be estimated bsed on the current velocity commands)
time_steps = | np.arange(0.2, 3.1, 0.1) | numpy.arange |
import numpy as np
import numba as nb
from dataclasses import dataclass
from numba import types
from numba.typed import Dict
from numba import njit
import pandas as pd
import time
import datetime
import csv
from openpyxl import load_workbook
from pyModbusTCP.client import ModbusClient
from pyModbusTCP import utils
@dataclass
class Data:
Ppv: np.array
Pbat: np.array
Pperi: np.array
soc: np.array
soc0: int
Pbs0: int
E: dict
class BatModDC(object):
"""Performance Simulation Class for DC-coupled PV-Battery systems
:param parameter: PV battery system parameters
:type parameter: dict
:param d: array containing parameters
:type d: numpy array
:param ppv: normalized DC power output of the PV generator
:type ppv: numpy array
:param pl: AC load power
:type pl: numpy array
:param Pr: Residual power for battery charging
:type Pr: numpy array
:param Prpv: AC residual power
:type Pr: numpy array
:param Ppv: DC power output of the PV generator
:type Ppv: numpy array
:param ppv2ac: Normalized AC output power of the PV2AC conversion pathway to cover the AC power demand
:type ppv2ac: numpy array
:param Ppv2ac_out: Target AC output power of the PV2AC conversion pathway
:type Ppv2ac_out: numpy array
:param dt: time step width in seconds
:type dt: integer
"""
_version = 0.1
def __init__(self, parameter, d, ppv, pl, dt):
"""Constructor method
"""
self.parameter = parameter
self.d = d
self.ppv = ppv
self.pl = pl
self.dt = dt
self.th = False # Start threshold for the recharging of the battery
self.spi = float()
# Initialization and preallocation
self.Real.Pr, self.Real.Prpv, self.Real.Ppv, self.Real.ppv2ac, self.Real.Ppv2ac_out = max_self_consumption(parameter, ppv, pl, pvmod=True)
self.Real.Ppv2ac_out0 = 0
self.Real.Ppv2bat_in0 = 0
self.Real.Pbat = np.zeros_like(self.ppv) # DC power of the battery in W
self.Real.soc = np.zeros_like(self.ppv) # State of charge of the battery
self.Real.soc0 = 0 # State of charge of the battery in the first time step
# Input power of the PV2BAT conversion pathway in W
self.Real.Ppv2bat_in = np.zeros_like(self.ppv)
# Output power of the BAT2AC conversion pathway in W
self.Real.Pbat2ac_out = np.zeros_like(self.ppv)
self.Real.Pbat2ac_out0 = 0
# AC power of the PV-battery system in W
self.Real.Ppvbs = np.zeros_like(self.ppv)
# Additional power consumption of other system components (e.g. AC power meter) in W
self.Real.Pperi = np.ones(self.ppv.size) * self.parameter['P_PERI_AC']
self.Ideal.Ppv = np.maximum(0, self.ppv) * self.parameter['P_PV'] * 1000
self.Ideal.Pr = self.Ideal.Ppv - self.pl
self.Ideal.Pbat = np.zeros_like(self.ppv)
self.Ideal.soc = np.zeros_like(self.ppv)
self.Ideal.Ppv2bat_in = np.zeros_like(self.ppv)
self.Ideal.Ppv2bat_in = np.zeros_like(self.ppv)
self.Ideal.Pbat2ac_out = np.zeros_like(self.ppv)
self.Ideal.Ppvbs = np.zeros_like(self.ppv)
@dataclass
class Real(Data):
Pr : np.array
Prpv : np.array
ppv2ac : np.array
Ppv2ac_out : np.array
Ppv2ac_out0 : int
Ppv2bat_in : np.array
Pbat2ac_out : np.array
Ppvbs : np.array
@dataclass
class Ideal(Real):
def __init__(self):
super().__init__()
def simulation(self, pvmod=True):
"""Manages the Performance Simulation Model for AC-coupled PV-Battery Systems
"""
self.Real.Ppv2ac_out, self.Real.Ppv2bat_in, self.Real.Ppv2bat_in0, self.Real.Pbat2ac_out, self.Real.Pbat2ac_out0, self.Real.Ppvbs, self.Real.Pbat, self.Real.soc, self.Real.soc0 = batmod_dc(
self.d, self.dt, self.Real.soc0, self.Real.soc, self.Real.Pr, self.Real.Prpv, self.Real.Ppv, self.Real.Ppv2bat_in0, self.Real.Ppv2bat_in,
self.Real.Pbat2ac_out0, self.Real.Pbat2ac_out, self.Real.Ppv2ac_out, self.Real.Ppvbs, self.Real.Pbat)
self.Ideal.Pbat, self.Ideal.soc, self.Ideal.soc0 = batmod_dc_ideal(self.d, self.dt, self.Ideal.soc0, self.Ideal.soc, self.Ideal.Pr, self.Ideal.Pbat)
# Define missing parameters
self.Real.Ppv2ac = self.Real.Ppv2ac_out # AC output power of the PV2AC conversion pathway
self.Real.Ppv2bat = self.Real.Ppv2bat_in # DC input power of the PV2BAT conversion pathway
self.Ideal.Ppvbs = self.Ideal.Ppv - np.maximum(0, self.Ideal.Pbat) - (np.minimum(0, self.Ideal.Pbat)) # Realized AC power of the PV-battery system
self.Ideal.Ppv2ac = self.Ideal.Ppv - np.maximum(0, self.Ideal.Pbat) # AC output power of the PV2AC conversion pathway
self.Ideal.Ppv2bat = np.maximum(0, self.Ideal.Pbat) # DC input power of the PV2BAT conversion pathway
print()
def bat_mod_res(self):
"""Function to calculate the power flows and energy sums including curtailment of PV power
"""
self.Real.E = bat_res_mod(self.parameter, self.pl, self.Real.Ppv, self.Real.Pbat,
self.dt, self.Real.Ppv2ac, self.Real.Ppv2bat, self.Real.Ppvbs, self.Real.Pperi)
self.Ideal.E = bat_res_mod_ideal(self.parameter, self.pl, self.Ideal.Ppv, self.Ideal.Pbat,
self.dt, self.Ideal.Ppv2ac, self.Ideal.Ppv2bat, self.Ideal.Ppvbs, self.Ideal.Pperi)
def calculate_spi(self):
self.spi = calculate_spi(_E_real=self.Real.E, _E_ideal=self.Ideal.E)
def get_E(self):
"""Returns the energy sums of the simulation
:return: Energy sums of the simulation in MWh
:rtype: dict
"""
return self.Real.E, self.Ideal.E
def get_soc(self):
"""Returns the state of charge of the battery
:return: state of charge of the battery
:rtype: numpy array
"""
return self.soc
def get_Pbat(self):
"""Returns the DC power of the battery in W
:return: DC power of the battery in W
:rtype: numpy array
"""
return self.Pbat
def get_SPI(self):
return self.spi
class BatModAC(object):
"""Performance Simulation Class for AC-coupled PV-Battery systems
:param parameter: PV battery system parameters
:type parameter: dict
:param d: array containing parameters
:type d: numpy array
:param ppv: normalized DC power output of the PV generator
:type ppv: numpy array
:param pl: AC load power
:type pl: numpy array
:param Pr: AC residual power
:type Pr: numpy array
:param Ppv: DC power output of the PV generator
:type Ppv: numpy array
:param Ppvs: AC power output of the PV inverter taking into account the conversion losses and maximum output power of the PV inverter
:type Ppvs: numpy array
:param Pperi: Additional power consumption of other system components (e.g. AC power meter) in W
:type Pperi: numpy array
:param dt: time step width in seconds
:type dt: integer
"""
_version = '0.1'
def __init__(self, parameter, d, ppv, pl, dt):
"""Constructor method
"""
self.parameter = parameter
self.d = d
self.ppv = ppv
self.pl = pl
self.dt = dt
self.spi = float()
self.th = False # Start threshold for the recharging of the battery
# Initialization and preallocation
self.Real.Pr, self.Real.Ppv, self.Real.Ppvs, self.Real.Pperi = max_self_consumption(parameter, ppv, pl, pvmod=True)
self.Real.Pbat = np.zeros_like(self.ppv) # DC power of the battery in W
self.Real.Pbs = np.zeros_like(self.ppv) # AC power of the battery system in W
self.Real.soc = np.zeros_like(self.ppv) # State of charge of the battery
self.Real.soc0 = 0 # State of charge of the battery in the first time step
self.Real.Pbs0 = 0 # State of the battery storage in the previous time step
self.Ideal.Ppv = np.maximum(0, ppv) * parameter['P_PV'] * 1000
self.Ideal.Pr = self.Ideal.Ppv - pl
self.Ideal.Pbat = np.zeros_like(self.ppv)
self.Ideal.Pbs = np.zeros_like(self.ppv)
self.Ideal.Pbs0 = 0
self.Ideal.soc = np.zeros_like(self.ppv)
self.Ideal.soc0 = 0
self.Ideal.Ppvs = self.Ideal.Ppv
self.Ideal.Pperi = np.zeros_like(self.ppv)
@dataclass
class Real(Data):
Pr : np.array
Ppvs : np.array
Pbs : np.array
@dataclass
class Ideal(Real):
def __init__(self):
super().__init__()
def simulation(self):
"""Manages the Performance Simulation Model for AC-coupled PV-Battery Systems
"""
self.Real.Pbat, self.Real.Pbs, self.Real.soc, self.Real.soc0, self.Real.Pbs0 = batmod_ac(
self.d, self.dt, self.Real.soc0, self.Real.soc, self.Real.Pr, self.Real.Pbs0, self.Real.Pbs, self.Real.Pbat)
self.Ideal.Pbs, self.Ideal.Pbat, self.Ideal.soc0, self.Ideal.soc = batmod_ac_ideal(
self.d, self.dt, self.Ideal.soc0, self.Ideal.soc, self.Ideal.Pr, self.Ideal.Pbat)
def bat_mod_res(self):
"""Function to calculate the power flows and energy sums including curtailment of PV power
"""
self.Real.E = bat_res_mod(
self.parameter, self.pl, self.Real.Ppv, self.Real.Pbat, self.dt, self.Real.Ppvs, self.Real.Pbs, self.Real.Pperi)
self.Ideal.E = bat_res_mod_ideal(
self.parameter, self.pl, self.Ideal.Ppv, self.Ideal.Pbat, self.dt, self.Ideal.Ppvs, self.Ideal.Pbs, self.Ideal.Pperi)
def calculate_spi(self):
self.spi = calculate_spi(_E_real=self.Real.E, _E_ideal=self.Ideal.E)
def get_E(self):
"""Returns the energy sums of the simulation
:return: Energy sums of the simulation in MWh
:rtype: dict
"""
return self.Real.E, self.Ideal.E
def get_soc(self):
"""Returns the state of charge of the battery
:return: state of charge of the battery
:rtype: numpy array
"""
return self.soc
def get_Pbat(self):
"""Returns the DC power of the battery in W
:return: DC power of the battery in W
:rtype: numpy array
"""
return self.Pbat
def get_Pbs(self):
"""Returns the AC power of the battery system in W
:return: AC power of the battery system in W
:rtype: numpy array
"""
return self.Pbs
def get_SPI(self):
return self.spi
class BatModPV(object):
"""Performance Simulation Class for PV-coupled PV-Battery systems
:param parameter: PV battery system parameters
:type parameter: dict
:param d: array containing parameters
:type d: numpy array
:param ppv: normalized DC power output of the PV generator
:type ppv: numpy array
:param pl: AC load power
:type pl: numpy array
:param Pac: Power demand on the AC side
:type Pac: numpy array
:param Ppv: DC power output of the PV generator
:type Ppv: numpy array
:param Pperi: Additional power consumption of other system components (e.g. AC power meter) in W
:type Pperi: numpy array
:param dt: time step width in seconds
:type dt: integer
"""
_version = '0.1'
def __init__(self, parameter, d, ppv, pl, Pac, Ppv, Pperi, dt):
"""Constructor method
"""
self.parameter = parameter
self.d = d
self.ppv = ppv
self.pl = pl
self.Pac = Pac
self.Ppv = Ppv
self.Pperi = Pperi
self.dt = dt
# Initialization and preallocation
self.Pbat = np.zeros_like(self.ppv) # DC power of the battery in W
self.soc = np.zeros_like(self.ppv) # State of charge of the battery
# Output power of the PV2AC conversion pathway in W
self.Ppv2ac_out = np.zeros_like(self.ppv)
# Input power of the PV2BAT conversion pathway in W
self.Ppv2bat_in = np.zeros_like(self.ppv)
self.Ppv2bat_in0 = 0
# Output power of the BAT2PV conversion pathway in W
self.Pbat2pv_out = np.zeros_like(self.ppv)
self.Pbat2pv_out0 = 0
# AC power of the PV-battery system in W
self.Ppvbs = np.zeros_like(self.ppv)
self.simulation()
self.bat_mod_res()
def simulation(self, pvmod=True):
"""Manages the Performance Simulation Model for AC-coupled PV-Battery Systems
"""
self.th = 0 # Start threshold for the recharging of the battery
self.soc0 = 0 # Initial state of charge of the battery in the first time step
# Simulation of the battery system
#start = time.process_time()
self.soc, self.soc0, self.Ppv, self.Ppvbs, self.Pbat, self.Ppv2ac_out, self.Pbat2pv_out, self.Ppv2bat_in = batmod_pv(self.d, self.dt, self.soc0, self.soc, self.Ppv, self.Pac, self.Ppv2bat_in0, self.Ppv2bat_in, self.Ppv2ac_out, self.Pbat2pv_out0, self.Pbat2pv_out, self.Ppvbs, self.Pbat)
#print(time.process_time()-start)
# Define missing parameters
self.Ppv2ac = self.Ppv2ac_out # AC output power of the PV2AC conversion pathway
self.Ppv2bat = self.Ppv2bat_in # DC input power of the PV2BAT conversion pathway
def bat_mod_res(self):
"""Function to calculate the power flows and energy sums including curtailment of PV power
"""
self.E = bat_res_mod(self.parameter, self.pl, self.Ppv, self.Pbat, self.dt, self.Ppv2ac, self.Ppv2bat, self.Ppvbs, self.Pperi)
def get_E(self):
"""Returns the energy sums of the simulation
:return: Energy sums of the simulation in MWh
:rtype: dict
"""
return self.E
def get_soc(self):
"""Returns the state of charge of the battery
:return: state of charge of the battery
:rtype: numpy array
"""
return self.soc
def get_Pbat(self):
"""Returns the DC power of the battery in W
:return: DC power of the battery in W
:rtype: numpy array
"""
return self.Pbat
class ModBus(object):
"""Establishes connection to a battery system via ModBus protocol
:param host: IP address of the host
:type host: string
:param port: Server port of the host
:type port: integer
:param unit_id: Unit-ID of the host
:type unit_id: integer
"""
def __init__(self, host, port, unit_id, input_vals, dt, fname):
"""Constructor method
"""
self.host = host
self.port = port
self.unit_id = unit_id
self.dt = dt
self.input_vals = input_vals
self.fname = fname
self.open_connection()
self.create_csv_file()
self.start_loop()
def open_connection(self):
"""Opens the connection to the host
"""
# Open ModBus connection
try:
self.c = ModbusClient(host=self.host, port=self.port,
unit_id=self.unit_id, auto_open=True, auto_close=True)
except ValueError:
print("Error with host: {}, port: {} or unit-ID: {} params".format(
self.host, self.port, self.unit_id))
def start_loop(self):
"""Starts the writing and reading process
"""
# Transform the array to fit the 1 minute time duration
#self.set_vals = np.repeat(self.input_vals, self.dt * 60)
i = 0
idx = pd.date_range(start=datetime.datetime.now(),
periods=(self.input_vals.size), freq='S')
while i < len(idx):
if datetime.datetime.now().second == idx[i].second:
# Set chrging value
self.set_val = int(self.input_vals[i])
if self.set_val < 0:
# Write negative value to battery charge power (AC) setpoint register
self.c.write_single_register(1024, self.set_val & 0xFFFF)
# Log writing time
self.set_time = datetime.datetime.now()
else:
# Write positive value to battery charge power (AC) setpoint to register
self.c.write_single_register(1024, self.set_val)
# Log writing time
self.set_time = datetime.datetime.now()
try:
# Read total AC power value from register
_P_ac = self.c.read_holding_registers(172, 2)
self.read_time_P_ac = datetime.datetime.now()
except:
print('Could not read register 172!')
try:
# Read actual battery charge/discharge power value from register
_P_bat = self.c.read_holding_registers(582, 1)
self.read_time_P_bat = datetime.datetime.now()
except:
print('Could not read register 582!')
# Load content of two registers into a single float value
zregs = utils.word_list_to_long(_P_ac, big_endian=False)
# Decode and store float value of the AC-power
self.P_ac = utils.decode_ieee(*zregs)
# Store the DC charging power
self.P_bat = np.int16(*_P_bat)
# Read actual soc
self.soc0 = self.read_soc(210)
try:
# Save the values to a csv file
self.save_to_csv()
except:
print('Could not save to csv!')
i += 1
def read_soc(self, reg):
"""Reads the state of charge of the battery
"""
# Load the actual state fo charge of the battery
regs = self.c.read_holding_registers(reg, 2)
# Load content of two registers into a single float value
zregs = utils.word_list_to_long(regs, big_endian=False)
return utils.decode_ieee(*zregs)
def create_csv_file(self):
"""Creates a csv file from set and read values
"""
# Create a new csv-file
with open(self.fname, 'w') as f:
writer = csv.writer(f, dialect='excel')
writer.writerow(['set_time',
'read_time_P_ac',
'read_time_P_bat',
'soc',
'set_value',
'P_ac',
'P_bat'])
def save_to_csv(self):
"""Saves the set and read values to s csv file
"""
# Save the read values to a csv file
with open(self.fname, "a") as f:
wr = csv.writer(f, dialect='excel')
wr.writerow([self.set_time, self.read_time_P_ac, self.read_time_P_bat,
self.soc0, self.set_val, self.P_ac, self.P_bat])
def max_self_consumption(parameter, ppv, pl, pvmod=True, ideal=False):
"""Function for maximizing self consumption
:param parameter: PV battery system parameters
:type parameter: dict
:param ppv: normalized DC power output of the PV generator
:type ppv: numpy array
:param pl: AC load power
:type pl: numpy array
"""
# Maximize self consumption for AC-coupled systems
if parameter['Top'] == 'AC':
# DC power output of the PV generator
if pvmod: # ppv: Normalized DC power output of the PV generator in kW/kWp
if ideal:
Ppv = np.maximum(0, ppv ) * parameter['P_PV'] * 1000
else:
Ppv = np.minimum(ppv * parameter['P_PV'], parameter['P_PV2AC_in']) * 1000
else: # ppv: DC power output of the PV generator in W
if ideal:
Ppv = np.maximum(0, ppv)
else:
Ppv = np.minimum(ppv, parameter['P_PV2AC_in'] * 1000)
# Normalized input power of the PV inverter
ppvinvin = Ppv / parameter['P_PV2AC_in'] / 1000
# AC power output of the PV inverter taking into account the conversion losses and maximum
# output power of the PV inverter
Ppvs = np.minimum(np.maximum(0, Ppv-(parameter['PV2AC_a_in'] * ppvinvin * ppvinvin + parameter['PV2AC_b_in'] * ppvinvin + parameter['PV2AC_c_in'])), parameter['P_PV2AC_out'] * 1000)
# 3.2 Residual power
# Additional power consumption of other system components (e.g. AC power meter) in W
Pperi = np.ones_like(ppv) * parameter['P_PERI_AC']
# Adding the standby consumption of the PV inverter in times without any AC power output of the PV system
# to the additional power consumption
Pperi[Ppvs == 0] += parameter['P_PVINV_AC']
# Residual power
if ideal:
Pr = Ppv - pl
else:
Pr = Ppvs - pl - Pperi
return Pr, Ppv, Ppvs, Pperi
# Maximize self consumption for DC-coupled systems
elif parameter['Top'] == 'DC':
# Initialization and preallocation
Ppv2ac_in_ac = np.zeros_like(ppv)
Ppv = np.empty_like(ppv) # DC power output of the PV generator
if pvmod: # ppv: Normalized DC power output of the PV generator in kW/kWp
Ppv = ppv * parameter['P_PV'] * 1000
else:
Ppv = ppv
# DC power output of the PV generator taking into account the maximum
# DC input power of the PV2AC conversion pathway
Ppv = np.minimum(Ppv, parameter['P_PV2AC_in'] * 1000)
# Residual power
# Power demand on the AC side
Pac = pl + parameter['P_PERI_AC']
# Normalized AC output power of the PV2AC conversion pathway to cover the AC
# power demand
ppv2ac = np.minimum(
Pac, parameter['P_PV2AC_out'] * 1000) / parameter['P_PV2AC_out'] / 1000
# Target DC input power of the PV2AC conversion pathway
Ppv2ac_in_ac = np.minimum(Pac, parameter['P_PV2AC_out'] * 1000) + (
parameter['PV2AC_a_out'] * ppv2ac**2 + parameter['PV2AC_b_out'] * ppv2ac + parameter['PV2AC_c_out'])
# Normalized DC input power of the PV2AC conversion pathway TODO 1
ppv2ac = Ppv / parameter['P_PV2AC_in'] / 1000
# Target AC output power of the PV2AC conversion pathway
Ppv2ac_out = np.maximum(
0, Ppv - (parameter['PV2AC_a_in'] * ppv2ac**2 + parameter['PV2AC_b_in'] * ppv2ac + parameter['PV2AC_c_in']))
# Residual power for battery charging
Prpv = Ppv - Ppv2ac_in_ac
# Residual power for battery discharging
Pr = Ppv2ac_out - Pac
return Pr, Prpv, Ppv, ppv2ac, Ppv2ac_out
# Maximize self consumption for PV-coupled systems
elif parameter['Top'] == 'PV':
# Preallocation
# Pbat = np.zeros_like(ppv) # DC power of the battery in W
# soc = np.zeros_like(ppv) # State of charge of the battery
# Ppv2ac_out = np.zeros_like(ppv) # Output power of the PV2AC conversion pathway in W
# Ppv2bat_in = np.zeros_like(ppv) # Input power of the PV2BAT conversion pathway in W
# Pbat2pv_out = np.zeros_like(ppv) # Output power of the BAT2PV conversion pathway in W
# Ppvbs = np.zeros_like(ppv) # AC power of the PV-battery system in W
Ppv = np.empty_like(ppv) # DC power output of the PV generator
# Additional power consumption of other system components (e.g. AC power meter) in W
Pperi = np.ones_like(ppv) * parameter['P_PERI_AC']
# dt = 1 # Time increment in s
# th = 0 # Start threshold for the recharging of the battery
# soc0 = 0 # State of charge of the battery in the first time step
# DC power output of the PV generator
if pvmod: # ppv: Normalized DC power output of the PV generator in kW/kWp
Ppv = ppv * parameter['P_PV'] * 1000
else: # ppv: DC power output of the PV generator in W
Ppv = ppv
# Power demand on the AC side
Pac = pl + Pperi
return Pac, Ppv, Pperi
@nb.jit(nopython=True)
def batmod_ac(d, _dt, _soc0, _soc, _Pr, _Pbs0, _Pbs, _Pbat):
"""Performance Simulation function for AC-coupled battery systems
:param d: array containing parameters
:type d: numpy array
:param dt: time step width
:type dt: integer
:param soc0: state of charge in the previous time step
:type soc0: float
:param Pr: residual power
:type Pr: numpy array
:param Pbs0: AC-power of the battery system in the previous time step
:type Pbs0: float
:param Pbs: AC-power of the battery syste
:type Pbs: numpy array
:param Pbat: DC-power oof the battery
:type Pbat: numpy array
"""
# Loading of particular variables
_E_BAT = d[0]
_eta_BAT = d[1]
_t_CONSTANT = d[2]
_P_SYS_SOC0_DC = d[3]
_P_SYS_SOC0_AC = d[4]
_P_SYS_SOC1_DC = d[5]
_P_SYS_SOC1_AC = d[6]
_AC2BAT_a_in = d[7]
_AC2BAT_b_in = d[8]
_AC2BAT_c_in = d[9]
_BAT2AC_a_out = d[10]
_BAT2AC_b_out = d[11]
_BAT2AC_c_out = d[12]
_P_AC2BAT_DEV = d[13]
_P_BAT2AC_DEV = d[14]
_P_BAT2AC_out = d[15]
_P_AC2BAT_in = d[16]
_t_DEAD = int(round(d[17]))
_SOC_h = d[18]
_P_AC2BAT_min = _AC2BAT_c_in
_P_BAT2AC_min = _BAT2AC_c_out
# Correction factor to avoid over charge and discharge the battery
corr = 0.1
# Initialization of particular variables
_tde = _t_CONSTANT > 0 # Binary variable to activate the first-order time delay element
# Factor of the first-order time delay element
_ftde = 1 - np.exp(-_dt / _t_CONSTANT)
# First time step with regard to the dead time of the system control
_tstart = np.maximum(2, 1 + _t_DEAD)
_tend = int(_Pr.size)
_th = 0
# Capacity of the battery, conversion from kWh to Wh
_E_BAT *= 1000
# Effiency of the battery in percent
_eta_BAT /= 100
# Check if the dead or settling time can be ignored and set flags accordingly
if _dt >= (3 * _t_CONSTANT) or _tend == 1:
_tstart = 1
T_DEAD = False
else:
T_DEAD = True
if _dt >= _t_DEAD + 3 * _t_CONSTANT:
SETTLING = False
else:
SETTLING = True
for t in range(_tstart - 1, _tend):
# Energy content of the battery in the previous time step
E_b0 = _soc0 * _E_BAT
# Calculate the AC power of the battery system from the residual power
# with regard to the dead time of the system control
if T_DEAD:
P_bs = _Pr[t - _t_DEAD]
else:
P_bs = _Pr[t]
# Check if the battery holds enough unused capacity for charging or discharging
# Estimated amount of energy in Wh that is supplied to or discharged from the storage unit.
E_bs_est = P_bs * _dt / 3600
# Reduce P_bs to avoid over charging of the battery
if E_bs_est > 0 and E_bs_est > (_E_BAT - E_b0):
P_bs = (_E_BAT - E_b0) * 3600 / _dt
# When discharging take the correction factor into account
elif E_bs_est < 0 and np.abs(E_bs_est) > (E_b0):
P_bs = (E_b0 * 3600 / _dt) * (1-corr)
# Adjust the AC power of the battery system due to the stationary
# deviations taking the minimum charging and discharging power into
# account
if P_bs > _P_AC2BAT_min:
P_bs = np.maximum(_P_AC2BAT_min, P_bs + _P_AC2BAT_DEV)
elif P_bs < -_P_BAT2AC_min:
P_bs = np.minimum(-_P_BAT2AC_min, P_bs - _P_BAT2AC_DEV)
else:
P_bs = 0
# Limit the AC power of the battery system to the rated power of the
# battery converter
P_bs = np.maximum(-_P_BAT2AC_out * 1000,
np.minimum(_P_AC2BAT_in * 1000, P_bs))
# Adjust the AC power of the battery system due to the settling time
# (modeled by a first-order time delay element) Hier hat der Schritt vorher eine Null?
# Muss der vorherige Wert mit übergeben werden?
if SETTLING:
if t > 0:
P_bs = _tde * _Pbs[t-1] + _tde * (P_bs - _Pbs[t-1]) * _ftde + P_bs * (not _tde)
else:
P_bs = _tde * _Pbs0 + _tde * (P_bs - _Pbs0) * _ftde + P_bs * (not _tde)
# Decision if the battery should be charged or discharged
if P_bs > 0 and _soc0 < 1 - _th * (1 - _SOC_h):
# The last term th*(1-SOC_h) avoids the alternation between
# charging and standby mode due to the DC power consumption of the
# battery converter when the battery is fully charged. The battery
# will not be recharged until the SOC falls below the SOC-threshold
# (SOC_h) for recharging from PV.
# Normalized AC power of the battery system
p_bs = P_bs / _P_AC2BAT_in / 1000
# DC power of the battery affected by the AC2BAT conversion losses
# of the battery converter
P_bat = np.maximum(
0, P_bs - (_AC2BAT_a_in * p_bs * p_bs + _AC2BAT_b_in * p_bs + _AC2BAT_c_in))
elif P_bs < 0 and _soc0 > 0:
# Normalized AC power of the battery system
p_bs = np.abs(P_bs / _P_BAT2AC_out / 1000)
# DC power of the battery affected by the BAT2AC conversion losses
# of the battery converter
P_bat = P_bs - (_BAT2AC_a_out * p_bs * p_bs +
_BAT2AC_b_out * p_bs + _BAT2AC_c_out)
else: # Neither charging nor discharging of the battery
# Set the DC power of the battery to zero
P_bat = 0
# Decision if the standby mode is active
if P_bat == 0 and _soc0 <= 0: # Standby mode in discharged state
# DC and AC power consumption of the battery converter
P_bat = -np.maximum(0, _P_SYS_SOC0_DC)
P_bs = _P_SYS_SOC0_AC
elif P_bat == 0 and _soc0 > 0: # Standby mode in fully charged state
# DC and AC power consumption of the battery converter
P_bat = -np.maximum(0, _P_SYS_SOC1_DC)
P_bs = _P_SYS_SOC1_AC
# Transfer the realized AC power of the battery system and
# the DC power of the battery
_Pbs0 = P_bs
_Pbs[t] = P_bs
_Pbat[t] = P_bat
# Change the energy content of the battery from Ws to Wh conversion
if P_bat > 0:
E_b = E_b0 + P_bat * np.sqrt(_eta_BAT) * _dt / 3600
elif P_bat < 0:
E_b = E_b0 + P_bat / np.sqrt(_eta_BAT) * _dt / 3600
else:
E_b = E_b0
# Calculate the state of charge of the battery
_soc0 = E_b / (_E_BAT)
_soc[t] = _soc0
# Adjust the hysteresis threshold to avoid alternation
# between charging and standby mode due to the DC power
# consumption of the battery converter.
if _th and _soc[t] > _SOC_h or _soc[t] > 1:
_th = True
else:
_th = False
return _Pbat, _Pbs, _soc, _soc0, _Pbs0
@nb.jit(nopython=True)
def batmod_ac_ideal(d, _dt, _soc0, _soc, _Pr, _Pbat):
_E_BAT = d[0]
for t in range(_Pr.size):
# Energy content of the battery in the previous time step
E_b0 = _soc0 * _E_BAT * 1000
# Calculate the DC power of the battery from the residual power
P_bat = _Pr[t]
# Decision if the battery should be charged or discharged
if P_bat > 0 and _soc0 < 1: # Battery charging
E_b = E_b0 + P_bat * _dt / 3600 # Change the energy content of the battery
elif P_bat < 0 and _soc0 > 0: # Battery discharging
# Change the energy content of the battery
E_b = E_b0 + P_bat * _dt / 3600
else: # Neither charging nor discharging of the battery
# Set the DC power of the battery to zero
P_bat = 0
# No change in the energy content of the battery
E_b = E_b0
# Transfer the realized DC power of the battery
_Pbat[t] = P_bat
# Calculate the state of charge of the battery
_soc0 = E_b / (_E_BAT * 1000)
_soc[t] = _soc0
# Define missing parameters
_Pbs = _Pbat # Realized AC power of the battery system
return _Pbs, _Pbat, _soc0, _soc
@nb.jit(nopython=True)
def batmod_dc(d, _dt, _soc0, _soc, _Pr, _Prpv, _Ppv, _Ppv2bat_in0, _Ppv2bat_in, _Pbat2ac_out0, _Pbat2ac_out, _Ppv2ac_out, _Ppvbs, _Pbat):
"""Performance simulation function for DC-coupled battery systems
:param d: array containing parameters
:type d: numpy array
:param dt: time step width
:type dt: integer
:param soc0: state of charge in the previous time step
:type soc0: float
:param Pr: residual power
:type Pr: numpy array
:param Prpv: residual power of the PV-system
:type Prpv: numpy array
:param Ppv: PV-power
:type Ppv: numpy array
:param Ppv2bat_in0: AC input power of the battery system in the previous time step
:type Ppv2bat_in0: float
:param Ppv2bat_in: AC input power of the battery system
:type Ppv2bat_in: numpy array
:param Pbat2ac_out0: AC output power of the battery system in the previous time step
:type Pbat2ac_out0: float
:param Pbat2ac_out: AC output power of the battery system
:type Pbat2ac_out: numpy array
:param Ppv2ac_out0: AC output power of the PV inverter in the previous time step
:type Ppv2ac_out0: float
:param Ppv2ac_out: AC output power of the PV inverter
:type Ppv2ac_out: numpy array
:param Ppvbs: AC power from the PV system to the battery system
:type Ppvbs: numpy array
:param Pbat: DC power of the battery
:type Pbat: float
"""
_E_BAT = d[0]
_P_PV2AC_in = d[1]
_P_PV2AC_out = d[2]
_P_PV2BAT_in = d[3]
_P_BAT2AC_out = d[4]
_PV2AC_a_in = d[5]
_PV2AC_b_in = d[6]
_PV2AC_c_in = d[7]
_PV2BAT_a_in = d[8]
_PV2BAT_b_in = d[9]
_BAT2AC_a_out = d[10]
_BAT2AC_b_out = d[11]
_BAT2AC_c_out = d[12]
_eta_BAT = d[13]
_SOC_h = d[14]
_P_PV2BAT_DEV = d[15]
_P_BAT2AC_DEV = d[16]
_t_DEAD = int(round(d[17]))
_t_CONSTANT = d[18]
_P_SYS_SOC1_DC = d[19]
_P_SYS_SOC0_AC = d[20]
_P_SYS_SOC0_DC = d[21]
_P_PV2AC_min = _PV2AC_c_in
# Capacity of the battery, conversion from kWh to Wh
_E_BAT *= 1000
# Effiency of the battery in percent
_eta_BAT /= 100
# Initialization of particular variables
# _P_PV2AC_min = _parameter['PV2AC_c_in'] # Minimum input power of the PV2AC conversion pathway
_tde = _t_CONSTANT > 0 # Binary variable to activate the first-order time delay element
# Factor of the first-order time delay element
_ftde = 1 - np.exp(-_dt / _t_CONSTANT)
# First time step with regard to the dead time of the system control
_tstart = np.maximum(2, 1 + _t_DEAD)
_tend = int(_Pr.size)
_th = 0
corr = 0.1
# Check if the dead or settling time can be ignored and set flags accordingly
if _dt >= (3 * _t_CONSTANT) or _tend == 1:
_tstart = 1
T_DEAD = False
else:
T_DEAD = True
if _dt >= _t_DEAD + 3 * _t_CONSTANT:
SETTLING = False
else:
SETTLING = True
for t in range(_tstart - 1, _tend):
# Energy content of the battery in the previous time step
E_b0 = _soc0 * _E_BAT
# Residual power with regard to the dead time of the system control
if T_DEAD:
P_rpv = _Prpv[t - _t_DEAD]
P_r = _Pr[t - _t_DEAD]
else:
P_rpv = _Prpv[t]
P_r = _Pr[t]
# Check if the battery holds enough unused capacity for charging or discharging
# Estimated amount of energy that is supplied to or discharged from the storage unit.
E_bs_rpv = P_rpv * _dt / 3600
E_bs_r = P_r * _dt / 3600
# Reduce P_bs to avoid over charging of the battery
if E_bs_rpv > 0 and E_bs_rpv > (_E_BAT - E_b0):
P_rpv = (_E_BAT - E_b0) * 3600 / _dt
# When discharging take the correction factor into account
elif E_bs_r < 0 and np.abs(E_bs_r) > (E_b0):
P_r = ((E_b0) * 3600 / _dt) * (1-corr)
# Decision if the battery should be charged or discharged
if P_rpv > 0 and _soc0 < 1 - _th * (1 - _SOC_h):
'''
The last term th*(1-SOC_h) avoids the alternation between
charging and standby mode due to the DC power consumption of the
battery converter when the battery is fully charged. The battery
will not be recharged until the SOC falls below the SOC-threshold
(SOC_h) for recharging from PV.
'''
# Charging power
P_pv2bat_in = P_rpv
# Adjust the charging power due to the stationary deviations
P_pv2bat_in = np.maximum(0, P_pv2bat_in + _P_PV2BAT_DEV)
# Limit the charging power to the maximum charging power
P_pv2bat_in = np.minimum(P_pv2bat_in, _P_PV2BAT_in * 1000)
# Adjust the charging power due to the settling time
# (modeled by a first-order time delay element)
if SETTLING:
if t > 0:
P_pv2bat_in = _tde * _Ppv2bat_in[(t-1)] + _tde * (
P_pv2bat_in - _Ppv2bat_in[(t-1)]) * _ftde + P_pv2bat_in * (not _tde)
else:
P_pv2bat_in = _tde * _Ppv2bat_in0 + _tde * \
(P_pv2bat_in - _Ppv2bat_in0) * \
_ftde + P_pv2bat_in * (not _tde)
# Limit the charging power to the current power output of the PV generator
P_pv2bat_in = np.minimum(P_pv2bat_in, _Ppv[t])
# Normalized charging power
ppv2bat = P_pv2bat_in / _P_PV2BAT_in / 1000
# DC power of the battery affected by the PV2BAT conversion losses
# (the idle losses of the PV2BAT conversion pathway are not taken
# into account)
P_bat = np.maximum(
0, P_pv2bat_in - (_PV2BAT_a_in * ppv2bat**2 + _PV2BAT_b_in * ppv2bat))
# Realized DC input power of the PV2AC conversion pathway
P_pv2ac_in = _Ppv[t] - P_pv2bat_in
# Normalized DC input power of the PV2AC conversion pathway
_ppv2ac = P_pv2ac_in / _P_PV2AC_in / 1000
# Realized AC power of the PV-battery system
P_pv2ac_out = np.maximum(
0, P_pv2ac_in - (_PV2AC_a_in * _ppv2ac**2 + _PV2AC_b_in * _ppv2ac + _PV2AC_c_in))
P_pvbs = P_pv2ac_out
# Transfer the final values
_Ppv2ac_out[t] = P_pv2ac_out
_Ppv2bat_in0 = P_pv2bat_in
_Ppv2bat_in[t] = P_pv2bat_in
elif P_rpv < 0 and _soc0 > 0:
# Discharging power
P_bat2ac_out = P_r * -1
# Adjust the discharging power due to the stationary deviations
P_bat2ac_out = np.maximum(0, P_bat2ac_out + _P_BAT2AC_DEV)
# Adjust the discharging power to the maximum discharging power
P_bat2ac_out = np.minimum(P_bat2ac_out, _P_BAT2AC_out * 1000)
# Adjust the discharging power due to the settling time
# (modeled by a first-order time delay element)
if SETTLING:
if t > 0:
P_bat2ac_out = _tde * _Pbat2ac_out[t-1] + _tde * (
P_bat2ac_out - _Pbat2ac_out[t-1]) * _ftde + P_bat2ac_out * (not _tde)
else:
P_bat2ac_out = _tde * _Pbat2ac_out0 + _tde * \
(P_bat2ac_out - _Pbat2ac_out0) * \
_ftde + P_bat2ac_out * (not _tde)
# Limit the discharging power to the maximum AC power output of the PV-battery system
P_bat2ac_out = np.minimum(
_P_PV2AC_out * 1000 - _Ppv2ac_out[t], P_bat2ac_out)
# Normalized discharging power
ppv2bat = P_bat2ac_out / _P_BAT2AC_out / 1000
# DC power of the battery affected by the BAT2AC conversion losses
# (if the idle losses of the PV2AC conversion pathway are covered by
# the PV generator, the idle losses of the BAT2AC conversion pathway
# are not taken into account)
if _Ppv[t] > _P_PV2AC_min:
P_bat = -1 * (P_bat2ac_out + (_BAT2AC_a_out *
ppv2bat**2 + _BAT2AC_b_out * ppv2bat))
else:
P_bat = -1 * (P_bat2ac_out + (_BAT2AC_a_out * ppv2bat **
2 + _BAT2AC_b_out * ppv2bat + _BAT2AC_c_out)) + _Ppv[t]
# Realized AC power of the PV-battery system
P_pvbs = _Ppv2ac_out[t] + P_bat2ac_out
# Transfer the final values
_Pbat2ac_out0 = P_bat2ac_out
_Pbat2ac_out[t] = P_bat2ac_out
else: # Neither charging nor discharging of the battery
# Set the DC power of the battery to zero
P_bat = 0
# Realized AC power of the PV-battery system
P_pvbs = _Ppv2ac_out[t]
# Decision if the standby mode is active
if P_bat == 0 and P_pvbs == 0 and _soc0 <= 0: # Standby mode in discharged state
# DC and AC power consumption of the PV-battery inverter
P_bat = -np.maximum(0, _P_SYS_SOC0_DC)
P_pvbs = -_P_SYS_SOC0_AC
elif P_bat == 0 and P_pvbs > 0 and _soc0 > 0: # Standby mode in fully charged state
# DC power consumption of the PV-battery inverter
P_bat = -np.maximum(0, _P_SYS_SOC1_DC)
# Transfer the realized AC power of the PV-battery system and the DC power of the battery
_Ppvbs[t] = P_pvbs
_Pbat[t] = P_bat
# Change the energy content of the battery Wx to Wh conversion
if P_bat > 0:
E_b = E_b0 + P_bat * np.sqrt(_eta_BAT) * _dt / 3600
elif P_bat < 0:
E_b = E_b0 + P_bat / np.sqrt(_eta_BAT) * _dt / 3600
else:
E_b = E_b0
# Calculate the state of charge of the battery
_soc0 = E_b / _E_BAT
_soc[t] = _soc0
# Adjust the hysteresis threshold to avoid alternation between charging
# and standby mode due to the DC power consumption of the
# PV-battery inverter
if _th and _soc[t] > _SOC_h or _soc[t] > 1:
_th = True
else:
_th = False
return _Ppv2ac_out, _Ppv2bat_in, _Ppv2bat_in0, _Pbat2ac_out, _Pbat2ac_out0, _Ppvbs, _Pbat, _soc, _soc0
@nb.jit(nopython=True)
def batmod_dc_ideal(d, _dt, _soc0, _soc, _Pr, _Pbat):
_E_BAT = d[0]
for t in range(_Pr.size):
# Energy content of the battery in the previous time step
E_b0 = _soc0 * _E_BAT * 1000
P_bat = _Pr[t]
if P_bat > 0 and _soc0 < 1: # Battery charging
# Change the energy content of the battery
E_b = E_b0 + P_bat * _dt / 3600
elif P_bat < 0 and _soc0 > 0: # Battery discharging
# Change the energy content of the battery
E_b = E_b0 + P_bat * _dt / 3600
else: # Neither charging nor discharging of the battery
P_bat = 0
E_b = E_b0
_Pbat[t] = P_bat
_soc0 = E_b / (_E_BAT * 1000)
_soc[t] = _soc0
return _Pbat, _soc, _soc0
@nb.jit(nopython=True)
def batmod_pv(d, _dt, _soc0, _soc, _Ppv, _Pac, _Ppv2bat_in0, _Ppv2bat_in, _Ppv2ac_out, _Pbat2pv_out0, _Pbat2pv_out, _Ppvbs, _Pbat):
"""Performance simulation function for PV-coupled battery systems
:param d: array containing parameters
:type d: numpy array
:param dt: time step width
:type dt: integer
:param soc0: state of charge of the battery in the previous time step
:type soc0: float
:param soc: state of charge of the battery
:type soc: numpy array
:param Pr: residual power
:type Pr: numpy array
:param Ppv: PV-power
:type Ppv: numpy array
:param Pac: AC output power of the PV inverter
:type Pac: numpy array
:param Ppv2bat_in: AC input power of the battery system
:type Ppv2bat_in: numpy array
:param Ppv2bat_in0: AC input power of the battery system in the previous time step
:type Ppv2bat_in0: float
:param Pbat2pv_out0: AC output power of the battery system in the previous time step
:type Pbat2pv_out0: float
:param Pbat2pv_out: AC output power of the battery system
:type Pbat2pv_out: numpy array
:param Ppvbs: AC power from the PV system to the battery system
:type Ppvbs: numpy array
:param Pbat: DC power of the battery
:type Pbat: float
"""
# Initialization of particular variables
_E_BAT = d[0]
_P_PV2AC_in = d[1]
_P_PV2AC_out = d[2]
_P_PV2BAT_in = d[3]
_P_BAT2PV_out = d[4]
_PV2AC_a_in = d[5]
_PV2AC_b_in = d[6]
_PV2AC_c_in = d[7]
_PV2BAT_a_in = d[8]
_PV2BAT_b_in = d[9]
_PV2BAT_c_in = d[10]
_PV2AC_a_out = d[11]
_PV2AC_b_out = d[12]
_PV2AC_c_out = d[13]
_BAT2PV_a_out = d[14]
_BAT2PV_b_out = d[15]
_BAT2PV_c_out = d[16]
_eta_BAT = d[17]
_SOC_h = d[18]
_P_PV2BAT_DEV = d[19]
_P_BAT2AC_DEV = d[20]
_P_SYS_SOC1_DC = d[21]
_P_SYS_SOC0_AC = d[22]
_P_SYS_SOC0_DC = d[23]
_t_DEAD = int(round(d[24]))
_t_CONSTANT = d[25]
# Correction factor to avoid over charge and discharge the battery
corr = 0.1
_P_PV2BAT_min = _PV2BAT_c_in # Minimum DC charging power
_P_BAT2PV_min = _BAT2PV_c_out # Minimum DC discharging power
# Initialization of particular variables
_tde = _t_CONSTANT > 0 # Binary variable to activate the first-order time delay element
# Factor of the first-order time delay element
_ftde = 1 - np.exp(-_dt / _t_CONSTANT)
# First time step with regard to the dead time of the system control
_tstart = np.maximum(2, 1 + _t_DEAD)
_tend = int(_Ppv.size)
_th = 0
_E_BAT *= 1000 # Conversion from W to kW
_eta_BAT /= 100
# Check if the dead or settling time can be ignored and set flags accordingly
if _dt >= (3 * _t_CONSTANT) or _tend == 1:
_tstart = 1
T_DEAD = False
else:
T_DEAD = True
if _dt >= _t_DEAD + 3 * _t_CONSTANT:
SETTLING = False
else:
SETTLING = True
for t in range(_tstart - 1, _tend):
# Energy content of the battery in the previous time step
E_b0 = _soc0 * _E_BAT
# Target AC output power of the PV-battery system to cover the AC power demand
if T_DEAD:
P_pvbs = np.minimum(_Pac[t - _t_DEAD], _P_PV2AC_out * 1000)
else:
P_pvbs = np.minimum(_Pac[t], _P_PV2AC_out * 1000)
# Normalized AC output power of the PV2AC conversion pathway
ppv2ac = P_pvbs / _P_PV2AC_out / 1000
# Target DC input power of the PV2AC conversion pathway
P_pv2ac_in = P_pvbs + (_PV2AC_a_out * ppv2ac **
2 + _PV2AC_b_out * ppv2ac + _PV2AC_c_out)
# Residual power
if T_DEAD:
P_rpv = _Ppv[t - _t_DEAD] - P_pv2ac_in
else:
P_rpv = _Ppv[t] - P_pv2ac_in
# Check if the battery holds enough unused capacity for charging or discharging
# Estimated amount of energy that is supplied to or discharged from the storage unit.
E_bs_rpv = P_rpv * _dt / 3600
# Reduce P_bs to avoid over charging of the battery
if E_bs_rpv > 0 and E_bs_rpv > (_E_BAT - E_b0):
P_rpv = ((_E_BAT - E_b0) * 3600) / _dt
# When charging take the correction factor into account
elif E_bs_rpv < 0 and np.abs(E_bs_rpv) > (E_b0):
P_rpv = ((E_b0) * 3600 / _dt) * (1-corr)
# Decision if the battery should be charged or discharged
if P_rpv > _P_PV2BAT_min and _soc0 < 1 - _th * (1 - _SOC_h):
'''
The last term th*(1-SOC_h) avoids the alternation between
charging and standby mode due to the DC power consumption of the
battery converter when the battery is fully charged. The battery
will not be recharged until the SOC falls below the SOC-threshold
(SOC_h) for recharging from PV.
'''
# Charging power
P_pv2bat_in = P_rpv
# Adjust the charging power due to stationary deviations
P_pv2bat_in = np.maximum(0, P_pv2bat_in + _P_PV2BAT_DEV)
# Limit the charging power to the maximum charging power
P_pv2bat_in = np.minimum(P_pv2bat_in, _P_PV2BAT_in * 1000)
# Adjust the charging power due to the settling time
# (modeled by a first-order time delay element)
if SETTLING:
if t > 0:
P_pv2bat_in = _tde * _Ppv2bat_in[t-1] + _tde * (
P_pv2bat_in - _Ppv2bat_in[t-1]) * _ftde + P_pv2bat_in * (not _tde)
else:
P_pv2bat_in = _tde * _Ppv2bat_in0 + _tde * \
(P_pv2bat_in - _Ppv2bat_in0) * \
_ftde + P_pv2bat_in * (not _tde)
# Limit the charging power to the current power output of the PV generator
P_pv2bat_in = np.minimum(P_pv2bat_in, _Ppv[t])
# Normalized charging power
ppv2bat = P_pv2bat_in / _P_PV2BAT_in / 1000
# DC power of the battery
P_bat = np.maximum(0, P_pv2bat_in - (_PV2BAT_a_in *
ppv2bat**2 + _PV2BAT_b_in * ppv2bat + _PV2BAT_c_in))
# Realized DC input power of the PV2AC conversion pathway
P_pv2ac_in = _Ppv[t] - P_pv2bat_in
# Limit the DC input power of the PV2AC conversion pathway
P_pv2ac_in = np.minimum(P_pv2ac_in, _P_PV2AC_in * 1000)
# Recalculate Ppv(t) with limited PV2AC input power
_Ppv[t] = P_pv2ac_in + P_pv2bat_in
# Normalized DC input power of the PV2AC conversion pathway
ppv2ac = P_pv2ac_in / _P_PV2AC_in / 1000
# Realized AC power of the PV-battery system
P_pv2ac_out = np.maximum(
0, P_pv2ac_in - (_PV2AC_a_in * ppv2ac**2 + _PV2AC_b_in * ppv2ac + _PV2AC_c_in))
P_pvbs = P_pv2ac_out
# Transfer the final values
_Ppv2ac_out[t] = P_pv2ac_out
_Ppv2bat_in0 = P_pv2bat_in
_Ppv2bat_in[t] = P_pv2bat_in
elif P_rpv < -_P_BAT2PV_min and _soc0 > 0:
# Target discharging power of the battery
P_bat2pv_out = np.abs(P_rpv)
# Adjust the discharging power due to the stationary deviations
P_bat2pv_out = np.maximum(0, P_bat2pv_out + _P_BAT2AC_DEV)
# Adjust the discharging power to the maximum discharging power
P_bat2pv_out = np.minimum(P_bat2pv_out, _P_BAT2PV_out * 1000)
# Adjust the discharging power due to the settling time
# (modeled by a first-order time delay element)
if SETTLING:
if t > 0:
P_bat2pv_out = _tde * _Pbat2pv_out[t-1] + _tde * (P_bat2pv_out - _Pbat2pv_out[t-1]) * _ftde + P_bat2pv_out * (not _tde)
else:
P_bat2pv_out = _tde * _Pbat2pv_out0 + _tde * (P_bat2pv_out - _Pbat2pv_out0) * _ftde + P_bat2pv_out * (not _tde)
# Recalculate Ppv(t) with limited PV2AC input power
_Ppv[t] = np.minimum(_P_PV2AC_in * 1000, _Ppv[t])
# Limit the discharging power to the maximum AC power output of the PV-battery system
P_bat2pv_out = np.minimum(_P_PV2AC_in * 1000 - _Ppv[t], P_bat2pv_out)
# Normalized discharging power
pbat2pv = P_bat2pv_out / _P_BAT2PV_out / 1000
# DC power of the battery affected by the BAT2PV conversion losses
P_bat = -1*(P_bat2pv_out+(_BAT2PV_a_out * pbat2pv**2 + _BAT2PV_b_out * pbat2pv + _BAT2PV_c_out))
# Realized DC input power of the PV2AC conversion pathway
P_pv2ac_in = _Ppv[t] + P_bat2pv_out
# Normalized DC input power of the PV2AC conversion pathway
ppv2ac = P_pv2ac_in / _P_PV2AC_in / 1000
# AC power of the PV-battery system
P_pvbs = np.maximum(0, P_pv2ac_in-(_PV2AC_a_in * ppv2ac**2 + _PV2AC_b_in * ppv2ac + _PV2AC_c_in))
P_pv2ac_out = P_pvbs
# Transfer the final values
_Ppv2ac_out[t] = P_pv2ac_out
_Pbat2pv_out0 = P_bat2pv_out
_Pbat2pv_out[t] = P_bat2pv_out
else: # Neither charging nor discharging of the battery
# Set the DC power of the battery to zero
P_bat = 0
# Limit the power output of the PV generator to the maximum input power
# of the PV inverter
_Ppv[t] = np.minimum(_Ppv[t], _P_PV2AC_in * 1000)
# Normalized DC input power of the PV2AC conversion pathway
ppv2ac = _Ppv[t] / _P_PV2AC_in / 1000
# Realized AC power of the PV-battery system
P_pvbs = np.maximum(0, _Ppv[t] - (_PV2AC_a_in * ppv2ac**2 + _PV2AC_b_in * ppv2ac + _PV2AC_c_in))
# Transfer the final values
_Ppv2ac_out[t] = P_pvbs
# Decision if the standby mode is active
if P_bat == 0 and _soc0 <= 0: # Standby mode in discharged state
# DC power consumption of the battery converter
P_bat = -np.maximum(0, _P_SYS_SOC0_DC)
if P_pvbs == 0:
P_pvbs = -_P_SYS_SOC0_AC
elif P_bat == 0 and P_pvbs > 0 and _soc0 > 0: # Standby mode in fully charged state
# DC power consumption of the battery converter
P_bat = -np.maximum(0, _P_SYS_SOC1_DC)
# Transfer the realized AC power of the battery system and
# the DC power of the battery
_Ppvbs[t] = P_pvbs
_Pbat[t] = P_bat
# Change the energy content of the battery Wx to Wh conversio
if P_bat > 0:
E_b = E_b0 + P_bat * np.sqrt(_eta_BAT) * _dt / 3600
elif P_bat < 0:
E_b = E_b0 + P_bat / np.sqrt(_eta_BAT) * _dt / 3600
else:
E_b = E_b0
# Calculate the state of charge of the battery
_soc0 = E_b / (_E_BAT)
_soc[t] = _soc0
# Adjust the hysteresis threshold to avoid alternation
# between charging and standby mode due to the DC power
# consumption of the battery converter.
if _th and _soc[t] > _SOC_h or _soc[t] > 1:
_th = True
else:
_th = False
return _soc, _soc0, _Ppv, _Ppvbs, _Pbat, _Ppv2ac_out, _Pbat2pv_out, _Ppv2bat_in
def bat_res_mod(_parameter, _Pl, _Ppv, _Pbat, _dt, *args):
"""Function for calculating energy sums
:param _parameter: parameter of the system
:type _parameter: dict
:param _Pl: load power
:type _Pl: numpy array
:param _Ppv: output power of the PV generator
:type _Ppv: numpy array
:param _Pbat: DC power of the battery
:type _Pbat: numpy array
:param _dt: time step width
:type _dt: integer
:return: energy sums
:rtype: dict
"""
_E = dict()
if _parameter['Top'] == 'AC': # AC-coupled systems
_Ppvs = args[0] # AC output power of the PV system
_Pbs = args[1] # AC power of the battery system
# Additional power consumption of the other system components
_Pperi = args[2]
elif _parameter['Top'] == 'DC' or _parameter['Top'] == 'PV': # DC- and PV-coupled systems
_Ppv2ac = args[0] # AC output power of the PV2AC conversion pathway
_Ppv2bat_in = args[1] # Input power of the PV2BAT conversion pathway
_Ppvbs = args[2] # AC power of the PV-battery system
# Additional power consumption of the other system components
_Pperi = args[3]
_Ppv2ac_in = _Ppv - _Ppv2bat_in # Input power of the PV2AC conversion pathway
# Total load including the power consumption of the other system components
_Plt = _Pl + _Pperi
# DC input power of the battery (charged)
_Pbatin = np.maximum(0, _Pbat)
# DC output power of the battery (discharged)
_Pbatout = np.minimum(0, _Pbat)
# Maximum PV feed-in power
_P_ac2g_max = _parameter['p_ac2g_max'] * _parameter['P_PV'] * 1000
if _parameter['Top'] == 'AC': # AC-coupled systems
# Residual power without curtailment
_Pr = _Ppvs - _Plt
# AC input power of the battery system
_Pac2bs = np.maximum(0, _Pbs)
# AC output power of the battery system
_Pbs2ac = np.minimum(0, _Pbs)
# Negative residual power (residual load demand)
_Prn = np.minimum(0, _Pr)
# Positive residual power (surplus PV power)
_Prp = np.maximum(0, _Pr)
# Direct use of PV power by the load
_Ppvs2l = np.minimum(_Ppvs, _Plt)
# PV charging power
_Ppvs2bs = np.minimum(_Prp, _Pac2bs)
# Grid charging power
_Pg2bs = np.maximum(_Pac2bs - _Prp, 0)
# Grid supply power of the load
_Pg2l = np.minimum(_Prn - _Pbs2ac, 0)
# Battery supply power of the load
_Pbs2l = np.maximum(_Prn, _Pbs2ac)
# Battery feed-in power
_Pbs2g = np.minimum(_Pbs2ac - _Prn, 0)
# PV feed-in power including curtailment
_Ppvs2g = np.minimum(np.maximum(_Prp - _Pac2bs, 0), _P_ac2g_max)
# Power demand from the grid
_Pg2ac = _Pg2l - _Pg2bs
# Feed-in power to the grid
_Pac2g = _Ppvs2g - _Pbs2g
# Grid power
_Pg = _Pac2g + _Pg2ac
# Curtailed PV power (AC output power)
_Pct = np.maximum(_Prp - _Pac2bs, 0) - _Ppvs2g
# AC output power of the PV system including curtailment
_Ppvs = _Ppvs - _Pct
# Residual power including curtailment
_Pr = _Ppvs - _Plt
# Index for PV curtailment
_idx = np.where(_Pct > 0)[0]
for i in range(len(_idx)):
_tct = _idx[i]
# Normalized output power of the PV inverter
_ppvinvout = _Ppvs[_tct] / _parameter['P_PV2AC_out'] / 1000
# DC output power of the PV generator taking into account the
# conversion and curtailment losses
_Ppv[_tct] = _Ppvs[_tct] + (_parameter['PV2AC_a_out'] * _ppvinvout **
2 + _parameter['PV2AC_b_out'] * _ppvinvout + _parameter['PV2AC_c_out'])
elif _parameter['Top'] == 'DC' or _parameter['Top'] == 'PV': # DC- and PV-coupled systems
# Grid power demand of the PV-battery system
_Pg2pvbs = np.minimum(0, _Ppvbs)
# AC input power of the PV-battery system
_Pac2pvbs = _Pg2pvbs
# AC output power of the PV-battery system
_Ppvbs2ac = np.maximum(0, _Ppvbs)
# Load supply power by the PV-battery system
_Ppvbs2l = np.minimum(_Plt, _Ppvbs2ac)
# Load supply power by the grid
_Pg2l = _Plt - _Ppvbs2l
# Direct use of PV power by the load
_Ppv2l = np.minimum(_Plt, _Ppv2ac)
# PV feed-in power including curtailment
_Ppv2g = np.minimum(_Ppv2ac - _Ppv2l, _P_ac2g_max)
# Curtailed PV power (AC output power)
_Pct = _Ppv2ac - _Ppv2l - _Ppv2g
if np.sum(_Pct) > 0:
# Power of the PV-battery system including curtailment
_Ppvbs = _Ppvbs - _Pct
# AC output power of the PV-battery system including curtailment
_Ppvbs2ac = np.maximum(0, _Ppvbs)
# AC output power of the PV2AC conversion pathway including curtailment
_Ppv2ac = _Ppv2ac - _Pct
# Index for PV curtailment
_idx = np.where(_Pct > 0)[0]
for i in range(len(_idx)):
_tct = _idx[i]
# Specific AC output power of the PV2AC conversion pathway
_ppv2ac = _Ppv2ac[_tct] / _parameter['P_PV2AC_out'] / 1000
# DC input power of the PV2AC conversion pathway including curtailment
_Ppv2ac_in[_tct] = _Ppv2ac[_tct] + (_parameter['PV2AC_a_out'] * _ppv2ac **
2 + _parameter['PV2AC_b_out'] * _ppv2ac + _parameter['PV2AC_c_out'])
# DC output power of the PV generator including curtailment
_Ppv = _Ppv2ac_in + _Ppv2bat_in
# Grid power including curtailment
_Pg = _Ppvbs-_Plt
# Feed-in power to the grid including curtailment
_Pac2g = np.maximum(0, _Pg)
# Power demand from the grid
_Pg2ac = np.minimum(0, _Pg)
# Energy sums in MWH
# Electrical demand including the energy consumption of the other system components
_E['El'] = np.sum(np.abs(_Plt)) * _dt / 3.6e9
# DC output of the PV generator including curtailment
_E['Epv'] = np.sum(np.abs(_Ppv)) * _dt / 3.6e9
# DC input of the battery (charged)
_E['Ebatin'] = np.sum(np.abs(_Pbatin)) * _dt / 3.6e9
# DC output of the battery (discharged)
_E['Ebatout'] = np.sum(np.abs(_Pbatout)) * _dt / 3.6e9
# Grid feed-in
_E['Eac2g'] = np.sum(np.abs(_Pac2g)) * _dt / 3.6e9
# Grid demand
_E['Eg2ac'] = np.sum(np.abs(_Pg2ac)) * _dt / 3.6e9
# Load supply by the grid
_E['Eg2l'] = np.sum(np.abs(_Pg2l)) * _dt / 3.6e9
# Demand of the other system components
_E['Eperi'] = np.sum(np.abs(_Pperi)) * _dt / 3.6e9
# Curtailed PV energy
_E['Ect'] = np.sum(np.abs(_Pct)) * _dt / 3.6e9
if _parameter['Top'] == 'AC': # AC-coupled systems
# AC output of the PV system including curtailment
_E['Epvs'] = np.sum(np.abs(_Ppvs)) * _dt / 3.6e9
# AC input of the battery system
_E['Eac2bs'] = np.sum(np.abs(_Pac2bs)) * _dt / 3.6e9
# AC output of the battery system
_E['Ebs2ac'] = np.sum(np.abs(_Pbs2ac)) * _dt / 3.6e9
# Direct use of PV energy
_E['Epvs2l'] = np.sum(np.abs(_Ppvs2l)) * _dt / 3.6e9
# PV charging
_E['Epvs2bs'] = np.sum(np.abs(_Ppvs2bs)) * _dt / 3.6e9
# Grid charging
_E['Eg2bs'] = np.sum(np.abs(_Pg2bs)) * _dt / 3.6e9
# PV feed-in
_E['Epvs2g'] = np.sum(np.abs(_Ppvs2g)) * _dt / 3.6e9
# Load supply by the battery system
_E['Ebs2l'] = np.sum(np.abs(_Pbs2l)) * _dt / 3.6e9
# Battery feed-in
_E['Ebs2g'] = np.sum(np.abs(_Pbs2g)) * _dt / 3.6e9
elif _parameter['Top'] == 'DC' or _parameter['Top'] == 'PV': # DC- and PV-coupled systems
# Grid demand of the PV-battery system
_E['Eg2pvbs'] = np.sum(np.abs(_Pg2pvbs)) * _dt / 3.6e9
# AC input of the PV-battery system
_E['Eac2pvbs'] = np.sum(np.abs(_Pac2pvbs)) * _dt / 3.6e9
# AC output of the PV-battery system
_E['Epvbs2ac'] = np.sum(np.abs(_Ppvbs2ac)) * _dt / 3.6e9
# Load supply by the PV-battery system
_E['Epvbs2l'] = np.sum(np.abs(_Ppvbs2l)) * _dt / 3.6e9
return _E
def bat_res_mod_ideal(_parameter, _Pl, _Ppv, _Pbat, _dt, *args):
E = dict() # Dictionary to store energy sums
if _parameter['Top'] == 'AC':
Ppvs = args[0] # AC output power of the PV system
Pbs = args[1] # AC power of the battery system
Pperi = args[2] # Additional power consumption of the other system components
elif _parameter['Top'] == 'DC':
Ppv2ac = args[0]
Ppv2bat_in = args[1]
Ppvbs = args[2]
Pperi = args[3]
Ppv2ac_in = _Ppv - Ppv2bat_in
# Additional power consumption of the other system components
Pperi = np.zeros_like(_Ppv)
# Total load including the power consumption of the other system components
Plt = _Pl
# DC input power of the battery (charged)
Pbatin = np.maximum(0, _Pbat)
# DC output power of the battery (discharged)
Pbatout = np.minimum(0, _Pbat)
if _parameter['Top'] == 'AC':
# Grid power
Pg = Ppvs - _Pl - Pbs
# Residual power
Pr = Ppvs - Plt
# AC input power of the battery system
Pac2bs = np.maximum(0, Pbs)
# AC output power of the battery system
Pbs2ac = np.minimum(0, Pbs)
# Negative residual power (residual load demand)
Prn = np.minimum(0, Pr)
# Positive residual power (surplus PV power)
Prp = np.maximum(0, Pr)
# Direct use of PV power by the load
Ppvs2l = np.minimum(Ppvs, Plt)
# PV charging power
Ppvs2bs=np.minimum(Prp, Pac2bs)
# Grid charging power
Pg2bs=np.maximum(Pac2bs - Prp, 0)
# Grid supply power of the load
Pg2l=np.minimum(Prn - Pbs2ac, 0)
# Battery supply power of the load
Pbs2l=np.maximum(Prn, Pbs2ac)
# Battery feed-in power
Pbs2g=np.minimum(Pbs2ac - Prn, 0)
# PV feed-in power
Ppvs2g=np.maximum(Prp - Pac2bs, 0)
elif _parameter['Top'] == 'DC':
# Grid power
Pg = Ppvbs - _Pl
# Grid power demand of the PV-battery system
Pg2pvbs = np.minimum(0, Ppvbs)
# AC input power of the PV-battery system
Pac2pvbs = Pg2pvbs
# AC output power of the PV-battery system
Ppvbs2ac = np.maximum(0, Ppvbs)
# Load supply power by the PV-battery system
Ppvbs2l = np.minimum(_Pl, Ppvbs2ac)
# Load supply power by the grid
Pg2l = (Plt - Ppvbs2l)
# Curtailed PV power (AC output power)
Pct = np.zeros_like(_Ppv)
# Power demand from the grid
Pg2ac = np.minimum(0, Pg)
# Feed-in power to the grid
Pac2g=np.maximum(0, Pg)
# Energy sums
# Electrical demand including the energy consumption of the other system components
E['El'] = np.sum(np.abs(Plt)) / 3.6e9
# DC output of the PV generator including curtailment
E['Epv'] = np.sum(np.abs(_Ppv)) / 3.6e9
# DC input of the battery (charged)
E['Ebatin'] = np.sum(np.abs(Pbatin)) / 3.6e9
# DC output of the battery (discharged)
E['Ebatout'] = np.sum(np.abs(Pbatout)) / 3.6e9
# Grid feed-in
E['Eac2g'] = np.sum(np.abs(Pac2g)) / 3.6e9
# Grid demand
E['Eg2ac'] = np.sum(np.abs(Pg2ac)) / 3.6e9
# Load supply by the grid
E['Eg2l'] = np.sum(np.abs(Pg2l)) / 3.6e9
# Demand of the other system components
E['Eperi'] = np.sum(np.abs(Pperi)) / 3.6e9
# Curtailed PV energy
E['Ect'] = np.sum(np.abs(Pct)) / 3.6e9
if _parameter['Top'] == 'AC':
# AC output of the PV system including curtailment
E['Epvs']=np.sum(np.abs(Ppvs)) / 3.6e9
# AC input of the battery system
E['Eac2bs']=np.sum(np.abs(Pac2bs)) / 3.6e9
# AC output of the battery system
E['Ebs2ac']=np.sum(np.abs(Pbs2ac)) / 3.6e9
# Direct use of PV energy
E['Epvs2l']=np.sum(np.abs(Ppvs2l)) / 3.6e9
# PV charging
E['Epvs2bs']=np.sum(np.abs(Ppvs2bs)) / 3.6e9
# Grid charging
E['Eg2bs']=np.sum(np.abs(Pg2bs)) / 3.6e9
# PV feed-in
E['Epvs2g']=np.sum(np.abs(Ppvs2g)) / 3.6e9
# Load supply by the battery system
E['Ebs2l']=np.sum( | np.abs(Pbs2l) | numpy.abs |
#!/usr/bin/env python
"""
Interpolation of scattered data using ordinary kriging/collocation
The program uses nearest neighbors interpolation and selects data from eight
quadrants around the prediction point and uses a third-order Gauss-Markov
covariance model, with a correlation length defined by the user.
Provides the possibility of pre-cleaning of the data using a spatial n-sigma
filter before interpolation.
Observations with provided noise/error estimates (for each observation) are
added to the diagonal of the covariance matrix if provided. User can also
provide a constant rms-noise added to the diagonal.
Takes as input a h5df file with needed data in geographical coordinates
and a-priori error if needed. The user provides the wanted projection
using the EPSG projection format.
Output consists of an hdf5 file containing the predictions, rmse and the
number of points used in the prediction, and the epsg number for the
projection.
Notes:
If both the a-priori errors are provided and constant rms all values
smaller then provided rms is set to this value providing a minimum
error for the observations.
To reduce the impact of highly correlated along-track measurements
(seen as streaks in the interpolated raster) the 'rand' option
can be used. This randomly samples N-observations in each quadrant
instead of using the closest data points.
Example:
python interpkrig.py ifile.h5 ofile.h5 -d 10 10 -n 25 -r 50 -a 25 -p 3031 \
-c 50 10 -v lon lat dhdt dummy -e 0.1 -m dist
python interpkrig.py ifile.h5 ofile.h5 -d 10 10 -n 25 -r 50 -a 25 -p 3031 \
-c 50 10 -v lon lat dhdt rmse -e 0.1 -m rand
Credits:
captoolkit - JPL Cryosphere Altimetry Processing Toolkit
<NAME> (<EMAIL>)
<NAME> (<EMAIL>)
<NAME> (<EMAIL>)
Jet Propulsion Laboratory, California Institute of Technology
"""
import h5py
import pyproj
import argparse
import numpy as np
from scipy import stats
from scipy.spatial import cKDTree
from scipy.spatial.distance import cdist
def rand(x, n):
"""Draws random samples from array"""
# Determine data density
if len(x) > n:
# Draw random samples from array
I = np.random.choice(np.arange(len(x)), n, replace=False)
else:
# Output boolean vector - true
I = np.ones(len(x), dtype=bool)
return I
def sort_dist(d, n):
""" Sort array by distance"""
# Determine if sorting needed
if len(d) >= n:
# Sort according to distance
I = np.argsort(d)
else:
# Output boolean vector - true
I = np.ones(len(x), dtype=bool)
return I
def transform_coord(proj1, proj2, x, y):
"""Transform coordinates from proj1 to proj2 (EPSG num)."""
# Set full EPSG projection strings
proj1 = pyproj.Proj("+init=EPSG:" + proj1)
proj2 = pyproj.Proj("+init=EPSG:" + proj2)
# Convert coordinates
return pyproj.transform(proj1, proj2, x, y)
def make_grid(xmin, xmax, ymin, ymax, dx, dy):
""" Construct output grid-coordinates. """
Nn = int((np.abs(ymax - ymin)) / dy) + 1 # ny
Ne = int((np.abs(xmax - xmin)) / dx) + 1 # nx
xi = np.linspace(xmin, xmax, num=Ne)
yi = np.linspace(ymin, ymax, num=Nn)
return np.meshgrid(xi, yi)
def spatial_filter(x, y, z, dx, dy, sigma=5.0):
""" Cleaning of spatial data """
# Grid dimensions
Nn = int((np.abs(y.max() - y.min())) / dy) + 1
Ne = int((np.abs(x.max() - x.min())) / dx) + 1
# Bin data
f_bin = stats.binned_statistic_2d(x, y, z, bins=(Ne, Nn))
# Get bin numbers for the data
index = f_bin.binnumber
# Unique indexes
ind = np.unique(index)
# Create output
zo = z.copy()
# Number of unique index
for i in range(len(ind)):
# index for each bin
idx, = np.where(index == ind[i])
# Get data
zb = z[idx]
# Make sure we have enough
if len(zb[~ | np.isnan(zb) | numpy.isnan |
import os
import sys
import yaml
import numpy as np
import torch
import torch.utils.data as data
import numpy as np
import numpy.random as npr
import cv2
import copy
import glob
import scipy
import datasets
from config.config import cfg
from transforms3d.quaternions import mat2quat, quat2mat
from utils.se3 import *
from utils.pose_error import *
from utils.cython_bbox import bbox_overlaps
_SUBJECTS = [
'20200709-subject-01',
'20200813-subject-02',
'20200820-subject-03',
'20200903-subject-04',
'20200908-subject-05',
'20200918-subject-06',
'20200928-subject-07',
'20201002-subject-08',
'20201015-subject-09',
'20201022-subject-10',
]
_SERIALS = [
'836212060125',
'839512060362',
'840412060917',
'841412060263',
'932122060857',
'932122060861',
'932122061900',
'932122062010',
]
_YCB_CLASSES = {
1: '002_master_chef_can',
2: '003_cracker_box',
3: '004_sugar_box',
4: '005_tomato_soup_can',
5: '006_mustard_bottle',
6: '007_tuna_fish_can',
7: '008_pudding_box',
8: '009_gelatin_box',
9: '010_potted_meat_can',
10: '011_banana',
11: '019_pitcher_base',
12: '021_bleach_cleanser',
13: '024_bowl',
14: '025_mug',
15: '035_power_drill',
16: '036_wood_block',
17: '037_scissors',
18: '040_large_marker',
19: '051_large_clamp',
20: '052_extra_large_clamp',
21: '061_foam_brick',
}
_MANO_JOINTS = [
'wrist',
'thumb_mcp',
'thumb_pip',
'thumb_dip',
'thumb_tip',
'index_mcp',
'index_pip',
'index_dip',
'index_tip',
'middle_mcp',
'middle_pip',
'middle_dip',
'middle_tip',
'ring_mcp',
'ring_pip',
'ring_dip',
'ring_tip',
'little_mcp',
'little_pip',
'little_dip',
'little_tip'
]
_MANO_JOINT_CONNECT = [
[0, 1], [ 1, 2], [ 2, 3], [ 3, 4],
[0, 5], [ 5, 6], [ 6, 7], [ 7, 8],
[0, 9], [ 9, 10], [10, 11], [11, 12],
[0, 13], [13, 14], [14, 15], [15, 16],
[0, 17], [17, 18], [18, 19], [19, 20],
]
_BOP_EVAL_SUBSAMPLING_FACTOR = 4
class dex_ycb_dataset(data.Dataset):
def __init__(self, setup, split, obj_list):
self._setup = setup
self._split = split
self._color_format = "color_{:06d}.jpg"
self._depth_format = "aligned_depth_to_color_{:06d}.png"
self._label_format = "labels_{:06d}.npz"
self._height = 480
self._width = 640
# paths
self._name = 'dex_ycb_' + setup + '_' + split
self._image_set = split
self._dex_ycb_path = self._get_default_path()
path = os.path.join(self._dex_ycb_path, 'data')
self._data_dir = path
self._calib_dir = os.path.join(self._data_dir, "calibration")
self._model_dir = os.path.join(self._data_dir, "models")
self._obj_file = {
k: os.path.join(self._model_dir, v, "textured_simple.obj")
for k, v in _YCB_CLASSES.items()
}
# define all the classes
self._classes_all = ('002_master_chef_can', '003_cracker_box', '004_sugar_box', '005_tomato_soup_can', '006_mustard_bottle', \
'007_tuna_fish_can', '008_pudding_box', '009_gelatin_box', '010_potted_meat_can', '011_banana', '019_pitcher_base', \
'021_bleach_cleanser', '024_bowl', '025_mug', '035_power_drill', '036_wood_block', '037_scissors', '040_large_marker', \
'051_large_clamp', '052_extra_large_clamp', '061_foam_brick')
self._num_classes_all = len(self._classes_all)
self._class_colors_all = [(255, 0, 0), (0, 255, 0), (0, 0, 255), (255, 255, 0), (255, 0, 255), (0, 255, 255), \
(128, 0, 0), (0, 128, 0), (0, 0, 128), (128, 128, 0), (128, 0, 128), (0, 128, 128), \
(64, 0, 0), (0, 64, 0), (0, 0, 64), (64, 64, 0), (64, 0, 64), (0, 64, 64),
(192, 0, 0), (0, 192, 0), (0, 0, 192)]
self._extents_all = self._load_object_extents()
self._posecnn_class_indexes = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21]
# compute class index
class_index = []
for name in obj_list:
for i in range(self._num_classes_all):
if name == self._classes_all[i]:
class_index.append(i)
break
print('class index:', class_index)
self._class_index = class_index
# select a subset of classes
self._classes = obj_list
self._num_classes = len(self._classes)
self._class_colors = [self._class_colors_all[i] for i in class_index]
self._extents = self._extents_all[class_index]
self._points, self._points_all = self._load_object_points(self._classes, self._extents)
# Seen subjects, camera views, grasped objects.
if self._setup == 's0':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 != 4]
if self._split == 'val':
subject_ind = [0, 1]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 == 4]
if self._split == 'test':
subject_ind = [2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 == 4]
# Unseen subjects.
if self._setup == 's1':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
if self._split == 'val':
subject_ind = [6]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
if self._split == 'test':
subject_ind = [7, 8]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
# Unseen camera views.
if self._setup == 's2':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5]
sequence_ind = list(range(100))
if self._split == 'val':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [6]
sequence_ind = list(range(100))
if self._split == 'test':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [7]
sequence_ind = list(range(100))
# Unseen grasped objects.
if self._setup == 's3':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [
i for i in range(100) if i // 5 not in (3, 7, 11, 15, 19)
]
if self._split == 'val':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i // 5 in (3, 19)]
if self._split == 'test':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i // 5 in (7, 11, 15)]
self._subjects = [_SUBJECTS[i] for i in subject_ind]
self._serials = [_SERIALS[i] for i in serial_ind]
self._intrinsics = []
for s in self._serials:
intr_file = os.path.join(self._calib_dir, "intrinsics", "{}_{}x{}.yml".format(s, self._width, self._height))
with open(intr_file, 'r') as f:
intr = yaml.load(f, Loader=yaml.FullLoader)
intr = intr['color']
self._intrinsics.append(intr)
# build mapping
self._sequences = []
self._mapping = []
self._ycb_ids = []
offset = 0
for n in self._subjects:
seq = sorted(os.listdir(os.path.join(self._data_dir, n)))
seq = [os.path.join(n, s) for s in seq]
assert len(seq) == 100
seq = [seq[i] for i in sequence_ind]
self._sequences += seq
for i, q in enumerate(seq):
meta_file = os.path.join(self._data_dir, q, "meta.yml")
with open(meta_file, 'r') as f:
meta = yaml.load(f, Loader=yaml.FullLoader)
c = np.arange(len(self._serials))
f = np.arange(meta['num_frames'])
f, c = np.meshgrid(f, c)
c = c.ravel()
f = f.ravel()
s = (offset + i) * np.ones_like(c)
m = np.vstack((s, c, f)).T
self._mapping.append(m)
self._ycb_ids.append(meta['ycb_ids'])
offset += len(seq)
self._mapping = np.vstack(self._mapping)
# sample a subset for training
if split == 'train':
self._mapping = self._mapping[::10]
# dataset size
self._size = len(self._mapping)
print('dataset %s with images %d' % (self._name, self._size))
def __len__(self):
return self._size
def get_bop_id_from_idx(self, idx):
s, c, f = map(lambda x: x.item(), self._mapping[idx])
scene_id = s * len(self._serials) + c
im_id = f
return scene_id, im_id
def __getitem__(self, idx):
s, c, f = self._mapping[idx]
is_testing = f % _BOP_EVAL_SUBSAMPLING_FACTOR == 0
if self._split == 'test' and not is_testing:
sample = {'is_testing': is_testing}
return sample
scene_id, im_id = self.get_bop_id_from_idx(idx)
video_id = '%04d' % (scene_id)
image_id = '%06d' % (im_id)
# posecnn result path
posecnn_result_path = os.path.join(self._dex_ycb_path, 'results_posecnn', self._name, 'vgg16_dex_ycb_epoch_16.checkpoint.pth',
video_id + '_' + image_id + '.mat')
d = os.path.join(self._data_dir, self._sequences[s], self._serials[c])
roidb = {
'color_file': os.path.join(d, self._color_format.format(f)),
'depth_file': os.path.join(d, self._depth_format.format(f)),
'label_file': os.path.join(d, self._label_format.format(f)),
'intrinsics': self._intrinsics[c],
'ycb_ids': self._ycb_ids[s],
'posecnn': posecnn_result_path,
}
# Get the input image blob
im_color, im_depth = self._get_image_blob(roidb['color_file'], roidb['depth_file'])
# build the label blob
im_label, intrinsic_matrix, poses, gt_boxes, poses_result, rois_result, labels_result \
= self._get_label_blob(roidb, self._num_classes)
is_syn = 0
im_scale = 1.0
im_info = np.array([im_color.shape[1], im_color.shape[2], im_scale, is_syn], dtype=np.float32)
sample = {'image_color': im_color[:, :, (2, 1, 0)],
'image_depth': im_depth,
'label': im_label,
'intrinsic_matrix': intrinsic_matrix,
'gt_poses': poses,
'gt_boxes': gt_boxes,
'poses_result': poses_result,
'rois_result': rois_result,
'labels_result': labels_result,
'extents': self._extents,
'points': self._points_all,
'im_info': im_info,
'video_id': video_id,
'image_id': image_id}
if self._split == 'test':
sample['is_testing'] = is_testing
return sample
def _get_image_blob(self, color_file, depth_file):
# rgba
rgba = cv2.imread(color_file, cv2.IMREAD_UNCHANGED)
if rgba.shape[2] == 4:
im = np.copy(rgba[:,:,:3])
alpha = rgba[:,:,3]
I = np.where(alpha == 0)
im[I[0], I[1], :] = 0
else:
im = rgba
im_color = im.astype('float') / 255.0
# depth image
im_depth = cv2.imread(depth_file, cv2.IMREAD_UNCHANGED)
im_depth = im_depth.astype('float') / 1000.0
return im_color, im_depth
def _get_label_blob(self, roidb, num_classes):
""" build the label blob """
# parse data
cls_indexes = roidb['ycb_ids']
classes = np.array(self._class_index)
fx = roidb['intrinsics']['fx']
fy = roidb['intrinsics']['fy']
px = roidb['intrinsics']['ppx']
py = roidb['intrinsics']['ppy']
intrinsic_matrix = np.eye(3, dtype=np.float32)
intrinsic_matrix[0, 0] = fx
intrinsic_matrix[1, 1] = fy
intrinsic_matrix[0, 2] = px
intrinsic_matrix[1, 2] = py
label = np.load(roidb['label_file'])
# label image
im_label = label['seg']
# poses
poses = label['pose_y']
if len(poses.shape) == 2:
poses = np.reshape(poses, (1, 3, 4))
num = poses.shape[0]
assert num == len(cls_indexes), 'number of poses not equal to number of objects'
# bounding boxes
gt_boxes = np.zeros((num, 5), dtype=np.float32)
for i in range(num):
cls = int(cls_indexes[i]) - 1
ind = np.where(classes == cls)[0]
if len(ind) > 0:
R = poses[i, :, :3]
T = poses[i, :, 3]
# compute box
x3d = np.ones((4, self._points_all.shape[1]), dtype=np.float32)
x3d[0, :] = self._points_all[ind,:,0]
x3d[1, :] = self._points_all[ind,:,1]
x3d[2, :] = self._points_all[ind,:,2]
RT = np.zeros((3, 4), dtype=np.float32)
RT[:3, :3] = R
RT[:, 3] = T
x2d = np.matmul(intrinsic_matrix, np.matmul(RT, x3d))
x2d[0, :] = np.divide(x2d[0, :], x2d[2, :])
x2d[1, :] = np.divide(x2d[1, :], x2d[2, :])
gt_boxes[i, 0] = np.min(x2d[0, :])
gt_boxes[i, 1] = np.min(x2d[1, :])
gt_boxes[i, 2] = np.max(x2d[0, :])
gt_boxes[i, 3] = np.max(x2d[1, :])
gt_boxes[i, 4] = ind
# load posecnn result if available
if os.path.exists(roidb['posecnn']):
result = scipy.io.loadmat(roidb['posecnn'])
n = result['poses'].shape[0]
poses_result = np.zeros((n, 9), dtype=np.float32)
poses_result[:, 0] = 1
poses_result[:, 1] = result['rois'][:, 1]
poses_result[:, 2:] = result['poses']
rois_result = result['rois'].copy()
labels_result = result['labels'].copy()
# select the classes, one object per class
index = []
flags = np.zeros((self._num_classes, ), dtype=np.int32)
for i in range(poses_result.shape[0]):
cls = self._posecnn_class_indexes[int(poses_result[i, 1])] - 1
ind = np.where(classes == cls)[0]
if len(ind) > 0 and flags[ind] == 0:
index.append(i)
poses_result[i, 1] = ind
rois_result[i, 1] = ind
flags[ind] = 1
poses_result = poses_result[index, :]
rois_result = rois_result[index, :]
else:
# print('no posecnn result %s' % (roidb['posecnn']))
poses_result = np.zeros((0, 9), dtype=np.float32)
rois_result = np.zeros((0, 7), dtype=np.float32)
labels_result = np.zeros((0, 1), dtype=np.float32)
poses = poses.transpose((1, 2, 0))
return im_label, intrinsic_matrix, poses, gt_boxes, poses_result, rois_result, labels_result
def _get_default_path(self):
"""
Return the default path where YCB_Video is expected to be installed.
"""
return os.path.join(datasets.ROOT_DIR, 'data', 'DEX_YCB')
def _load_object_extents(self):
extents = np.zeros((self._num_classes_all, 3), dtype=np.float32)
for i in range(self._num_classes_all):
point_file = os.path.join(self._model_dir, self._classes_all[i], 'points.xyz')
print(point_file)
assert os.path.exists(point_file), 'Path does not exist: {}'.format(point_file)
points = np.loadtxt(point_file)
extents[i, :] = 2 * np.max(np.absolute(points), axis=0)
return extents
def _load_object_points(self, classes, extents):
points = [[] for _ in range(len(classes))]
num = np.inf
num_classes = len(classes)
for i in range(num_classes):
point_file = os.path.join(self._model_dir, classes[i], 'points.xyz')
print(point_file)
assert os.path.exists(point_file), 'Path does not exist: {}'.format(point_file)
points[i] = np.loadtxt(point_file)
if points[i].shape[0] < num:
num = points[i].shape[0]
points_all = np.zeros((num_classes, num, 3), dtype=np.float32)
for i in range(num_classes):
points_all[i, :, :] = points[i][:num, :]
return points, points_all
def write_dop_results(self, output_dir, modality):
# only write the result file
filename = os.path.join(output_dir, 'poserbpf_' + self._name + '_' + modality + '.csv')
f = open(filename, 'w')
f.write('scene_id,im_id,obj_id,score,R,t,time\n')
# list the mat file
filename = os.path.join(output_dir, '*.mat')
files = sorted(glob.glob(filename))
# for each image
for i in range(len(files)):
filename = os.path.basename(files[i])
# parse filename
pos = filename.find('_')
scene_id = int(filename[:pos])
im_id = int(filename[pos+1:-4])
# load result
print(files[i])
result = scipy.io.loadmat(files[i])
if len(result['rois']) == 0:
continue
rois = result['rois']
num = rois.shape[0]
for j in range(num):
obj_id = self._class_index[int(rois[j, 1])] + 1
if obj_id == 0:
continue
score = rois[j, -1]
run_time = -1
# pose from network
R = quat2mat(result['poses'][j, :4].flatten())
t = result['poses'][j, 4:] * 1000
line = '{scene_id},{im_id},{obj_id},{score},{R},{t},{time}\n'.format(
scene_id=scene_id,
im_id=im_id,
obj_id=obj_id,
score=score,
R=' '.join(map(str, R.flatten().tolist())),
t=' '.join(map(str, t.flatten().tolist())),
time=run_time)
f.write(line)
# close file
f.close()
# compute box
def compute_box(self, cls, intrinsic_matrix, RT):
ind = np.where(self._class_index == cls)[0]
x3d = np.ones((4, self._points_all.shape[1]), dtype=np.float32)
x3d[0, :] = self._points_all[ind,:,0]
x3d[1, :] = self._points_all[ind,:,1]
x3d[2, :] = self._points_all[ind,:,2]
x2d = np.matmul(intrinsic_matrix, np.matmul(RT, x3d))
x2d[0, :] = np.divide(x2d[0, :], x2d[2, :])
x2d[1, :] = np.divide(x2d[1, :], x2d[2, :])
x1 = np.min(x2d[0, :])
y1 = np.min(x2d[1, :])
x2 = np.max(x2d[0, :])
y2 = np.max(x2d[1, :])
return [x1, y1, x2, y2]
def evaluation(self, output_dir, modality):
self.write_dop_results(output_dir, modality)
filename = os.path.join(output_dir, 'results_poserbpf.mat')
if os.path.exists(filename):
results_all = scipy.io.loadmat(filename)
print('load results from file')
print(filename)
distances_sys = results_all['distances_sys']
distances_non = results_all['distances_non']
errors_rotation = results_all['errors_rotation']
errors_translation = results_all['errors_translation']
results_seq_id = results_all['results_seq_id'].flatten()
results_frame_id = results_all['results_frame_id'].flatten()
results_object_id = results_all['results_object_id'].flatten()
results_cls_id = results_all['results_cls_id'].flatten()
else:
# save results
num_max = 200000
num_results = 1
distances_sys = np.zeros((num_max, num_results), dtype=np.float32)
distances_non = np.zeros((num_max, num_results), dtype=np.float32)
errors_rotation = np.zeros((num_max, num_results), dtype=np.float32)
errors_translation = np.zeros((num_max, num_results), dtype=np.float32)
results_seq_id = np.zeros((num_max, ), dtype=np.float32)
results_frame_id = np.zeros((num_max, ), dtype=np.float32)
results_object_id = np.zeros((num_max, ), dtype=np.float32)
results_cls_id = np.zeros((num_max, ), dtype=np.float32)
# for each image
count = -1
for i in range(len(self._mapping)):
s, c, f = self._mapping[i]
is_testing = f % _BOP_EVAL_SUBSAMPLING_FACTOR == 0
if not is_testing:
continue
# intrinsics
intrinsics = self._intrinsics[c]
intrinsic_matrix = np.eye(3, dtype=np.float32)
intrinsic_matrix[0, 0] = intrinsics['fx']
intrinsic_matrix[1, 1] = intrinsics['fy']
intrinsic_matrix[0, 2] = intrinsics['ppx']
intrinsic_matrix[1, 2] = intrinsics['ppy']
# parse keyframe name
scene_id, im_id = self.get_bop_id_from_idx(i)
# load result
filename = os.path.join(output_dir, '%04d_%06d.mat' % (scene_id, im_id))
print(filename)
result = scipy.io.loadmat(filename)
# load gt
d = os.path.join(self._data_dir, self._sequences[s], self._serials[c])
label_file = os.path.join(d, self._label_format.format(f))
label = np.load(label_file)
cls_indexes = np.array(self._ycb_ids[s]).flatten()
# poses
poses = label['pose_y']
if len(poses.shape) == 2:
poses = np.reshape(poses, (1, 3, 4))
num = poses.shape[0]
assert num == len(cls_indexes), 'number of poses not equal to number of objects'
# instance label
im_label = label['seg']
instance_ids = np.unique(im_label)
if instance_ids[0] == 0:
instance_ids = instance_ids[1:]
if instance_ids[-1] == 255:
instance_ids = instance_ids[:-1]
# for each gt poses
for j in range(len(instance_ids)):
cls = instance_ids[j]
# find the number of pixels of the object
pixels = np.sum(im_label == cls)
if pixels < 200:
continue
count += 1
# find the pose
object_index = np.where(cls_indexes == cls)[0][0]
RT_gt = poses[object_index, :, :]
box_gt = self.compute_box(cls - 1, intrinsic_matrix, RT_gt)
results_seq_id[count] = scene_id
results_frame_id[count] = im_id
results_object_id[count] = object_index
results_cls_id[count] = cls
# network result
roi_index = []
if len(result['rois']) > 0:
for k in range(result['rois'].shape[0]):
ind = int(result['rois'][k, 1])
if cls == self._class_index[ind] + 1:
roi_index.append(k)
# select the roi
if len(roi_index) > 1:
# overlaps: (rois x gt_boxes)
roi_blob = result['rois'][roi_index, :]
roi_blob = roi_blob[:, (0, 2, 3, 4, 5, 1)]
gt_box_blob = np.zeros((1, 5), dtype=np.float32)
gt_box_blob[0, 1:] = box_gt
overlaps = bbox_overlaps(
np.ascontiguousarray(roi_blob[:, :5], dtype=np.float),
np.ascontiguousarray(gt_box_blob, dtype=np.float)).flatten()
assignment = overlaps.argmax()
roi_index = [roi_index[assignment]]
if len(roi_index) > 0:
RT = np.zeros((3, 4), dtype=np.float32)
ind = int(result['rois'][roi_index, 1])
points = self._points[ind]
# pose from network
RT[:3, :3] = quat2mat(result['poses'][roi_index, :4].flatten())
RT[:, 3] = result['poses'][roi_index, 4:]
distances_sys[count, 0] = adi(RT[:3, :3], RT[:, 3], RT_gt[:3, :3], RT_gt[:, 3], points)
distances_non[count, 0] = add(RT[:3, :3], RT[:, 3], RT_gt[:3, :3], RT_gt[:, 3], points)
errors_rotation[count, 0] = re(RT[:3, :3], RT_gt[:3, :3])
errors_translation[count, 0] = te(RT[:, 3], RT_gt[:, 3])
else:
distances_sys[count, :] = np.inf
distances_non[count, :] = np.inf
errors_rotation[count, :] = np.inf
errors_translation[count, :] = np.inf
distances_sys = distances_sys[:count+1, :]
distances_non = distances_non[:count+1, :]
errors_rotation = errors_rotation[:count+1, :]
errors_translation = errors_translation[:count+1, :]
results_seq_id = results_seq_id[:count+1]
results_frame_id = results_frame_id[:count+1]
results_object_id = results_object_id[:count+1]
results_cls_id = results_cls_id[:count+1]
results_all = {'distances_sys': distances_sys,
'distances_non': distances_non,
'errors_rotation': errors_rotation,
'errors_translation': errors_translation,
'results_seq_id': results_seq_id,
'results_frame_id': results_frame_id,
'results_object_id': results_object_id,
'results_cls_id': results_cls_id }
filename = os.path.join(output_dir, 'results_poserbpf.mat')
scipy.io.savemat(filename, results_all)
# print the results
# for each class
import matplotlib.pyplot as plt
max_distance = 0.1
index_plot = [0]
color = ['r']
leng = ['PoseRBPF']
num = len(leng)
ADD = np.zeros((self._num_classes_all + 1, num), dtype=np.float32)
ADDS = np.zeros((self._num_classes_all + 1, num), dtype=np.float32)
TS = np.zeros((self._num_classes_all + 1, num), dtype=np.float32)
classes = list(copy.copy(self._classes_all))
classes.append('all')
for k in range(self._num_classes_all + 1):
fig = plt.figure(figsize=(16.0, 10.0))
if k == self._num_classes_all:
index = range(len(results_cls_id))
else:
index = np.where(results_cls_id == k + 1)[0]
if len(index) == 0:
continue
print('%s: %d objects' % (classes[k], len(index)))
# distance symmetry
ax = fig.add_subplot(2, 3, 1)
lengs = []
for i in index_plot:
D = distances_sys[index, i]
ind = np.where(D > max_distance)[0]
D[ind] = np.inf
d = np.sort(D)
n = len(d)
accuracy = np.cumsum(np.ones((n, ), np.float32)) / n
plt.plot(d, accuracy, color[i], linewidth=2)
ADDS[k, i] = VOCap(d, accuracy)
lengs.append('%s (%.2f)' % (leng[i], ADDS[k, i] * 100))
print('%s, %s: %d objects missed' % (classes[k], leng[i], np.sum(np.isinf(D))))
ax.legend(lengs)
plt.xlabel('Average distance threshold in meter (symmetry)')
plt.ylabel('accuracy')
ax.set_title(classes[k])
# distance non-symmetry
ax = fig.add_subplot(2, 3, 2)
lengs = []
for i in index_plot:
D = distances_non[index, i]
ind = np.where(D > max_distance)[0]
D[ind] = np.inf
d = np.sort(D)
n = len(d)
accuracy = np.cumsum(np.ones((n, ), np.float32)) / n
plt.plot(d, accuracy, color[i], linewidth=2)
ADD[k, i] = VOCap(d, accuracy)
lengs.append('%s (%.2f)' % (leng[i], ADD[k, i] * 100))
print('%s, %s: %d objects missed' % (classes[k], leng[i], np.sum(np.isinf(D))))
ax.legend(lengs)
plt.xlabel('Average distance threshold in meter (non-symmetry)')
plt.ylabel('accuracy')
ax.set_title(classes[k])
# translation
ax = fig.add_subplot(2, 3, 3)
lengs = []
for i in index_plot:
D = errors_translation[index, i]
ind = np.where(D > max_distance)[0]
D[ind] = np.inf
d = np.sort(D)
n = len(d)
accuracy = np.cumsum(np.ones((n, ), np.float32)) / n
plt.plot(d, accuracy, color[i], linewidth=2)
TS[k, i] = VOCap(d, accuracy)
lengs.append('%s (%.2f)' % (leng[i], TS[k, i] * 100))
print('%s, %s: %d objects missed' % (classes[k], leng[i], np.sum( | np.isinf(D) | numpy.isinf |
"""
This script contains all necessary code to extract and convert the patients data from the Sciensano hospital survey into parameters usable by the BIOMATH COVID-19 SEIRD model.
You must place the super secret detailed hospitalization dataset `COVID19BE_CLINIC.csv` in the same folder as this script in order to run it.
Further, you must MANUALLY replace décédé and rétabli in the file `COVID19BE_CLINIC.csv` with D and R.
To load the resulting .xlsx into a pandas dataframe use:
dataframe = pd.read_excel('../../data/interim/model_parameters/COVID19_SEIRD/sciensano_hospital_parameters.xlsx', sheet_name='residence_times', index_col=0, header=[0,1])
"""
__author__ = "<NAME>"
__copyright__ = "Copyright (c) 2020 by <NAME>, BIOMATH, Ghent University. All Rights Reserved."
# ----------------------
# Load required packages
# ----------------------
import os
import math
import numpy as np
import pandas as pd
from scipy.stats import mannwhitneyu, ttest_ind, gamma, exponweib, weibull_min
import matplotlib.pyplot as plt
import datetime
from datetime import timedelta
import argparse
# ----------------
# Script arguments
# ----------------
parser = argparse.ArgumentParser()
parser.add_argument("-s", "--subset_size", help="Size of subset drawn from total population during bootstrapping", default=1000, type=int)
parser.add_argument("-n", "--number_iterations", help="Total number of bootstraps", default=100, type=int)
parser.add_argument("-a", "--age_stratification_size", help="Total number of age groups", default=9, type=int)
# Save as dict
args = parser.parse_args()
# Set correct age_classes
if args.age_stratification_size == 3:
age_classes = pd.IntervalIndex.from_tuples([(0,20),(20,60),(60,120)], closed='left')
age_path = '0_20_60/'
elif args.age_stratification_size == 9:
age_classes = pd.IntervalIndex.from_tuples([(0,10),(10,20),(20,30),(30,40),(40,50),(50,60),(60,70),(70,80),(80,120)], closed='left')
age_path = '0_10_20_30_40_50_60_70_80/'
elif args.age_stratification_size == 10:
age_classes =pd.IntervalIndex.from_tuples([(0,12),(12,18),(18,25),(25,35),(35,45),(45,55),(55,65),(65,75),(75,85),(85,120)], closed='left')
age_path = '0_12_18_25_35_45_55_65_75_85/'
else:
raise ValueError(
"age_stratification_size '{0}' is not legitimate. Valid options are 3, 9 or 10".format(args.age_stratification_size)
)
# -----
# Paths
# -----
fig_path = '../../results/analysis/hospital/'+age_path
data_path = '../../data/interim/model_parameters/COVID19_SEIQRD/hospitals/' + age_path
# Verify that the paths exist and if not, generate them
for directory in [fig_path, data_path]:
if not os.path.exists(directory):
os.makedirs(directory)
# -----------------------------
# Helper functions and settings
# -----------------------------
plot_fit=False
colorscale_okabe_ito = {"orange" : "#E69F00", "light_blue" : "#56B4E9",
"green" : "#009E73", "yellow" : "#F0E442",
"blue" : "#0072B2", "red" : "#D55E00",
"pink" : "#CC79A7", "black" : "#000000"}
def adjacent_values(vals, q1, q3):
upper_adjacent_value = q3 + (q3 - q1) * 1.5
upper_adjacent_value = np.clip(upper_adjacent_value, q3, vals[-1])
lower_adjacent_value = q1 - (q3 - q1) * 1.5
lower_adjacent_value = np.clip(lower_adjacent_value, vals[0], q1)
return lower_adjacent_value, upper_adjacent_value
def set_axis_style(ax, labels):
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(labels)
ax.set_xlim(0.25, len(labels) + 0.75)
ax.set_xlabel('Sample name')
def fit_weibull(v):
sample_size_lst=[]
shape_lst=[]
loc_lst=[]
scale_lst=[]
for age_group in v.index.get_level_values(0).unique().values:
if isinstance(v[age_group],list):
values = [x for x in v[age_group] if (math.isnan(x) == False)]
shape, loc, scale = weibull_min.fit(values,floc=0)
sample_size_lst.append(len(v[age_group]))
else:
v[age_group][v[age_group]==0] = 0.01
v = v.dropna()
shape, loc, scale = weibull_min.fit(v[age_group].values,floc=0)
sample_size_lst.append(len(v[age_group].values))
shape_lst.append(shape)
loc_lst.append(loc)
scale_lst.append(scale)
return sample_size_lst, shape_lst, loc_lst, scale_lst
def plot_weibull_fit(v,par,max_val):
fig,axes = plt.subplots(nrows=3,ncols=3,sharex=True,figsize=(12,12))
axes = axes.flatten()
for idx,age_group in enumerate(v.index.get_level_values(0).unique().values):
bins = np.linspace(0, max_val, 10)
axes[idx].hist(v[age_group], bins=bins, density=True)
x = np.linspace (0.5, max_val, 1000)
#y = gamma.pdf(x, a=residence_times[par,'shape'][age_group], loc=residence_times[par,'loc'][age_group], scale=residence_times[par,'scale'][age_group])
y = weibull_min.pdf(x, c=residence_times[par,'shape'][age_group], loc=residence_times[par,'loc'][age_group], scale=residence_times[par,'scale'][age_group])
axes[idx].plot(x,y)
axes[idx].text(x=0.70,y=0.82,s='Shape: '+"{:.2f}".format(residence_times[par,'shape'][age_group]) + '\nScale: ' + "{:.2f}".format(residence_times[par,'scale'][age_group]) + '\nLoc: '+ "{:.2f}".format(residence_times[par,'loc'][age_group]), transform=axes[idx].transAxes, fontsize=8)
axes[idx].set_title('Age group: ' + str(age_group), fontsize=12)
axes[idx].set_xlim([0,max_val])
fig.suptitle(par,fontsize=16)
plt.show()
plt.close()
#######################################################
## Load and format Sciensano hospital survey dataset ##
#######################################################
df = pd.read_csv('COVID19BE_CLINIC.csv')
n_orig = df.shape[0]
print('The original dataset contains ' + str(n_orig) + ' entries.')
# Drop the columns on admission_data and discharge_data --> do this myself
df=df.drop(columns=['admission_data','discharge_data'])
# Drop the columns with missing age
df.dropna(subset=['age'], inplace=True)
n_filtering_age = df.shape[0]
print(str(n_orig-n_filtering_age) + ' entries were removed because the age was missing.')
# Only if admission data, discharge data, status of discharge and ICU transfer is known, the data can be used by our model
df.dropna(subset=['dt_admission'], inplace=True)
df.dropna(subset=['dt_discharge'], inplace=True)
df.dropna(subset=['status_discharge'], inplace=True)
df.dropna(subset=['ICU_transfer'], inplace=True)
df.drop(df[df.status_discharge == 'Autre'].index, inplace=True)
df.drop(df[df.status_discharge == 'Inconnu'].index, inplace=True)
df.drop(df[df.status_discharge == 'Transfert'].index, inplace=True)
n_filtering_dates = df.shape[0]
print(str(n_filtering_age-n_filtering_dates) + ' entries were removed because the admission date, discharge date, status at discharge or ICU transfer was missing.')
# Convert dates to pd.datetimes
df['dt_admission'] = pd.to_datetime(df['dt_admission'])
df['dt_admission'] = df['dt_admission'].dt.date
df['dt_discharge'] = pd.to_datetime(df['dt_discharge'])
df['dt_discharge'] = df['dt_discharge'].dt.date
df['dt_onset'] = pd.to_datetime(df['dt_onset'])
df['dt_onset'] = df['dt_onset'].dt.date
df['dt_icu_transfer'] = pd.to_datetime(df['dt_icu_transfer'])
df['dt_icu_transfer'] = df['dt_icu_transfer'].dt.date
# Add column with the age classes
df['age_class'] = pd.cut(df.age, bins=age_classes)
# Remove the negative residence times
df.drop(df[((df['dt_discharge'] - df['dt_admission'])/datetime.timedelta(days=1)) < 0].index, inplace=True)
# Remove the negative admission to onset times
df.drop(df[((df['dt_admission'] - df['dt_onset'])/datetime.timedelta(days=1)) < 0].index, inplace=True)
# Remove all residence times larger than 180 days
df.drop(df[((df['dt_discharge'] - df['dt_admission'])/datetime.timedelta(days=1)) >= 180].index, inplace=True)
n_filtering_times = df.shape[0]
print(str(n_filtering_dates-n_filtering_times) + ' entries were removed because the residence time or onset time were negative.')
# Drop retirement home patients from dataset
exclude_homes = True
if exclude_homes:
df.drop(df[df.Expo_retirement_home == 'Oui'].index, inplace=True)
n_filtering_homes = df.shape[0]
print(str(n_filtering_times-n_filtering_homes) + ' additional entries were removed because the patient came from a retirement home.')
# Print a summary of the filtering
print(str(n_orig-n_filtering_homes)+' entries were removed during filtering. '+str(n_filtering_homes)+' entries remained.')
else:
# Print a summary of the filtering
print(str(n_orig-n_filtering_times)+' entries were removed during filtering. '+str(n_filtering_times)+' entries remained.')
###################################################
## Compute fractions: c, m0, m0_{ICU} and m0_{C} ##
###################################################
quantiles = [25,75,2.5,97.5]
# ------------------------------------------------------
# Initialize dataframe for results and population totals
# ------------------------------------------------------
columns = [[],[]]
tuples = list(zip(*columns))
columns = pd.MultiIndex.from_tuples(tuples, names=["parameter", "quantity"])
fractions = pd.DataFrame(index=age_classes, columns=columns)
averages = pd.DataFrame(index=['population'],columns=columns)
# -------------------------------------------
# Compute fraction parameters point estimates
# -------------------------------------------
# Sample size
fractions['total_sample_size','point estimate']=df.groupby(by='age_class').apply(lambda x: x.age.count())
# Hospitalization propensity
fractions['admission_propensity','point estimate']=df.groupby(by='age_class').apply(lambda x: x.age.count())/df.shape[0]
# Distribution cohort/icu
fractions['c','point estimate'] = df.groupby(by='age_class').apply(lambda x: x[x.ICU_transfer=='Non'].age.count()/x[x.ICU_transfer.isin(['Oui', 'Non'])].age.count())
# Mortalities
fractions['m0','point estimate']=df.groupby(by='age_class').apply(
lambda x: x[( (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Oui', 'Non'])].age.count())
fractions['m0_{ICU}','point estimate']= df.groupby(by='age_class').apply(
lambda x: x[((x.ICU_transfer=='Oui') & (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Oui'])].age.count())
fractions['m0_{C}','point estimate']= df.groupby(by='age_class').apply(
lambda x: x[((x.ICU_transfer=='Non') & (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Non'])].age.count())
# -----------------------------
# Bootstrap fraction parameters
# -----------------------------
subset_size = args.subset_size
n = args.number_iterations
# First initialize a numpy array for the results
# First axis: parameter: c, m0, m0_C, m0_ICU
# Second axis: age group
# Third axis: bootstrap sample
bootstrap_fractions_age = np.zeros([4, len(age_classes), n])
# Loop over parameters
for idx in range(4):
for jdx in range(n):
smpl = df.groupby(by='age_class').apply(lambda x: x.sample(n=subset_size,replace=True))
smpl=smpl.drop(columns='age_class')
if idx == 0:
bootstrap_fractions_age[idx,:,jdx] = smpl.groupby(by='age_class').apply(lambda x: x[x.ICU_transfer=='Non'].age.count()/
x[x.ICU_transfer.isin(['Oui', 'Non'])].age.count()).values
elif idx == 1:
bootstrap_fractions_age[idx,:,jdx] = smpl.groupby(by='age_class').apply(lambda x: x[( (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Oui', 'Non'])].age.count()).values
elif idx == 2:
bootstrap_fractions_age[idx,:,jdx] = smpl.groupby(by='age_class').apply(lambda x: x[((x.ICU_transfer=='Non') & (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Non'])].age.count()).values
elif idx == 3:
bootstrap_fractions_age[idx,:,jdx] = smpl.groupby(by='age_class').apply(lambda x: x[((x.ICU_transfer=='Oui') & (x.status_discharge=='D'))].age.count()/
x[x.ICU_transfer.isin(['Oui'])].age.count()).values
# Compute summary statistics
for idx,par in enumerate(['c', 'm0', 'm0_{C}', 'm0_{ICU}']):
fractions[par,'bootstrap mean'] = np.median(bootstrap_fractions_age[idx,:,:], axis=1)
fractions[par,'bootstrap median'] = np.median(bootstrap_fractions_age[idx,:,:], axis=1)
for quantile in quantiles:
fractions[par,'bootstrap Q'+str(quantile)] = np.quantile(bootstrap_fractions_age[idx,:,:], q=quantile/100, axis=1)
# Save raw samples as a .npy
with open(data_path+'sciensano_bootstrap_fractions.npy', 'wb') as f:
np.save(f,bootstrap_fractions_age)
# Compute population average/total point estimate
averages['total_sample_size','point estimate'] = fractions['total_sample_size','point estimate'].sum()
averages['admission_propensity', 'point estimate'] = sum(((fractions['total_sample_size','point estimate']*fractions['admission_propensity', 'point estimate']).values)/(np.ones(len(age_classes))*fractions['total_sample_size', 'point estimate'].sum()))
averages['c', 'point estimate'] = df[df.ICU_transfer=='Non'].age.count()/df[df.ICU_transfer.isin(['Oui', 'Non'])].age.count()
averages['m0', 'point estimate'] = df[((df.status_discharge=='D'))].age.count()/df[df.ICU_transfer.isin(['Oui', 'Non'])].age.count()
averages['m0_{ICU}', 'point estimate'] = df[((df.ICU_transfer=='Oui') & (df.status_discharge=='D'))].age.count()/df[df.ICU_transfer.isin(['Oui'])].age.count()
averages['m0_{C}', 'point estimate'] = df[((df.ICU_transfer=='Non') & (df.status_discharge=='D'))].age.count()/df[df.ICU_transfer.isin(['Non'])].age.count()
# Bootstrap total population
bootstrap_fractions = np.zeros([4, n])
# Loop over parameters
for idx in range(4):
for jdx in range(n):
smpl = df.sample(n=subset_size,replace=True)
if idx == 0:
bootstrap_fractions[idx,jdx] = smpl[smpl.ICU_transfer=='Non'].age.count()/smpl[smpl.ICU_transfer.isin(['Oui', 'Non'])].age.count()
elif idx == 1:
bootstrap_fractions[idx,jdx] = smpl[((smpl.status_discharge=='D'))].age.count()/smpl[smpl.ICU_transfer.isin(['Oui', 'Non'])].age.count()
elif idx == 2:
bootstrap_fractions[idx,jdx] = smpl[((smpl.ICU_transfer=='Non') & (smpl.status_discharge=='D'))].age.count()/smpl[smpl.ICU_transfer.isin(['Non'])].age.count()
elif idx == 3:
bootstrap_fractions[idx,jdx] = smpl[((smpl.ICU_transfer=='Oui') & (smpl.status_discharge=='D'))].age.count()/smpl[smpl.ICU_transfer.isin(['Oui'])].age.count()
# Compute summary statistics
for idx,par in enumerate(['c', 'm0', 'm0_{C}', 'm0_{ICU}']):
averages[par,'bootstrap mean'] = np.median(bootstrap_fractions[idx,:])
averages[par,'bootstrap median'] = np.median(bootstrap_fractions[idx,:])
for quantile in quantiles:
averages[par,'bootstrap Q'+str(quantile)] = np.quantile(bootstrap_fractions[idx,:], q=quantile/100)
# -------------------------------------------
# Perform Mann-Whitney U-tests on mortalities
# -------------------------------------------
# Difference in mortality, ICU vs. Cohort
# Boxplot
x = bootstrap_fractions[2,:]
y = bootstrap_fractions[3,:]
stat, p_tt = ttest_ind(x, y)
stat, p_mwu = mannwhitneyu(x, y)
fig, ax = plt.subplots(figsize=(8,6))
bp = ax.boxplot([x, y], positions=[1,2])
plt.setp(bp['medians'], color='k')
ax.set_ylabel('mortality (-)')
ax.set_ylim(0,1)
ax.set_xticklabels(['Cohort mortality (N={}) \n median = {:.2f} \n mean = {:.2f}'.format(len(x), np.median(x), np.mean(x)),
'ICU mortality (N={}) \n median = {:.2f} \n mean = {:.2f}'.format(len(y), np.median(y), np.mean(y))])
ax.set_title('Difference in overall mortality, \ntwo-sided t-test: p={:.2e} \nMann-Withney U-test: p={:.2e}'.format(p_tt,p_mwu))
plt.savefig(fig_path+'SCIENSANO_test_mortalities.pdf', dpi=600, bbox_inches='tight',orientation='portrait', papertype='a4')
plt.close()
# -----------------------------------------------------------------
# Make a violin plot of mortalities in ICU and cohort per age group
# -----------------------------------------------------------------
data = []
for idx,age_class in enumerate(age_classes):
data.append(bootstrap_fractions_age[2,idx,:])
# Violin plot
fig,ax = plt.subplots(figsize=(12,4))
parts = ax.violinplot(
data, positions=range(1,len(age_classes)+1), vert=False,showmeans=False, showmedians=False,
showextrema=False)
for idx,pc in enumerate(parts['bodies']):
pc.set_facecolor(colorscale_okabe_ito['green'])
pc.set_edgecolor('black')
pc.set_alpha(1)
quartiles = [25, 50, 75]
quartile1 = np.zeros(len(data))
medians = np.zeros(len(data))
quartile3 = np.zeros(len(data))
for i,x in enumerate(data):
quartile1[i],medians[i],quartile3[i] = np.percentile(x, quartiles)
whiskers = np.array([
adjacent_values(sorted_array, q1, q3)
for sorted_array, q1, q3 in zip(data, quartile1, quartile3)])
whiskers_min, whiskers_max = whiskers[:, 0], whiskers[:, 1]
inds = np.arange(1, len(medians)+1)
ax.scatter( medians, inds, marker='o', color='white', s=30, zorder=3)
ax.hlines(inds, quartile1, quartile3, color='k', linestyle='-', lw=5)
ax.hlines(inds, whiskers_min, whiskers_max, color='k', linestyle='-', lw=1)
data = []
for idx,age_class in enumerate(age_classes):
data.append(bootstrap_fractions_age[3,idx,:])
parts = ax.violinplot(
data, positions=range(1,len(age_classes)+1), vert=False,showmeans=False, showmedians=False,
showextrema=False)
for idx,pc in enumerate(parts['bodies']):
pc.set_facecolor(colorscale_okabe_ito['red'])
pc.set_edgecolor('black')
pc.set_alpha(1)
quartiles = [25, 50, 75]
quartile1 = np.zeros(len(data))
medians = np.zeros(len(data))
quartile3 = np.zeros(len(data))
for i,x in enumerate(data):
quartile1[i],medians[i],quartile3[i] = | np.percentile(x, quartiles) | numpy.percentile |
from typing import Union
import numpy as np
from objects.basis_functions import BasisFunctions
from tests.objects.polynomial_basis_test import PolynomialBasisFunctionsTest
class BasisFunctionsTest(PolynomialBasisFunctionsTest):
def setUp(self):
super().setUp()
self.basis_fun = BasisFunctions()
def test_eval(self):
M = 1000
x = np.array([1] * M)
returns = self.basis_fun.eval(x=x)
self.assertEqual(np.shape(returns)[1], M)
self.assertEqual(np.shape(returns)[0], 3)
# TODO test and improve the following 2 methods
def compute_exp_batch(self, n: float, x: Union[float, np.ndarray], u: Union[float, np.ndarray]):
out = np.zeros((self.K, self.M, self.U))
for k in range(self.K):
# TODO remove this if, should not be necessary
if k == 0:
out[k, :, :] = self.basis_function_expectation[k](x, u.T)
else:
out[k, :, :] = self.basis_function_expectation[k][0](x, u.T).T
return out
def compute_exp(self, n: float, x: Union[float, np.ndarray], u: Union[float, np.ndarray]):
out = | np.zeros((self.K, self.M)) | numpy.zeros |
import astropy.units as u
import numpy as np
from lofti_gaia.loftitools import *
from lofti_gaia.cFunctions import calcOFTI_C
#from loftitools import *
import pickle
import time
import matplotlib.pyplot as plt
# Astroquery throws some warnings we can ignore:
import warnings
warnings.filterwarnings("ignore")
'''This module obtaines measurements from Gaia EDR3 (Gaia DR2 is also available as a secondary option) and runs through the LOFTI Gaia/OFTI
wide stellar binary orbit fitting technique.
'''
class Fitter(object):
'''Initialize the Fitter object for the binary system, and compute observational constraints
to be used in the orbit fit. User must provide Gaia source ids, tuples of mass estimates for
both objects, specify the number of desired orbits in posterior sample. Fit will be
for object 2 relative to object 1.
Attributes are tuples of (value,uncertainty) unless otherwise indicated. Attributes
with astropy units are retrieved from Gaia archive, attributes without units are
computed from Gaia values. All relative values are for object 2 relative to object 1.
Args:
sourceid1, sourceid2 (int): Gaia source ids for the two objects, fit will be for motion of \
object 2 relative to object 1
mass1, mass2 (tuple, flt): tuple os mass estimate for object 1 and 2, of the form (value, uncertainty)
Norbits (int): Number of desired orbits in posterior sample. Default = 100000
results_filename (str): Filename for fit results files. If none, results will be written to files \
named FitResults.yr.mo.day.hr.min.s
astrometry (dict): User-supplied astrometric measurements. Must be dictionary or table or pandas dataframe with\
column names "sep,seperr,pa,paerr,dates" or "ra,raerr,dec,decerr,dates". May be same as the rv table. \
Sep, deltaRA, and deltaDEC must be in arcseconds, PA in degrees, dates in decimal years. \
Default = None
user_rv (dict): User-supplied radial velocity measurements. Must be dictionary or table or pandas dataframe with\
column names "rv,rverr,rv_dates". May be same as the astrometry table. Default = None.
catalog (str): name of Gaia catalog to query. Default = 'gaiaedr3.gaia_source'
ruwe1, ruwe2 (flt): RUWE value from Gaia archive
ref_epoch (flt): reference epoch in decimal years. For Gaia DR2 this is 2015.5, for Gaia EDR3 it is 2016.0
plx1, plx2 (flt): parallax from Gaia in mas
RA1, RA2 (flt): right ascension from Gaia; RA in deg, uncertainty in mas
Dec1, Dec2 (flt): declination from Gaia; Dec in deg, uncertainty in mas
pmRA1, pmRA2 (flt): proper motion in RA in mas yr^-1 from Gaia
pmDec1, pmDec2 (flt): proper motion in DEC in mas yr^-1 from Gaia
rv1, rv2 (flt, optional): radial velocity in km s^-1 from Gaia
rv (flt, optional): relative RV of 2 relative to 1, if both are present in Gaia
plx (flt): weighted mean parallax for the binary system in mas
distance (flt): distance of system in pc, computed from Gaia parallax using method \
of Bailer-Jones et. al 2018.
deltaRA, deltaDec (flt): relative separation in RA and Dec directions, in mas
pmRA, pmDec (flt): relative proper motion in RA/Dec directions in km s^-1
sep (flt): total separation vector in mas
pa (flt): postion angle of separation vector in degrees from North
sep_au (flt): separation in AU
sep_km (flt): separation in km
total_vel (flt): total velocity vector in km s^-1. If RV is available for both, \
this is the 3d velocity vector; if not it is just the plane of sky velocity.
total_planeofsky_vel (flt): total velocity in the plane of sky in km s^-1. \
In the absence of RV this is equivalent to the total velocity vector.
deltaGmag (flt): relative contrast in Gaia G magnitude. Does not include uncertainty.
inflateProperMOtionError (flt): an optional factor to mulitply default gaia proper motion error by.
Written by <NAME>, 2020
'''
def __init__(self, sourceid1, sourceid2, mass1, mass2, Norbits = 100000, \
results_filename = None,
astrometry = None,
user_rv = None,
catalog = 'gaiaedr3.gaia_source',
inflateProperMotionError=1
):
self.sourceid1 = sourceid1
self.sourceid2 = sourceid2
try:
self.mass1 = mass1[0]
self.mass1err = mass1[1]
self.mass2 = mass2[0]
self.mass2err = mass2[1]
self.mtot = [self.mass1 + self.mass2, np.sqrt((self.mass1err**2) + (self.mass2err**2))]
except:
raise ValueError('Masses must be tuples of (value,error), ex: mass1 = (1.0,0.05)')
self.Norbits = Norbits
if not results_filename:
self.results_filename = 'FitResults.'+time.strftime("%Y.%m.%d.%H.%M.%S")+'.txt'
self.stats_filename = 'FitResults.Stats.'+time.strftime("%Y.%m.%d.%H.%M.%S")+'.txt'
else:
self.results_filename = results_filename
self.stats_filename = results_filename+'.Stats.txt'
self.astrometry = False
# check if user supplied astrometry:
if astrometry is not None:
# if so, set astrometric flag to True:
self.astrometry = True
# store observation dates:
self.astrometric_dates = astrometry['dates']
# if in sep/pa, convert to ra/dec:
if 'sep' in astrometry:
try:
astr_ra = [MonteCarloIt([astrometry['sep'][i],astrometry['seperr'][i]]) * \
np.sin(np.radians(MonteCarloIt([astrometry['pa'][i],astrometry['paerr'][i]]))) \
for i in range(len(astrometry['sep']))]
astr_dec = [MonteCarloIt([astrometry['sep'][i],astrometry['seperr'][i]]) * \
np.cos(np.radians(MonteCarloIt([astrometry['pa'][i],astrometry['paerr'][i]]))) \
for i in range(len(astrometry['sep']))]
self.astrometric_ra = np.array([
[np.mean(astr_ra[i]) for i in range(len(astrometry['sep']))],
[np.std(astr_ra[i]) for i in range(len(astrometry['sep']))]
])
self.astrometric_dec = np.array([
[np.mean(astr_dec[i]) for i in range(len(astrometry['sep']))],
[np.std(astr_dec[i]) for i in range(len(astrometry['sep']))]
])
except:
raise ValueError('Astrometry keys not recognized. Please provide dictionary or table or pandas dataframe with\
column names "sep,seperr,pa,paerr,dates" or "ra,raerr,dec,decerr,dates"')
elif 'ra' in astrometry:
# else store the ra/dec as attributes:
try:
self.astrometric_ra = np.array([astrometry['ra'], astrometry['raerr']])
self.astrometric_dec = np.array([astrometry['dec'], astrometry['decerr']])
except:
raise ValueError('Astrometry keys not recognized. Please provide dictionary or table or pandas dataframe with\
column names "sep,seperr,pa,paerr,dates" or "ra,raerr,dec,decerr,dates"')
else:
raise ValueError('Astrometry keys not recognized. Please provide dictionary or table or pandas dataframe with\
column names "sep,seperr,pa,paerr,dates" or "ra,raerr,dec,decerr,dates"')
# Check if user supplied rv:
self.use_user_rv = False
if user_rv is not None:
# set user rv flag to true:
self.use_user_rv = True
try:
# set attributes; multiply rv by -1 due to difference in coordinate systems:
self.user_rv = np.array([user_rv['rv']*-1,user_rv['rverr']])
self.user_rv_dates = np.array(user_rv['rv_dates'])
except:
raise ValueError('RV keys not recognized. Please use column names "rv,rverr,rv_dates"')
self.catalog = catalog
# Get Gaia measurements, compute needed constraints, and add to object:
self.PrepareConstraints(catalog=self.catalog,inflateFactor=inflateProperMotionError)
def edr3ToICRF(self,pmra,pmdec,ra,dec,G):
''' Corrects for biases in proper motion. The function is from https://arxiv.org/pdf/2103.07432.pdf
Args:
pmra,pmdec (float): proper motion
ra, dec (float): right ascension and declination
G (float): G magnitude
Written by <NAME>, 2021
'''
if G>=13:
return pmra , pmdec
import numpy as np
def sind(x):
return np.sin(np.radians(x))
def cosd(x):
return np.cos(np.radians(x))
table1="""
0.0 9.0 9.0 9.5 9.5 10.0 10.0 10.5 10.5 11.0 11.0 11.5 11.5 11.75 11.75 12.0 12.0 12.25 12.25 12.5 12.5 12.75 12.75 13.0
18.4 33.8 -11.3 14.0 30.7 -19.4 12.8 31.4 -11.8 13.6 35.7 -10.5 16.2 50.0 2.1 19.4 59.9 0.2 21.8 64.2 1.0 17.7 65.6 -1.9 21.3 74.8 2.1 25.7 73.6 1.0 27.3 76.6 0.5
34.9 68.9 -2.9 """
table1 = np.fromstring(table1,sep=" ").reshape((12,5)).T
Gmin = table1[0]
Gmax = table1[1]
#pick the appropriate omegaXYZ for the source’s magnitude:
omegaX = table1[2][(Gmin<=G)&(Gmax>G)][0]
omegaY = table1[3][(Gmin<=G)&(Gmax>G)][0]
omegaZ = table1[4][(Gmin<=G)&(Gmax>G)][0]
pmraCorr = -1*sind(dec)*cosd(ra)*omegaX -sind(dec)*sind(ra)*omegaY + cosd(dec)*omegaZ
pmdecCorr = sind(ra)*omegaX -cosd(ra)*omegaY
return pmra-pmraCorr/1000., pmdec-pmdecCorr/1000.
def PrepareConstraints(self, rv=False, catalog='gaiaedr3.gaia_source', inflateFactor=1.):
'''Retrieves parameters for both objects from Gaia EDR3 archive and computes system attriubtes,
and assigns them to the Fitter object class.
Args:
rv (bool): flag for handling the presence or absence of RV measurements for both objects \
in EDR3. Gets set to True if both objects have Gaia RV measurements. Default = False
catalog (str): name of Gaia catalog to query. Default = 'gaiaedr3.gaia_source'
inflateFactor (flt): Factor by which to inflate the errors on Gaia proper motions to \
account for improper uncertainty estimates. Default = 1.0
Written by <NAME>, 2020
'''
from astroquery.gaia import Gaia
deg_to_mas = 3600000.
mas_to_deg = 1./3600000.
# Retrieve astrometric solution from Gaia EDR3
job = Gaia.launch_job("SELECT * FROM "+catalog+" WHERE source_id = "+str(self.sourceid1))
j = job.get_results()
job = Gaia.launch_job("SELECT * FROM "+catalog+" WHERE source_id = "+str(self.sourceid2))
k = job.get_results()
if catalog == 'gaiadr2.gaia_source':
# Retrieve RUWE from RUWE catalog for both sources and add to object state:
job = Gaia.launch_job("SELECT * FROM gaiadr2.ruwe WHERE source_id = "+str(self.sourceid1))
jruwe = job.get_results()
job = Gaia.launch_job("SELECT * FROM gaiadr2.ruwe WHERE source_id = "+str(self.sourceid2))
kruwe = job.get_results()
self.ruwe1 = jruwe['ruwe'][0]
self.ruwe2 = kruwe['ruwe'][0]
else:
# EDR3 contains ruwe in the main catalog:
self.ruwe1 = j['ruwe'][0]
self.ruwe2 = k['ruwe'][0]
# Check RUWE for both objects and warn if too high:
if self.ruwe1>1.2 or self.ruwe2>1.2:
print('''WARNING: RUWE for one or more of your solutions is greater than 1.2. This indicates
that the source might be an unresolved binary or experiencing acceleration
during the observation. Orbit fit results may not be trustworthy.''')
# reference epoch:
self.ref_epoch = j['ref_epoch'][0]
# parallax:
self.plx1 = [j[0]['parallax']*u.mas, j[0]['parallax_error']*u.mas]
self.plx2 = [k[0]['parallax']*u.mas, k[0]['parallax_error']*u.mas]
# RA/DEC
self.RA1 = [j[0]['ra']*u.deg, j[0]['ra_error']*mas_to_deg*u.deg]
self.RA2 = [k[0]['ra']*u.deg, k[0]['ra_error']*mas_to_deg*u.deg]
self.Dec1 = [j[0]['dec']*u.deg, j[0]['dec_error']*mas_to_deg*u.deg]
self.Dec2 = [k[0]['dec']*u.deg, k[0]['dec_error']*mas_to_deg*u.deg]
# Proper motions
pmRACorrected1,pmDecCorrected1 = self.edr3ToICRF(j[0]['pmra'],j[0]['pmdec'],j[0]['ra'],j[0]['dec'],j[0]["phot_g_mean_mag"])
pmRACorrected2,pmDecCorrected2 = self.edr3ToICRF(k[0]['pmra'],k[0]['pmdec'],k[0]['ra'],k[0]['dec'],k[0]["phot_g_mean_mag"])
self.pmRA1 = [pmRACorrected1*u.mas/u.yr, j[0]['pmra_error']*u.mas/u.yr*inflateFactor]
self.pmRA2 = [pmRACorrected2*u.mas/u.yr, k[0]['pmra_error']*u.mas/u.yr*inflateFactor]
self.pmDec1 = [pmDecCorrected1*u.mas/u.yr, j[0]['pmdec_error']*u.mas/u.yr*inflateFactor]
self.pmDec2 = [pmDecCorrected2*u.mas/u.yr, k[0]['pmdec_error']*u.mas/u.yr*inflateFactor]
# See if both objects have RV's in DR2:
if catalog == 'gaiaedr3.gaia_source':
key = 'dr2_radial_velocity'
error_key = 'dr2_radial_velocity_error'
elif catalog == 'gaiadr2.gaia_source':
key = 'radial_velocity'
error_key = 'radial_velocity_error'
if type(k[0][key]) == np.float64 and type(j[0][key]) == np.float64 or type(k[0][key]) == np.float32 and type(j[0][key]) == np.float32:
rv = True
self.rv1 = [j[0][key]*u.km/u.s,j[0][error_key]*u.km/u.s]
self.rv2 = [k[0][key]*u.km/u.s,k[0][error_key]*u.km/u.s]
rv1 = MonteCarloIt(self.rv1)
rv2 = MonteCarloIt(self.rv2)
self.rv = [ -np.mean(rv2-rv1) , np.std(rv2-rv1) ] # km/s
# negative to relfect change in coordinate system from RV measurements to lofti
# pos RV = towards observer in this coord system
else:
self.rv = [0,0]
# weighted mean of parallax values:
plx = np.average([self.plx1[0].value,self.plx2[0].value], weights = [self.plx1[1].value,self.plx2[1].value])
plxerr = np.max([self.plx1[1].value,self.plx2[1].value])
self.plx = [plx,plxerr] # mas
self.distance = distance(*self.plx) # pc
# Compute separations of component 2 relative to 1:
r1 = MonteCarloIt(self.RA1)
r2 = MonteCarloIt(self.RA2)
d1 = MonteCarloIt(self.Dec1)
d2 = MonteCarloIt(self.Dec2)
ra = (r2*deg_to_mas - r1*deg_to_mas) * np.cos(np.radians(np.mean([self.Dec1[0].value,self.Dec2[0].value])))
dec = ((d2 - d1)*u.deg).to(u.mas).value
self.deltaRA = [np.mean(ra),np.std(ra)] # mas
self.deltaDec = [np.mean(dec),np.std(dec)] # mas
# compute relative proper motion:
pr1 = MonteCarloIt(self.pmRA1)
pr2 = MonteCarloIt(self.pmRA2)
pd1 = MonteCarloIt(self.pmDec1)
pd2 = MonteCarloIt(self.pmDec2)
pmRA = [np.mean(pr2 - pr1), np.std(pr2-pr1)] # mas/yr
pmDec = [np.mean(pd2 - pd1), np.std(pd2 - pd1)] # mas/yr
self.pmRA = masyr_to_kms(pmRA,self.plx) # km/s
self.pmDec = masyr_to_kms(pmDec,self.plx) # km/s
# Compute separation/position angle:
r, p = to_polar(r1,r2,d1,d2)
self.sep = tuple([np.mean(r).value, np.std(r).value]) # mas
self.pa = tuple([np.mean(p).value, np.std(p).value]) # deg
self.sep_au = tuple([((self.sep[0]/1000)*self.distance[0]), ((self.sep[1]/1000)*self.distance[0])])
self.sep_km = tuple([ self.sep_au[0]*u.au.to(u.km) , self.sep_au[1]*u.au.to(u.km)])
# compute total velocities:
if rv:
self.total_vel = [ add_in_quad([self.pmRA[0],self.pmDec[0],self.rv[0]]) ,
add_in_quad([self.pmRA[1],self.pmDec[1],self.rv[1]]) ] # km/s
self.total_planeofsky_vel = [ add_in_quad([self.pmRA[0],self.pmDec[0]]) ,
add_in_quad([self.pmRA[1],self.pmDec[1]]) ] # km/s
else:
self.total_vel = [ add_in_quad([self.pmRA[0],self.pmDec[0]]) ,
add_in_quad([self.pmRA[1],self.pmDec[1]]) ] # km/s
self.total_planeofsky_vel = self.total_vel.copy() # km/s
# compute deltamag:
self.deltaGmag = j[0]['phot_g_mean_mag'] - k[0]['phot_g_mean_mag']
class FitOrbit(object):
''' Object for performing an orbit fit. Takes attributes from Fitter class.
ex: orbits = FitOrbit(fitterobject)
Args:
fitterobject (Fitter object): Fitter object initialized from the Fitter class
write_stats (bool): If True, write out summary statistics of orbit sample at \
conclusion of fit. Default = True.
write_results (bool): If True, write out the fit results to a pickle file \
in addition to the text file created during the fit. Default = True.
deltaRA, deltaDec (flt): relative separation in RA and Dec directions, in mas
pmRA, pmDec (flt): relative proper motion in RA/Dec directions in km s^-1
rv (flt, optional): relative RV of 2 relative to 1, if both are present in Gaia EDR3
mtot_init (flt): initial total system mass in Msun from user input
distance (flt): distance of system in pc, computed from Gaia parallax using method of Bailer-Jones et. al 2018.
sep (flt): separation vector in mas
pa (flt): postion angle of separation vector in degrees from North
ref_epoch (flt): epoch of the measurement, 2016.0 for Gaia EDR3 and 2015.5 for Gaia DR2.
Norbits (int): number of desired orbit samples
write_stats (bool): if True, write summary of sample statistics to human-readable file at end of run. Default = True
write_results (bool): if True, write out current state of sample orbits in pickle file in periodic intervals during \
run, and again at the end of the run. RECOMMENDED. Default = True
results_filename (str): name of file for saving pickled results to disk. If not supplied, \
defaul name is FitResults.y.mo.d.h.m.s.pkl, saved in same directory as fit was run.
stats_filename (str): name of file for saving human-readable file of stats of sample results. If not supplied, \
defaul name is FitResults.Stats.y.mo.d.h.m.s.pkl, saved in same directory as fit was run.
run_time (flt): run time for the last fit. astropy units object
Written by <NAME>, 2020
'''
def __init__(self, fitterobject, write_stats = True, write_results = True, python_version=False, \
use_pm_cross_term = False, corr_coeff = None):
# establish fit parameters:
self.deltaRA = fitterobject.deltaRA
self.deltaDec = fitterobject.deltaDec
self.pmRA = fitterobject.pmRA
self.pmDec = fitterobject.pmDec
self.rv = fitterobject.rv
self.mtot_init = fitterobject.mtot
self.distance = fitterobject.distance
self.sep = fitterobject.sep
self.pa = fitterobject.pa
self.ref_epoch = fitterobject.ref_epoch
self.Norbits = fitterobject.Norbits
self.write_results = write_results
self.write_stats = write_stats
self.results_filename = fitterobject.results_filename
self.stats_filename = fitterobject.stats_filename
self.astrometry = fitterobject.astrometry
if self.astrometry:
self.astrometric_ra = fitterobject.astrometric_ra
self.astrometric_dec = fitterobject.astrometric_dec
self.astrometric_dates = fitterobject.astrometric_dates
self.use_user_rv = fitterobject.use_user_rv
if self.use_user_rv:
self.user_rv = fitterobject.user_rv
self.user_rv_dates = fitterobject.user_rv_dates
# run orbit fitter:
self.fitorbit(python_fitOFTI=python_version, use_pm_cross_term = use_pm_cross_term, corr_coeff = corr_coeff)
def fitorbit(self, save_results_every_X_loops = 100, python_fitOFTI=False, use_pm_cross_term = False, corr_coeff = None):
'''Run the OFTI fitting run on the Fitter object. Called when FitOrbit object
is created.
Args:
save_results_every_X_loops (int): on every Xth loop, save status of the \
orbit sample arrays to a pickle file, if write_results = True (Default)
python_fitOFTI (bool): If True, fit using python only without using C Kepler's equation solver. Default = False
use_pm_cross_term (bool): If True, include the proper motion correlation cross term in the Chi^2 computation \
Default = False
Written by <NAME>, 2020
'''
# write header:
print('Saving orbits in',self.results_filename)
k = open(self.results_filename, 'w')
output_file_header = '# sma [arcsec] period [yrs] orbit phase t_0 [yr] ecc incl [deg]\
argp [deg] lan [deg] m_tot [Msun] dist [pc] chi^2 ln(prob) ln(randn)'
k.write(output_file_header + "\n")
k.close()
import time as tm
########### Perform initial run to get initial chi-squared: #############
# Draw random orbits:
#parameters = a,T,const,to,e,i,w,O,m1,dist
numSamples = 10000
parameters_init = draw_samples(numSamples, self.mtot_init, self.distance, self.ref_epoch)
# Compute positions and velocities:
if(python_fitOFTI):
X,Y,Z,Xdot,Ydot,Zdot,Xddot,Yddot,Zddot,parameters=calc_OFTI(parameters_init,self.ref_epoch,self.sep,self.pa)
else:
returnArray = np.zeros((19,numSamples))
returnArray = calcOFTI_C(parameters_init,self.ref_epoch,self.sep,self.pa,returnArray.copy())
X,Y,Z,Xdot,Ydot,Zdot,Xddot,Yddot,Zddot = returnArray[0:9]
parameters = returnArray[9:]
# Compute chi squared:
if self.rv[0] != 0:
model = np.array([Y,X,Ydot,Xdot,Zdot])
data = np.array([self.deltaRA, self.deltaDec, self.pmRA, self.pmDec, self.rv])
else:
model = np.array([Y,X,Ydot,Xdot])
data = np.array([self.deltaRA, self.deltaDec, self.pmRA, self.pmDec])
chi2 = ComputeChi2(data,model)
if use_pm_cross_term:
chi2 -= ( 2 * corr_coeff * (data[2][0] - model[2]) * (data[3][0] - model[3]) ) / (data[2][1] * data[3][1])
if self.astrometry:
p = parameters.copy()
a,T,const,to,e,i,w,O,m1,dist = p[0],p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9]
chi2_astr = np.zeros(10000)
# Calculate predicted positions at astr observation dates for each orbit:
for j in range(self.astrometric_ra.shape[1]):
# for each date, compute XYZ for each 10000 trial orbit. We can
# skip scale and rotate because that was accomplished in the calc_OFTI call above.
X1,Y1,Z1,E1 = calc_XYZ(a,T,to,e,i,w,O,self.astrometric_dates[j])
# Place astrometry into data array where: data[0][0]=ra obs, data[0][1]=ra err, etc:
data = np.array([self.astrometric_ra[:,j], self.astrometric_dec[:,j]])
# place corresponding predicited positions at that date for each trial orbit in arcsec:
model = np.array([Y1*1000,X1*1000])
# compute chi2 for trial orbits at that date and add to the total chi2 sum:
chi2_astr += ComputeChi2(data,model)
chi2 = chi2 + chi2_astr
if self.use_user_rv:
p = parameters.copy()
a,T,const,to,e,i,w,O,m1,dist = p[0],p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9]
chi2_rv = np.zeros(10000)
for j in range(self.user_rv.shape[1]):
# compute ecc anomaly at that date:
X1,Y1,Z1,E1 = calc_XYZ(a,T,to,e,i,w,O,self.user_rv_dates[j])
# compute velocities at that ecc anom:
Xdot,Ydot,Zdot = calc_velocities(a,T,to,e,i,w,O,dist,E1)
# compute chi2:
chi2_rv += ComputeChi2(np.array([self.user_rv[:,j]]),np.array([Zdot]))
chi2 = chi2 + chi2_rv
print('inital chi min',np.nanmin(chi2))
self.chi_min = np.nanmin(chi2)
# Accept/reject:
accepted, lnprob, lnrand = AcceptOrReject(chi2,self.chi_min)
# count number accepted:
number_orbits_accepted = np.size(accepted)
# tack on chi2, log probability, log random unif number to parameters array:
parameters = np.concatenate((parameters,chi2[None,:],lnprob[None,:],lnrand[None,:]), axis = 0)
# transpose:
parameters=np.transpose(parameters)
# write results to file:
k = open(self.results_filename, 'a')
for params in parameters[accepted]:
string = ' '.join([str(p) for p in params])
k.write(string + "\n")
k.close()
###### start loop ########
# initialize:
loop_count = 0
start=tm.time()
while number_orbits_accepted < self.Norbits:
# Draw random orbits:
numSamples = 10000
parameters_init = draw_samples(numSamples, self.mtot_init, self.distance, self.ref_epoch)
# Compute positions and velocities and new parameters array with scaled and rotated values:
if(python_fitOFTI):
X,Y,Z,Xdot,Ydot,Zdot,Xddot,Yddot,Zddot,parameters=calc_OFTI(parameters_init,self.ref_epoch,self.sep,self.pa)
else:
returnArray = np.zeros((19,numSamples))
returnArray = calcOFTI_C(parameters_init,self.ref_epoch,self.sep,self.pa,returnArray.copy())
X,Y,Z,Xdot,Ydot,Zdot,Xddot,Yddot,Zddot = returnArray[0:9]
parameters = returnArray[9:]
returnArray = None
# compute chi2 for orbits using Gaia observations:
if self.rv[0] != 0:
model = np.array([Y,X,Ydot,Xdot,Zdot])
data = np.array([self.deltaRA, self.deltaDec, self.pmRA, self.pmDec, self.rv])
else:
model = np.array([Y,X,Ydot,Xdot])
data = np.array([self.deltaRA, self.deltaDec, self.pmRA, self.pmDec])
chi2 = ComputeChi2(data,model)
if use_pm_cross_term:
chi2 -= ( 2 * (data[2][0] - model[2]) * (data[3][0] - model[3]) ) / (data[2][1] * data[3][1])
# add user astrometry if given:
if self.astrometry:
p = parameters.copy()
a,T,const,to,e,i,w,O,m1,dist = p[0],p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9]
chi2_astr = np.zeros(10000)
# Calculate predicted positions at astr observation dates for each orbit:
for j in range(self.astrometric_ra.shape[1]):
# for each date, compute XYZ for each 10000 trial orbit. We can
# skip scale and rotate because that was accomplished in the calc_OFTI call above.
X1,Y1,Z1,E1 = calc_XYZ(a,T,to,e,i,w,O,self.astrometric_dates[j])
# Place astrometry into data array where: data[0][0]=ra obs, data[0][1]=ra err, etc:
data = np.array([self.astrometric_ra[:,j], self.astrometric_dec[:,j]])
# place corresponding predicited positions at that date for each trial orbit:
model = np.array([Y1*1000,X1*1000])
# compute chi2 for trial orbits at that date and add to the total chi2 sum:
chi2_astr += ComputeChi2(data,model)
chi2 = chi2 + chi2_astr
# add user rv if given:
if self.use_user_rv:
p = parameters.copy()
a,T,const,to,e,i,w,O,m1,dist = p[0],p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9]
chi2_rv = np.zeros(10000)
for j in range(self.user_rv.shape[1]):
# compute ecc anomaly at that date:
X1,Y1,Z1,E1 = calc_XYZ(a,T,to,e,i,w,O,self.user_rv_dates[j])
# compute velocities at that ecc anom:
Xdot,Ydot,Zdot = calc_velocities(a,T,to,e,i,w,O,dist,E1)
# compute chi2:
chi2_rv += ComputeChi2(np.array([self.user_rv[:,j]]),np.array([Zdot]))
chi2 = chi2 + chi2_rv
# Accept/reject:
accepted, lnprob, lnrand = AcceptOrReject(chi2,self.chi_min)
if np.size(accepted) == 0:
pass
else:
# count num accepted
p = parameters.copy()
a,T,const,to,e,i,w,O,m1,dist = p[0],p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9]
sampleResults = calc_XYZ(a,T,to,e,i/180*np.pi,w/180*np.pi,O/180*np.pi,2016.0)
number_orbits_accepted += | np.size(accepted) | numpy.size |
import numpy as np
from text_selection.kld.kld_iterator import get_minimun_indices
def test_one_entry__returns_zero():
array = np.array([1.2], dtype=np.float64)
min_value, min_indices = get_minimun_indices(array)
assert min_value == 1.2
np.testing.assert_array_equal(min_indices, np.array([0]))
def test_two_same_entries__returns_zero_and_one():
array = np.array([1.2, 1.2], dtype=np.float64)
min_value, min_indices = get_minimun_indices(array)
assert min_value == 1.2
np.testing.assert_array_equal(min_indices, np.array([0, 1]))
def test_two_different_entries__returns_min():
array = np.array([1, 0.2], dtype=np.float64)
min_value, min_indices = get_minimun_indices(array)
assert min_value == 0.2
np.testing.assert_array_equal(min_indices, np.array([1]))
def test_two_same_entries_with_one_different_entry__returns_min():
array = np.array([0.2, 1, 0.2], dtype=np.float64)
min_value, min_indices = get_minimun_indices(array)
assert min_value == 0.2
np.testing.assert_array_equal(min_indices, np.array([0, 2]))
def test_inf_and_one__returns_min():
array = np.array([np.inf, 1.2], dtype=np.float64)
min_value, min_indices = get_minimun_indices(array)
assert min_value == 1.2
np.testing.assert_array_equal(min_indices, | np.array([1]) | numpy.array |
import numpy as np
import sys
from random import randint
class MazeMap:
"""A Class that establishes a maze's environment"""
def __init__(self,
dimensions,
wall=-1,
blank=0,
goal=-2):
# Tuple argument for the length and width of the maze
self.dims = dimensions
# By default, maze will generate as blank
self.maze = | np.zeros(self.dims, dtype=int) | numpy.zeros |
"""
Tests for smoothing and estimation of unobserved states and disturbances
- Predicted states: :math:`E(\alpha_t | Y_{t-1})`
- Filtered states: :math:`E(\alpha_t | Y_t)`
- Smoothed states: :math:`E(\alpha_t | Y_n)`
- Smoothed disturbances :math:`E(\varepsilon_t | Y_n), E(\eta_t | Y_n)`
Tested against R (FKF, KalmanRun / KalmanSmooth), Stata (sspace), and
MATLAB (ssm toolbox)
Author: <NAME>
License: Simplified-BSD
"""
from __future__ import division, absolute_import, print_function
import numpy as np
import pandas as pd
import os
from statsmodels import datasets
from statsmodels.tsa.statespace import mlemodel, sarimax
from statsmodels.tsa.statespace.tools import compatibility_mode
from statsmodels.tsa.statespace.kalman_filter import (
FILTER_CONVENTIONAL, FILTER_COLLAPSED, FILTER_UNIVARIATE)
from statsmodels.tsa.statespace.kalman_smoother import (
SMOOTH_CONVENTIONAL, SMOOTH_CLASSICAL, SMOOTH_ALTERNATIVE,
SMOOTH_UNIVARIATE)
from numpy.testing import assert_allclose, assert_almost_equal, assert_equal, assert_raises
from nose.exc import SkipTest
current_path = os.path.dirname(os.path.abspath(__file__))
class TestStatesAR3(object):
@classmethod
def setup_class(cls, alternate_timing=False, *args, **kwargs):
# Dataset / Stata comparison
path = current_path + os.sep + 'results/results_wpi1_ar3_stata.csv'
cls.stata = pd.read_csv(path)
cls.stata.index = pd.date_range(start='1960-01-01', periods=124,
freq='QS')
# Matlab comparison
path = current_path + os.sep+'results/results_wpi1_ar3_matlab_ssm.csv'
matlab_names = [
'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3',
'detV', 'eps', 'epsvar', 'eta', 'etavar'
]
cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names)
cls.model = sarimax.SARIMAX(
cls.stata['wpi'], order=(3, 1, 0), simple_differencing=True,
hamilton_representation=True, *args, **kwargs
)
if alternate_timing:
cls.model.ssm.timing_init_filtered = True
# Parameters from from Stata's sspace MLE estimation
params = np.r_[.5270715, .0952613, .2580355, .5307459]
cls.results = cls.model.smooth(params, cov_type='none')
# Calculate the determinant of the covariance matrices (for easy
# comparison to other languages without having to store 2-dim arrays)
cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
for i in range(cls.model.nobs):
cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
cls.results.filter_results.predicted_state_cov[:, :, i])
cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
cls.results.smoother_results.smoothed_state_cov[:, :, i])
if not compatibility_mode:
# Perform simulation smoothing
n_disturbance_variates = (
(cls.model.k_endog + cls.model.ssm.k_posdef) * cls.model.nobs
)
cls.sim = cls.model.simulation_smoother(filter_timing=0)
cls.sim.simulate(
disturbance_variates=np.zeros(n_disturbance_variates),
initial_state_variates=np.zeros(cls.model.k_states)
)
def test_predict_obs(self):
assert_almost_equal(
self.results.filter_results.predict().forecasts[0],
self.stata.ix[1:, 'dep1'], 4
)
def test_standardized_residuals(self):
assert_almost_equal(
self.results.filter_results.standardized_forecasts_error[0],
self.stata.ix[1:, 'sr1'], 4
)
def test_predicted_states(self):
assert_almost_equal(
self.results.filter_results.predicted_state[:, :-1].T,
self.stata.ix[1:, ['sp1', 'sp2', 'sp3']], 4
)
assert_almost_equal(
self.results.filter_results.predicted_state[:, :-1].T,
self.matlab_ssm[['a1', 'a2', 'a3']], 4
)
def test_predicted_states_cov(self):
assert_almost_equal(
self.results.det_predicted_state_cov.T,
self.matlab_ssm[['detP']], 4
)
def test_filtered_states(self):
assert_almost_equal(
self.results.filter_results.filtered_state.T,
self.stata.ix[1:, ['sf1', 'sf2', 'sf3']], 4
)
def test_smoothed_states(self):
assert_almost_equal(
self.results.smoother_results.smoothed_state.T,
self.stata.ix[1:, ['sm1', 'sm2', 'sm3']], 4
)
assert_almost_equal(
self.results.smoother_results.smoothed_state.T,
self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4
)
def test_smoothed_states_cov(self):
assert_almost_equal(
self.results.det_smoothed_state_cov.T,
self.matlab_ssm[['detV']], 4
)
def test_smoothed_measurement_disturbance(self):
assert_almost_equal(
self.results.smoother_results.smoothed_measurement_disturbance.T,
self.matlab_ssm[['eps']], 4
)
def test_smoothed_measurement_disturbance_cov(self):
res = self.results.smoother_results
assert_almost_equal(
res.smoothed_measurement_disturbance_cov[0].T,
self.matlab_ssm[['epsvar']], 4
)
def test_smoothed_state_disturbance(self):
assert_almost_equal(
self.results.smoother_results.smoothed_state_disturbance.T,
self.matlab_ssm[['eta']], 4
)
def test_smoothed_state_disturbance_cov(self):
assert_almost_equal(
self.results.smoother_results.smoothed_state_disturbance_cov[0].T,
self.matlab_ssm[['etavar']], 4
)
class TestStatesAR3AlternateTiming(TestStatesAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesAR3AlternateTiming, cls).setup_class(
alternate_timing=True, *args, **kwargs)
class TestStatesAR3AlternativeSmoothing(TestStatesAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesAR3AlternativeSmoothing, cls).setup_class(
smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs)
def test_smoothed_states(self):
# Initialization issues can change the first few smoothed states
assert_almost_equal(
self.results.smoother_results.smoothed_state.T[2:],
self.stata.ix[3:, ['sm1', 'sm2', 'sm3']], 4
)
assert_almost_equal(
self.results.smoother_results.smoothed_state.T[2:],
self.matlab_ssm.ix[2:, ['alphahat1', 'alphahat2', 'alphahat3']], 4
)
def test_smoothed_states_cov(self):
assert_almost_equal(
self.results.det_smoothed_state_cov.T[1:],
self.matlab_ssm.ix[1:, ['detV']], 4
)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother.smooth_method,
SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_ALTERNATIVE)
class TestStatesAR3UnivariateSmoothing(TestStatesAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesAR3UnivariateSmoothing, cls).setup_class(
filter_method=FILTER_UNIVARIATE, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_UNIVARIATE)
class TestStatesMissingAR3(object):
@classmethod
def setup_class(cls, alternate_timing=False, *args, **kwargs):
# Dataset
path = current_path + os.sep + 'results/results_wpi1_ar3_stata.csv'
cls.stata = pd.read_csv(path)
cls.stata.index = pd.date_range(start='1960-01-01', periods=124,
freq='QS')
# Matlab comparison
path = current_path + os.sep+'results/results_wpi1_missing_ar3_matlab_ssm.csv'
matlab_names = [
'a1','a2','a3','detP','alphahat1','alphahat2','alphahat3',
'detV','eps','epsvar','eta','etavar'
]
cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names)
# KFAS comparison
path = current_path + os.sep+'results/results_smoothing3_R.csv'
cls.R_ssm = pd.read_csv(path)
# Create missing observations
cls.stata['dwpi'] = cls.stata['wpi'].diff()
cls.stata.ix[10:21, 'dwpi'] = np.nan
cls.model = sarimax.SARIMAX(
cls.stata.ix[1:,'dwpi'], order=(3, 0, 0),
hamilton_representation=True, *args, **kwargs
)
if alternate_timing:
cls.model.ssm.timing_init_filtered = True
# Parameters from from Stata's sspace MLE estimation
params = np.r_[.5270715, .0952613, .2580355, .5307459]
cls.results = cls.model.smooth(params, return_ssm=True)
# Calculate the determinant of the covariance matrices (for easy
# comparison to other languages without having to store 2-dim arrays)
cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
for i in range(cls.model.nobs):
cls.results.det_predicted_state_cov[0,i] = np.linalg.det(
cls.results.predicted_state_cov[:,:,i])
cls.results.det_smoothed_state_cov[0,i] = np.linalg.det(
cls.results.smoothed_state_cov[:,:,i])
if not compatibility_mode:
# Perform simulation smoothing
n_disturbance_variates = (
(cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs
)
cls.sim = cls.model.simulation_smoother()
cls.sim.simulate(
disturbance_variates=np.zeros(n_disturbance_variates),
initial_state_variates=np.zeros(cls.model.k_states)
)
def test_predicted_states(self):
assert_almost_equal(
self.results.predicted_state[:,:-1].T,
self.matlab_ssm[['a1', 'a2', 'a3']], 4
)
def test_predicted_states_cov(self):
assert_almost_equal(
self.results.det_predicted_state_cov.T,
self.matlab_ssm[['detP']], 4
)
def test_smoothed_states(self):
assert_almost_equal(
self.results.smoothed_state.T,
self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4
)
def test_smoothed_states_cov(self):
assert_almost_equal(
self.results.det_smoothed_state_cov.T,
self.matlab_ssm[['detV']], 4
)
def test_smoothed_measurement_disturbance(self):
assert_almost_equal(
self.results.smoothed_measurement_disturbance.T,
self.matlab_ssm[['eps']], 4
)
def test_smoothed_measurement_disturbance_cov(self):
assert_almost_equal(
self.results.smoothed_measurement_disturbance_cov[0].T,
self.matlab_ssm[['epsvar']], 4
)
# There is a discrepancy between MATLAB ssm toolbox and
# statsmodels.tsa.statespace on the following variables in the case of
# missing data. Tests against the R package KFAS confirm our results
def test_smoothed_state_disturbance(self):
# assert_almost_equal(
# self.results.smoothed_state_disturbance.T,
# self.matlab_ssm[['eta']], 4
# )
assert_almost_equal(
self.results.smoothed_state_disturbance.T,
self.R_ssm[['etahat']], 9
)
def test_smoothed_state_disturbance_cov(self):
# assert_almost_equal(
# self.results.smoothed_state_disturbance_cov[0].T,
# self.matlab_ssm[['etavar']], 4
# )
assert_almost_equal(
self.results.smoothed_state_disturbance_cov[0,0,:],
self.R_ssm['detVeta'], 9
)
class TestStatesMissingAR3AlternateTiming(TestStatesMissingAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesMissingAR3AlternateTiming, cls).setup_class(alternate_timing=True, *args, **kwargs)
class TestStatesMissingAR3AlternativeSmoothing(TestStatesMissingAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesMissingAR3AlternativeSmoothing, cls).setup_class(
smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother.smooth_method,
SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_ALTERNATIVE)
class TestStatesMissingAR3UnivariateSmoothing(TestStatesMissingAR3):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestStatesMissingAR3UnivariateSmoothing, cls).setup_class(
filter_method=FILTER_UNIVARIATE, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_UNIVARIATE)
class TestMultivariateMissing(object):
"""
Tests for most filtering and smoothing variables against output from the
R library KFAS.
Note that KFAS uses the univariate approach which generally will result in
different predicted values and covariance matrices associated with the
measurement equation (e.g. forecasts, etc.). In this case, although the
model is multivariate, each of the series is truly independent so the values
will be the same regardless of whether the univariate approach is used or
not.
"""
@classmethod
def setup_class(cls, **kwargs):
# Results
path = current_path + os.sep + 'results/results_smoothing_R.csv'
cls.desired = pd.read_csv(path)
# Data
dta = datasets.macrodata.load_pandas().data
dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS')
obs = dta[['realgdp','realcons','realinv']].diff().ix[1:]
obs.ix[0:50, 0] = np.nan
obs.ix[19:70, 1] = np.nan
obs.ix[39:90, 2] = np.nan
obs.ix[119:130, 0] = np.nan
obs.ix[119:130, 2] = np.nan
# Create the model
mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs)
mod['design'] = np.eye(3)
mod['obs_cov'] = np.eye(3)
mod['transition'] = np.eye(3)
mod['selection'] = np.eye(3)
mod['state_cov'] = np.eye(3)
mod.initialize_approximate_diffuse(1e6)
cls.model = mod
cls.results = mod.smooth([], return_ssm=True)
# Calculate the determinant of the covariance matrices (for easy
# comparison to other languages without having to store 2-dim arrays)
cls.results.det_scaled_smoothed_estimator_cov = (
np.zeros((1, cls.model.nobs)))
cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_disturbance_cov = (
np.zeros((1, cls.model.nobs)))
for i in range(cls.model.nobs):
cls.results.det_scaled_smoothed_estimator_cov[0,i] = (
np.linalg.det(
cls.results.scaled_smoothed_estimator_cov[:,:,i]))
cls.results.det_predicted_state_cov[0,i] = np.linalg.det(
cls.results.predicted_state_cov[:,:,i+1])
cls.results.det_smoothed_state_cov[0,i] = np.linalg.det(
cls.results.smoothed_state_cov[:,:,i])
cls.results.det_smoothed_state_disturbance_cov[0,i] = (
np.linalg.det(
cls.results.smoothed_state_disturbance_cov[:,:,i]))
def test_loglike(self):
assert_allclose(np.sum(self.results.llf_obs), -205310.9767)
def test_scaled_smoothed_estimator(self):
assert_allclose(
self.results.scaled_smoothed_estimator.T,
self.desired[['r1', 'r2', 'r3']]
)
def test_scaled_smoothed_estimator_cov(self):
assert_allclose(
self.results.det_scaled_smoothed_estimator_cov.T,
self.desired[['detN']]
)
def test_forecasts(self):
assert_allclose(
self.results.forecasts.T,
self.desired[['m1', 'm2', 'm3']]
)
def test_forecasts_error(self):
assert_allclose(
self.results.forecasts_error.T,
self.desired[['v1', 'v2', 'v3']]
)
def test_forecasts_error_cov(self):
assert_allclose(
self.results.forecasts_error_cov.diagonal(),
self.desired[['F1', 'F2', 'F3']]
)
def test_predicted_states(self):
assert_allclose(
self.results.predicted_state[:,1:].T,
self.desired[['a1', 'a2', 'a3']]
)
def test_predicted_states_cov(self):
assert_allclose(
self.results.det_predicted_state_cov.T,
self.desired[['detP']]
)
def test_smoothed_states(self):
assert_allclose(
self.results.smoothed_state.T,
self.desired[['alphahat1', 'alphahat2', 'alphahat3']]
)
def test_smoothed_states_cov(self):
assert_allclose(
self.results.det_smoothed_state_cov.T,
self.desired[['detV']]
)
def test_smoothed_forecasts(self):
assert_allclose(
self.results.smoothed_forecasts.T,
self.desired[['muhat1','muhat2','muhat3']]
)
def test_smoothed_state_disturbance(self):
assert_allclose(
self.results.smoothed_state_disturbance.T,
self.desired[['etahat1','etahat2','etahat3']]
)
def test_smoothed_state_disturbance_cov(self):
assert_allclose(
self.results.det_smoothed_state_disturbance_cov.T,
self.desired[['detVeta']]
)
def test_smoothed_measurement_disturbance(self):
assert_allclose(
self.results.smoothed_measurement_disturbance.T,
self.desired[['epshat1','epshat2','epshat3']]
)
def test_smoothed_measurement_disturbance_cov(self):
assert_allclose(
self.results.smoothed_measurement_disturbance_cov.diagonal(),
self.desired[['Veps1','Veps2','Veps3']]
)
class TestMultivariateMissingClassicalSmoothing(TestMultivariateMissing):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestMultivariateMissingClassicalSmoothing, cls).setup_class(
smooth_method=SMOOTH_CLASSICAL, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL)
assert_equal(self.model.ssm._kalman_smoother.smooth_method,
SMOOTH_CLASSICAL)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_CLASSICAL)
class TestMultivariateMissingAlternativeSmoothing(TestMultivariateMissing):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestMultivariateMissingAlternativeSmoothing, cls).setup_class(
smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother.smooth_method,
SMOOTH_ALTERNATIVE)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_ALTERNATIVE)
class TestMultivariateMissingUnivariateSmoothing(TestMultivariateMissing):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestMultivariateMissingUnivariateSmoothing, cls).setup_class(
filter_method=FILTER_UNIVARIATE, *args, **kwargs)
def test_smooth_method(self):
assert_equal(self.model.ssm.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
assert_equal(self.model.ssm._kalman_smoother._smooth_method,
SMOOTH_UNIVARIATE)
class TestMultivariateVAR(object):
"""
Tests for most filtering and smoothing variables against output from the
R library KFAS.
Note that KFAS uses the univariate approach which generally will result in
different predicted values and covariance matrices associated with the
measurement equation (e.g. forecasts, etc.). In this case, although the
model is multivariate, each of the series is truly independent so the values
will be the same regardless of whether the univariate approach is used or
not.
"""
@classmethod
def setup_class(cls, *args, **kwargs):
# Results
path = current_path + os.sep + 'results/results_smoothing2_R.csv'
cls.desired = pd.read_csv(path)
# Data
dta = datasets.macrodata.load_pandas().data
dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS')
obs = np.log(dta[['realgdp','realcons','realinv']]).diff().ix[1:]
# Create the model
mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs)
mod['design'] = np.eye(3)
mod['obs_cov'] = np.array([[ 0.0000640649, 0. , 0. ],
[ 0. , 0.0000572802, 0. ],
[ 0. , 0. , 0.0017088585]])
mod['transition'] = np.array([[-0.1119908792, 0.8441841604, 0.0238725303],
[ 0.2629347724, 0.4996718412, -0.0173023305],
[-3.2192369082, 4.1536028244, 0.4514379215]])
mod['selection'] = np.eye(3)
mod['state_cov'] = np.array([[ 0.0000640649, 0.0000388496, 0.0002148769],
[ 0.0000388496, 0.0000572802, 0.000001555 ],
[ 0.0002148769, 0.000001555 , 0.0017088585]])
mod.initialize_approximate_diffuse(1e6)
cls.model = mod
cls.results = mod.smooth([], return_ssm=True)
# Calculate the determinant of the covariance matrices (for easy
# comparison to other languages without having to store 2-dim arrays)
cls.results.det_scaled_smoothed_estimator_cov = (
np.zeros((1, cls.model.nobs)))
cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
cls.results.det_smoothed_state_disturbance_cov = (
np.zeros((1, cls.model.nobs)))
for i in range(cls.model.nobs):
cls.results.det_scaled_smoothed_estimator_cov[0,i] = (
np.linalg.det(
cls.results.scaled_smoothed_estimator_cov[:,:,i]))
cls.results.det_predicted_state_cov[0,i] = np.linalg.det(
cls.results.predicted_state_cov[:,:,i+1])
cls.results.det_smoothed_state_cov[0,i] = np.linalg.det(
cls.results.smoothed_state_cov[:,:,i])
cls.results.det_smoothed_state_disturbance_cov[0,i] = (
np.linalg.det(
cls.results.smoothed_state_disturbance_cov[:,:,i]))
def test_loglike(self):
assert_allclose(np.sum(self.results.llf_obs), 1695.34872)
def test_scaled_smoothed_estimator(self):
assert_allclose(
self.results.scaled_smoothed_estimator.T,
self.desired[['r1', 'r2', 'r3']], atol=1e-4
)
def test_scaled_smoothed_estimator_cov(self):
# Last obs is zero, so exclude it
assert_allclose(
np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]),
np.log(self.desired[['detN']][:-1]), atol=1e-6
)
def test_forecasts(self):
assert_allclose(
self.results.forecasts.T,
self.desired[['m1', 'm2', 'm3']], atol=1e-6
)
def test_forecasts_error(self):
assert_allclose(
self.results.forecasts_error.T[:, 0],
self.desired['v1'], atol=1e-6
)
def test_forecasts_error_cov(self):
assert_allclose(
self.results.forecasts_error_cov.diagonal()[:, 0],
self.desired['F1'], atol=1e-6
)
def test_predicted_states(self):
assert_allclose(
self.results.predicted_state[:,1:].T,
self.desired[['a1', 'a2', 'a3']], atol=1e-6
)
def test_predicted_states_cov(self):
assert_allclose(
self.results.det_predicted_state_cov.T,
self.desired[['detP']], atol=1e-16
)
def test_smoothed_states(self):
assert_allclose(
self.results.smoothed_state.T,
self.desired[['alphahat1', 'alphahat2', 'alphahat3']], atol=1e-6
)
def test_smoothed_states_cov(self):
assert_allclose(
self.results.det_smoothed_state_cov.T,
self.desired[['detV']], atol=1e-16
)
def test_smoothed_forecasts(self):
assert_allclose(
self.results.smoothed_forecasts.T,
self.desired[['muhat1','muhat2','muhat3']], atol=1e-6
)
def test_smoothed_state_disturbance(self):
assert_allclose(
self.results.smoothed_state_disturbance.T,
self.desired[['etahat1','etahat2','etahat3']], atol=1e-6
)
def test_smoothed_state_disturbance_cov(self):
assert_allclose(
self.results.det_smoothed_state_disturbance_cov.T,
self.desired[['detVeta']], atol=1e-18
)
def test_smoothed_measurement_disturbance(self):
assert_allclose(
self.results.smoothed_measurement_disturbance.T,
self.desired[['epshat1','epshat2','epshat3']], atol=1e-6
)
def test_smoothed_measurement_disturbance_cov(self):
assert_allclose(
self.results.smoothed_measurement_disturbance_cov.diagonal(),
self.desired[['Veps1','Veps2','Veps3']], atol=1e-6
)
class TestMultivariateVARAlternativeSmoothing(TestMultivariateVAR):
@classmethod
def setup_class(cls, *args, **kwargs):
if compatibility_mode:
raise SkipTest
super(TestMultivariateVARAlternativeSmoothing, cls).setup_class(
smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs)
def test_smooth_method(self):
| assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) | numpy.testing.assert_equal |
# -*- coding: utf-8 -*-
__all__ = ['points', 'costfunction', 'station']
# todo add grid definitions of reanalysis
# for plotting
era5_grid = {'lon': None, 'lat': None}
erai_grid = None
jra55_grid = None
cera_grid = None
def station(lon, lat, label=None, marker='o', markersize=20, bounds=1, ax=None, data=None, **kwargs):
import numpy as np
import cartopy as cpy
import matplotlib.pyplot as plt
from ..fun import check_kw
# from cartopy.feature import NaturalEarthFeature
# coast = NaturalEarthFeature(category='physical', scale='10m', facecolor='none', name='coastline')
# have a time component? -> plot as time series
if data is not None:
if lon in data:
lon = data[lon].values
if lat in data:
lat = data[lat].values
else:
lon = np.asarray(lon)
lat = np.asarray(lat)
itx = np.isfinite(lon) & np.isfinite(lat)
lon = lon[itx]
lat = lat[itx]
if lon.size != lat.size:
raise ValueError("Lon and Lat need same size")
# todo add number of points plotted / median distance
ilon = np.median(lon)
ilat = np.median(lat)
projection = kwargs.get('projection', cpy.crs.PlateCarree())
if ax is None:
ax = plt.axes(projection=projection)
ax.set_extent((ilon - bounds, ilon + bounds, ilat - bounds, ilat + bounds), crs=projection)
if check_kw('ocean', value=True, **kwargs):
ax.add_feature(cpy.feature.OCEAN.with_scale('10m'), zorder=0)
if check_kw('land', value=True, **kwargs):
ax.add_feature(cpy.feature.LAND.with_scale('10m'), zorder=0)
if check_kw('coastline', value=True, **kwargs):
ax.add_feature(cpy.feature.COASTLINE.with_scale('10m'), zorder=0)
# ax.coastlines()
if check_kw('rivers', value=True, **kwargs):
ax.add_feature(cpy.feature.RIVERS.with_scale('10m'), zorder=1)
if check_kw('lakes', value=True, **kwargs):
ax.add_feature(cpy.feature.LAKES.with_scale('10m'), zorder=1)
if check_kw('borders', value=True, **kwargs):
ax.add_feature(cpy.feature.BORDERS.with_scale('10m'), zorder=1)
if check_kw('states', value=True, **kwargs):
ax.add_feature(cpy.feature.STATES.with_scale('10m'), zorder=1)
ax.scatter(lon, lat, s=markersize, c=kwargs.get('color', 'r'), transform=projection, zorder=10,
edgecolor='k') # ontop
try:
gl = ax.gridlines(draw_labels=True, xlocs=kwargs.get('xlocs', None), ylocs=kwargs.get('ylocs', None),
linewidth=0.5, linestyle='--', color='k')
gl.xformatter = cpy.mpl.gridliner.LONGITUDE_FORMATTER
gl.yformatter = cpy.mpl.gridliner.LATITUDE_FORMATTER
gl.xlabels_top = False
gl.ylabels_right = False
except:
ax.gridlines(draw_labels=False)
ax.set_extent((ilon - bounds, ilon + bounds, ilat - bounds, ilat + bounds), crs=projection)
left = 0.5
bottom = 0.13
width = 0.3
height = 0.2
rect = [left, bottom, width, height]
ax2 = plt.axes(rect, projection=cpy.crs.PlateCarree())
ax2.set_extent((ilon - 30, ilon + 30, ilat - 30, ilat + 30))
# ax2.set_global() #will show the whole world as context
ax2.coastlines(resolution='110m', zorder=2)
ax2.add_feature(cpy.feature.LAND)
ax2.add_feature(cpy.feature.OCEAN)
ax2.gridlines()
lon0, lon1, lat0, lat1 = ax.get_extent()
box_x = [lon0, lon1, lon1, lon0, lon0]
box_y = [lat0, lat0, lat1, lat1, lat0]
plt.plot(box_x, box_y, color='red', transform=cpy.crs.Geodetic())
return ax
def points(lon, lat, labels=None, values=None, markersize=80, ocean=True, land=True, coastlines=True, rivers=False,
grid=True, posneg=False, extent=None, lloffset=0.2, showcost=False, clabel=None, cbars={}, colorlevels=None,
data=None, vmin=None, vmax=None, dropna=False, figure=None, gridspecs=None, **kwargs):
""" Plot stations on a map
Args:
lon (np.array, list): Longitudes
lat (np.array, list): Latidutes
labels (np.array, list): Labels
values (np.array, list): Values for scatterplot
markersize (int): markersize
ocean (bool): plot ocean ?
land (bool): plot land ?
coastlines (bool): plot coastlines ?
rivers (bool): plot river ?
grid (bool): plot gridlines ?
posneg (bool): different markers for positive and negative
extent (str): neither (default), both, min, max
lloffset (float): label offset
showcost (bool): Estimate Cost function and add to title
clabel (str): Colorbar Label
cbars (dict): Colorbar Options
colorlevels (list, str): scatterplot colorlevels
data (xr.DataArray): Data
vmin (float): minimum value
vmax (float): maximum value
dropna (bool): Remove missing values?
figure (plt.figure): figure handle
gridspecs (dict): gridspec options for figure
**kwargs:
Returns:
plt.axes
"""
import numpy as np
import cartopy as cpy
from matplotlib.colors import BoundaryNorm
import matplotlib.pyplot as plt
from ._helpers import cost, plot_arange as pa, plot_levels as pl
if data is not None:
lon = data[lon]
lat = data[lat]
values = data
lon = np.asarray(lon)
lat = np.asarray(lat)
if lon.size != lat.size:
raise ValueError("Lon and Lat need same size")
if values is not None:
values = np.asarray(values, dtype=float)
nn = np.size(values)
if lon.size != lat.size or lon.size != values.size:
raise ValueError("Lon, Lat and Values need same size", lon.size, lat.size, values.size)
if vmin is not None:
idx = values < vmin
values[idx] = np.nan
print("vmin", idx.sum(), nn)
if vmax is not None:
idx = values > vmax
values[idx] = np.nan
print("vmax", idx.sum(), nn)
if dropna:
idx = np.isfinite(values)
values = values[idx]
lon = lon[idx]
lat = lat[idx]
print("NA", nn - idx.sum(), nn)
projection = kwargs.get('projection', cpy.crs.PlateCarree())
if figure is None:
ax = plt.axes(projection=projection)
else:
ax = figure.add_subplot(gridspecs, projection=projection)
if ocean:
ax.add_feature(cpy.feature.OCEAN, zorder=0, facecolor=kwargs.get('ocean_facecolor', cpy.feature.COLORS['water']))
if land:
ax.add_feature(cpy.feature.LAND, zorder=0, facecolor=kwargs.get('land_facecolor', cpy.feature.COLORS['land']))
if coastlines:
ax.coastlines()
if rivers:
ax.add_feature(cpy.feature.LAKES, zorder=0)
ax.add_feature(cpy.feature.RIVERS, zorder=1)
if labels is not None:
labels = np.asarray(labels)
if values is None:
ax.scatter(lon, lat, s=markersize, c=kwargs.get('color', 'r'), transform=cpy.crs.PlateCarree(), zorder=10,
edgecolor='k') # ontop
else:
if posneg:
kwargs['marker'] = np.where(values < 0, 'd', 'o')
cmap = plt.get_cmap(kwargs.pop('cmap', None))
norm = None
if colorlevels is not None:
if isinstance(colorlevels, str):
colorlevels = eval(colorlevels) # plot_levels, plot_arange
norm = BoundaryNorm(colorlevels, cmap.N)
idx = np.isfinite(values)
cs = ax.scatter(lon[idx], lat[idx], s=markersize, c=values[idx],
transform=cpy.crs.PlateCarree(),
zorder=10,
cmap=cmap,
edgecolor='k',
marker=kwargs.get('marker', 'o'),
norm=norm)
cbars['fraction'] = cbars.get('fraction', 0.01)
cbars['aspect'] = cbars.get('aspect', 50)
cbars['shrink'] = cbars.get('shrink', 0.8)
cbars['extend'] = cbars.get('extend', 'both')
cb = plt.colorbar(cs, ax=ax, **cbars)
if clabel is not None:
cb.set_label(clabel)
if showcost:
tcost = cost(lon, lat, values)
if np.isfinite(values).sum() != np.size(values):
itx = ~np.isfinite(values)
ax.scatter(lon[itx], lat[itx], s=markersize, marker='s', c='w', transform=cpy.crs.PlateCarree(), zorder=9,
edgecolor='k')
if labels is not None:
if not hasattr(lloffset, '__iter__'):
lloffset = [lloffset] * len(labels)
for i, j, l, k in zip(lon, lat, labels, lloffset):
ax.text(i + k, j, str(l), horizontalalignment='left', verticalalignment='top',
transform=cpy.crs.PlateCarree(), fontsize=kwargs.get('fontsize', 8), zorder=12,
clip_on=True)
if grid:
try:
gl = ax.gridlines(draw_labels=True, xlocs=kwargs.get('xlocs', None), ylocs=kwargs.get('ylocs', None),
linewidth=0.5, linestyle='--', color='k')
gl.xformatter = cpy.mpl.gridliner.LONGITUDE_FORMATTER
gl.yformatter = cpy.mpl.gridliner.LATITUDE_FORMATTER
gl.xlabels_top = False
gl.ylabels_right = False
except:
ax.gridlines(draw_labels=False)
if values is not None:
nn = np.sum(np.isfinite(values))
title = '(# %d / %d)' % (nn, np.size(values))
# COST Summary
if showcost:
tscost = np.nansum(tcost) / np.sum(np.isfinite(values))
title += ' Cost: %5.2f' % tscost
else:
title = 'Stations # %d' % np.size(lon)
ax.set_title(kwargs.get('title', '') + ' ' + title)
if 'xlabel' in kwargs.keys():
ax.set_xlabel(kwargs.get('xlabel'))
if 'ylabel' in kwargs.keys():
ax.set_ylabel(kwargs.get('ylabel'))
if extent is not None:
ax.set_extent(extent, crs=cpy.crs.PlateCarree())
return ax
def costfunction(lon, lat, values, **kwargs):
import numpy as np
from ._helpers import cost
# plot cost values instead
tcost = cost(lon, lat, values)
values = np.where(np.isfinite(values), tcost, np.nan) # Plot Cost Values instead of real values
return points(lon, lat, values=values, **kwargs)
def values_zonal_meridional(lon, lat, values, zonal=True, ax=None, label=None, lat_bands=10, lon_bands=10, func=None,
fkwargs={}, **kwargs):
import numpy as np
import cartopy as cpy
import matplotlib.pyplot as plt
lon = | np.asarray(lon) | numpy.asarray |
import datetime
import json
import numpy as np
import os
import pandas as pd
import pickle
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
os.environ['TF_CPP_MIN_VLOG_LEVEL'] = '0'
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '0'
import random
from absl import logging
logging.set_verbosity(logging.INFO)
from itertools import chain
from sklearn.linear_model import LinearRegression
from statsmodels.tsa.api import VAR
from statsmodels.tsa.stattools import adfuller
from statsmodels.tools.eval_measures import rmse, aic
import local_settings
from climate_ae.models import utils
from climate_ae.data_generator.datahandler import input_fn
import climate_ae.models.ae.eval_utils as eval_utils
import climate_ae.models.ae.climate_utils as climate_utils
import climate_ae.models.ae.train as train
from climate_ae.models.ae.train_linear_model import load_data, predict_latents_and_decode
DEBUG = False
def get_forecasts(model_fitted, annos, var_order, n_steps):
forecasts_ = []
if n_steps == 0:
n_steps = annos.shape[0] - var_order
n_to_predict = (annos.shape[0] - var_order)//n_steps
for i in range(n_to_predict):
forecasts_.append(
model_fitted.forecast(
y=annos[(i*n_steps):((i*n_steps)+var_order),:],
steps=n_steps))
forecasts_np = np.concatenate(forecasts_)
residuals = annos[var_order:(var_order+n_to_predict*n_steps),:] - forecasts_np
return forecasts_np, residuals
def generate_bts_sample_parametric(model, reg, fitted_, resids_, block_size,
dim_x, dim_out, precip):
n_blocks = int(np.floor(fitted_.shape[0]/block_size))
n_blocks_dict = {}
for b in range(n_blocks):
n_blocks_dict[b] = list(range((b*block_size), ((b+1)*block_size)))
ho_annos_bts = np.zeros([n_blocks*block_size, dim_x])
for b in range(n_blocks):
# get a random block
block_id = random.randint(0, n_blocks-1)
# get residuals from this random block
resampled_resid = resids_[n_blocks_dict[block_id],:]
fitted_to_add = fitted_[(b*block_size):((b+1)*block_size),:]
# add to fitted values
ho_annos_bts[(b*block_size):((b+1)*block_size),:] = (fitted_to_add +
resampled_resid)
# get decoded predictions for bootstrap sample
shape_ = [ho_annos_bts.shape[0], *dim_out[1:]]
ho_xhatexp_bts = predict_latents_and_decode(model, reg, ho_annos_bts, shape_)
# if precipitation: transform back to original scale
if precip:
ho_xhatexp_bts = ho_xhatexp_bts ** 2
return ho_xhatexp_bts
def generate_bts_sample_simple(model, reg, annos, block_size, dim_out,
precip):
dim_x = annos.shape[1]
n_blocks = int(np.floor(annos.shape[0]/block_size))
n_blocks_dict = {}
for b in range(n_blocks):
n_blocks_dict[b] = list(range((b*block_size), ((b+1)*block_size)))
annos_bts = np.zeros([n_blocks*block_size, dim_x])
for b in range(n_blocks):
# get a random block
block_id = random.randint(0, n_blocks-1)
annos_bts[(b*block_size):((b+1)*block_size),:] = \
annos[n_blocks_dict[block_id],:]
# get decoded predictions for bootstrap sample
shape_ = [annos_bts.shape[0], *dim_out[1:]]
xhatexp_bts = predict_latents_and_decode(model, reg, annos_bts, shape_)
# if precipitation: transform back to original scale
if precip:
xhatexp_bts = xhatexp_bts ** 2
return xhatexp_bts
def train_linear_model_and_generate(checkpoint_path, n_bts_samples, var_order,
block_size, n_steps, precip, save_nc, seed=1):
# set seed
np.random.seed(seed)
# get configs from model
with open(os.path.join(checkpoint_path, "hparams.pkl"), 'rb') as f:
config = pickle.load(f)
config = utils.config_to_namedtuple(config)
model, _ = train.get_models(config)
# input function
def input_anno(params, mode, repeat, n_repeat=None):
dataset = input_fn(params=params, mode=mode, repeat=repeat,
n_repeat=n_repeat, shuffle=False)
if len(params.temp_indices) == 0 and len(params.psl_indices) == 0:
dataset = dataset.map(lambda x:
{"inputs": x["inputs"],
"anno": tf.gather(x["anno"], params.anno_indices, axis=1),
"year": x["year"],
"month": x["month"],
"day": x["day"]
})
elif len(params.temp_indices) == 0:
dataset = dataset.map(lambda x:
{"inputs": x["inputs"],
"anno": tf.concat(
(tf.gather(x["anno"], params.anno_indices, axis=1),
tf.gather(x["psl_mean_ens"], params.psl_indices, axis=1)),
axis=1),
"year": x["year"],
"month": x["month"],
"day": x["day"]
})
elif len(params.psl_indices) == 0:
dataset = dataset.map(lambda x:
{"inputs": x["inputs"],
"anno": tf.concat(
(tf.gather(x["anno"], params.anno_indices, axis=1),
tf.gather(x["temp_mean_ens"], params.temp_indices, axis=1)),
axis=1),
"year": x["year"],
"month": x["month"],
"day": x["day"]
})
else:
dataset = dataset.map(lambda x:
{"inputs": x["inputs"],
"anno": tf.concat(
(tf.gather(x["anno"], params.anno_indices, axis=1),
tf.gather(x["psl_mean_ens"], params.psl_indices, axis=1),
tf.gather(x["temp_mean_ens"], params.temp_indices, axis=1)),
axis=1),
"year": x["year"],
"month": x["month"],
"day": x["day"]
})
return dataset
global_step = tf.Variable(initial_value=0, dtype=tf.int64, trainable=False,
name="global_step")
train_inputs = input_anno(params=config, mode="train",
repeat=False)
test_inputs = input_anno(params=config, mode="test1",
repeat=False)
holdout_inputs = input_anno(params=config, mode="test2",
repeat=False)
# dummy run - otherwise, the model wouldn't be fully build
show_inputs = iter(train_inputs)
_ = model(next(show_inputs)["inputs"])
# restore model from checkpoint
checkpoint = tf.train.Checkpoint(model=model, global_step=global_step)
manager = tf.train.CheckpointManager(checkpoint, checkpoint_path, max_to_keep=3)
status = checkpoint.restore(manager.latest_checkpoint)
status.assert_consumed()
# get training data for linear latent space model
tr_inputs, _, tr_latents, tr_annos, _, _, _ = load_data(
train_inputs, model, subset=True, debug=DEBUG)
# fit linear model
reg = LinearRegression().fit(tr_annos, tr_latents)
# get test data
te_inputs, te_recons, _, te_annos, _, _, _ = load_data(test_inputs, model,
debug=DEBUG)
# predict latents for test set and decode
te_xhatexp = predict_latents_and_decode(model, reg, te_annos,
| np.shape(te_inputs) | numpy.shape |
"""
Author: <NAME>
Email: <EMAIL>
Description: Part of the code package corresponding to my master thesis. This file implements a 2d
optimal control problem example.
Year: 2019/2020
"""
########################################################################################################################
# importing stuff
########################################################################################################################
import numpy as np
import random
import logging
import re
from matplotlib import pyplot as plt
from collections import deque
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import time
from valueFunctionApprox.myValueFunctionApproximation import MyValueFunctionApproximation
from misc.myLoggingFunctions import createSetupFile
from misc.myLoggingFunctions import depositeIntermediateTrainingResults
import sys
sys.path.append('../functionApproximation/cpd')
from myALSOptimiser import MyALSRbfOptimiser
########################################################################################################################
# definition of functions
########################################################################################################################
def terminalCostFunc(xList, domainBox):
"""
@param[in] ### xList ### list of length two containing data points, where
xList[0] corresponds to the x1 data, and xList[1] corresponds to the x2 data
NOTE:
> data can be given in scalar or in matrix form!
@param[in] ### domainBox ### list of two tuples representing the boundary of the domain the vehicle should
not leave
@return ### retVal ### a scalar or a matrix modeling the cost of achieving the states
given in xList at the final time
"""
# take care of the following:
# > there are logical operators in python for boolean arrays and for boolean scalars - there is no approach to
# cover both cases ...
# > hence distinguish two cases: is xList a list of two scalars or is it a list of arrays ....
tmp = 100.0
if np.isscalar(xList[0]) == True:
if (domainBox[0][0] <= xList[0] <= domainBox[0][1]) and (domainBox[1][0] <= xList[1] <= domainBox[1][1]):
return 0.0
else:
return tmp
else:
retVal = tmp * | np.ones(xList[0].shape) | numpy.ones |
# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
import itertools
import typing as tp
import numpy as np
from nevergrad.parametrization import parameter as p
from .base import ExperimentFunction
from . import corefuncs
class PBT(ExperimentFunction):
"""Population-Based Training, also known as Lamarckism or Meta-Optimization."""
def __init__(
self,
names: tp.Tuple[str, ...] = ("sphere", "cigar", "ellipsoid"),
dimensions: tp.Tuple[int, ...] = (7, 7, 7),
num_workers: int = 10,
):
for name in names:
if name not in corefuncs.registry:
available = ", ".join(sorted(corefuncs.registry))
raise ValueError(
f'Unknown core function "{name}" in PBT. Available names are:\n-----\n{available}'
)
self._funcs = [corefuncs.registry[name] for name in names]
self._optima = [np.random.normal(size=d) for d in dimensions]
assert len(names) == len(dimensions)
self._hyperparameter_dimension = len(names)
self._dimensions = dimensions
self._total_dimension = sum(dimensions)
parametrization = p.Array(shape=(self._hyperparameter_dimension,)).set_name("")
# Population of checkpoints (that are optimized by the underlying optimization method)
# and parameters (that we do optimize).
self._population_checkpoints: tp.List[np.ndarray] = [np.zeros(self._total_dimension)] * num_workers
self._population_parameters: tp.List[np.ndarray] = [
| np.zeros(self._hyperparameter_dimension) | numpy.zeros |
"""Module that handles shared information for all network objects."""
import xml.etree.ElementTree as et
import numbers
import numpy as np
import pandas as pd
import scipy.sparse as sps
from paminco.utils.readin import parse_number, xml_find_root
from paminco.utils.misc import Cache
from paminco.utils.typing import sparse_format, is_int, is_iterable, IntEnum2
import paminco._doc as _doc
ID_UNMAPPED = -9999
LBL_UNMAPPED = "Invalid"
class FlowDirection(IntEnum2):
"""Enum defining the type flow for the graph."""
DIRECTED = 0
"""All edges can only take flow >= 0."""
UNDIRECTED = 1
"""All edges can take any flow."""
MIXED = 2
"""Some edges may only take flow >= 0."""
class Edges:
"""
Class that contains the edges/links of a network.
An edges object can be instantiated in several ways:
Edges(e)
where ``e`` is an Edges object. Data in ``e`` will be
copied if specfied by parameter ``copy``.
Edges(st)
where ``st`` is array_like. Parameter st is converted to
ndarray and is expected to me of shape (m, 2). Can be
node indices or node labels specifying an edge. If labels
are given, indices are mapped by ``map_labels_to_indices``,
given indices are mapped by ``map_indices_to_labels``. Edge
bounds are determined by the parameter ``directed``.
Edges((st, bounds))
where ``st`` is array_like and ``bounds`` is tuple (lower,
upper) specifying bounds used for all edges or array_like
of shape (m, 2) marking individual bounds for all edges.
Edges((labels, indices, bounds))
where ``labels``, ``indices`` are array_like of shape
(m, 2) and ``bounds`` is tuple (lower, upper) specifying
bounds used for all edges or array_like of shape (m, 2)
containing individual bounds for all edges.
Parameters
----------
data : ndarray, or tuple of ndarray
Edge data.
directed_flow : bool, default=True
Controls default values for ``None`` in bounds. If ``True``, lower
bounds are set to 0 and ``False`` to -inf. Missing upper bounds are
set to inf.
map_labels_to_indices : None, bool, dict, or callable, default=True
Determines mapping of labels to indices if no indices are
given. If ``None`` or ``False``, indices of edges will be set
to -9999, denoting invalid edge indices. If ``dict``,
labels will be mapped by this dict. If ``True``, node indices
are set to 0, 1, ..., n-1. If ``callable``, use callable with
signature ``indices = callable(labels)``.
map_indices_to_labels : None, bool, dict, or callable, default=True
Determines mapping of indices to indices if no labels are
given. If ``None`` or ``False``, indices of edges will be set
to 'invalid', denoting invalid edge labels. If ``dict``,
indices will be mapped by this dict. If ``True``, node labels
are set to node indices as str. If ``callable``, use callable
with signature ``labels = callable(indices)``.
dtype_float : dtype, default=numpy.float_
Datatype for edge bounds.
dtype_int : dtype, default=int
Datatype for edge bounds.
copy : bool, default=False
Whether to create a copy of the inputs in data.
Attributes
----------
flow_directions : ndarray
Ndarray of shape (m, ). A ``-1`` denotes an edge with lb < 0 and
ub <= 0. A ``0`` denotes an edge with lb < 0 and ub > 0.
A ``1`` denotes an edge with lb >=0 and ub > 0.
"""
def __init__(
self,
data,
directed_flow: bool = True,
map_labels_to_indices=True, # optional
map_indices_to_labels=True, # optional
dtype_float=None,
dtype_int=None,
copy: bool = False,
) -> None:
# Collect kwargs
kw = {
"directed_flow": directed_flow,
"map_labels_to_indices": map_labels_to_indices,
"map_indices_to_labels": map_indices_to_labels,
"dtype_float": dtype_float,
"dtype_int": dtype_int,
"copy": copy,
}
if isinstance(data, Edges):
d = (data.labels, data.indices, data.bounds)
return self.__init__(d,
dtype_float=data.dtype_float,
dtype_int=data.dtype_int)
elif isinstance(data, tuple):
if len(data) == 3:
pass
elif len(data) == 2:
# (labels or indices, bounds)
st, bounds = data
st = np.array(st)
if st.dtype.kind in {'U', 'S'}:
# (labels, bounds)
if isinstance(map_labels_to_indices, dict):
st_ids = np.vectorize(map_labels_to_indices.__getitem__)(st)
elif map_labels_to_indices is True:
# Automap labels
# Get unique labels and sort them if quasi-ints
unique_lbl = np.unique(st)
try:
unique_lbl = sorted(unique_lbl, key=int)
except ValueError:
pass
d = dict(zip(unique_lbl, np.arange(len(unique_lbl))))
st_ids = np.vectorize(d.__getitem__)(st)
elif map_labels_to_indices is None or map_labels_to_indices is False:
# Set to invalid indices
st_ids = np.full(st.shape, ID_UNMAPPED, dtype=int)
else:
# Map labels by callable
st_ids = map_labels_to_indices(st)
return self.__init__((st, st_ids, bounds), **kw)
elif issubclass(st.dtype.type, numbers.Integral):
# (indices, bounds)
unique_st = np.unique(st)
if np.array_equal(np.sort(unique_st), np.arange(len(unique_st))) is False:
raise ValueError(f"Indices must be all integers from 0 to {len(unique_st) - 1}.")
if isinstance(map_indices_to_labels, dict):
st_lbl = np.vectorize(map_indices_to_labels.__getitem__)(st)
elif map_indices_to_labels is True:
st_lbl = st.astype(str)
elif map_indices_to_labels is None or map_indices_to_labels is False:
# Set to invalid indices
st_lbl = np.full(st.shape, LBL_UNMAPPED)
else:
st_lbl = map_indices_to_labels(st)
return self.__init__((st_lbl, st, bounds), **kw)
else:
raise ValueError(f"Invalid edge data: {data}.")
else:
raise ValueError(f"Invalid edge data: {data}.")
else:
# Only labels or indices given -> build lower and upper bounds by directed
if directed_flow is True:
return self.__init__((data, (0, np.inf)), **kw)
return self.__init__((data, (-np.inf, np.inf)), **kw)
# Handle datatypes
if dtype_float is None:
dtype_float = np.float64
if dtype_int is None:
dtype_int = int
self._dtype_float = dtype_float
self._dtype_int = dtype_int
# Unpack data
labels, indices, bounds = data
self.labels = np.array(labels, dtype=str, copy=copy)
self.indices = np.array(indices, dtype=dtype_int, copy=copy)
# Broadcast bounds if lower, upper for all edges given
if not isinstance(bounds, np.ndarray):
bounds = np.array(bounds)
if len(bounds.shape) == 1:
bounds = bounds.reshape(1, -1)
bounds = np.repeat(bounds, len(labels), axis=0)
# Handle 'None' bounds
bkw = {"posinf": np.inf, "neginf": -np.inf}
self.bounds = np.array(bounds, dtype=dtype_float, copy=copy)
self.bounds[:, 1] = np.nan_to_num(self.bounds[:, 1],
copy=False,
nan=np.inf,
**bkw)
if directed_flow is True:
self.bounds[:, 0] = np.nan_to_num(self.bounds[:, 0],
copy=False,
nan=0.,
**bkw)
else:
self.bounds[:, 0] = np.nan_to_num(self.bounds[:, 0],
copy=False,
nan=-np.inf,
**bkw)
# Check consistency of labels, indices and bounds
if self.labels.shape[1] != 2:
raise ValueError(
f"Invalid edge data, labels are of shape {self.labels.shape}."
)
if (self.labels.shape == self.indices.shape == self.bounds.shape) is False:
raise ValueError(
"Inconsistent shapes. "
f"Labels: {self.labels.shape}, "
f"indices: {self.indices.shape}, "
f"bounds: {self.bounds.shape}."
)
# Set edge directions and get type of graph
self.flow_directions = np.zeros(len(self))
self.flow_directions[self.lb < 0] -= 1
self.flow_directions[self.ub > 0] += 1
if len(self.flow_undirected) == len(self):
self.flow_dir = FlowDirection.UNDIRECTED
elif len(self.flow_undirected) == 0:
self.flow_dir = FlowDirection.DIRECTED
else:
self.flow_dir = FlowDirection.MIXED
self.cache = Cache()
def __eq__(self, other) -> bool:
for att in ["labels", "indices", "bounds"]:
if np.array_equal(getattr(self, att), getattr(other, att)) is False:
return False
return True
def __len__(self) -> int:
return len(self.indices)
def __getitem__(self, idx):
if is_iterable(idx):
return [self[i] for i in idx]
return {att: getattr(self, att)[idx]
for att in ["source_lbl", "target_lbl", "s", "t", "lb", "ub"]}
def to_df(self, **kwargs) -> pd.DataFrame:
"""Get object as DataFrame.
Parameters
----------
**kwargs : keyword arguments, optional
Passed to DataFrame constructor.
Returns
-------
df : pandas.DataFrame
Edges with source/target labels, source/target ids, lower
and upper bounds.
"""
data = np.hstack([self.labels, self.indices, self.bounds])
df = pd.DataFrame(data, **kwargs)
df.columns = ["source_lbl", "target_lbl", "s", "t", "lb", "ub"]
df[["source_lbl", "target_lbl"]] = df[["source_lbl", "target_lbl"]].astype(str)
df[["s", "t"]] = df[["s", "t"]].astype(self._dtype_int)
df[["lb", "ub"]] = df[["lb", "ub"]].astype(self._dtype_float)
return df
def get_flow_df(
self,
x,
labels: bool = True,
colname_flow: str = "flow"
) -> pd.DataFrame:
if isinstance(x, (int, float)):
x = np.full(len(self), x)
if labels is True:
s, t = self.source_lbl, self.target_lbl
dtype = str
else:
s, t = self.s, self.t
dtype = int
df = pd.DataFrame({"source": s,
"target": t,
colname_flow: x})
df[["source", "target"]] = df[["source", "target"]].astype(dtype)
return df
def get_directed(
self,
w=None,
backward_positive: bool = True
) -> tuple:
if self.cache.is_valid("directed_elements") is False:
forward = self.ub > 0
backward = self.lb < 0
s_fw, t_fw = self.indices[forward, :].T
t_bw, s_bw = self.indices[backward, :].T
s = np.hstack((s_fw, s_bw))
t = np.hstack((t_fw, t_bw))
self.cache["directed_elements"] = (forward, backward, s, t)
else:
(forward, backward, s, t) = self.cache["directed_elements"]
if w is not None:
w_fw = w[forward]
w_bw = w[backward]
if backward_positive is False:
w_bw = - w_bw
# Stack weight similar to source, target
w = np.hstack((w_fw, w_bw))
return s, t, w
return s, t
def get_duplicate_edges(self) -> np.ndarray:
# Dubplicates -> s/t both are the same
st = pd.Series([str(a) + "-" + str(b) for (a, b) in self.indices])
return np.where(st.duplicated())[0]
def map_labels(self, d: dict) -> None:
"""Map edge labels by d."""
self.indices = np.vectorize(d.__getitem__)(self.labels).astype(self.dtype_int)
def _delete_edges(
self,
del_idx,
return_indices: bool = False
):
del_idx = np.array(del_idx)
# Delete edges in all numpy arrays
self.labels = np.delete(self.labels, del_idx, axis=0)
self.indices = np.delete(self.indices, del_idx, axis=0)
self.bounds = | np.delete(self.bounds, del_idx, axis=0) | numpy.delete |
import numpy as np
import os
import sys
import yaml
from .fgcmUtilities import FocalPlaneProjectorFromOffsets
from .fgcmLogger import FgcmLogger
class ConfigField(object):
"""
A validatable field with a default
"""
def __init__(self, datatype, value=None, default=None, required=False, length=None):
self._datatype = datatype
self._value = value
self._required = required
self._length = length
_default = default
if self._datatype == np.ndarray:
if default is not None:
_default = | np.atleast_1d(default) | numpy.atleast_1d |
from __future__ import print_function
import os
import sys
import numpy as np
import torch
# import networkx as nx
import random
from torch.autograd import Variable
from torch.nn.parameter import Parameter
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from tqdm import tqdm
from copy import deepcopy
from pygcn.models import SGCNModel
from rl.dqn import DQN
import itertools as it
# from .q_net_node import QNetNode, NStepQNetNode, node_greedy_actions
# from .node_attack_common import load_base_model, NodeAttakEnv, init_setup
# sys.path.append('%s/../common' % os.path.dirname(os.path.realpath(__file__)))
# from common.cmd_args import cmd_args
# sys.path.append('%s/../node_classification' % os.path.dirname(os.path.realpath(__file__)))
# from node_classification.node_utils import run_test, load_raw_graph
# sys.path.append('%s/../graph_attack' % os.path.dirname(os.path.realpath(__file__)))
# from graph_attack.nstep_replay_mem import NstepReplayMem
class Memory:
def __init__(self, memory_size):
self.memory_size = memory_size
self.memory = [None] * memory_size
self.occ = set()
self.avail = set(range(memory_size))
def add(self, record):
i = self.avail.pop()
self.memory[i] = record
self.occ.add(i)
def sample(self):
i = self.occ.pop()
record = self.memory[i]
self.memory[i] = None
self.avail.add(i)
return record
class Agent(object):
def __init__(self, args, env, target_dict, adv_start):
self.mem_pool = Memory(memory_size=500000)
self.env = env
self.args = args
self.target_dict = target_dict
self.actions1 = | np.arange(args.num_adv) | numpy.arange |
import numpy as np
def sqrt_gain_db(gain_db):
return gain_db / 2
def design_low_shelving_filter(g_db, f, q, fs):
k = np.tan((np.pi * f) / fs);
v0 = np.power(10.0, g_db / 20.0);
root2 = 1.0 / q
if v0 < 1:
v0 = 1 / v0
if g_db > 0:
b0 = (1 + np.sqrt(v0) * root2 * k + v0 * k * k) / (1 + root2 * k + k * k)
b1 = (2 * (v0 * k * k - 1)) / (1 + root2 * k + k * k)
b2 = (1 - np.sqrt(v0) * root2 * k + v0 * k * k) / (1 + root2 * k + k * k)
a0 = 1
a1 = (2 * (k * k - 1)) / (1 + root2 * k + k * k)
a2 = (1 - root2 * k + k * k) / (1 + root2 * k + k * k)
elif g_db < 0:
b0 = (1 + root2 * k + k * k) / (1 + root2 * np.sqrt(v0) * k + v0 * k * k)
b1 = (2 * (k * k - 1)) / (1 + root2 * np.sqrt(v0) * k + v0 * k * k)
b2 = (1 - root2 * k + k * k) / (1 + root2 * np.sqrt(v0) * k + v0 * k * k)
a0 = 1
a1 = (2 * (v0 * k * k - 1)) / (1 + root2 * np.sqrt(v0) * k + v0 * k * k)
a2 = (1 - root2 * np.sqrt(v0) * k + v0 * k * k) / (1 + root2 * np.sqrt(v0) * k + v0 * k * k)
else:
b0 = 1
b1 = 0
b2 = 0
a0 = 1
a1 = 0
a2 = 0
return np.array([b0, b1, b2, a0, a1, a2])
def design_high_shelving_filter(g_db, f, q, fs):
k = np.tan(np.pi * f / fs)
v0 = np.power(10, g_db / 20)
root2 = 1 / q
if v0 < 1:
v0 = 1 / v0
if g_db > 0:
b0 = (v0 + root2 * np.sqrt(v0) * k + k * k) / (1 + root2 * k + k * k)
b1 = (2 * (k * k - v0)) / (1 + root2 * k + k * k)
b2 = (v0 - root2 * np.sqrt(v0) * k + k * k) / (1 + root2 * k + k * k)
a0 = 1
a1 = (2 * (k * k - 1)) / (1 + root2 * k + k * k)
a2 = (1 - root2 * k + k * k) / (1 + root2 * k + k * k)
elif g_db < 0:
b0 = (1 + root2 * k + k * k) / (v0 + root2 * np.sqrt(v0) * k + k * k)
b1 = (2 * (k * k - 1)) / (v0 + root2 * np.sqrt(v0) * k + k * k)
b2 = (1 - root2 * k + k * k) / (v0 + root2 * np.sqrt(v0) * k + k * k)
a0 = 1
a1 = (2 * ((k * k) / v0 - 1)) / (1 + root2 / np.sqrt(v0) * k + (k * k) / v0)
a2 = (1 - root2 / np.sqrt(v0) * k + (k * k) / v0) / (1 + root2 / | np.sqrt(v0) | numpy.sqrt |
"""Bokeh Violinplot."""
import numpy as np
from bokeh.models.annotations import Title
from ....stats import hdi
from ....stats.density_utils import get_bins, histogram, kde
from ...plot_utils import _scale_fig_size, make_label
from .. import show_layout
from . import backend_kwarg_defaults, create_axes_grid
def plot_violin(
ax,
plotters,
figsize,
rows,
cols,
sharex,
sharey,
shade_kwargs,
shade,
rug,
rug_kwargs,
bw,
textsize,
circular,
hdi_prob,
quartiles,
backend_kwargs,
show,
):
"""Bokeh violin plot."""
if backend_kwargs is None:
backend_kwargs = {}
backend_kwargs = {
**backend_kwarg_defaults(("dpi", "plot.bokeh.figure.dpi"),),
**backend_kwargs,
}
(figsize, *_, linewidth, _) = _scale_fig_size(figsize, textsize, rows, cols)
shade_kwargs = {} if shade_kwargs is None else shade_kwargs
rug_kwargs = {} if rug_kwargs is None else rug_kwargs
rug_kwargs.setdefault("fill_alpha", 0.1)
rug_kwargs.setdefault("line_alpha", 0.1)
if ax is None:
ax = create_axes_grid(
len(plotters),
rows,
cols,
sharex=sharex,
sharey=sharey,
figsize=figsize,
backend_kwargs=backend_kwargs,
)
else:
ax = np.atleast_2d(ax)
for (var_name, selection, x), ax_ in zip(
plotters, (item for item in ax.flatten() if item is not None)
):
val = x.flatten()
if val[0].dtype.kind == "i":
dens = cat_hist(val, rug, shade, ax_, **shade_kwargs)
else:
dens = _violinplot(val, rug, shade, bw, circular, ax_, **shade_kwargs)
if rug:
rug_x = -np.abs(np.random.normal(scale=max(dens) / 3.5, size=len(val)))
ax_.scatter(rug_x, val, **rug_kwargs)
per = np.percentile(val, [25, 75, 50])
hdi_probs = hdi(val, hdi_prob, multimodal=False)
if quartiles:
ax_.line(
[0, 0], per[:2], line_width=linewidth * 3, line_color="black", line_cap="round"
)
ax_.line([0, 0], hdi_probs, line_width=linewidth, line_color="black", line_cap="round")
ax_.circle(
0,
per[-1],
line_color="white",
fill_color="white",
size=linewidth * 1.5,
line_width=linewidth,
)
_title = Title()
_title.text = make_label(var_name, selection)
ax_.title = _title
ax_.xaxis.major_tick_line_color = None
ax_.xaxis.minor_tick_line_color = None
ax_.xaxis.major_label_text_font_size = "0pt"
show_layout(ax, show)
return ax
def _violinplot(val, rug, shade, bw, circular, ax, **shade_kwargs):
"""Auxiliary function to plot violinplots."""
if bw == "default":
if circular:
bw = "taylor"
else:
bw = "experimental"
x, density = kde(val, circular=circular, bw=bw)
if not rug:
x = np.concatenate([x, x[::-1]])
density = np.concatenate([-density, density[::-1]])
ax.harea(y=x, x1=density, x2= | np.zeros_like(density) | numpy.zeros_like |
import math
import numpy as np
def split_patients(patient_admission: dict, admission_codes: dict, code_map: dict, seed=6669) -> (np.ndarray, np.ndarray, np.ndarray):
print('splitting train, valid, and test pids')
np.random.seed(seed)
common_pids = set()
for i, code in enumerate(code_map):
print('\r\t%.2f%%' % ((i + 1) * 100 / len(code_map)), end='')
for pid, admissions in patient_admission.items():
for admission in admissions:
codes = admission_codes[admission['admission_id']]
if code in codes:
common_pids.add(pid)
break
else:
continue
break
print('\r\t100%')
max_admission_num = 0
pid_max_admission_num = 0
for pid, admissions in patient_admission.items():
if len(admissions) > max_admission_num:
max_admission_num = len(admissions)
pid_max_admission_num = pid
common_pids.add(pid_max_admission_num)
remaining_pids = np.array(list(set(patient_admission.keys()).difference(common_pids)))
np.random.shuffle(remaining_pids)
train_num = 6000
valid_num = 125
train_pids = np.array(list(common_pids.union(set(remaining_pids[:(train_num - len(common_pids))].tolist()))))
valid_pids = remaining_pids[(train_num - len(common_pids)):(train_num + valid_num - len(common_pids))]
test_pids = remaining_pids[(train_num + valid_num - len(common_pids)):]
return train_pids, valid_pids, test_pids
def build_code_xy(pids: np.ndarray,
patient_admission: dict,
admission_codes_encoded: dict,
max_admission_num: int,
code_num: int,
max_code_num_in_a_visit: int) -> (np.ndarray, np.ndarray, np.ndarray):
print('building train/valid/test codes features and labels ...')
n = len(pids)
x = | np.zeros((n, max_admission_num, max_code_num_in_a_visit), dtype=int) | numpy.zeros |
#! /usr/bin/env python
# -*- coding: utf-8 -*-
""" This modules handles the CCD based images """
"""
// Full usage of ccd functionalities requires: shapely, astrobject, pynverse (all pipable) //
// ccd-x axis is refered to as 'i', y as "j".
show: plot the ccd as imshow.
show_traceindex: plot the ccd using `show()` and overplot the trace coutours.
"""
import warnings
import numpy as np
# Propobject
from propobject import BaseObject
# Astrobject
from astrobject.photometry import Image
# PyIFU
from pyifu.spectroscopy import Spectrum
from .utils.tools import kwargs_update
"""
The Idea of the CCD calibration is to first estimate the Spectral Matching.
Then to set this Matching to all the ScienceCCD objects.
- Tracematch holds the spaxel->pixel_area relation.
"""
__all__ = ["get_dome","get_ccd"]
##################################
# #
# Object Generators #
# #
##################################
def get_ccd(lampfile, ccdspec_mask=None,
tracematch=None, background=None,
correct_traceflexure=False, savefile_traceflexure=None,
**kwargs):
""" Load a SEDmachine ccd image.
Parameters
-----------
lampfile: [string]
Location of the file containing the object
tracematch: [Tracematch (pysedm object)] -optional-
Tracematch object containing the Spectral property on the CCD
background: [bool] -optional-
which kind of background do you want (i.e. background=0)
**kwargs goes to _get_default_background_()
Returns
-------
ScienceCCD (Child of CCD which is a Child of an astrobjec's Image)
"""
lamp = ScienceCCD(lampfile, background=0)
if tracematch is not None:
lamp.set_tracematch(tracematch)
# Trace Flexure Correction (if any)
if correct_traceflexure:
from .flexure import get_ccd_jflexure
from .sedm import TRACE_DISPERSION
# Save the flexure plot
j_offset = get_ccd_jflexure(lamp, ntraces=200, tracewidth=1, jscan=[-3,3,10],
savefile=savefile_traceflexure, get_object=False)
new_tracematch = lamp.tracematch.get_shifted_tracematch(0, j_offset)
new_tracematch.set_buffer( TRACE_DISPERSION)
lamp.set_tracematch(new_tracematch )
lamp.header["JFLXCORR"] = (True, "Is TraceMatch corrected for j flexure?")
lamp.header["CCDJFLX"] = (j_offset, "amplitude in pixel of the j flexure Trace correction")
else:
lamp.header["JFLXCORR"] = (False, "Is TraceMatch corrected for j flexure?")
lamp.header["CCDJFLX"] = (0, "amplitude in pixel of the j flexure Trace correction")
if background is None:
lamp.set_background(lamp._get_default_background_(**kwargs), force_it=True)
elif not background == 0:
lamp.set_background(background, force_it=True)
return lamp
def get_dome(domefile, tracematch=None, load_sep=False, **kwargs):
""" Load a SEDmachine domeflat image.
(special version of get_ccd. might be moved to get_ccd...)
Parameters
-----------
domefile: [string]
Location of the file containing the object
tracematch: [Tracematch (pysedm object)] -optional-
Tracematch object containing the Spectral property on the CCD
**kwargs goes to DomeCCD.__init__() if tracematch is None
else to _get_default_background_
Returns
-------
DomeCCD (Child of CCD which is a Child of an astrobjec's Image)
"""
if tracematch is not None:
kwargs["background"] = 0
dome = DomeCCD(domefile, **kwargs)
if load_sep:
dome.datadet = dome.data/np.sqrt(np.abs(dome.data))
dome.sep_extract(thresh=50., on="datadet")
if tracematch is not None:
# = Tracematch that gonna help the background
dome.set_tracematch(tracematch)
dome.set_background(dome._get_default_background_(**kwargs), force_it=True)
return dome
#####################################
# #
# Raw CCD Images for SED machine #
# #
#####################################
class BaseCCD( Image ):
""" """
def __build__(self,bw=64, bh=64,
fw=3, fh=3,**kwargs):
""" build the structure of the class
// Doc from SEP
bw, bh : int, -optional-
Size of background boxes in pixels. Default is 64 [ndlr (in SEP)].
fw, fh : int, -optional-
Filter width and height in boxes. Default is 3 [ndlr (in SEP)].
"""
super(BaseCCD,self).__build__(**kwargs)
# -- How to read the image
self._build_properties["bkgdbox"]={"bh":bh,"bw":bw,"fh":fh,"fw":fw}
# ==================== #
# Internal tools #
# ==================== #
def _get_sep_threshold_(self, thresh):
""" Trick to automatically get the proper threshold for SEP extract """
if thresh is None:
return np.median(self.rawdata)
return thresh
# ==================== #
# Properties #
# ==================== #
@property
def data_log(self):
return np.log10(self.data)
# ============================== #
# #
# Main CCD Object #
# Tracing <-> CCD <-> Cube #
# #
# ============================== #
class CCD( BaseCCD ):
""" Virtual Class For CCD images that have input light """
PROPERTIES = ["tracematch"]
DERIVED_PROPERTIES = ["matched_septrace_index"]
# ------------------- #
# Tracematch <-> CCD #
# ------------------- #
def set_tracematch(self, tracematch):
""" Attach to this instance the Tracematch """
from .spectralmatching import TraceMatch
if TraceMatch not in tracematch.__class__.__mro__:
raise TypeError("The given tracematch must be a TraceMatch object")
self._properties["tracematch"] = tracematch
def match_trace_to_sep(self):
""" matches the SEP ellipse with the current trace vertices.
You must have ran sep_extract() to be able to use this method.
(This method need Shapely.)
You can then use the methods:
- sepindex_to_traceindex()
- traceindex_to_sepindex()
Returns
-------
Void
"""
# -> import and tests
try:
from shapely import geometry, vectorized
except ImportError:
raise AttributeError("Matching traces to sep requires Shapely. pip install Shapely")
if not self.has_sepobjects():
raise AttributeError("sep has not been ran. Do so to be able to match sep output with traces")
# -> actual code
x,y,a,b,theta = self.sepobjects.get(["x","y","a","b","theta"]).T
self._derived_properties["matched_septrace_index"] =\
{idx: np.argwhere(vectorized.contains( geometry.Polygon(self.tracematch.get_trace_vertices(idx)), x,y)).ravel()
for idx in self.tracematch.trace_indexes}
def sepindex_to_traceindex(self, sepindex):
""" Give the index of an sep entry. This will give the corresponding trace index """
if not self.has_matchedindex():
raise AttributeError("spectral match traces has not been matched with sep indexes. Run match_tracematch_and_sep()")
return [traceindex for traceindex, sepindexes in self.matchedindex.items() if sepindex in sepindexes]
def traceindex_to_sepindex(self, traceindex):
""" Give the index of an sep entry. This will give the corresponding trace index """
if not self.has_matchedindex():
self.match_trace_to_sep()
return self.matchedindex[traceindex]
def set_default_variance(self, force_it=False):
""" define a default variance using the following formula:
rawdata + ( median(data) - percentile(data, 16) )**2,
it supposed to account for poisson noise + potential additional variance.
This is a really poor's man tools...
Returns
-------
Void
"""
if self.has_var() and not force_it:
raise AttributeError("Cannot reset the variance. Set force_it to True to allow overwritting of the variance.")
delta_sigma = np.percentile(self.data, [16,50])
self._properties['var'] = self.rawdata+(delta_sigma[1]-delta_sigma[0])**2
# ----------- #
# GETTER #
# ----------- #
def get_trace_cutout(self, traceindex, masked=True, on="data"):
""" returns a 2D array containg the cutout around the requested trace.
The trace could be either with or without tracematch mask (i.e. 0 outside
the trace).
Parameters
----------
traceindex: [int]
index of the spaxel trace.
masked: [bool] -optional-
do you want the data (see `on`) to be masked out (i.e. ==0) outside
the trace
on: [string] -optional-
On which data source do you want the trace (e.g. data, rawdata, background, variance)
Returns
-------
2d-array
"""
xmin, xmax = self.tracematch.get_trace_xbounds(traceindex)
ymin, ymax = self.tracematch.get_trace_ybounds(traceindex)
if masked:
return self.get_trace_mask(traceindex)[ymin:ymax,xmin:xmax]*eval("self.%s"%on)[ymin:ymax,xmin:xmax]
return eval("self.%s"%on)[ymin:ymax,xmin:xmax]
def get_finetuned_trace(self, traceindex, polydegree=2,
width=None, trace_position=False, **kwargs):
""" The builds a fine tuned trace of the given traceindex.
The tuning uses detected object from sep.
=> You must have run match_tracematch_and_sep()
Parameters
----------
traceindex: [int]
Index of the trace you want to fine tune
polydegree: [positive-int] -optional-
Degree of the polynome that will be used to define the trace.
(See 'width' for details on the width of the trace polygon)
=> If polydegree is higher than the number of sep object detected
belonging to this trace, polydegree will the reduced to that number
=> If polydegree ends up being lower of equal to 0, None is returned
width: [float / None] -optional-
Width of the polygon (in pixels)
If None, width will be estimated based on the b-values of the
sep detected objects.
trace_position: [bool] -optional-
Get the expected trace central position instead of the vertices of the polygon containing it.
**kwargs goes to spectralmatching.get_boxing_polygone()
Returns
-------
One of these:
- None if no fit possible (one of less sep object for this trace )
- array (vertices)
- array (x,y if trace_position=True)
"""
if not self.has_sepobjects():
warnings.warn("No SEP object loaded. run sep_extract() to enable finetuning. Original vertices returned")
return self.tracematch.copy()
_cannot_finetune = False
try:
x, y, b = self.sepobjects.get(["x","y","b"], self.traceindex_to_sepindex(traceindex)).T
except:
_cannot_finetune = True
x,y,b = [],[],[]
if len(x) < polydegree:
warnings.warn("less sep-points than polynom degree. Degree reduced ")
polydegree = len(x)-1
if polydegree <=0:
_cannot_finetune = True
if _cannot_finetune:
warnings.warn("cannot build finetune tracing for %s. Normal vertices returned"%traceindex)
return self.tracematch.get_trace_vertices(traceindex)
else:
if trace_position:
return self.tracematch.get_finetuned_trace(traceindex, x, y, polydegree=polydegree, **kwargs)
else:
return self.tracematch.get_finetuned_trace_vertices(traceindex, x, y,
width= np.nanmedian(b)*2. if width is None else width,
polydegree=polydegree, **kwargs)
def get_trace_mask(self, traceindex, finetune=False, polydegree=2,
subpixelisation=5, **kwargs):
""" Build a weightmask based on the trace vertices.
Parameters
----------
traceindex: [int]
index of the trace for which you want a mask
finetune: [bool] -optional-
Should the trace be remeasured based on potential detected sources?
// The following options apply if finetune is True
polydegree: [int] -optional-
Degree of the polynome used to define the traces
subpixelisation: [int] -optional-
Our much should the pixel be subdivided to do the polygon-to-image
interpolation? (the higher the slower)
Set 1 for no subdivition (fastest)
**kwargs goes to the method `get_finetuned_trace`
"""
if not finetune:
return self.tracematch.get_trace_mask(traceindex)
from .spectralmatching import polygon_mask, _HAS_SKIMAGE
if not _HAS_SKIMAGE:
warnings.warn("get_trace needs skimage to be able to use subpixelisation")
subpixelisation = 1
verts = self.get_finetuned_trace(traceindex, polydegree=polydegree, **kwargs)
mask = np.asarray(polygon_mask( verts*subpixelisation,
self.shape[0]*subpixelisation, self.shape[1]*subpixelisation,
get_fullcolor=False),
dtype="float")
if subpixelisation==1:
return mask/np.nanmax(mask)
from .spectralmatching import measure
return measure.block_reduce(mask, (subpixelisation,subpixelisation) )/float(subpixelisation**2)
def get_finetuned_tracematch(self, indexes, polydegree=2, width=None, build_masking=False, **kwargs):
""" """
from .spectralmatching import TraceMatch
tmap = TraceMatch()
tmap.set_trace_vertices({i:self.get_finetuned_trace(i, polydegree=polydegree, width=width, **kwargs)
for i in indexes}, build_masking=build_masking)
return tmap
# ---------------- #
# Tracematch #
# ---------------- #
def get_spectrum(self, traceindex, on="data", finetune=False):
""" Get the basic spectrum extracted for the CCD based on the
TraceMatch object.
Parameters
----------
traceindex: [int, list of]
index(es) of the spectrum(a) to return
on: [str] -optional-
on which 2d image shall the spectrum be extracted.
By Default 'data', but you can set e.g. rawdata, background
or anything accessible as 'self.%s'%on.
finetune: [bool] -optional-
Should the trace masking come from finetunning of spectral trace?
(Remark: The spectral match loaded might already be finetuned ones.)
Returns
-------
flux (or list of) as a function of pixels
"""
if not self.has_tracematch():
raise AttributeError("The TraceMatch has not been set. see set_tracematch() ")
if hasattr(traceindex, "__iter__"):
return [self.get_spectrum(id_) for id_ in traceindex]
maskidx = self.get_trace_mask(traceindex, finetune=finetune)
return np.sum(eval("self.%s"%on)*maskidx, axis=0)
def get_xslice(self, i, on="data"):
""" build a `CCDSlice` based on the ith-column.
Returns
-------
CCDSlice (child of Spectrum)
"""
slice_ = CCDSlice(None)
if "data" in on and not self.has_var():
warnings.warn("Setting the default variance for 'get_xslice' ")
self.set_default_variance()
var = self.var.T[i] if 'data' in on else np.ones(np.shape("self.%s"%on))*np.nanstd("self.%s"%on)
slice_.create(eval("self.%s.T[i]"%on), variance = var,
lbda = np.arange(len(self.data.T[i])), logwave=False)
slice_.set_tracebounds(self.tracematch.get_traces_crossing_x_ybounds(i))
return slice_
def fit_background(self, start=2, jump=10, multiprocess=True, set_it=True, smoothing=[0,5], **kwargs):
""" """
from .background import get_background, fit_background
self._background = get_background( fit_background(self, start=start, jump=jump,
multiprocess=multiprocess, **kwargs),
smoothing=smoothing )
if set_it:
self.set_background(self._background.background, force_it=True)
def fetch_background(self, set_it=True, build_if_needed=True, ncore=None, **kwargs):
"""
ncore is used only if build_background() is called.
"""
from .background import load_background
from .io import filename_to_background_name
# ---------------- #
# Test it exists #
# ---------------- #
from glob import glob
if len(glob(filename_to_background_name(self.filename)))==0:
warnings.warn("No background has been found for %s"%self.filename)
if not build_if_needed:
raise IOError("Since build_if_needed=False, No background available.")
from .background import build_background
build_background(self, ncore=ncore, **kwargs)
warnings.warn("A background has been built")
self._background = load_background( filename_to_background_name( self.filename ))
if set_it:
self.set_background( self._background.background, force_it=True)
def extract_spectrum(self, traceindex, wavesolution, lbda=None, kind="cubic",
get_spectrum=True, pixel_shift=0.):
""" Build the `traceindex` spectrum based on the given wavelength solution.
The returned object could be an pyifu's Spectrum or three arrays, lbda, flux, variance.
The method works as follow for the given traceindex:
1) Get the flux per pixels [using the get_spectrum() method]
(Get the variance the same way if any)
2) Convert the given lbda into pixels
[using the lbda_to_pixels() method from wavesolution]
3) Interpolate the flux per pixels into flux per lbda
(Interpolate the variance the same way)
[using interp1d from scipy.interpolate]
Parameters
----------
traceindex: [int]
The index of the spectrum you want to extract
wavesolution: [WaveSolution]
Object containing the method to go from pixels to lbda
lbda: [array] -optional-
Shape of the lbda array you want the spectrum to have.
kind: [str or int] -optional-
Specifies the kind of interpolation as a string
('linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic'
where 'slinear', 'quadratic' and 'cubic' refer to a spline
interpolation of first, second or third order) or as an integer
specifying the order of the spline interpolator to use.
get_spectrum: [bool] -optional-
Which form the returned data should have?
finetune: [bool] -optional-
Should the trace masking come from finetunning of spectral trace?
(Remark: The spectral match loaded might already be a finetuned ones.)
Returns
-------
Spectrum or
array, array, array/None (lbda, flux, variance)
"""
f = self.get_spectrum(traceindex, finetune=False)
v = self.get_spectrum(traceindex, finetune=False, on="var") if self.has_var() else None
pixs = np.arange(len(f))[::-1]
minpix, maxpix = self.tracematch.get_trace_xbounds(traceindex)
mask = pixs[(pixs>minpix)* (pixs<maxpix)][::-1]
if lbda is not None:
from scipy.interpolate import interp1d
pxl_wanted = wavesolution.lbda_to_pixels(lbda, traceindex) + pixel_shift
flux = interp1d(pixs[mask], f[mask], kind=kind)(pxl_wanted)
var = interp1d(pixs[mask], v[mask], kind=kind)(pxl_wanted) if v is not None else v
else:
lbda = wavesolution.pixels_to_lbda(pixs[mask], traceindex)
flux = f[mask]
var = v[mask]
if get_spectrum:
spec = Spectrum(None)
spec.create(flux,variance=var,lbda=lbda)
return spec
return lbda, flux, var
# --------------- #
# Extract Cube #
# --------------- #
def extract_cube(self, wavesolution, lbda,
hexagrid=None, traceindexes=None, show_progress=False,
pixel_shift=0., rotation=None):
""" Create a cube from the ccd.
------------------------------------
| Central method of the ccd object |
------------------------------------
The method works as follow (see the extract_spectrum() method):
for each trace (loop object traceindexes)
1) Get the flux per pixels [using the get_spectrum() method]
(Get the variance the same way if any)
2) Convert the given lbda into pixels
[using the lbda_to_pixels() method from wavesolution]
3) Interpolate the flux per pixels into flux per lbda
(Interpolate the variance the same way)
[using interp1d from scipy.interpolate]
4) Get the x,y position of the traceindex
[using the ids_to_index() and index_to_xy() methods from hexagrid]
If anything false (most likely the interpolation because of wavelength matching)
the flux (or variance) per lbda will be set to an array of NaNs
All the spaxels fluxes will be set to a cube (SEDMCube see .sedm)
Parameters
----------
wavesolution: [WaveSolution]
The object containing the pixels<->wavelength relation of the night.
lbda: [float array]
wavelength array of the cube to be created (in Angstrom)
hexagrid: [HexagoneProjection] -optional-
object containing the x,y position of the traces.
If not given, this will be created based on the instance's TraceMatch.
(it is advised to give the night hexagrid.)
traceindexes: [list of int] -optional-
Which trace should be extracted to build the cube?
If not given (None) this will used all the traceindexes for which there
is a wavelength solution (wavesolution)
show_progress: [bool] -optional-
Should the progress within the loop over traceindexes should be
shown (using astropy's ProgressBar)
Returns
-------
SEDMCube (child of pyifu's Cube)
"""
from .sedm import SEDMSPAXELS, SEDMCube, SEDM_INVERT, SEDM_ROT
if rotation is None:
rotation = SEDM_ROT
# - index check
if traceindexes is None:
traceindexes = np.sort(list(wavesolution.wavesolutions.keys()))
elif np.any(~np.in1d(traceindexes, list(wavesolution.wavesolutions.keys()))):
raise ValueError("At least some given indexes in `used_indexes` do not have a wavelength solution")
# - Hexagonal Grid
if hexagrid is None:
hexagrid = self.tracematch.extract_hexgrid(traceindexes)
used_indexes = [i_ for i_ in traceindexes if i_ in hexagrid.ids_index.keys()]
# - data
cube = SEDMCube(None)
cubeflux_ = {}
cubevar_ = {} if self.has_var() else None
# ------------ #
# MultiProcess #
# ------------ #
def _build_ith_flux_(i_):
try:
lbda_, flux_, variance_ = self.extract_spectrum(i_, wavesolution, lbda=lbda,
get_spectrum=False,
pixel_shift=pixel_shift)
except:
warnings.warn("FAILING EXTRACT_SPECTRUM for trace index %d: most likely wavesolution failed for this trace. *NaN Spectrum set*"%i_)
flux_ = np.ones(len(lbda) )*np.NaN
variance_ = np.ones(len(lbda) )*np.inf
cubeflux_[i_] = flux_
if cubevar_ is not None:
cubevar_[i_] = variance_
#except:
# warnings.warn("FAILED FOR %s. Most likely, the requested wavelength are not fully covered by the trace"%i_)
# cubeflux_[i_] = np.zeros(len(lbda))*np.NaN
# if cubevar_ is not None:
# cubevar_[i_] = np.zeros(len(lbda))*np.NaN
# ------------ #
# - MultiThreading to speed this up
if show_progress:
print("show_progress removed from extract_cube()")
_ = [_build_ith_flux_(i) for i in used_indexes]
cubeflux = np.asarray([cubeflux_[i] for i in used_indexes])
cubevar = np.asarray([cubevar_[i] for i in used_indexes]) if cubevar_ is not None else None
# - Fill the Cube
# SEDM DEPENDENT
hexagrid.set_rot_degree(rotation)
spaxels_position = np.asarray(hexagrid.index_to_xy( hexagrid.ids_to_index(used_indexes),
invert_rotation=False,
switch_axis=SEDM_INVERT)).T
spaxel_map = {i:c for i,c in zip(used_indexes, spaxels_position)}
cube.create(cubeflux.T,lbda=lbda, spaxel_mapping=spaxel_map, variance=cubevar.T)
cube.set_spaxel_vertices(np.dot(hexagrid.grid_rotmatrix,SEDMSPAXELS.T).T)
return cube
# --------------- #
# Extract Cube #
# --------------- #
def show(self, toshow="data", ax=None,
logscale= False, cmap = None, show_sepobjects=False,
vmin = None, vmax = None, savefile=None, show=True, **kwargs):
""" Highlight the trace on top of the CCD image.
This method requires that the spectral match has been loaded.
Parameters
----------
idx: [int]
vmin, vmax: [float /string / None]
Upper and lower value for the colormap. 3 Format are available
- float: Value in data unit
- string: percentile. Give a float (between 0 and 100) in string format.
This will be converted in float and passed to numpy.percentile
- None: The default will be used (percentile 0.5 and 99.5 percent respectively).
(NB: vmin and vmax are independent, i.e. one can be None and the other '98' for instance)
Returns
-------
dict ({ax, fig, imshow's output})
"""
from .utils.mpl import figout, mpl
if ax is None:
fig = mpl.figure(figsize=[8,8])
ax = fig.add_axes([0.13,0.13,0.8,0.8])
ax.set_xlabel(r"$\mathrm{x\ [ccd]}$",fontsize = "large")
ax.set_ylabel(r"$\mathrm{y\ [ccd]}$",fontsize = "large")
elif "imshow" not in dir(ax):
raise TypeError("The given 'ax' most likely is not a matplotlib axes. "+\
"No imshow available")
else:
fig = ax.figure
# What To Show
data_ = eval("self.%s"%toshow) if type(toshow) == str else toshow
if logscale:
data_ = np.log10(data_)
if cmap is None: cmap=mpl.cm.viridis
vmin = np.percentile(data_, 0.5) if vmin is None else \
np.percentile(data_, float(vmin)) if type(vmin) == str else\
vmin
vmax = np.percentile(data_, 99.5) if vmax is None else \
np.percentile(data_, float(vmax)) if type(vmax) == str else\
vmax
prop = kwargs_update(dict(origin="lower", aspect='auto', vmin=vmin, vmax=vmax), **kwargs)
# Show It
sc = ax.imshow(data_, **prop)
# - sepobject
if show_sepobjects and self.has_sepobjects():
self.sepobjects.display(ax)
fig.figout(savefile=savefile, show=show)
return {"ax":ax, "fig" : fig, "imshow":sc}
def show_traceindex(self, traceindex, ax=None,
logscale= False, toshow="data", show_finetuned_traces=False,
cmap = None, facecolor = "None", edgecolor="k",
vmin = None, vmax = None, savefile=None, show=True, **kwargs):
""" Highlight the trace on top of the CCD image.
This method requires that the spectral match has been loaded.
Parameters
----------
traceindex: [int]
"""
from .utils.mpl import figout
pl = self.show( toshow=toshow, ax=ax, logscale=logscale, cmap = cmap,
vmin = vmin, vmax = vmax, savefile=None, show=False, **kwargs)
ax, fig = pl["ax"], pl["fig"]
pl["patch"] = self.display_traces(ax, traceindex, facecolors=facecolor, edgecolors=edgecolor)
if show_finetuned_traces and self.has_matchedindex():
from matplotlib import patches
traces = traceindex if hasattr(traceindex, "__iter__") else [traceindex]
for idx_ in traces:
self.sepobjects.display_ellipses(pl["ax"], self.traceindex_to_sepindex(idx_))
p_ = patches.Polygon(self.get_finetuned_trace(idx_),
facecolor="None", edgecolor="C1")
pl["ax"].add_patch(p_)
# Output
fig.figout(savefile=savefile, show=show)
return pl
def show_xslice(self, xpixel, toshow="data", savefile=None, ax=None, show=True,
ls="-", color=None, lw=1,
show_tracebounds=True,
bandalpha=0.5, bandfacecolor="0.7", bandedgecolor="None",bandedgewidth=0,
**kwargs):
""" """
from .utils.mpl import figout, mpl
if ax is None:
fig = mpl.figure(figsize=[9,5])
ax = fig.add_subplot(111)
else:
fig = ax.figure
# This plot
ax.plot( eval("self.%s.T[xpixel]"%toshow), ls=ls, color=color, lw=lw,**kwargs)
if show_tracebounds:
[ax.axvspan(*y_, alpha=bandalpha, facecolor=bandfacecolor,
edgecolor=bandedgecolor,linewidth=bandedgewidth)
for y_ in self.tracematch.get_traces_crossing_x_ybounds(xpixel)]
fig.figout(savefile=savefile, show=show)
def show_as_slicer(self, traceindexes, vmin=0 , vmax="90",
masked=True, toshow="rawdata"):
""" """
import matplotlib.pyplot as mpl
data = eval("self.%s"%toshow)
if vmin is None:
vmin = 0
if type(vmin) == str:
vmin = np.percentile(data, vmin)
if vmax is None:
vmax = "95"
if type(vmax) == str:
vmax = np.percentile(data, vmax)
# parameters
ntraces = len(traceindexes)
height = 0.85/ntraces
# Build the figure
fig = mpl.figure(figsize=[8,4])
# draw the traces
for i,index_ in enumerate(traceindexes):
ax = fig.add_axes([0.1,0.1+height*i, 0.8,height])
ax.imshow(self.get_trace_cutout(index_, masked=masked, on=toshow), origin="lower", aspect="auto", vmin=vmin, vmax=vmax)
ax.set_yticks([])
if i>0:
ax.set_xticks([])
else:
ax.set_xlabel("pixels since trace origin")
return {"fig":fig}
def display_traces(self, ax, traceindex, facecolors="None", edgecolors="k",
update_limits=True):
""" """
pl = self.tracematch.display_traces(ax, traceindex,
facecolors =facecolors, edgecolors=edgecolors)
# Fancy It
if update_limits:
[xmin, xmax], [ymin, ymax] = np.percentile(self.tracematch.trace_vertices[traceindex] if not hasattr(traceindex,"__iter__") else\
np.concatenate([self.tracematch.trace_vertices[idx] for idx in traceindex], axis=0),
[0,100], axis=0).T
ax.set_xlim(xmin-20, xmax+20)
ax.set_ylim(ymin-5, ymax+5)
return pl
# ================== #
# Internal Tools #
# ================== #
def _get_default_background_(self, add_mask=None,
cut_bright_pixels=None,
exclude_edges=False,
scaleup_sepmask=2, apply_sepmask=True,
**kwargs):
""" This Background has been optimized for SEDm Calibration Lamps """
if add_mask is None and self.has_tracematch():
add_mask = np.asarray(~self.tracematch.get_notrace_mask(), dtype="bool")
if add_mask is not None and cut_bright_pixels is not None:
data_ = self.rawdata.copy()
data_[add_mask] = np.NaN
add_mask = add_mask + (data_>np.percentile(data_[data_==data_],50))
if exclude_edges:
falses = np.zeros(self.shape)
# - x cuts
xremove, yremove =100, 20
falses[:,(np.arange(self.shape[1])<xremove) + (np.arange(self.shape[1])>(self.shape[1]-xremove)) ] = 1.
falses[(np.arange(self.shape[0])<yremove) + (np.arange(self.shape[0])>(self.shape[0]-yremove)),:] = 1.
add_mask = add_mask + np.asarray(falses, dtype="bool")
return self.get_sep_background(doublepass=False, update_background=False,
add_mask=add_mask,
apply_sepmask=apply_sepmask, scaleup_sepmask=scaleup_sepmask,
**kwargs)
# ================== #
# Properties #
# ================== #
# - TraceMatching association
@property
def tracematch(self):
""" """
return self._properties["tracematch"]
def has_tracematch(self):
return self.tracematch is not None
@property
def matchedindex(self):
""" Object containing the relation between the sepindex and the trace index.
see the methods sepindex_to_traceindex() and traceindex_to_sepindex() """
if self._derived_properties["matched_septrace_index"] is None:
self._derived_properties["matched_septrace_index"] = {}
return self._derived_properties["matched_septrace_index"]
def has_matchedindex(self):
""" Is the sep<-> trace index matching done? """
return self.matchedindex is not None and len(self.matchedindex.keys())>0
# - Generic properties
@property
def objname(self):
if "Calib" in self.header.get("NAME","no-name"):
return self.header["NAME"].split()[1]
return self.header.get("NAME","no-name")
# ============================== #
# #
# Childs Of CCD #
# #
# ============================== #
class ScienceCCD( CCD ):
""" Should be used to improve the trace matching. """
class DomeCCD( ScienceCCD ):
""" Object Build to handle the CCD images of the Dome exposures"""
# ================== #
# Main Tools #
# ================== #
def get_tracematch(self, bound_pixels=None, width="optimal"):
""" """
xlim, ylim = self.get_trace_position(bound_pixels=bound_pixels)
if width is None:
b = self.sepobjects.get("b")
width = np.median(b)*2 if width=="median" else \
b*2 if width!="optimal" else np.clip(b,np.median(b)-2*np.std(b),np.median(b)+2*np.std(b))*2
return [np.concatenate(v_) for v_ in zip(np.asarray([xlim,ylim+width]).T,np.asarray([xlim[::-1],ylim[::-1]-width]).T)]
def get_trace_position(self, bound_pixels=None):
""" """
x, y, a, b, theta = self.sepobjects.get(["x","y","a","b","theta"]).T
# This enables to remove cosmics
flagout = a/b<10
x, y, theta = x[~flagout], y[~flagout], theta[~flagout]
if bound_pixels is not None:
print("BOUNDS")
xlim = np.asarray([x-bound_pixels[0], x+bound_pixels[1]])
ylim = | np.sin(theta) | numpy.sin |
import numpy as np
import numba
from src.data import Problem, Case, Matter
@numba.jit('i8[:, :](i8[:, :], i8)', nopython=True)
def is_rot_symmetry_point(x_arr: np.array, background: np.int) -> np.array:
res_arr = np.zeros(x_arr.shape, dtype=np.int64)
# center point
for i0 in range(x_arr.shape[0]):
for j0 in range(x_arr.shape[1]):
# right-down
x_arr_1 = x_arr[i0:, j0:]
# right-up
x_arr_2 = x_arr[i0::-1, j0:].transpose()
# left-up
x_arr_3 = x_arr[i0::-1, j0::-1]
# left-down
x_arr_4 = x_arr[i0:, j0::-1].transpose()
new_shape_0 = max([x_arr_1.shape[0], x_arr_2.shape[0], x_arr_3.shape[0], x_arr_4.shape[0]])
new_shape_1 = max([x_arr_1.shape[1], x_arr_2.shape[1], x_arr_3.shape[1], x_arr_4.shape[1]])
x_arr_1_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_1_exp[:x_arr_1.shape[0], :x_arr_1.shape[1]] = x_arr_1
x_arr_2_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_2_exp[:x_arr_2.shape[0], :x_arr_2.shape[1]] = x_arr_2
x_arr_3_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_3_exp[:x_arr_3.shape[0], :x_arr_3.shape[1]] = x_arr_3
x_arr_4_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_4_exp[:x_arr_4.shape[0], :x_arr_4.shape[1]] = x_arr_4
# break if gap
if ((x_arr_1_exp != x_arr_2_exp) * (x_arr_1_exp != background) * (x_arr_2_exp != background)).sum():
res_arr[i0, j0] = -2
continue
# break if gap
if ((x_arr_1_exp != x_arr_3_exp) * (x_arr_1_exp != background) * (x_arr_3_exp != background)).sum():
res_arr[i0, j0] = -2
continue
# break if gap
if ((x_arr_1_exp != x_arr_4_exp) * (x_arr_1_exp != background) * (x_arr_4_exp != background)).sum():
res_arr[i0, j0] = -2
continue
# break if gap
if ((x_arr_2_exp != x_arr_3_exp) * (x_arr_2_exp != background) * (x_arr_3_exp != background)).sum():
res_arr[i0, j0] = -2
continue
# break if gap
if ((x_arr_2_exp != x_arr_4_exp) * (x_arr_2_exp != background) * (x_arr_4_exp != background)).sum():
res_arr[i0, j0] = -2
continue
# break if gap
if ((x_arr_3_exp != x_arr_4_exp) * (x_arr_3_exp != background) * (x_arr_4_exp != background)).sum():
res_arr[i0, j0] = -2
continue
score_arr = (x_arr_1_exp != background).astype(np.int64) + (x_arr_2_exp != background).astype(np.int64) + \
(x_arr_3_exp != background).astype(np.int64) + (x_arr_4_exp != background).astype(np.int64)
res_arr[i0, j0] = (score_arr * (score_arr - 1)).sum()
# center should be same
if 1 <= score_arr[0, 1] <= 2:
flag_todo = 1
elif 1 <= score_arr[1, 1] <= 2:
flag_todo = 1
else:
flag_todo = 0
if flag_todo == 1:
# unless it is the center
if i0 == j0 == x_arr.shape[0] // 2 and x_arr.shape[0] == x_arr.shape[1] and x_arr.shape[0] % 2 == 1:
pass
else:
res_arr[i0, j0] = -2
return res_arr // 2
@numba.jit('i8[:, :](i8[:, :], i8)', nopython=True)
def is_rot_symmetry_valley(x_arr: np.array, background: np.int) -> np.array:
res_arr = np.zeros(x_arr.shape, dtype=np.int64)
res_arr[-1, :] = -1
res_arr[:, -1] = -1
# center point
for i0 in range(x_arr.shape[0] - 1):
for j0 in range(x_arr.shape[1] - 1):
# right-down
x_arr_1 = x_arr[i0 + 1:, j0 + 1:]
# right-up
x_arr_2 = x_arr[i0::-1, j0 + 1:].transpose()
# left-up
x_arr_3 = x_arr[i0::-1, j0::-1]
# left-down
x_arr_4 = x_arr[i0 + 1:, j0::-1].transpose()
new_shape_0 = max([x_arr_1.shape[0], x_arr_2.shape[0], x_arr_3.shape[0], x_arr_4.shape[0]])
new_shape_1 = max([x_arr_1.shape[1], x_arr_2.shape[1], x_arr_3.shape[1], x_arr_4.shape[1]])
x_arr_1_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_1_exp[:x_arr_1.shape[0], :x_arr_1.shape[1]] = x_arr_1
x_arr_2_exp = background * np.ones((new_shape_0, new_shape_1), dtype=np.int64)
x_arr_2_exp[:x_arr_2.shape[0], :x_arr_2.shape[1]] = x_arr_2
x_arr_3_exp = background * | np.ones((new_shape_0, new_shape_1), dtype=np.int64) | numpy.ones |
# coding: utf-8
# In[20]:
import numpy as np
import pydensecrf.densecrf as dcrf
import os
import cv2
import random
from tqdm import tqdm
# In[21]:
from skimage.color import gray2rgb
from skimage.color import rgb2gray
import matplotlib.pyplot as plt
from sklearn.metrics import f1_score, accuracy_score
from pydensecrf.utils import unary_from_labels, create_pairwise_bilateral, create_pairwise_gaussian, unary_from_softmax
#from osgeo import gdal
get_ipython().run_line_magic('matplotlib', 'inline')
# In[22]:
# Color maps for direction map
COLOR_LR = [0,128,128]
COLOR_UD = [128,0,128]
COLOR_DIAG = [255,215,0]
COLOR_ADIAG = [1,255,255]
INF = 10000
# In[23]:
MAX = 0
SUM = 1
VEC = 0
MAT = 1
# In[24]:
def dir_to_features(dir_map):
"""Converts direction color map to feature used for crf kernel. The
feature is obtained by computing the intersections of the x, y axis and the
line determined by the position of one point and its direction. (More details in
the report)
Parameters
____________
dir_map: numpy.array
Direction map that maps each pixel to a direction in
[left_right, up_down, diagonal, anti-diagonal], each direction
is represented by a color.
"""
(h, w, c) = dir_map.shape
feature_map = np.zeros((h,w,2))
for i in range(h):
for j in range(w):
dir_color = dir_map[i,j]
if dir_color[0] == COLOR_LR[0]: # dir = lr
feature_map[i,j] = np.array([INF,i])
if dir_color[0] == COLOR_UP[0]: # dir = ud
feature_map[i,j] = np.array([j,INF])
if dir_color[1] == COLOR_DIAG[0]: # dir = diag
feature_map[i,j] = np.array([j-i,i-j])
if dir_color[1] == COLOR_ADIAG[0]: # dir = adiag
feature_map[i,j] = np.array([i+j, i+j])
return feature_map
# In[25]:
def gen_dir_map(img):
"""Generate direction map from a rgb img
Parameters
____________
img: numpy.array
Rgb img with width = height
"""
window_size = 101
half_size = int((window_size-1)/2)
sigma_1 = 2
sigma_2 = 40
(h, w, c) = img.shape
assert h==w, "h and w are not equal"
dir_map = np.zeros((h,w))
pos_mat = np.zeros((h,w,2))
for i in range(h):
for j in range(w):
pos_mat[i,j,0]=i
pos_mat[i,j,1]=j
padded_pos = np.pad(pos_mat, ((half_size, half_size), (half_size, half_size), (0,0)))
padded_img = np.pad(img, ((half_size, half_size), (half_size, half_size), (0,0)))
index_mask_lr = np.zeros((window_size, window_size)).astype("bool")
index_mask_lr[half_size,:]=True
index_mask_ud = np.zeros((window_size, window_size)).astype("bool")
index_mask_ud[:,half_size]=True
index_mask_diag = np.identity(window_size).astype("bool")
index_mask_adiag = np.fliplr(np.identity(window_size)).astype("bool")
mask_list = [index_mask_lr, index_mask_ud, index_mask_diag, index_mask_adiag]
for i in range(h):
for j in range(w):
img_nbr = padded_img[i:i+window_size,j:j+window_size]
pos_nbr = padded_pos[i:i+window_size,j:j+window_size]
img_nbr = img_nbr - img[i,j,:]
pos_nbr = pos_nbr - np.array([i,j])
dir_intensity = np.zeros(4)
for dir_index, index_mask in enumerate(mask_list):
img_nbr_dir = img_nbr[index_mask]
pos_nbr_dir = pos_nbr[index_mask]
img_nbr_dir = np.sum(img_nbr_dir**2, axis=1)/(2*sigma_1**2)
pos_nbr_dir = np.sum(pos_nbr_dir**2, axis=1)/(2*sigma_2**2)
k = np.exp(-img_nbr_dir-pos_nbr_dir)
dir_intensity[dir_index]=np.sum(k)
dir_map[i,j]=np.argmax(dir_intensity)+1
return dir_map
# In[26]:
def visualize_dir_map(img, dir_map, save_file=False,
filename=None, vis_path=None, dir_path=None):
"""Visualize a direction map
Parameters
____________
img: numpy.array
Rgb img
dir_map: numpy.array
Correspongding direction map
...
"""
h = img.shape[0]
w = img.shape[1]
vis_dir = np.zeros(img.shape)
vis_dir[dir_map==1] = np.array(COLOR_LR)
vis_dir[dir_map==2] = np.array(COLOR_UD)
vis_dir[dir_map==3] = np.array(COLOR_DIAG)
vis_dir[dir_map==4] = np.array(COLOR_ADIAG)
plt.figure(figsize=(10,5))
plt.subplot(1,2,1); plt.imshow(img); plt.title('Original Image (blurred)'); plt.axis('off');
plt.subplot(1,2,2); plt.imshow(dir_map); plt.title('Direction map'); plt.axis('off');
if save_file:
plt.savefig(os.path.join(vis_path, filename),dpi=300)
plt.close()
cv2.imwrite(os.path.join(dir_path, filename), vis_dir)
# In[27]:
def gen_dir_map_and_visualize(image_path= './images/',
vis_path='./vis_dir_blur_/',
dir_path='./dir_map_/',
process_all=True):
"""Generate direction color map for images in image_path
Parameters
____________
image_path: string
Image path
vis_path: string
Path to save visualization results
dir_path: string
Path to save direction map
process_all: Bool
False to generate a single visualization result without save. True to
generate and save visualizaiton results for all images.
"""
if not os.path.exists(dir_path):
os.mkdir(dir_path)
if not os.path.exists(vis_path):
os.mkdir(vis_path)
if process_all:
for file in tqdm(os.listdir(image_path)):
img = cv2.imread(os.path.join(image_path, file))
img = cv2.GaussianBlur(img,(5,5),0)
dir_map = gen_dir_map(img)
visualize_dir_map(img, dir_map, filename=file, save_file=True,
vis_path=vis_path, dir_path=dir_path)
else:
img = cv2.imread('./images/satImage_001.png')
img = cv2.GaussianBlur(img,(5,5),0)
dir_map = gen_dir_map(img)
visualize_dir_map(img, dir_map, save_file=False)
# In[28]:
def crf_with_dir_kernel(original_img, dir_feature, prob,
iter_num, compat_smooth, compat_appearance, compat_struct,
w_smooth, w_appearance, w_struct,
sigma_smooth, sigma_app_color, sigma_app_pos,
sigma_struct_pos, sigma_struct_feat):
"""CRF with a Gaussian smoothing kernel, an appearance kernel and a structural kernel
"""
(h,w) = prob.shape
y = np.zeros((h,w,2))
y[:,:,1] = prob
y[:,:,0] = 1-y[:,:,1]
annotated_image=y.transpose((2, 0, 1))
#Gives no of class labels in the annotated image
n_labels = 2
#Setting up the CRF model
d = dcrf.DenseCRF2D(original_img.shape[1], original_img.shape[0], n_labels)
# get unary potentials (neg log probability)
U = unary_from_softmax(annotated_image)
unary = np.ascontiguousarray(U)
d.setUnaryEnergy(unary)
compat_smooth = compat_smooth * w_smooth
compat_appearance = compat_appearance * w_appearance
compat_struct = compat_struct * w_struct
# Smooth kernel
d.addPairwiseGaussian(sxy=(sigma_smooth, sigma_smooth), compat=compat_smooth.astype(np.float32),
kernel=dcrf.DIAG_KERNEL,
normalization=dcrf.NORMALIZE_SYMMETRIC)
# Appearance kernel
d.addPairwiseBilateral(sxy=(sigma_app_pos, sigma_app_pos),
srgb=(sigma_app_color, sigma_app_color, sigma_app_color),
rgbim=original_image,
compat=compat_appearance.astype(np.float32),
kernel=dcrf.DIAG_KERNEL,
normalization=dcrf.NORMALIZE_SYMMETRIC)
# Structural kernel
pairwise_energy = create_pairwise_bilateral(sdims=(sigma_struct_pos,sigma_struct_pos),
schan=(sigma_struct_feat,sigma_struct_feat),
img=dir_feature, chdim=2)
d.addPairwiseEnergy(pairwise_energy, compat=compat_struct.astype(np.float32))
Q = d.inference(iter_num)
proba = np.array(Q)
return proba[1].reshape((dir_feature.shape[0], dir_feature.shape[1]))
# In[29]:
def crf(original_image, prob,
iter_num=4, compat_smooth = np.array([[-0.4946432, 1.27117338],[0.59452892, 0.23182234]]),
compat_appearance = np.array([[-0.30571318, 0.83015124],[1.3217825, -0.13046645]]),
w_smooth=3.7946478055761963, w_appearance=1.8458537690881878,
sigma_smooth=8.575103751642672, sigma_color=2.0738539891571977, sigma_color_pos=20):
"""Basic CRF with a Gaussian smoothing kernel and an appearance kernel
"""
(h,w) = prob.shape
y = np.zeros((h,w,2))
y[:,:,1] = prob
y[:,:,0] = 1-y[:,:,1]
annotated_image=y.transpose((2, 0, 1))
#Gives no of class labels in the annotated image
n_labels = 2
#print("No of labels in the Image are ")
#print(n_labels)
#Setting up the CRF model
d = dcrf.DenseCRF2D(original_image.shape[1], original_image.shape[0], n_labels)
# get unary potentials (neg log probability)
U = unary_from_softmax(annotated_image)
unary = np.ascontiguousarray(U)
d.setUnaryEnergy(unary)
compat_smooth=compat_smooth*w_smooth
compat_appearance=compat_appearance*w_appearance
# This adds the color-independent term, features are the locations only.
d.addPairwiseGaussian(sxy=(sigma_smooth, sigma_smooth), compat=compat_smooth.astype(np.float32), kernel=dcrf.DIAG_KERNEL,
normalization=dcrf.NORMALIZE_SYMMETRIC)
# This adds the color-dependent term, i.e. features are (x,y,r,g,b).
d.addPairwiseBilateral(sxy=(sigma_color_pos, sigma_color_pos), srgb=(sigma_color, sigma_color, sigma_color), rgbim=original_image,
compat=compat_appearance.astype(np.float32),
kernel=dcrf.DIAG_KERNEL,
normalization=dcrf.NORMALIZE_SYMMETRIC)
Q = d.inference(iter_num)
proba = np.array(Q)
return proba[1].reshape((original_image.shape[0], original_image.shape[1]))
# In[30]:
def crf_smooth(original_image, prob, use_2d = True, iter_num=1, w=4.921522279119057, sigma_sm=4.325251720130304):
"""CRF with only a smoothing kernel
"""
(h,w) = prob.shape
y = np.zeros((h,w,2))
y[:,:,1] = prob
y[:,:,0] = 1-y[:,:,1]
annotated_image=y.transpose((2, 0, 1))
#Gives no of class labels in the annotated image
n_labels = 2
#Setting up the CRF model
if use_2d :
d = dcrf.DenseCRF2D(original_image.shape[1], original_image.shape[0], n_labels)
# get unary potentials (neg log probability)
U = unary_from_softmax(annotated_image)
unary = np.ascontiguousarray(U)
d.setUnaryEnergy(unary)
# This adds the color-independent term, features are the locations only.
d.addPairwiseGaussian(sxy=(sigma_sm, sigma_sm), compat=w, kernel=dcrf.DIAG_KERNEL,
normalization=dcrf.NORMALIZE_SYMMETRIC)
Q = d.inference(iter_num)
proba = np.array(Q)
return proba[1].reshape((original_image.shape[0], original_image.shape[1]))
# In[31]:
def propagate_max_mat(img, prob):
"""Probability propagation (max) in 4 directions via matrix multiplication
"""
prob_out = prob.copy()
prop_size = 51
half_size = int((prop_size-1)/2)
prop_num = 3
sigma_1 = 5
sigma_2 = 42
(h, w) = prob.shape
pos_mat = np.zeros((h,w,2))
for i in range(h):
for j in range(w):
pos_mat[i,j,0]=i
pos_mat[i,j,1]=j
padded_pos = np.pad(pos_mat, ((half_size, half_size), (half_size, half_size), (0,0)))
padded_img = np.pad(img, ((half_size, half_size), (half_size, half_size), (0,0)))
index_mask = np.zeros((prop_size, prop_size)).astype("bool")
for i in range(prop_size):
index_mask[i,half_size]=1
index_mask[half_size,i]=1
index_mask[i,i]=1
index_mask[prop_size-1-i,i]=1
for iteration in range(prop_num):
padded_prob = np.pad(prob_out, ((half_size, half_size), (half_size, half_size)))
# propagate prob (maximum)
for i in range(h):
for j in range(w):
if prob_out[i,j]<0.01:
continue
img_nbr = padded_img[i:i+prop_size,j:j+prop_size]
pos_nbr = padded_pos[i:i+prop_size,j:j+prop_size]
img_nbr = img_nbr - img[i,j,:]
pos_nbr = pos_nbr - np.array([i,j])
img_nbr[~index_mask]=0
pos_nbr[~index_mask]=0
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr)*prob_out[i,j]
k = k*index_mask
padded_prob[i:i+prop_size,j:j+prop_size] = np.maximum(padded_prob[i:i+prop_size,j:j+prop_size], k)
prob_out = padded_prob[half_size:h+half_size,half_size:w+half_size]
return prob_out
# In[32]:
def propagate_max_vec(img, prob, prop_size=11,
prop_num=16, sigma_1=1.039316347691348, sigma_2=40):
"""
vec means only do propagation along x and y axis
max means propagate using max function
Args:
prop_size: neighborhood size
prop_num: number of iteration/propagation
sigma_1: variance of color
sigma_2: variance of distance
"""
prob_out = prob.copy()
half_size = int((prop_size-1)/2)
(h, w, c) = img.shape
pos_mat = np.zeros((h,w,2)) # position matrix
for i in range(h):
for j in range(w):
pos_mat[i,j,0]=i
pos_mat[i,j,1]=j
padded_pos = np.pad(pos_mat, ((half_size, half_size), (half_size, half_size), (0,0)))
padded_img = np.pad(img, ((half_size, half_size), (half_size, half_size), (0,0)))
for iteration in range(prop_num):
padded_prob = np.pad(prob_out, ((half_size, half_size), (half_size, half_size)))
padded_prob_fix = padded_prob.copy()
# propagate prob (maximum)
assert h==w, "h and w are not equal"
for i in range(h):
# prop along y for row i
img_nbr = padded_img[i:i+prop_size,:]
pos_nbr = padded_pos[i:i+prop_size,:]
img_nbr = img_nbr - padded_img[i+half_size,:,:]
pos_nbr = pos_nbr - padded_pos[i+half_size,:,:]
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr)*padded_prob_fix[i+half_size,:]
padded_prob[i:i+prop_size,:] = np.maximum(padded_prob[i:i+prop_size,:], k)
# prop along x for col i
img_nbr = padded_img[:,i:i+prop_size]
pos_nbr = padded_pos[:,i:i+prop_size]
img_nbr = img_nbr - padded_img[:,i+half_size,:].reshape((padded_img.shape[0],1,c))
pos_nbr = pos_nbr - padded_pos[:,i+half_size,:].reshape((padded_img.shape[0],1,2))
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr)*padded_prob_fix[:,i+half_size].reshape((-1,1))
padded_prob[:,i:i+prop_size] = np.maximum(padded_prob[:,i:i+prop_size], k)
prob_out = padded_prob[half_size:h+half_size,half_size:w+half_size]
return prob_out
# In[33]:
def propagate_sum_vec(img, prob, prop_size=11, prop_num=1, sigma_1=1.5319569104856783, sigma_2=80):
"""
vec means only do propagation along x and y axis
sum means propagate in a additive schema (with total probability fixed)
Args:
prop_size: neighborhood size
prop_num: number of iteration/propagation
sigma_1: variance of color
sigma_2: variance of distance
"""
# print(np.sum(prob))
prob_out = prob.copy()
half_size = int((prop_size-1)/2)
(h, w, c) = img.shape
pos_mat = np.zeros((h,w,2)) # position matrix
for i in range(h):
for j in range(w):
pos_mat[i,j,0]=i
pos_mat[i,j,1]=j
padded_pos = np.pad(pos_mat, ((half_size, half_size), (half_size, half_size), (0,0)))
padded_img = np.pad(img, ((half_size, half_size), (half_size, half_size), (0,0)))
padded_prob = np.pad(prob, ((half_size, half_size), (half_size, half_size)))
for iteration in range(prop_num):
padded_prob_fix = padded_prob.copy()
padded_prob = np.pad(np.zeros((h,w)), ((half_size, half_size), (half_size, half_size)))
# propagate prob (sum)
assert h==w, "h and w are not equal"
# compute the degree mat
deg_mat = np.zeros((h+2*half_size,w+2*half_size))
for i in range(h):
# prop along y for row i
img_nbr = padded_img[i:i+prop_size,:]
pos_nbr = padded_pos[i:i+prop_size,:]
img_nbr = img_nbr - padded_img[i+half_size,:,:]
pos_nbr = pos_nbr - padded_pos[i+half_size,:,:]
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr)
deg_mat[i+half_size,:] = deg_mat[i+half_size,:]+np.sum(k,axis=0)
# prop along x for col i
img_nbr = padded_img[:,i:i+prop_size]
pos_nbr = padded_pos[:,i:i+prop_size]
img_nbr = img_nbr - padded_img[:,i+half_size,:].reshape((padded_img.shape[0],1,c))
pos_nbr = pos_nbr - padded_pos[:,i+half_size,:].reshape((padded_img.shape[0],1,2))
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr)
deg_mat[:,i+half_size] = deg_mat[:,i+half_size]+np.sum(k,axis=1)
for i in range(h):
# prop along y for row i
img_nbr = padded_img[i:i+prop_size,:]
pos_nbr = padded_pos[i:i+prop_size,:]
img_nbr = img_nbr - padded_img[i+half_size,:,:]
pos_nbr = pos_nbr - padded_pos[i+half_size,:,:]
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr) # similarity matrix
k = k/deg_mat[i+half_size,:] #devided by degree
prop_prob = k * padded_prob_fix[i+half_size,:]
padded_prob[i:i+prop_size,:] = padded_prob[i:i+prop_size,:] + prop_prob
# prop along x for col i
img_nbr = padded_img[:,i:i+prop_size]
pos_nbr = padded_pos[:,i:i+prop_size]
img_nbr = img_nbr - padded_img[:,i+half_size,:].reshape((padded_img.shape[0],1,c))
pos_nbr = pos_nbr - padded_pos[:,i+half_size,:].reshape((padded_img.shape[0],1,2))
img_nbr = np.sum(img_nbr**2, axis=2)/(2*sigma_1**2)
pos_nbr = np.sum(pos_nbr**2, axis=2)/(2*sigma_2**2)
k = np.exp(-img_nbr-pos_nbr) # similarity matrix
k = k/deg_mat[:,i+half_size].reshape((-1,1)) #devided by degree
prop_prob = k * padded_prob_fix[:,i+half_size].reshape((-1,1))
padded_prob[:,i:i+prop_size] = padded_prob[:,i:i+prop_size]+ prop_prob
# padded_prob = padded_prob + 0.5 * padded_prob_fix # lazy propagation
prob_out = padded_prob[half_size:h+half_size,half_size:w+half_size]
# print(np.sum(prob_out))
prob_out[prob_out>1]=1
return prob_out
# In[34]:
def prob_to_patch(im):
"""Convert pixel level probability prediction to patch version
"""
patch_list = []
patch_size = 16
for j in range(0, im.shape[1], patch_size):
for i in range(0, im.shape[0], patch_size):
patch = im[i:i + patch_size, j:j + patch_size]
df = np.mean(patch)
patch_list.append(df)
return | np.array(patch_list) | numpy.array |
from youtube_discussion_tree_api._conflicts import _tf_idf_automatic_algorithm, _calculate_document_frequency, _calculate_tf_idf, _cosine_sim, _cosine_similarity, _gen_vector, _in_doc_freq, _preprocessing
from unittest import TestCase
from youtube_discussion_tree_api.utils import Node
import numpy as np
class TestConflistSolvingAlgorithm(TestCase):
def setUp(self):
self.candidates = [
Node(
id = "comment1",
author_name = "Ororo",
author_id = "author1",
text = "Hello, I love turtles and dogs",
like_count = 10000000,
parent_id = None,
published_at = "12-12-2012"
),
Node(
id = "comment2",
author_name = "<NAME>",
author_id = "author2",
text = "Cats are the best animals in the whole world",
like_count = 10000000,
parent_id = None,
published_at = "12-12-2012"
),
Node(
id = "comment3",
author_name = "Kekino",
author_id = "author3",
text = "I'm more of a dogs person, they are so cute",
like_count = 10000000,
parent_id = None,
published_at = "12-12-2012"
)
]
self.candidates_preprocessed = [["hello", "love", "turtl", "dog"]
, ["cat", "best", "anim", "whole", "world"]
, ["dog", "person", "cute"]]
def test_preprocessing(self):
self.assertEqual(self.candidates_preprocessed, _preprocessing(self.candidates))
def test_calculate_document_frequency(self):
expected = {
"hello" : 1,
"love" : 1,
"turtl" : 1,
"dog" : 2,
"cat" : 1,
"best" : 1,
"anim" : 1,
"whole" : 1,
"world" : 1,
"person" : 1,
"cute" : 1
}
self.assertEqual(expected, _calculate_document_frequency(self.candidates_preprocessed))
def test_in_doc_frequency(self):
df = {
"hello" : 1,
"love" : 1,
"turtl" : 1,
"dog" : 2,
"cat" : 1,
"best" : 1,
"anim" : 1,
"whole" : 1,
"world" : 1,
"person" : 1,
"cute" : 1
}
self.assertEqual(1, _in_doc_freq("love", df))
self.assertEqual(2, _in_doc_freq("dog", df))
self.assertEqual(0, _in_doc_freq("patata", df))
def test_calculate_tf_idf(self):
df = {
"hello" : 1,
"love" : 1,
"turtl" : 1,
"dog" : 2,
"cat" : 1,
"best" : 1,
"anim" : 1,
"whole" : 1,
"world" : 1,
"person" : 1,
"cute" : 1
}
tf_idf = _calculate_tf_idf( self.candidates_preprocessed
,df
,len(self.candidates_preprocessed)
,len(df.keys()))
self.assertDictEqual({
(0, "hello") : (1/11 * np.log(3/2)),
(0, "love") : (1/11 * np.log(3/2)),
(0, "turtl") : (1/11 * np.log(3/2)),
(0, "dog") : (1/11 * np.log(3/3)),
(1, "cat") : (1/11 * np.log(3/2)),
(1, "best") : (1/11 * np.log(3/2)),
(1, "anim") : (1/11 * np.log(3/2)),
(1, "whole") : (1/11 * np.log(3/2)),
(1, "world") : (1/11 * np.log(3/2)),
(2, "dog") : (1/11 * np.log(3/3)),
(2, "person") : (1/11 * np.log(3/2)),
(2, "cute") : (1/11 * np.log(3/2)),
}, tf_idf)
def test_cosine_sim(self):
v1 = [1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/3),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2),1/11 * np.log(3/2)]
v2 = [0,0,0,0,1,1,1,1,1,0,0]
self.assertEqual(np.dot(v1, v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)), _cosine_sim(v1,v2))
def test_gen_vector(self):
df = {
"hello" : 1,
"love" : 1,
"turtl" : 1,
"dog" : 2,
"cat" : 1,
"best" : 1,
"anim" : 1,
"whole" : 1,
"world" : 1,
"person" : 1,
"cute" : 1
}
expected = np.zeros(len(df.keys()))
expected[1]= 1/11 * np.log(4/2)
expected[2]= 1/11 * np.log(4/2)
expected[10] = 1/11 * np.log(4/2)
self.assertEqual(
expected.all(),_gen_vector(['hey', 'dude', 'also', 'love', 'turtl', 'cute', 'slow'], list(df.keys()), df , 3).all()
)
def test_cosine_similarity(self):
reply = Node(
id = "comment1",
author_name = "Quim10^-12",
author_id = "author1",
text = "Hey dude! I also love turtle, they are so cute and slow.",
like_count = 10000000,
parent_id = None,
published_at = "12-12-2012"
)
df = {
"hello" : 1,
"love" : 1,
"turtl" : 1,
"dog" : 2,
"cat" : 1,
"best" : 1,
"anim" : 1,
"whole" : 1,
"world" : 1,
"person" : 1,
"cute" : 1
}
D = [[1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,1,1,1,1,1,0,0],
[0,0,0,1,0,0,0,0,0,1,1]]
cosines = _cosine_similarity( reply
, D
, list(df.keys())
, df,
3)
v = [0, 1/7 * np.log(4/2), 1/7 * np.log(4/2), 0, 0, 0, 0, 0, 0, 0, 1/7 * np.log(4/2)]
self.assertEqual([
(1,np.dot(v, D[0])/( | np.linalg.norm(v) | numpy.linalg.norm |
import sys, os
sys.path.append(os.path.join(os.path.dirname(__file__), '..'))
import argparse, glob, json
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.offsetbox import *
from matplotlib.patches import *
from PIL import Image
def load_results(path):
res = []
skip_count = 0
for cur_path in glob.glob(os.path.join(path, '*.json')):
with open(cur_path, 'r', encoding='utf8') as fop:
cur_res = json.load(fop)
# skip incomplete sessions
if None in cur_res:
skip_count += 1
continue
res.append(cur_res)
if skip_count > 0: print("[Warning] Skipped %d incomplete sessions." % skip_count)
return np.array(res)
def load_task(config):
truths, options = [], []
options = [task['options'] for task in config['tasks']]
truths = [task['options'][task['truth']] for task in config['tasks']]
truth_idcs = [task['truth'] for task in config['tasks']]
return np.array(truth_idcs), np.array(truths), np.array(options)
def get_choice_matrix(results, options):
# convert results into (task, choices) choice count matrix
mat_choices = np.zeros((results.shape[1], 3))
for res_idx in range(results.shape[0]):
for task_idx in range(results.shape[1]):
choice_idx = np.where(options[task_idx] == results[res_idx, task_idx])
mat_choices[task_idx, choice_idx] += 1
return mat_choices
def calc_accuracies(results, truths):
mat_truths = np.repeat(truths.reshape((1, truths.shape[0])), results.shape[0], axis=0)
matches = np.sum(results == mat_truths, axis=1)
accuracies = matches / truths.shape[0]
return accuracies
def calc_kappa(choices, num_choices=3):
'''Calculate Fleiss' Kappa (based on https://en.wikibooks.org/wiki/Algorithm_Implementation/Statistics/Fleiss'_kappa)'''
num_evals = np.sum(choices[0])
num_tasks = choices.shape[0]
p = [0.0] * num_choices
for j in range(num_choices):
p[j] = 0.0
for i in range(num_tasks):
p[j] += choices[i][j]
p[j] /= num_tasks * num_evals
P = [0.0] * num_tasks
for i in range(num_tasks):
P[i] = 0.0
for j in range(num_choices):
P[i] += choices[i][j] * choices[i][j]
P[i] = (P[i] - num_evals) / (num_evals * (num_evals - 1))
Pbar = sum(P) / num_tasks
PbarE = 0.0
for pj in p:
PbarE += pj * pj
kappa = (Pbar - PbarE) / (1 - PbarE)
return kappa
if __name__ == '__main__':
arg_parser = argparse.ArgumentParser(description='SynEval Result Aggregation')
arg_parser.add_argument('config_path', help='path evaluation configuration JSON')
arg_parser.add_argument('result_path', help='path result files')
arg_parser.add_argument('--plot', action='store_true', help='plot results')
arg_parser.add_argument('--data_path', help='path to data (required for plotting)')
args = arg_parser.parse_args()
# load config
with open(args.config_path, 'r', encoding='utf8') as fop:
config = json.load(fop)
truth_idcs, truths, options = load_task(config)
# load results
results = load_results(args.result_path)
print("Loaded %d evaluation sessions with %d tasks each." % (results.shape[0], truths.shape[0]))
# calculate accuracy
accuracies = calc_accuracies(results, truths)
print("Accuracy: %.2f avg, %.2f stddev, %.2f max, %.2f min" % (np.mean(accuracies), np.std(accuracies), np.max(accuracies), np.min(accuracies)))
print(" ", accuracies)
# calculate accuracy per class
choices = get_choice_matrix(results, options)
print("Accuracy per class:")
for class_idx, class_dsc in enumerate(config['classes']):
class_correct = choices[[ti for ti, t in enumerate(truth_idcs) if t == class_idx], class_idx]
class_accuracy = | np.sum(class_correct) | numpy.sum |
# emacs: -*- mode: python; py-indent-offset: 4; indent-tabs-mode: nil -*-
# vi: set ft=python sts=4 ts=4 sw=4 et:
#
# Copyright 2021 The NiPreps Developers <<EMAIL>>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# We support and encourage derived works from this project, please read
# about our expectations at
#
# https://www.nipreps.org/community/licensing/
#
"""The :math:`B_0` unwarping transform formalism."""
from pathlib import Path
import attr
import numpy as np
from scipy import ndimage as ndi
from scipy.sparse import vstack as sparse_vstack, csr_matrix, kron
import nibabel as nb
from bids.utils import listify
@attr.s(slots=True)
class B0FieldTransform:
"""Represents and applies the transform to correct for susceptibility distortions."""
coeffs = attr.ib(default=None)
shifts = attr.ib(default=None, init=False)
def fit(self, spatialimage):
r"""
Generate the interpolation matrix (and the VSM with it).
Implements Eq. :math:`\eqref{eq:1}`, interpolating :math:`f(\mathbf{s})`
for all voxels in the target-image's extent.
"""
# Calculate the physical coordinates of target grid
if isinstance(spatialimage, (str, bytes, Path)):
spatialimage = nb.load(spatialimage)
if self.shifts is not None:
newaff = spatialimage.affine
newshape = spatialimage.shape
if np.all(newshape == self.shifts.shape) and np.allclose(
newaff, self.shifts.affine
):
return
weights = []
coeffs = []
# Generate tensor-product B-Spline weights
for level in listify(self.coeffs):
wmat = grid_bspline_weights(spatialimage, level)
weights.append(wmat)
coeffs.append(level.get_fdata(dtype="float32").reshape(-1))
# Interpolate the VSM (voxel-shift map)
vsm = np.zeros(spatialimage.shape[:3], dtype="float32")
vsm = (np.squeeze(np.vstack(coeffs).T) @ sparse_vstack(weights)).reshape(
vsm.shape
)
# Cache
self.shifts = nb.Nifti1Image(vsm, spatialimage.affine, None)
def apply(
self,
spatialimage,
pe_dir,
ro_time,
order=3,
mode="constant",
cval=0.0,
prefilter=True,
output_dtype=None,
):
"""
Apply a transformation to an image, resampling on the reference spatial object.
Parameters
----------
spatialimage : `spatialimage`
The image object containing the data to be resampled in reference
space
reference : spatial object, optional
The image, surface, or combination thereof containing the coordinates
of samples that will be sampled.
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
mode : {'constant', 'reflect', 'nearest', 'mirror', 'wrap'}, optional
Determines how the input image is extended when the resamplings overflows
a border. Default is 'constant'.
cval : float, optional
Constant value for ``mode='constant'``. Default is 0.0.
prefilter: bool, optional
Determines if the image's data array is prefiltered with
a spline filter before interpolation. The default is ``True``,
which will create a temporary *float64* array of filtered values
if *order > 1*. If setting this to ``False``, the output will be
slightly blurred if *order > 1*, unless the input is prefiltered,
i.e. it is the result of calling the spline filter on the original
input.
Returns
-------
resampled : `spatialimage` or ndarray
The data imaged after resampling to reference space.
"""
# Ensure the vsm has been computed
self.fit(spatialimage)
vsm = self.shifts.get_fdata().copy()
# Reverse shifts if reversed blips
if pe_dir.endswith("-"):
vsm *= -1.0
# Generate warp field
pe_axis = "ijk".index(pe_dir[0])
# Map voxel coordinates applying the VSM
ijk_axis = tuple([np.arange(s) for s in vsm.shape])
voxcoords = np.array(np.meshgrid(*ijk_axis, indexing="ij"), dtype="float32")
voxcoords[pe_axis, ...] += vsm * ro_time
# Prepare data
data = np.squeeze(np.asanyarray(spatialimage.dataobj))
output_dtype = output_dtype or data.dtype
# Resample
resampled = ndi.map_coordinates(
data,
voxcoords.reshape(3, -1),
output=output_dtype,
order=order,
mode=mode,
cval=cval,
prefilter=prefilter,
).reshape(spatialimage.shape)
moved = spatialimage.__class__(
resampled, spatialimage.affine, spatialimage.header
)
moved.header.set_data_dtype(output_dtype)
return moved
def to_displacements(self, ro_time, pe_dir):
"""
Generate a NIfTI file containing a displacements field transform compatible with ITK/ANTs.
The displacements field can be calculated following
`Eq. (2) in the fieldmap fitting section
<sdcflows.workflows.fit.fieldmap.html#mjx-eqn-eq%3Afieldmap-2>`__.
Parameters
----------
ro_time : :obj:`float`
The total readout time in seconds (only if ``vsm=False``).
pe_dir : :obj:`str`
The ``PhaseEncodingDirection`` metadata value (only if ``vsm=False``).
Returns
-------
spatialimage : :obj:`nibabel.nifti.Nifti1Image`
A NIfTI 1.0 object containing the distortion.
"""
from math import pi
from nibabel.affines import voxel_sizes, obliquity
from nibabel.orientations import io_orientation
# Generate warp field
data = self.shifts.get_fdata(dtype="float32").copy()
pe_axis = "ijk".index(pe_dir[0])
pe_sign = -1.0 if pe_dir.endswith("-") else 1.0
pe_size = self.shifts.header.get_zooms()[pe_axis]
data *= pe_sign * ro_time * pe_size
fieldshape = tuple(list(data.shape[:3]) + [3])
# Compose a vector field
field = np.zeros((data.size, 3), dtype="float32")
field[..., pe_axis] = data.reshape(-1)
# If coordinate system is oblique, project displacements through directions matrix
aff = self.shifts.affine
if obliquity(aff).max() * 180 / pi > 0.01:
dirmat = | np.eye(4) | numpy.eye |
"""
Linear Algebra solvers and other helpers
"""
from __future__ import print_function
from statsmodels.compat.python import range
import numpy as np
from scipy.linalg import pinv, pinv2, lstsq # noqa:F421
def logdet_symm(m, check_symm=False):
"""
Return log(det(m)) asserting positive definiteness of m.
Parameters
----------
m : array-like
2d array that is positive-definite (and symmetric)
Returns
-------
logdet : float
The log-determinant of m.
"""
from scipy import linalg
if check_symm:
if not np.all(m == m.T): # would be nice to short-circuit check
raise ValueError("m is not symmetric.")
c, _ = linalg.cho_factor(m, lower=True)
return 2*np.sum(np.log(c.diagonal()))
def stationary_solve(r, b):
"""
Solve a linear system for a Toeplitz correlation matrix.
A Toeplitz correlation matrix represents the covariance of a
stationary series with unit variance.
Parameters
----------
r : array-like
A vector describing the coefficient matrix. r[0] is the first
band next to the diagonal, r[1] is the second band, etc.
b : array-like
The right-hand side for which we are solving, i.e. we solve
Tx = b and return b, where T is the Toeplitz coefficient matrix.
Returns
-------
The solution to the linear system.
"""
db = r[0:1]
dim = b.ndim
if b.ndim == 1:
b = b[:, None]
x = b[0:1, :]
for j in range(1, len(b)):
rf = r[0:j][::-1]
a = (b[j, :] - np.dot(rf, x)) / (1 - | np.dot(rf, db[::-1]) | numpy.dot |
import tensorflow as tf
import numpy as np
from config import cfg
def compute_area(xmin, xmax, ymin, ymax):
return ((xmax>xmin)*(xmax-xmin)*(ymax>ymin)*(ymax-ymin)).astype(np.float32)
def bbox_overlaps(boxes, query):
'''
boxes: (N, 4) array
query: (M, 4) array
RETURN: (N, M) array where ai,j is the distance matrix
'''
bxmin, bxmax = np.reshape(boxes[:,0], [-1,1]), np.reshape(boxes[:,2], [-1,1])
bymin, bymax = np.reshape(boxes[:,1], [-1,1]), np.reshape(boxes[:,3], [-1,1])
qxmin, qxmax = np.reshape(query[:,0], [1,-1]), np.reshape(query[:,2], [1,-1])
qymin, qymax = np.reshape(query[:,1], [1,-1]), np.reshape(query[:,3], [1,-1])
ixmin, ixmax = np.maximum(bxmin, qxmin), np.minimum(bxmax, qxmax)
iymin, iymax = np.maximum(bymin, qymin), np.minimum(bymax, qymax)
intersection = compute_area(ixmin, ixmax, iymin, iymax)
area_boxes = compute_area(bxmin, bxmax, bymin, bymax)
area_query = compute_area(qxmin, qxmax, qymin, qymax)
union = area_boxes + area_query - intersection
overlap = intersection / (union + cfg.eps)
return overlap
def minmax2ctrwh(boxes):
widths = np.maximum(0.0, boxes[:,2] - boxes[:,0])
heights = np.maximum(0.0, boxes[:,3] - boxes[:,1])
ctrx = boxes[:,0] + widths * 0.5
ctry = boxes[:,1] + heights * 0.5
return widths, heights, ctrx, ctry
def encode_roi(anchors, boxes):
'''
- anchors: (N, 4) tensors
- boxes: (N, 4) tensors
RETURN
- terms: (N, 4) encoded terms
'''
anc_w, anc_h, anc_ctrx, anc_ctry = minmax2ctrwh(anchors)
box_w, box_h, box_ctrx, box_ctry = minmax2ctrwh(boxes)
tx = (box_ctrx - anc_ctrx) / (anc_w + cfg.eps)
ty = (box_ctry - anc_ctry) / (anc_h + cfg.eps)
tw = np.log(box_w / (anc_w + cfg.eps) + cfg.log_eps)
th = np.log(box_h / (anc_h + cfg.eps) + cfg.log_eps)
return np.stack((tx, ty, tw, th), axis=1)
def rpn_target_one_batch(anchors, gt_boxes):
'''
Propose rpn_targt for one batch
- anchors: (N, 4) array
- gt_boxes: (M, 4) groundtruths boxes
RETURN
- labels: (N,), 1 for positive, 0 for negative, -1 for don't care
- terms: (N, 4), regression terms for each positive anchors
'''
N, M = anchors.shape[0], gt_boxes.shape[0]
iou = bbox_overlaps(gt_boxes, anchors)
max_iou_ind = iou.argmax(axis=1)
max_iou = iou[range(M), max_iou_ind]
max_gt_ind = iou.argmax(axis=0)
max_gt_iou = iou[max_gt_ind, range(N)]
# decide labels
labels = np.zeros(N, np.int32)-1
labels[max_gt_iou < cfg.rpn_negative_iou] = 0 # iou < negative_thresh
labels[max_gt_iou > cfg.rpn_positive_iou] = 1 # iou > postive_thresh
labels[max_iou_ind] = 1 # maximum iou with each groundtruth
# filter out too many positive or negative
pos_inds = np.where(labels == 1)[0]
neg_inds = | np.where(labels == 0) | numpy.where |
import numpy as np
import torch
from torchvision.transforms import ToTensor
def batchComputeFlowImage(uv):
flow_im = torch.zeros(uv.size(0), 3, uv.size(2), uv.size(3) )
uv_np = uv.numpy()
for i in range(uv.size(0)):
flow_im[i] = ToTensor()(computeFlowImage(uv_np[i][0], uv_np[i][1]))
return flow_im
def computeFlowImage(u,v,logscale=True,scaledown=6,output=False):
"""
topleft is zero, u is horiz, v is vertical
red is 3 o'clock, yellow is 6, light blue is 9, blue/purple is 12
"""
colorwheel = makecolorwheel()
ncols = colorwheel.shape[0]
radius = | np.sqrt(u**2 + v**2) | numpy.sqrt |
import numpy as np
import configparser
import os
import motmetrics as mm
# from numba import jit
import torch
from torch.nn.functional import cosine_similarity
from scipy.optimize import linear_sum_assignment as linear_assignment
from .tn_utils import *
from .kalman_box import KalmanBoxTracker, TrackState
# read config file
config = configparser.ConfigParser()
config.read(os.path.join("src", "configs", "tracking.config"))
# detector params
det_mode = config.get("Detector", "det_mode")
nms_thres = config.getfloat("Detector", "nms_thres")
nms_flag = config.getboolean("Detector", "nms_flag")
high_thres = config.getfloat("Detector", "high_thres")
low_thres = config.getfloat("Detector", "low_thres")
track_init_thres = config.getfloat("Detector", "track_init_thres")
exp_file = config.get("Detector", "exp_file")
detector_model_file = config.get("Detector", "chkpt_file")
half = config.getboolean("Detector", "half")
# TrackerInfo
pretext_model_path = config.get("TrackerInfo", "pretext_model_path")
embedding_size = config.getint("TrackerInfo", "embedding_size")
tracking_filename = config.get("TrackerInfo", "tracking_filename")
experiment_name = config.get("TrackerInfo", "experiment_name")
# TrackerParams
max_age = config.getint("TrackerParams", "max_age")
min_hits = config.getint("TrackerParams", "min_hits")
beta = config.getfloat("TrackerParams", "beta")
iou_thres = config.getfloat("TrackerParams", "iou_thres")
min_box_area = config.getfloat("TrackerParams", "min_box_area")
iou_thres_2 = config.getfloat("TrackerParams", "iou_thres_2")
visual = config.getboolean("TrackerParams", "visual")
# @jit
def iou(bb_test, bb_gt):
"""
Computes IUO between two bboxes in the form [x1,y1,x2,y2]
"""
xx1 = | np.maximum(bb_test[0], bb_gt[0]) | numpy.maximum |
import unittest
import qteasy as qt
import pandas as pd
from pandas import Timestamp
import numpy as np
import math
from numpy import int64
import itertools
import datetime
from qteasy.utilfuncs import list_to_str_format, regulate_date_format, time_str_format, str_to_list
from qteasy.utilfuncs import maybe_trade_day, is_market_trade_day, prev_trade_day, next_trade_day
from qteasy.utilfuncs import next_market_trade_day, unify, mask_to_signal, list_or_slice, labels_to_dict
from qteasy.utilfuncs import weekday_name, prev_market_trade_day, is_number_like, list_truncate, input_to_list
from qteasy.space import Space, Axis, space_around_centre, ResultPool
from qteasy.core import apply_loop
from qteasy.built_in import SelectingFinanceIndicator, TimingDMA, TimingMACD, TimingCDL, TimingTRIX
from qteasy.tsfuncs import income, indicators, name_change, get_bar
from qteasy.tsfuncs import stock_basic, trade_calendar, new_share, get_index
from qteasy.tsfuncs import balance, cashflow, top_list, index_indicators, composite
from qteasy.tsfuncs import future_basic, future_daily, options_basic, options_daily
from qteasy.tsfuncs import fund_basic, fund_net_value, index_basic, stock_company
from qteasy.evaluate import eval_alpha, eval_benchmark, eval_beta, eval_fv
from qteasy.evaluate import eval_info_ratio, eval_max_drawdown, eval_sharp
from qteasy.evaluate import eval_volatility
from qteasy.tafuncs import bbands, dema, ema, ht, kama, ma, mama, mavp, mid_point
from qteasy.tafuncs import mid_price, sar, sarext, sma, t3, tema, trima, wma, adx, adxr
from qteasy.tafuncs import apo, bop, cci, cmo, dx, macd, macdext, aroon, aroonosc
from qteasy.tafuncs import macdfix, mfi, minus_di, minus_dm, mom, plus_di, plus_dm
from qteasy.tafuncs import ppo, roc, rocp, rocr, rocr100, rsi, stoch, stochf, stochrsi
from qteasy.tafuncs import trix, ultosc, willr, ad, adosc, obv, atr, natr, trange
from qteasy.tafuncs import avgprice, medprice, typprice, wclprice, ht_dcperiod
from qteasy.tafuncs import ht_dcphase, ht_phasor, ht_sine, ht_trendmode, cdl2crows
from qteasy.tafuncs import cdl3blackcrows, cdl3inside, cdl3linestrike, cdl3outside
from qteasy.tafuncs import cdl3starsinsouth, cdl3whitesoldiers, cdlabandonedbaby
from qteasy.tafuncs import cdladvanceblock, cdlbelthold, cdlbreakaway, cdlclosingmarubozu
from qteasy.tafuncs import cdlconcealbabyswall, cdlcounterattack, cdldarkcloudcover
from qteasy.tafuncs import cdldoji, cdldojistar, cdldragonflydoji, cdlengulfing
from qteasy.tafuncs import cdleveningdojistar, cdleveningstar, cdlgapsidesidewhite
from qteasy.tafuncs import cdlgravestonedoji, cdlhammer, cdlhangingman, cdlharami
from qteasy.tafuncs import cdlharamicross, cdlhighwave, cdlhikkake, cdlhikkakemod
from qteasy.tafuncs import cdlhomingpigeon, cdlidentical3crows, cdlinneck
from qteasy.tafuncs import cdlinvertedhammer, cdlkicking, cdlkickingbylength
from qteasy.tafuncs import cdlladderbottom, cdllongleggeddoji, cdllongline, cdlmarubozu
from qteasy.tafuncs import cdlmatchinglow, cdlmathold, cdlmorningdojistar, cdlmorningstar
from qteasy.tafuncs import cdlonneck, cdlpiercing, cdlrickshawman, cdlrisefall3methods
from qteasy.tafuncs import cdlseparatinglines, cdlshootingstar, cdlshortline, cdlspinningtop
from qteasy.tafuncs import cdlstalledpattern, cdlsticksandwich, cdltakuri, cdltasukigap
from qteasy.tafuncs import cdlthrusting, cdltristar, cdlunique3river, cdlupsidegap2crows
from qteasy.tafuncs import cdlxsidegap3methods, beta, correl, linearreg, linearreg_angle
from qteasy.tafuncs import linearreg_intercept, linearreg_slope, stddev, tsf, var, acos
from qteasy.tafuncs import asin, atan, ceil, cos, cosh, exp, floor, ln, log10, sin, sinh
from qteasy.tafuncs import sqrt, tan, tanh, add, div, max, maxindex, min, minindex, minmax
from qteasy.tafuncs import minmaxindex, mult, sub, sum
from qteasy.history import get_financial_report_type_raw_data, get_price_type_raw_data
from qteasy.history import stack_dataframes, dataframe_to_hp, HistoryPanel
from qteasy.database import DataSource
from qteasy.strategy import Strategy, SimpleTiming, RollingTiming, SimpleSelecting, FactoralSelecting
from qteasy._arg_validators import _parse_string_kwargs, _valid_qt_kwargs
from qteasy.blender import _exp_to_token, blender_parser, signal_blend
class TestCost(unittest.TestCase):
def setUp(self):
self.amounts = np.array([10000., 20000., 10000.])
self.op = np.array([0., 1., -0.33333333])
self.amounts_to_sell = np.array([0., 0., -3333.3333])
self.cash_to_spend = np.array([0., 20000., 0.])
self.prices = np.array([10., 20., 10.])
self.r = qt.Cost(0.0)
def test_rate_creation(self):
"""测试对象生成"""
print('testing rates objects\n')
self.assertIsInstance(self.r, qt.Cost, 'Type should be Rate')
self.assertEqual(self.r.buy_fix, 0)
self.assertEqual(self.r.sell_fix, 0)
def test_rate_operations(self):
"""测试交易费率对象"""
self.assertEqual(self.r['buy_fix'], 0.0, 'Item got is incorrect')
self.assertEqual(self.r['sell_fix'], 0.0, 'Item got is wrong')
self.assertEqual(self.r['buy_rate'], 0.003, 'Item got is incorrect')
self.assertEqual(self.r['sell_rate'], 0.001, 'Item got is incorrect')
self.assertEqual(self.r['buy_min'], 5., 'Item got is incorrect')
self.assertEqual(self.r['sell_min'], 0.0, 'Item got is incorrect')
self.assertEqual(self.r['slipage'], 0.0, 'Item got is incorrect')
self.assertEqual(np.allclose(self.r.calculate(self.amounts),
[0.003, 0.003, 0.003]),
True,
'fee calculation wrong')
def test_rate_fee(self):
"""测试买卖交易费率"""
self.r.buy_rate = 0.003
self.r.sell_rate = 0.001
self.r.buy_fix = 0.
self.r.sell_fix = 0.
self.r.buy_min = 0.
self.r.sell_min = 0.
self.r.slipage = 0.
print('\nSell result with fixed rate = 0.001 and moq = 0:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell))
test_rate_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 0., -3333.3333]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], 33299.999667, msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 33.333332999999996, msg='result incorrect')
print('\nSell result with fixed rate = 0.001 and moq = 1:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 1.))
test_rate_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 1)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 0., -3333]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], 33296.67, msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 33.33, msg='result incorrect')
print('\nSell result with fixed rate = 0.001 and moq = 100:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 100))
test_rate_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 100)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 0., -3300]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], 32967.0, msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 33, msg='result incorrect')
print('\nPurchase result with fixed rate = 0.003 and moq = 0:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 0))
test_rate_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 0)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 997.00897308, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], -20000.0, msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 59.82053838484547, msg='result incorrect')
print('\nPurchase result with fixed rate = 0.003 and moq = 1:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 1))
test_rate_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 1)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 997., 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], -19999.82, msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 59.82, msg='result incorrect')
print('\nPurchase result with fixed rate = 0.003 and moq = 100:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 100))
test_rate_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 100)
self.assertIs(np.allclose(test_rate_fee_result[0], [0., 900., 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_fee_result[1], -18054., msg='result incorrect')
self.assertAlmostEqual(test_rate_fee_result[2], 54.0, msg='result incorrect')
def test_min_fee(self):
"""测试最低交易费用"""
self.r.buy_rate = 0.
self.r.sell_rate = 0.
self.r.buy_fix = 0.
self.r.sell_fix = 0.
self.r.buy_min = 300
self.r.sell_min = 300
self.r.slipage = 0.
print('\npurchase result with fixed cost rate with min fee = 300 and moq = 0:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 0))
test_min_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 0)
self.assertIs(np.allclose(test_min_fee_result[0], [0., 985, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], -20000.0, msg='result incorrect')
self.assertAlmostEqual(test_min_fee_result[2], 300.0, msg='result incorrect')
print('\npurchase result with fixed cost rate with min fee = 300 and moq = 10:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 10))
test_min_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 10)
self.assertIs(np.allclose(test_min_fee_result[0], [0., 980, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], -19900.0, msg='result incorrect')
self.assertAlmostEqual(test_min_fee_result[2], 300.0, msg='result incorrect')
print('\npurchase result with fixed cost rate with min fee = 300 and moq = 100:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 100))
test_min_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 100)
self.assertIs(np.allclose(test_min_fee_result[0], [0., 900, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], -18300.0, msg='result incorrect')
self.assertAlmostEqual(test_min_fee_result[2], 300.0, msg='result incorrect')
print('\nselling result with fixed cost rate with min fee = 300 and moq = 0:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell))
test_min_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell)
self.assertIs(np.allclose(test_min_fee_result[0], [0, 0, -3333.3333]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], 33033.333)
self.assertAlmostEqual(test_min_fee_result[2], 300.0)
print('\nselling result with fixed cost rate with min fee = 300 and moq = 1:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 1))
test_min_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 1)
self.assertIs(np.allclose(test_min_fee_result[0], [0, 0, -3333]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], 33030)
self.assertAlmostEqual(test_min_fee_result[2], 300.0)
print('\nselling result with fixed cost rate with min fee = 300 and moq = 100:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 100))
test_min_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 100)
self.assertIs(np.allclose(test_min_fee_result[0], [0, 0, -3300]), True, 'result incorrect')
self.assertAlmostEqual(test_min_fee_result[1], 32700)
self.assertAlmostEqual(test_min_fee_result[2], 300.0)
def test_rate_with_min(self):
"""测试最低交易费用对其他交易费率参数的影响"""
self.r.buy_rate = 0.0153
self.r.sell_rate = 0.01
self.r.buy_fix = 0.
self.r.sell_fix = 0.
self.r.buy_min = 300
self.r.sell_min = 333
self.r.slipage = 0.
print('\npurchase result with fixed cost rate with buy_rate = 0.0153, min fee = 300 and moq = 0:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 0))
test_rate_with_min_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 0)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0., 984.9305624, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], -20000.0, msg='result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[2], 301.3887520929774, msg='result incorrect')
print('\npurchase result with fixed cost rate with buy_rate = 0.0153, min fee = 300 and moq = 10:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 10))
test_rate_with_min_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 10)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0., 980, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], -19900.0, msg='result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[2], 300.0, msg='result incorrect')
print('\npurchase result with fixed cost rate with buy_rate = 0.0153, min fee = 300 and moq = 100:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 100))
test_rate_with_min_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 100)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0., 900, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], -18300.0, msg='result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[2], 300.0, msg='result incorrect')
print('\nselling result with fixed cost rate with sell_rate = 0.01, min fee = 333 and moq = 0:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell))
test_rate_with_min_result = self.r.get_selling_result(self.prices, self.amounts_to_sell)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0, 0, -3333.3333]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], 32999.99967)
self.assertAlmostEqual(test_rate_with_min_result[2], 333.33333)
print('\nselling result with fixed cost rate with sell_rate = 0.01, min fee = 333 and moq = 1:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 1))
test_rate_with_min_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 1)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0, 0, -3333]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], 32996.7)
self.assertAlmostEqual(test_rate_with_min_result[2], 333.3)
print('\nselling result with fixed cost rate with sell_rate = 0.01, min fee = 333 and moq = 100:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 100))
test_rate_with_min_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 100)
self.assertIs(np.allclose(test_rate_with_min_result[0], [0, 0, -3300]), True, 'result incorrect')
self.assertAlmostEqual(test_rate_with_min_result[1], 32667.0)
self.assertAlmostEqual(test_rate_with_min_result[2], 333.0)
def test_fixed_fee(self):
"""测试固定交易费用"""
self.r.buy_rate = 0.
self.r.sell_rate = 0.
self.r.buy_fix = 200
self.r.sell_fix = 150
self.r.buy_min = 0
self.r.sell_min = 0
self.r.slipage = 0
print('\nselling result of fixed cost with fixed fee = 150 and moq=0:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 0))
test_fixed_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0, 0, -3333.3333]), True, 'result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[1], 33183.333, msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 150.0, msg='result incorrect')
print('\nselling result of fixed cost with fixed fee = 150 and moq=100:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell, 100))
test_fixed_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell, 100)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0, 0, -3300.]), True,
f'result incorrect, {test_fixed_fee_result[0]} does not equal to [0,0,-3400]')
self.assertAlmostEqual(test_fixed_fee_result[1], 32850., msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 150., msg='result incorrect')
print('\npurchase result of fixed cost with fixed fee = 200:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 0))
test_fixed_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 0)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0., 990., 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[1], -20000.0, msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 200.0, msg='result incorrect')
print('\npurchase result of fixed cost with fixed fee = 200:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 100))
test_fixed_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 100)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0., 900., 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[1], -18200.0, msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 200.0, msg='result incorrect')
def test_slipage(self):
"""测试交易滑点"""
self.r.buy_fix = 0
self.r.sell_fix = 0
self.r.buy_min = 0
self.r.sell_min = 0
self.r.buy_rate = 0.003
self.r.sell_rate = 0.001
self.r.slipage = 1E-9
print('\npurchase result of fixed rate = 0.003 and slipage = 1E-10 and moq = 0:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 0))
print('\npurchase result of fixed rate = 0.003 and slipage = 1E-10 and moq = 100:')
print(self.r.get_purchase_result(self.prices, self.cash_to_spend, 100))
print('\nselling result with fixed rate = 0.001 and slipage = 1E-10:')
print(self.r.get_selling_result(self.prices, self.amounts_to_sell))
test_fixed_fee_result = self.r.get_selling_result(self.prices, self.amounts_to_sell)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0, 0, -3333.3333]), True,
f'{test_fixed_fee_result[0]} does not equal to [0, 0, -10000]')
self.assertAlmostEqual(test_fixed_fee_result[1], 33298.88855591,
msg=f'{test_fixed_fee_result[1]} does not equal to 99890.')
self.assertAlmostEqual(test_fixed_fee_result[2], 34.44444409,
msg=f'{test_fixed_fee_result[2]} does not equal to -36.666663.')
test_fixed_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 0)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0., 996.98909294, 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[1], -20000.0, msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 60.21814121353513, msg='result incorrect')
test_fixed_fee_result = self.r.get_purchase_result(self.prices, self.cash_to_spend, 100)
self.assertIs(np.allclose(test_fixed_fee_result[0], [0., 900., 0.]), True, 'result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[1], -18054.36, msg='result incorrect')
self.assertAlmostEqual(test_fixed_fee_result[2], 54.36, msg='result incorrect')
class TestSpace(unittest.TestCase):
def test_creation(self):
"""
test if creation of space object is fine
"""
# first group of inputs, output Space with two discr axis from [0,10]
print('testing space objects\n')
# pars_list = [[(0, 10), (0, 10)],
# [[0, 10], [0, 10]]]
#
# types_list = ['discr',
# ['discr', 'discr']]
#
# input_pars = itertools.product(pars_list, types_list)
# for p in input_pars:
# # print(p)
# s = qt.Space(*p)
# b = s.boes
# t = s.types
# # print(s, t)
# self.assertIsInstance(s, qt.Space)
# self.assertEqual(b, [(0, 10), (0, 10)], 'boes incorrect!')
# self.assertEqual(t, ['discr', 'discr'], 'types incorrect')
#
pars_list = [[(0, 10), (0, 10)],
[[0, 10], [0, 10]]]
types_list = ['foo, bar',
['foo', 'bar']]
input_pars = itertools.product(pars_list, types_list)
for p in input_pars:
# print(p)
s = Space(*p)
b = s.boes
t = s.types
# print(s, t)
self.assertEqual(b, [(0, 10), (0, 10)], 'boes incorrect!')
self.assertEqual(t, ['enum', 'enum'], 'types incorrect')
pars_list = [[(0, 10), (0, 10)],
[[0, 10], [0, 10]]]
types_list = [['discr', 'foobar']]
input_pars = itertools.product(pars_list, types_list)
for p in input_pars:
# print(p)
s = Space(*p)
b = s.boes
t = s.types
# print(s, t)
self.assertEqual(b, [(0, 10), (0, 10)], 'boes incorrect!')
self.assertEqual(t, ['discr', 'enum'], 'types incorrect')
pars_list = [(0., 10), (0, 10)]
s = Space(pars=pars_list, par_types=None)
self.assertEqual(s.types, ['conti', 'discr'])
self.assertEqual(s.dim, 2)
self.assertEqual(s.size, (10.0, 11))
self.assertEqual(s.shape, (np.inf, 11))
self.assertEqual(s.count, np.inf)
self.assertEqual(s.boes, [(0., 10), (0, 10)])
pars_list = [(0., 10), (0, 10)]
s = Space(pars=pars_list, par_types='conti, enum')
self.assertEqual(s.types, ['conti', 'enum'])
self.assertEqual(s.dim, 2)
self.assertEqual(s.size, (10.0, 2))
self.assertEqual(s.shape, (np.inf, 2))
self.assertEqual(s.count, np.inf)
self.assertEqual(s.boes, [(0., 10), (0, 10)])
pars_list = [(1, 2), (2, 3), (3, 4)]
s = Space(pars=pars_list)
self.assertEqual(s.types, ['discr', 'discr', 'discr'])
self.assertEqual(s.dim, 3)
self.assertEqual(s.size, (2, 2, 2))
self.assertEqual(s.shape, (2, 2, 2))
self.assertEqual(s.count, 8)
self.assertEqual(s.boes, [(1, 2), (2, 3), (3, 4)])
pars_list = [(1, 2, 3), (2, 3, 4), (3, 4, 5)]
s = Space(pars=pars_list)
self.assertEqual(s.types, ['enum', 'enum', 'enum'])
self.assertEqual(s.dim, 3)
self.assertEqual(s.size, (3, 3, 3))
self.assertEqual(s.shape, (3, 3, 3))
self.assertEqual(s.count, 27)
self.assertEqual(s.boes, [(1, 2, 3), (2, 3, 4), (3, 4, 5)])
pars_list = [((1, 2, 3), (2, 3, 4), (3, 4, 5))]
s = Space(pars=pars_list)
self.assertEqual(s.types, ['enum'])
self.assertEqual(s.dim, 1)
self.assertEqual(s.size, (3,))
self.assertEqual(s.shape, (3,))
self.assertEqual(s.count, 3)
pars_list = ((1, 2, 3), (2, 3, 4), (3, 4, 5))
s = Space(pars=pars_list)
self.assertEqual(s.types, ['enum', 'enum', 'enum'])
self.assertEqual(s.dim, 3)
self.assertEqual(s.size, (3, 3, 3))
self.assertEqual(s.shape, (3, 3, 3))
self.assertEqual(s.count, 27)
self.assertEqual(s.boes, [(1, 2, 3), (2, 3, 4), (3, 4, 5)])
def test_extract(self):
"""
:return:
"""
pars_list = [(0, 10), (0, 10)]
types_list = ['discr', 'discr']
s = Space(pars=pars_list, par_types=types_list)
extracted_int, count = s.extract(3, 'interval')
extracted_int_list = list(extracted_int)
print('extracted int\n', extracted_int_list)
self.assertEqual(count, 16, 'extraction count wrong!')
self.assertEqual(extracted_int_list, [(0, 0), (0, 3), (0, 6), (0, 9), (3, 0), (3, 3),
(3, 6), (3, 9), (6, 0), (6, 3), (6, 6), (6, 9),
(9, 0), (9, 3), (9, 6), (9, 9)],
'space extraction wrong!')
extracted_rand, count = s.extract(10, 'rand')
extracted_rand_list = list(extracted_rand)
self.assertEqual(count, 10, 'extraction count wrong!')
print('extracted rand\n', extracted_rand_list)
for point in list(extracted_rand_list):
self.assertEqual(len(point), 2)
self.assertLessEqual(point[0], 10)
self.assertGreaterEqual(point[0], 0)
self.assertLessEqual(point[1], 10)
self.assertGreaterEqual(point[1], 0)
pars_list = [(0., 10), (0, 10)]
s = Space(pars=pars_list, par_types=None)
extracted_int2, count = s.extract(3, 'interval')
self.assertEqual(count, 16, 'extraction count wrong!')
extracted_int_list2 = list(extracted_int2)
self.assertEqual(extracted_int_list2, [(0, 0), (0, 3), (0, 6), (0, 9), (3, 0), (3, 3),
(3, 6), (3, 9), (6, 0), (6, 3), (6, 6), (6, 9),
(9, 0), (9, 3), (9, 6), (9, 9)],
'space extraction wrong!')
print('extracted int list 2\n', extracted_int_list2)
self.assertIsInstance(extracted_int_list2[0][0], float)
self.assertIsInstance(extracted_int_list2[0][1], (int, int64))
extracted_rand2, count = s.extract(10, 'rand')
self.assertEqual(count, 10, 'extraction count wrong!')
extracted_rand_list2 = list(extracted_rand2)
print('extracted rand list 2:\n', extracted_rand_list2)
for point in extracted_rand_list2:
self.assertEqual(len(point), 2)
self.assertIsInstance(point[0], float)
self.assertLessEqual(point[0], 10)
self.assertGreaterEqual(point[0], 0)
self.assertIsInstance(point[1], (int, int64))
self.assertLessEqual(point[1], 10)
self.assertGreaterEqual(point[1], 0)
pars_list = [(0., 10), ('a', 'b')]
s = Space(pars=pars_list, par_types='enum, enum')
extracted_int3, count = s.extract(1, 'interval')
self.assertEqual(count, 4, 'extraction count wrong!')
extracted_int_list3 = list(extracted_int3)
self.assertEqual(extracted_int_list3, [(0., 'a'), (0., 'b'), (10, 'a'), (10, 'b')],
'space extraction wrong!')
print('extracted int list 3\n', extracted_int_list3)
self.assertIsInstance(extracted_int_list3[0][0], float)
self.assertIsInstance(extracted_int_list3[0][1], str)
extracted_rand3, count = s.extract(3, 'rand')
self.assertEqual(count, 3, 'extraction count wrong!')
extracted_rand_list3 = list(extracted_rand3)
print('extracted rand list 3:\n', extracted_rand_list3)
for point in extracted_rand_list3:
self.assertEqual(len(point), 2)
self.assertIsInstance(point[0], (float, int))
self.assertLessEqual(point[0], 10)
self.assertGreaterEqual(point[0], 0)
self.assertIsInstance(point[1], str)
self.assertIn(point[1], ['a', 'b'])
pars_list = [((0, 10), (1, 'c'), ('a', 'b'), (1, 14))]
s = Space(pars=pars_list, par_types='enum')
extracted_int4, count = s.extract(1, 'interval')
self.assertEqual(count, 4, 'extraction count wrong!')
extracted_int_list4 = list(extracted_int4)
it = zip(extracted_int_list4, [(0, 10), (1, 'c'), (0, 'b'), (1, 14)])
for item, item2 in it:
print(item, item2)
self.assertTrue(all([tuple(ext_item) == item for ext_item, item in it]))
print('extracted int list 4\n', extracted_int_list4)
self.assertIsInstance(extracted_int_list4[0], tuple)
extracted_rand4, count = s.extract(3, 'rand')
self.assertEqual(count, 3, 'extraction count wrong!')
extracted_rand_list4 = list(extracted_rand4)
print('extracted rand list 4:\n', extracted_rand_list4)
for point in extracted_rand_list4:
self.assertEqual(len(point), 2)
self.assertIsInstance(point[0], (int, str))
self.assertIn(point[0], [0, 1, 'a'])
self.assertIsInstance(point[1], (int, str))
self.assertIn(point[1], [10, 14, 'b', 'c'])
self.assertIn(point, [(0., 10), (1, 'c'), ('a', 'b'), (1, 14)])
pars_list = [((0, 10), (1, 'c'), ('a', 'b'), (1, 14)), (1, 4)]
s = Space(pars=pars_list, par_types='enum, discr')
extracted_int5, count = s.extract(1, 'interval')
self.assertEqual(count, 16, 'extraction count wrong!')
extracted_int_list5 = list(extracted_int5)
for item, item2 in extracted_int_list5:
print(item, item2)
self.assertTrue(all([tuple(ext_item) == item for ext_item, item in it]))
print('extracted int list 5\n', extracted_int_list5)
self.assertIsInstance(extracted_int_list5[0], tuple)
extracted_rand5, count = s.extract(5, 'rand')
self.assertEqual(count, 5, 'extraction count wrong!')
extracted_rand_list5 = list(extracted_rand5)
print('extracted rand list 5:\n', extracted_rand_list5)
for point in extracted_rand_list5:
self.assertEqual(len(point), 2)
self.assertIsInstance(point[0], tuple)
print(f'type of point[1] is {type(point[1])}')
self.assertIsInstance(point[1], (int, np.int64))
self.assertIn(point[0], [(0., 10), (1, 'c'), ('a', 'b'), (1, 14)])
print(f'test incremental extraction')
pars_list = [(10., 250), (10., 250), (10., 250), (10., 250), (10., 250), (10., 250)]
s = Space(pars_list)
ext, count = s.extract(64, 'interval')
self.assertEqual(count, 4096)
points = list(ext)
# 已经取出所有的点，围绕其中10个点生成十个subspaces
# 检查是否每个subspace都为Space，是否都在s范围内，使用32生成点集，检查生成数量是否正确
for point in points[1000:1010]:
subspace = s.from_point(point, 64)
self.assertIsInstance(subspace, Space)
self.assertTrue(subspace in s)
self.assertEqual(subspace.dim, 6)
self.assertEqual(subspace.types, ['conti', 'conti', 'conti', 'conti', 'conti', 'conti'])
ext, count = subspace.extract(32)
points = list(ext)
self.assertGreaterEqual(count, 512)
self.assertLessEqual(count, 4096)
print(f'\n---------------------------------'
f'\nthe space created around point <{point}> is'
f'\n{subspace.boes}'
f'\nand extracted {count} points, the first 5 are:'
f'\n{points[:5]}')
def test_axis_extract(self):
# test axis object with conti type
axis = Axis((0., 5))
self.assertIsInstance(axis, Axis)
self.assertEqual(axis.axis_type, 'conti')
self.assertEqual(axis.axis_boe, (0., 5.))
self.assertEqual(axis.count, np.inf)
self.assertEqual(axis.size, 5.0)
self.assertTrue(np.allclose(axis.extract(1, 'int'), [0., 1., 2., 3., 4.]))
self.assertTrue(np.allclose(axis.extract(0.5, 'int'), [0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5]))
extracted = axis.extract(8, 'rand')
self.assertEqual(len(extracted), 8)
self.assertTrue(all([(0 <= item <= 5) for item in extracted]))
# test axis object with discrete type
axis = Axis((1, 5))
self.assertIsInstance(axis, Axis)
self.assertEqual(axis.axis_type, 'discr')
self.assertEqual(axis.axis_boe, (1, 5))
self.assertEqual(axis.count, 5)
self.assertEqual(axis.size, 5)
self.assertTrue(np.allclose(axis.extract(1, 'int'), [1, 2, 3, 4, 5]))
self.assertRaises(ValueError, axis.extract, 0.5, 'int')
extracted = axis.extract(8, 'rand')
self.assertEqual(len(extracted), 8)
self.assertTrue(all([(item in [1, 2, 3, 4, 5]) for item in extracted]))
# test axis object with enumerate type
axis = Axis((1, 5, 7, 10, 'A', 'F'))
self.assertIsInstance(axis, Axis)
self.assertEqual(axis.axis_type, 'enum')
self.assertEqual(axis.axis_boe, (1, 5, 7, 10, 'A', 'F'))
self.assertEqual(axis.count, 6)
self.assertEqual(axis.size, 6)
self.assertEqual(axis.extract(1, 'int'), [1, 5, 7, 10, 'A', 'F'])
self.assertRaises(ValueError, axis.extract, 0.5, 'int')
extracted = axis.extract(8, 'rand')
self.assertEqual(len(extracted), 8)
self.assertTrue(all([(item in [1, 5, 7, 10, 'A', 'F']) for item in extracted]))
def test_from_point(self):
"""测试从一个点生成一个space"""
# 生成一个space，指定space中的一个点以及distance，生成一个sub-space
pars_list = [(0., 10), (0, 10)]
s = Space(pars=pars_list, par_types=None)
self.assertEqual(s.types, ['conti', 'discr'])
self.assertEqual(s.dim, 2)
self.assertEqual(s.size, (10., 11))
self.assertEqual(s.shape, (np.inf, 11))
self.assertEqual(s.count, np.inf)
self.assertEqual(s.boes, [(0., 10), (0, 10)])
print('create subspace from a point in space')
p = (3, 3)
distance = 2
subspace = s.from_point(p, distance)
self.assertIsInstance(subspace, Space)
self.assertEqual(subspace.types, ['conti', 'discr'])
self.assertEqual(subspace.dim, 2)
self.assertEqual(subspace.size, (4.0, 5))
self.assertEqual(subspace.shape, (np.inf, 5))
self.assertEqual(subspace.count, np.inf)
self.assertEqual(subspace.boes, [(1, 5), (1, 5)])
print('create subspace from a 6 dimensional discrete space')
s = Space(pars=[(10, 250), (10, 250), (10, 250), (10, 250), (10, 250), (10, 250)])
p = (15, 200, 150, 150, 150, 150)
d = 10
subspace = s.from_point(p, d)
self.assertIsInstance(subspace, Space)
self.assertEqual(subspace.types, ['discr', 'discr', 'discr', 'discr', 'discr', 'discr'])
self.assertEqual(subspace.dim, 6)
self.assertEqual(subspace.volume, 65345616)
self.assertEqual(subspace.size, (16, 21, 21, 21, 21, 21))
self.assertEqual(subspace.shape, (16, 21, 21, 21, 21, 21))
self.assertEqual(subspace.count, 65345616)
self.assertEqual(subspace.boes, [(10, 25), (190, 210), (140, 160), (140, 160), (140, 160), (140, 160)])
print('create subspace from a 6 dimensional continuous space')
s = Space(pars=[(10., 250), (10., 250), (10., 250), (10., 250), (10., 250), (10., 250)])
p = (15, 200, 150, 150, 150, 150)
d = 10
subspace = s.from_point(p, d)
self.assertIsInstance(subspace, Space)
self.assertEqual(subspace.types, ['conti', 'conti', 'conti', 'conti', 'conti', 'conti'])
self.assertEqual(subspace.dim, 6)
self.assertEqual(subspace.volume, 48000000)
self.assertEqual(subspace.size, (15.0, 20.0, 20.0, 20.0, 20.0, 20.0))
self.assertEqual(subspace.shape, (np.inf, np.inf, np.inf, np.inf, np.inf, np.inf))
self.assertEqual(subspace.count, np.inf)
self.assertEqual(subspace.boes, [(10, 25), (190, 210), (140, 160), (140, 160), (140, 160), (140, 160)])
print('create subspace with different distances on each dimension')
s = Space(pars=[(10., 250), (10., 250), (10., 250), (10., 250), (10., 250), (10., 250)])
p = (15, 200, 150, 150, 150, 150)
d = [10, 5, 5, 10, 10, 5]
subspace = s.from_point(p, d)
self.assertIsInstance(subspace, Space)
self.assertEqual(subspace.types, ['conti', 'conti', 'conti', 'conti', 'conti', 'conti'])
self.assertEqual(subspace.dim, 6)
self.assertEqual(subspace.volume, 6000000)
self.assertEqual(subspace.size, (15.0, 10.0, 10.0, 20.0, 20.0, 10.0))
self.assertEqual(subspace.shape, (np.inf, np.inf, np.inf, np.inf, np.inf, np.inf))
self.assertEqual(subspace.count, np.inf)
self.assertEqual(subspace.boes, [(10, 25), (195, 205), (145, 155), (140, 160), (140, 160), (145, 155)])
class TestCashPlan(unittest.TestCase):
def setUp(self):
self.cp1 = qt.CashPlan(['2012-01-01', '2010-01-01'], [10000, 20000], 0.1)
self.cp1.info()
self.cp2 = qt.CashPlan(['20100501'], 10000)
self.cp2.info()
self.cp3 = qt.CashPlan(pd.date_range(start='2019-01-01',
freq='Y',
periods=12),
[i * 1000 + 10000 for i in range(12)],
0.035)
self.cp3.info()
def test_creation(self):
self.assertIsInstance(self.cp1, qt.CashPlan, 'CashPlan object creation wrong')
self.assertIsInstance(self.cp2, qt.CashPlan, 'CashPlan object creation wrong')
self.assertIsInstance(self.cp3, qt.CashPlan, 'CashPlan object creation wrong')
# test __repr__()
print(self.cp1)
print(self.cp2)
print(self.cp3)
# test __str__()
self.cp1.info()
self.cp2.info()
self.cp3.info()
# test assersion errors
self.assertRaises(AssertionError, qt.CashPlan, '2016-01-01', [10000, 10000])
self.assertRaises(KeyError, qt.CashPlan, '2020-20-20', 10000)
def test_properties(self):
self.assertEqual(self.cp1.amounts, [20000, 10000], 'property wrong')
self.assertEqual(self.cp1.first_day, Timestamp('2010-01-01'))
self.assertEqual(self.cp1.last_day, Timestamp('2012-01-01'))
self.assertEqual(self.cp1.investment_count, 2)
self.assertEqual(self.cp1.period, 730)
self.assertEqual(self.cp1.dates, [Timestamp('2010-01-01'), Timestamp('2012-01-01')])
self.assertEqual(self.cp1.ir, 0.1)
self.assertAlmostEqual(self.cp1.closing_value, 34200)
self.assertAlmostEqual(self.cp2.closing_value, 10000)
self.assertAlmostEqual(self.cp3.closing_value, 220385.3483685)
self.assertIsInstance(self.cp1.plan, pd.DataFrame)
self.assertIsInstance(self.cp2.plan, pd.DataFrame)
self.assertIsInstance(self.cp3.plan, pd.DataFrame)
def test_operation(self):
cp_self_add = self.cp1 + self.cp1
cp_add = self.cp1 + self.cp2
cp_add_int = self.cp1 + 10000
cp_mul_int = self.cp1 * 2
cp_mul_float = self.cp2 * 1.5
cp_mul_time = 3 * self.cp2
cp_mul_time2 = 2 * self.cp1
cp_mul_time3 = 2 * self.cp3
cp_mul_float2 = 2. * self.cp3
self.assertIsInstance(cp_self_add, qt.CashPlan)
self.assertEqual(cp_self_add.amounts, [40000, 20000])
self.assertEqual(cp_add.amounts, [20000, 10000, 10000])
self.assertEqual(cp_add_int.amounts, [30000, 20000])
self.assertEqual(cp_mul_int.amounts, [40000, 20000])
self.assertEqual(cp_mul_float.amounts, [15000])
self.assertEqual(cp_mul_float.dates, [Timestamp('2010-05-01')])
self.assertEqual(cp_mul_time.amounts, [10000, 10000, 10000])
self.assertEqual(cp_mul_time.dates, [Timestamp('2010-05-01'),
Timestamp('2011-05-01'),
Timestamp('2012-04-30')])
self.assertEqual(cp_mul_time2.amounts, [20000, 10000, 20000, 10000])
self.assertEqual(cp_mul_time2.dates, [Timestamp('2010-01-01'),
Timestamp('2012-01-01'),
Timestamp('2014-01-01'),
Timestamp('2016-01-01')])
self.assertEqual(cp_mul_time3.dates, [Timestamp('2019-12-31'),
Timestamp('2020-12-31'),
Timestamp('2021-12-31'),
Timestamp('2022-12-31'),
Timestamp('2023-12-31'),
Timestamp('2024-12-31'),
Timestamp('2025-12-31'),
Timestamp('2026-12-31'),
Timestamp('2027-12-31'),
Timestamp('2028-12-31'),
Timestamp('2029-12-31'),
Timestamp('2030-12-31'),
Timestamp('2031-12-29'),
Timestamp('2032-12-29'),
Timestamp('2033-12-29'),
Timestamp('2034-12-29'),
Timestamp('2035-12-29'),
Timestamp('2036-12-29'),
Timestamp('2037-12-29'),
Timestamp('2038-12-29'),
Timestamp('2039-12-29'),
Timestamp('2040-12-29'),
Timestamp('2041-12-29'),
Timestamp('2042-12-29')])
self.assertEqual(cp_mul_float2.dates, [Timestamp('2019-12-31'),
Timestamp('2020-12-31'),
Timestamp('2021-12-31'),
Timestamp('2022-12-31'),
Timestamp('2023-12-31'),
Timestamp('2024-12-31'),
Timestamp('2025-12-31'),
Timestamp('2026-12-31'),
Timestamp('2027-12-31'),
Timestamp('2028-12-31'),
Timestamp('2029-12-31'),
Timestamp('2030-12-31')])
self.assertEqual(cp_mul_float2.amounts, [20000.0,
22000.0,
24000.0,
26000.0,
28000.0,
30000.0,
32000.0,
34000.0,
36000.0,
38000.0,
40000.0,
42000.0])
class TestPool(unittest.TestCase):
def setUp(self):
self.p = ResultPool(5)
self.items = ['first', 'second', (1, 2, 3), 'this', 24]
self.perfs = [1, 2, 3, 4, 5]
self.additional_result1 = ('abc', 12)
self.additional_result2 = ([1, 2], -1)
self.additional_result3 = (12, 5)
def test_create(self):
self.assertIsInstance(self.p, ResultPool)
def test_operation(self):
self.p.in_pool(self.additional_result1[0], self.additional_result1[1])
self.p.cut()
self.assertEqual(self.p.item_count, 1)
self.assertEqual(self.p.items, ['abc'])
for item, perf in zip(self.items, self.perfs):
self.p.in_pool(item, perf)
self.assertEqual(self.p.item_count, 6)
self.assertEqual(self.p.items, ['abc', 'first', 'second', (1, 2, 3), 'this', 24])
self.p.cut()
self.assertEqual(self.p.items, ['second', (1, 2, 3), 'this', 24, 'abc'])
self.assertEqual(self.p.perfs, [2, 3, 4, 5, 12])
self.p.in_pool(self.additional_result2[0], self.additional_result2[1])
self.p.in_pool(self.additional_result3[0], self.additional_result3[1])
self.assertEqual(self.p.item_count, 7)
self.p.cut(keep_largest=False)
self.assertEqual(self.p.items, [[1, 2], 'second', (1, 2, 3), 'this', 24])
self.assertEqual(self.p.perfs, [-1, 2, 3, 4, 5])
class TestCoreSubFuncs(unittest.TestCase):
"""Test all functions in core.py"""
def setUp(self):
pass
def test_input_to_list(self):
print('Testing input_to_list() function')
input_str = 'first'
self.assertEqual(qt.utilfuncs.input_to_list(input_str, 3), ['first', 'first', 'first'])
self.assertEqual(qt.utilfuncs.input_to_list(input_str, 4), ['first', 'first', 'first', 'first'])
self.assertEqual(qt.utilfuncs.input_to_list(input_str, 2, None), ['first', 'first'])
input_list = ['first', 'second']
self.assertEqual(qt.utilfuncs.input_to_list(input_list, 3), ['first', 'second', None])
self.assertEqual(qt.utilfuncs.input_to_list(input_list, 4, 'padder'), ['first', 'second', 'padder', 'padder'])
self.assertEqual(qt.utilfuncs.input_to_list(input_list, 1), ['first', 'second'])
self.assertEqual(qt.utilfuncs.input_to_list(input_list, -5), ['first', 'second'])
def test_point_in_space(self):
sp = Space([(0., 10.), (0., 10.), (0., 10.)])
p1 = (5.5, 3.2, 7)
p2 = (-1, 3, 10)
self.assertTrue(p1 in sp)
print(f'point {p1} is in space {sp}')
self.assertFalse(p2 in sp)
print(f'point {p2} is not in space {sp}')
sp = Space([(0., 10.), (0., 10.), range(40, 3, -2)], 'conti, conti, enum')
p1 = (5.5, 3.2, 8)
self.assertTrue(p1 in sp)
print(f'point {p1} is in space {sp}')
def test_space_in_space(self):
print('test if a space is in another space')
sp = Space([(0., 10.), (0., 10.), (0., 10.)])
sp2 = Space([(0., 10.), (0., 10.), (0., 10.)])
self.assertTrue(sp2 in sp)
self.assertTrue(sp in sp2)
print(f'space {sp2} is in space {sp}\n'
f'and space {sp} is in space {sp2}\n'
f'they are equal to each other\n')
sp2 = Space([(0, 5.), (2, 7.), (3., 9.)])
self.assertTrue(sp2 in sp)
self.assertFalse(sp in sp2)
print(f'space {sp2} is in space {sp}\n'
f'and space {sp} is not in space {sp2}\n'
f'{sp2} is a sub space of {sp}\n')
sp2 = Space([(0, 5), (2, 7), (3., 9)])
self.assertFalse(sp2 in sp)
self.assertFalse(sp in sp2)
print(f'space {sp2} is not in space {sp}\n'
f'and space {sp} is not in space {sp2}\n'
f'they have different types of axes\n')
sp = Space([(0., 10.), (0., 10.), range(40, 3, -2)])
self.assertFalse(sp in sp2)
self.assertFalse(sp2 in sp)
print(f'space {sp2} is not in space {sp}\n'
f'and space {sp} is not in space {sp2}\n'
f'they have different types of axes\n')
def test_space_around_centre(self):
sp = Space([(0., 10.), (0., 10.), (0., 10.)])
p1 = (5.5, 3.2, 7)
ssp = space_around_centre(space=sp, centre=p1, radius=1.2)
print(ssp.boes)
print('\ntest multiple diameters:')
self.assertEqual(ssp.boes, [(4.3, 6.7), (2.0, 4.4), (5.8, 8.2)])
ssp = space_around_centre(space=sp, centre=p1, radius=[1, 2, 1])
print(ssp.boes)
self.assertEqual(ssp.boes, [(4.5, 6.5), (1.2000000000000002, 5.2), (6.0, 8.0)])
print('\ntest points on edge:')
p2 = (5.5, 3.2, 10)
ssp = space_around_centre(space=sp, centre=p1, radius=3.9)
print(ssp.boes)
self.assertEqual(ssp.boes, [(1.6, 9.4), (0.0, 7.1), (3.1, 10.0)])
print('\ntest enum spaces')
sp = Space([(0, 100), range(40, 3, -2)], 'discr, enum')
p1 = [34, 12]
ssp = space_around_centre(space=sp, centre=p1, radius=5, ignore_enums=False)
self.assertEqual(ssp.boes, [(29, 39), (22, 20, 18, 16, 14, 12, 10, 8, 6, 4)])
print(ssp.boes)
print('\ntest enum space and ignore enum axis')
ssp = space_around_centre(space=sp, centre=p1, radius=5)
self.assertEqual(ssp.boes, [(29, 39),
(40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4)])
print(sp.boes)
def test_get_stock_pool(self):
print(f'start test building stock pool function\n')
share_basics = stock_basic(fields='ts_code,symbol,name,area,industry,market,list_date,exchange')
print(f'\nselect all stocks by area')
stock_pool = qt.get_stock_pool(area='上海')
print(f'{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stock areas are "上海"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['area'].eq('上海').all())
print(f'\nselect all stocks by multiple areas')
stock_pool = qt.get_stock_pool(area='贵州,北京,天津')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stock areas are in list of ["贵州", "北京", "天津"]\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['area'].isin(['贵州',
'北京',
'天津']).all())
print(f'\nselect all stocks by area and industry')
stock_pool = qt.get_stock_pool(area='四川', industry='银行, 金融')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stock areas are "四川", and industry in ["银行", "金融"]\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['industry'].isin(['银行', '金融']).all())
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['area'].isin(['四川']).all())
print(f'\nselect all stocks by industry')
stock_pool = qt.get_stock_pool(industry='银行, 金融')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stocks industry in ["银行", "金融"]\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['industry'].isin(['银行', '金融']).all())
print(f'\nselect all stocks by market')
stock_pool = qt.get_stock_pool(market='主板')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stock market is "主板"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['market'].isin(['主板']).all())
print(f'\nselect all stocks by market and list date')
stock_pool = qt.get_stock_pool(date='2000-01-01', market='主板')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all stock market is "主板", and list date after "2000-01-01"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['market'].isin(['主板']).all())
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['list_date'].le('2000-01-01').all())
print(f'\nselect all stocks by list date')
stock_pool = qt.get_stock_pool(date='1997-01-01')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all list date after "1997-01-01"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['list_date'].le('1997-01-01').all())
print(f'\nselect all stocks by exchange')
stock_pool = qt.get_stock_pool(exchange='SSE')
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all exchanges are "SSE"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['exchange'].eq('SSE').all())
print(f'\nselect all stocks by industry, area and list date')
industry_list = ['银行', '全国地产', '互联网', '环境保护', '区域地产',
'酒店餐饮', '运输设备', '综合类', '建筑工程', '玻璃',
'家用电器', '文教休闲', '其他商业', '元器件', 'IT设备',
'其他建材', '汽车服务', '火力发电', '医药商业', '汽车配件',
'广告包装', '轻工机械', '新型电力', '多元金融', '饲料']
area_list = ['深圳', '北京', '吉林', '江苏', '辽宁', '广东',
'安徽', '四川', '浙江', '湖南', '河北', '新疆',
'山东', '河南', '山西', '江西', '青海', '湖北',
'内蒙', '海南', '重庆', '陕西', '福建', '广西',
'上海']
stock_pool = qt.get_stock_pool(date='19980101',
industry=industry_list,
area=area_list)
print(f'\n{len(stock_pool)} shares selected, first 5 are: {stock_pool[0:5]}\n'
f'check if all exchanges are "SSE"\n'
f'{share_basics[np.isin(share_basics.ts_code, stock_pool)].head()}')
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['list_date'].le('1998-01-01').all())
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['industry'].isin(industry_list).all())
self.assertTrue(share_basics[np.isin(share_basics.ts_code, stock_pool)]['area'].isin(area_list).all())
self.assertRaises(KeyError, qt.get_stock_pool, industry=25)
self.assertRaises(KeyError, qt.get_stock_pool, share_name='000300.SH')
self.assertRaises(KeyError, qt.get_stock_pool, markets='SSE')
class TestEvaluations(unittest.TestCase):
"""Test all evaluation functions in core.py"""
# 以下手动计算结果在Excel文件中
def setUp(self):
"""用np.random生成测试用数据，使用cumsum()模拟股票走势"""
self.test_data1 = pd.DataFrame([5.34892759, 5.65768696, 5.79227076, 5.56266871, 5.88189632,
6.24795001, 5.92755558, 6.38748165, 6.31331899, 5.86001665,
5.61048472, 5.30696736, 5.40406792, 5.03180571, 5.37886353,
5.78608307, 6.26540339, 6.59348026, 6.90943801, 6.70911677,
6.33015954, 6.06697417, 5.9752499, 6.45786408, 6.95273763,
6.7691991, 6.70355481, 6.28048969, 6.61344541, 6.24620003,
6.47409983, 6.4522311, 6.8773094, 6.99727832, 6.59262674,
6.59014938, 6.63758237, 6.38331869, 6.09902105, 6.35390109,
6.51993567, 6.87244592, 6.83963485, 7.08797815, 6.88003144,
6.83657323, 6.97819483, 7.01600276, 7.12554256, 7.58941523,
7.61014457, 7.21224091, 7.48174399, 7.66490854, 7.51371968,
7.11586198, 6.97147399, 6.67453301, 6.2042138, 6.33967015,
6.22187938, 5.98426993, 6.37096079, 6.55897161, 6.26422645,
6.69363762, 7.12668015, 6.83232926, 7.30524081, 7.4262041,
7.54031383, 7.17545919, 7.20659257, 7.44886016, 7.37094393,
6.88011022, 7.08142491, 6.74992833, 6.5967097, 6.21336693,
6.35565105, 6.82347596, 6.44773408, 6.84538053, 6.47966466,
6.09699528, 5.63927014, 6.01081024, 6.20585303, 6.60528206,
7.01594726, 7.03684251, 6.76574977, 7.08740846, 6.65336462,
7.07126686, 6.80058956, 6.79241977, 6.47843472, 6.39245474],
columns=['value'])
self.test_data2 = pd.DataFrame([5.09276527, 4.83828592, 4.6000911, 4.63170487, 4.63566451,
4.50546921, 4.96390044, 4.64557907, 4.25787855, 3.76585551,
3.38826334, 3.76243422, 4.06365426, 3.87084726, 3.91400935,
4.13438822, 4.27064542, 4.56776104, 5.03800296, 5.31070529,
5.39902276, 5.21186286, 5.05683114, 4.68842046, 5.11895168,
5.27151571, 5.72294993, 6.09961056, 6.26569635, 6.48806151,
6.16058885, 6.2582459, 6.38934791, 6.57831057, 6.19508831,
5.70155153, 5.20435735, 5.36538825, 5.40450056, 5.2227697,
5.37828693, 5.53058991, 6.02996797, 5.76802181, 5.66166713,
6.07988994, 5.61794367, 5.63218151, 6.10728013, 6.0324168,
6.27164431, 6.27551239, 6.52329665, 7.00470007, 7.34163113,
7.33699083, 7.67661334, 8.09395749, 7.68086668, 7.58341161,
7.46219819, 7.58671899, 7.19348298, 7.40088323, 7.47562005,
7.93342043, 8.2286081, 8.3521632, 8.43590025, 8.34977395,
8.57563095, 8.81586328, 9.08738649, 9.01542031, 8.8653815,
9.21763111, 9.04233017, 8.59533999, 8.47590075, 8.70857222,
8.78890756, 8.92697606, 9.35743773, 9.68280866, 10.15622021,
10.55908549, 10.6337894, 10.55197128, 10.65435176, 10.54611045,
10.19432562, 10.48320884, 10.36176768, 10.03186854, 10.23656092,
10.0062843, 10.13669686, 10.30758958, 9.87904176, 10.05126375],
columns=['value'])
self.test_data3 = pd.DataFrame([5.02851874, 5.20700348, 5.02410709, 5.49836387, 5.06834371,
5.10956737, 5.15314979, 5.02256472, 5.09746382, 5.23909247,
4.93410336, 4.96316186, 5.40026682, 5.7353255, 5.53438319,
5.79092139, 5.67528173, 5.89840855, 5.75379463, 6.10855386,
5.77322365, 5.84538021, 5.6103973, 5.7518655, 5.49729695,
5.13610628, 5.30524121, 5.68093462, 5.73251319, 6.04420783,
6.26929843, 6.59610234, 6.09872345, 6.25475121, 6.72927396,
6.91395783, 7.00693283, 7.36217783, 7.71516676, 7.67580263,
7.62477511, 7.73600568, 7.53457914, 7.46170277, 7.83658014,
8.11481319, 8.03705544, 7.64948845, 7.52043731, 7.67247943,
7.46511982, 7.43541798, 7.58856517, 7.9392717, 8.25406287,
7.77031632, 8.03223447, 7.86799055, 7.57630999, 7.33230519,
7.22378732, 6.85972264, 7.17548456, 7.5387846, 7.2392632,
6.8455644, 6.59557185, 6.6496796, 6.73685623, 7.18598015,
7.13619128, 6.88060157, 7.1399681, 7.30308077, 6.94942434,
7.0247815, 7.37567798, 7.50080197, 7.59719284, 7.14520561,
7.29913484, 7.79551341, 8.15497781, 8.40456095, 8.86516528,
8.53042688, 8.94268762, 8.52048006, 8.80036284, 8.91602364,
9.19953385, 8.70828953, 8.24613093, 8.18770453, 7.79548389,
7.68627967, 7.23205036, 6.98302636, 7.06515819, 6.95068113],
columns=['value'])
self.test_data4 = pd.DataFrame([4.97926539, 5.44016005, 5.45122915, 5.74485615, 5.45600553,
5.44858945, 5.2435413, 5.47315161, 5.58464303, 5.36179749,
5.38236326, 5.29614981, 5.76523508, 5.75102892, 6.15316618,
6.03852528, 6.01442228, 5.70510182, 5.22748133, 5.46762379,
5.78926267, 5.8221362, 5.61236849, 5.30615725, 5.24200611,
5.41042642, 5.59940342, 5.28306781, 4.99451932, 5.08799266,
5.38865647, 5.58229139, 5.33492845, 5.48206276, 5.09721379,
5.39190493, 5.29965087, 5.0374415, 5.50798022, 5.43107577,
5.22759507, 4.991809, 5.43153084, 5.39966868, 5.59916352,
5.66412137, 6.00611838, 5.63564902, 5.66723484, 5.29863863,
4.91115153, 5.3749929, 5.75082334, 6.08308148, 6.58091182,
6.77848803, 7.19588758, 7.64862286, 7.99818347, 7.91824794,
8.30341071, 8.45984973, 7.98700002, 8.18924931, 8.60755649,
8.66233396, 8.91018407, 9.0782739, 9.33515448, 8.95870245,
8.98426422, 8.50340317, 8.64916085, 8.93592407, 8.63145745,
8.65322862, 8.39543204, 8.37969997, 8.23394504, 8.04062872,
7.91259763, 7.57252171, 7.72670114, 7.74486117, 8.06908188,
7.99166889, 7.92155906, 8.39956136, 8.80181323, 8.47464091,
8.06557064, 7.87145573, 8.0237959, 8.39481998, 8.68525692,
8.81185461, 8.98632237, 9.0989835, 8.89787405, 8.86508591],
columns=['value'])
self.test_data5 = pd.DataFrame([4.50258923, 4.35142568, 4.07459514, 3.87791297, 3.73715985,
3.98455684, 4.07587908, 4.00042472, 4.28276612, 4.01362051,
4.13713565, 4.49312372, 4.48633159, 4.4641207, 4.13444605,
3.79107217, 4.22941629, 4.56548511, 4.92472163, 5.27723158,
5.67409193, 6.00176917, 5.88889928, 5.55256103, 5.39308314,
5.2610492, 5.30738908, 5.22222408, 4.90332238, 4.57499908,
4.96097146, 4.81531011, 4.39115442, 4.63200662, 5.04588813,
4.67866025, 5.01705123, 4.83562258, 4.60381702, 4.66187576,
4.41292828, 4.86604507, 4.42280124, 4.07517294, 4.16317319,
4.10316596, 4.42913598, 4.06609666, 3.96725913, 4.15965746,
4.12379564, 4.04054068, 3.84342851, 3.45902867, 3.17649855,
3.09773586, 3.5502119, 3.66396995, 3.66306483, 3.29131401,
2.79558533, 2.88319542, 3.03671098, 3.44645857, 3.88167161,
3.57961874, 3.60180276, 3.96702102, 4.05429995, 4.40056979,
4.05653231, 3.59600456, 3.60792477, 4.09989922, 3.73503663,
4.01892626, 3.94597242, 3.81466605, 3.71417992, 3.93767156,
4.42806557, 4.06988106, 4.03713636, 4.34408673, 4.79810156,
5.18115011, 4.89798406, 5.3960077, 5.72504875, 5.61894017,
5.1958197, 4.85275896, 5.17550207, 4.71548987, 4.62408567,
4.55488535, 4.36532649, 4.26031979, 4.25225607, 4.58627048],
columns=['value'])
self.test_data6 = pd.DataFrame([5.08639513, 5.05761083, 4.76160923, 4.62166504, 4.62923183,
4.25070173, 4.13447513, 3.90890013, 3.76687608, 3.43342482,
3.67648224, 3.6274775, 3.9385404, 4.39771627, 4.03199346,
3.93265288, 3.50059789, 3.3851961, 3.29743973, 3.2544872,
2.93692949, 2.70893003, 2.55461976, 2.20922332, 2.29054475,
2.2144714, 2.03726827, 2.39007617, 2.29866155, 2.40607111,
2.40440444, 2.79374649, 2.66541922, 2.27018079, 2.08505127,
2.55478864, 2.22415625, 2.58517923, 2.58802256, 2.94870959,
2.69301739, 2.19991535, 2.69473146, 2.64704637, 2.62753542,
2.14240825, 2.38565154, 1.94592117, 2.32243877, 2.69337246,
2.51283854, 2.62484451, 2.15559054, 2.35410875, 2.31219177,
1.96018265, 2.34711266, 2.58083322, 2.40290041, 2.20439791,
2.31472425, 2.16228248, 2.16439749, 2.20080737, 1.73293206,
1.9264407, 2.25089861, 2.69269101, 2.59296687, 2.1420998,
1.67819153, 1.98419023, 2.14479494, 1.89055376, 1.96720648,
1.9916694, 2.37227761, 2.14446036, 2.34573903, 1.86162546,
2.1410721, 2.39204939, 2.52529064, 2.47079939, 2.9299031,
3.09452923, 2.93276708, 3.21731309, 3.06248964, 2.90413406,
2.67844632, 2.45621213, 2.41463398, 2.7373913, 3.14917045,
3.4033949, 3.82283446, 4.02285451, 3.7619638, 4.10346795],
columns=['value'])
self.test_data7 = pd.DataFrame([4.75233583, 4.47668283, 4.55894263, 4.61765848, 4.622892,
4.58941116, 4.32535872, 3.88112797, 3.47237806, 3.50898953,
3.82530406, 3.6718017, 3.78918195, 4.1800752, 4.01818557,
4.40822582, 4.65474654, 4.89287256, 4.40879274, 4.65505126,
4.36876403, 4.58418934, 4.75687172, 4.3689799, 4.16126498,
4.0203982, 3.77148242, 3.38198096, 3.07261764, 2.9014741,
2.5049543, 2.756105, 2.28779058, 2.16986991, 1.8415962,
1.83319008, 2.20898291, 2.00128981, 1.75747025, 1.26676663,
1.40316876, 1.11126484, 1.60376367, 1.22523829, 1.58816681,
1.49705679, 1.80244138, 1.55128293, 1.35339409, 1.50985759,
1.0808451, 1.05892796, 1.43414812, 1.43039101, 1.73631655,
1.43940867, 1.82864425, 1.71088265, 2.12015154, 2.45417128,
2.84777618, 2.7925612, 2.90975121, 3.25920745, 3.13801182,
3.52733677, 3.65468491, 3.69395211, 3.49862035, 3.24786017,
3.64463138, 4.00331929, 3.62509565, 3.78013949, 3.4174012,
3.76312271, 3.62054004, 3.67206716, 3.60596058, 3.38636199,
3.42580676, 3.32921095, 3.02976759, 3.28258676, 3.45760838,
3.24917528, 2.94618304, 2.86980011, 2.63191259, 2.39566759,
2.53159917, 2.96273967, 3.25626185, 2.97425402, 3.16412191,
3.58280763, 3.23257727, 3.62353556, 3.12806399, 2.92532313],
columns=['value'])
# 建立一个长度为 500 个数据点的测试数据, 用于测试数据点多于250个的情况下的评价过程
self.long_data = pd.DataFrame([9.879, 9.916, 10.109, 10.214, 10.361, 10.768, 10.594, 10.288,
10.082, 9.994, 10.125, 10.126, 10.384, 10.734, 10.4, 10.87,
11.338, 11.061, 11.415, 11.724, 12.077, 12.196, 12.064, 12.423,
12.19, 11.729, 11.677, 11.448, 11.485, 10.989, 11.242, 11.239,
11.113, 11.075, 11.471, 11.745, 11.754, 11.782, 12.079, 11.97,
12.178, 11.95, 12.438, 12.612, 12.804, 12.952, 12.612, 12.867,
12.832, 12.832, 13.015, 13.315, 13.249, 12.904, 12.776, 12.64,
12.543, 12.287, 12.225, 11.844, 11.985, 11.945, 11.542, 11.871,
12.245, 12.228, 12.362, 11.899, 11.962, 12.374, 12.816, 12.649,
12.252, 12.579, 12.3, 11.988, 12.177, 12.312, 12.744, 12.599,
12.524, 12.82, 12.67, 12.876, 12.986, 13.271, 13.606, 13.82,
14.161, 13.833, 13.831, 14.137, 13.705, 13.414, 13.037, 12.759,
12.642, 12.948, 13.297, 13.483, 13.836, 14.179, 13.709, 13.655,
13.198, 13.508, 13.953, 14.387, 14.043, 13.987, 13.561, 13.391,
12.923, 12.555, 12.503, 12.292, 11.877, 12.34, 12.141, 11.687,
11.992, 12.458, 12.131, 11.75, 11.739, 11.263, 11.762, 11.976,
11.578, 11.854, 12.136, 12.422, 12.311, 12.56, 12.879, 12.861,
12.973, 13.235, 13.53, 13.531, 13.137, 13.166, 13.31, 13.103,
13.007, 12.643, 12.69, 12.216, 12.385, 12.046, 12.321, 11.9,
11.772, 11.816, 11.871, 11.59, 11.518, 11.94, 11.803, 11.924,
12.183, 12.136, 12.361, 12.406, 11.932, 11.684, 11.292, 11.388,
11.874, 12.184, 12.002, 12.16, 11.741, 11.26, 11.123, 11.534,
11.777, 11.407, 11.275, 11.679, 11.62, 11.218, 11.235, 11.352,
11.366, 11.061, 10.661, 10.582, 10.899, 11.352, 11.792, 11.475,
11.263, 11.538, 11.183, 10.936, 11.399, 11.171, 11.214, 10.89,
10.728, 11.191, 11.646, 11.62, 11.195, 11.178, 11.18, 10.956,
11.205, 10.87, 11.098, 10.639, 10.487, 10.507, 10.92, 10.558,
10.119, 9.882, 9.573, 9.515, 9.845, 9.852, 9.495, 9.726,
10.116, 10.452, 10.77, 11.225, 10.92, 10.824, 11.096, 11.542,
11.06, 10.568, 10.585, 10.884, 10.401, 10.068, 9.964, 10.285,
10.239, 10.036, 10.417, 10.132, 9.839, 9.556, 9.084, 9.239,
9.304, 9.067, 8.587, 8.471, 8.007, 8.321, 8.55, 9.008,
9.138, 9.088, 9.434, 9.156, 9.65, 9.431, 9.654, 10.079,
10.411, 10.865, 10.51, 10.205, 10.519, 10.367, 10.855, 10.642,
10.298, 10.622, 10.173, 9.792, 9.995, 9.904, 9.771, 9.597,
9.506, 9.212, 9.688, 10.032, 9.723, 9.839, 9.918, 10.332,
10.236, 9.989, 10.192, 10.685, 10.908, 11.275, 11.72, 12.158,
12.045, 12.244, 12.333, 12.246, 12.552, 12.958, 13.11, 13.53,
13.123, 13.138, 13.57, 13.389, 13.511, 13.759, 13.698, 13.744,
13.467, 13.795, 13.665, 13.377, 13.423, 13.772, 13.295, 13.073,
12.718, 12.388, 12.399, 12.185, 11.941, 11.818, 11.465, 11.811,
12.163, 11.86, 11.935, 11.809, 12.145, 12.624, 12.768, 12.321,
12.277, 11.889, 12.11, 12.606, 12.943, 12.945, 13.112, 13.199,
13.664, 14.051, 14.189, 14.339, 14.611, 14.656, 15.112, 15.086,
15.263, 15.021, 15.346, 15.572, 15.607, 15.983, 16.151, 16.215,
16.096, 16.089, 16.32, 16.59, 16.657, 16.752, 16.583, 16.743,
16.373, 16.662, 16.243, 16.163, 16.491, 16.958, 16.977, 17.225,
17.637, 17.344, 17.684, 17.892, 18.036, 18.182, 17.803, 17.588,
17.101, 17.538, 17.124, 16.787, 17.167, 17.138, 16.955, 17.148,
17.135, 17.635, 17.718, 17.675, 17.622, 17.358, 17.754, 17.729,
17.576, 17.772, 18.239, 18.441, 18.729, 18.319, 18.608, 18.493,
18.069, 18.122, 18.314, 18.423, 18.709, 18.548, 18.384, 18.391,
17.988, 17.986, 17.653, 17.249, 17.298, 17.06, 17.36, 17.108,
17.348, 17.596, 17.46, 17.635, 17.275, 17.291, 16.933, 17.337,
17.231, 17.146, 17.148, 16.751, 16.891, 17.038, 16.735, 16.64,
16.231, 15.957, 15.977, 16.077, 16.054, 15.797, 15.67, 15.911,
16.077, 16.17, 15.722, 15.258, 14.877, 15.138, 15., 14.811,
14.698, 14.407, 14.583, 14.704, 15.153, 15.436, 15.634, 15.453,
15.877, 15.696, 15.563, 15.927, 16.255, 16.696, 16.266, 16.698,
16.365, 16.493, 16.973, 16.71, 16.327, 16.605, 16.486, 16.846,
16.935, 17.21, 17.389, 17.546, 17.773, 17.641, 17.485, 17.794,
17.354, 16.904, 16.675, 16.43, 16.898, 16.819, 16.921, 17.201,
17.617, 17.368, 17.864, 17.484],
columns=['value'])
self.long_bench = pd.DataFrame([9.7, 10.179, 10.321, 9.855, 9.936, 10.096, 10.331, 10.662,
10.59, 11.031, 11.154, 10.945, 10.625, 10.233, 10.284, 10.252,
10.221, 10.352, 10.444, 10.773, 10.904, 11.104, 10.797, 10.55,
10.943, 11.352, 11.641, 11.983, 11.696, 12.138, 12.365, 12.379,
11.969, 12.454, 12.947, 13.119, 13.013, 12.763, 12.632, 13.034,
12.681, 12.561, 12.938, 12.867, 13.202, 13.132, 13.539, 13.91,
13.456, 13.692, 13.771, 13.904, 14.069, 13.728, 13.97, 14.228,
13.84, 14.041, 13.963, 13.689, 13.543, 13.858, 14.118, 13.987,
13.611, 14.028, 14.229, 14.41, 14.74, 15.03, 14.915, 15.207,
15.354, 15.665, 15.877, 15.682, 15.625, 15.175, 15.105, 14.893,
14.86, 15.097, 15.178, 15.293, 15.238, 15., 15.283, 14.994,
14.907, 14.664, 14.888, 15.297, 15.313, 15.368, 14.956, 14.802,
14.506, 14.257, 14.619, 15.019, 15.049, 14.625, 14.894, 14.978,
15.434, 15.578, 16.038, 16.107, 16.277, 16.365, 16.204, 16.465,
16.401, 16.895, 17.057, 16.621, 16.225, 16.075, 15.863, 16.292,
16.551, 16.724, 16.817, 16.81, 17.192, 16.86, 16.745, 16.707,
16.552, 16.133, 16.301, 16.08, 15.81, 15.75, 15.909, 16.127,
16.457, 16.204, 16.329, 16.748, 16.624, 17.011, 16.548, 16.831,
16.653, 16.791, 16.57, 16.778, 16.928, 16.932, 17.22, 16.876,
17.301, 17.422, 17.689, 17.316, 17.547, 17.534, 17.409, 17.669,
17.416, 17.859, 17.477, 17.307, 17.245, 17.352, 17.851, 17.412,
17.144, 17.138, 17.085, 16.926, 16.674, 16.854, 17.064, 16.95,
16.609, 16.957, 16.498, 16.552, 16.175, 15.858, 15.697, 15.781,
15.583, 15.36, 15.558, 16.046, 15.968, 15.905, 16.358, 16.783,
17.048, 16.762, 17.224, 17.363, 17.246, 16.79, 16.608, 16.423,
15.991, 15.527, 15.147, 14.759, 14.792, 15.206, 15.148, 15.046,
15.429, 14.999, 15.407, 15.124, 14.72, 14.713, 15.022, 15.092,
14.982, 15.001, 14.734, 14.713, 14.841, 14.562, 15.005, 15.483,
15.472, 15.277, 15.503, 15.116, 15.12, 15.442, 15.476, 15.789,
15.36, 15.764, 16.218, 16.493, 16.642, 17.088, 16.816, 16.645,
16.336, 16.511, 16.2, 15.994, 15.86, 15.929, 16.316, 16.416,
16.746, 17.173, 17.531, 17.627, 17.407, 17.49, 17.768, 17.509,
17.795, 18.147, 18.63, 18.945, 19.021, 19.518, 19.6, 19.744,
19.63, 19.32, 18.933, 19.297, 19.598, 19.446, 19.236, 19.198,
19.144, 19.159, 19.065, 19.032, 18.586, 18.272, 18.119, 18.3,
17.894, 17.744, 17.5, 17.083, 17.092, 16.864, 16.453, 16.31,
16.681, 16.342, 16.447, 16.715, 17.068, 17.067, 16.822, 16.673,
16.675, 16.592, 16.686, 16.397, 15.902, 15.597, 15.357, 15.162,
15.348, 15.603, 15.283, 15.257, 15.082, 14.621, 14.366, 14.039,
13.957, 14.141, 13.854, 14.243, 14.414, 14.033, 13.93, 14.104,
14.461, 14.249, 14.053, 14.165, 14.035, 14.408, 14.501, 14.019,
14.265, 14.67, 14.797, 14.42, 14.681, 15.16, 14.715, 14.292,
14.411, 14.656, 15.094, 15.366, 15.055, 15.198, 14.762, 14.294,
13.854, 13.811, 13.549, 13.927, 13.897, 13.421, 13.037, 13.32,
13.721, 13.511, 13.999, 13.529, 13.418, 13.881, 14.326, 14.362,
13.987, 14.015, 13.599, 13.343, 13.307, 13.689, 13.851, 13.404,
13.577, 13.395, 13.619, 13.195, 12.904, 12.553, 12.294, 12.649,
12.425, 11.967, 12.062, 11.71, 11.645, 12.058, 12.136, 11.749,
11.953, 12.401, 12.044, 11.901, 11.631, 11.396, 11.036, 11.244,
10.864, 11.207, 11.135, 11.39, 11.723, 12.084, 11.8, 11.471,
11.33, 11.504, 11.295, 11.3, 10.901, 10.494, 10.825, 11.054,
10.866, 10.713, 10.875, 10.846, 10.947, 11.422, 11.158, 10.94,
10.521, 10.36, 10.411, 10.792, 10.472, 10.305, 10.525, 10.853,
10.556, 10.72, 10.54, 10.583, 10.299, 10.061, 10.004, 9.903,
9.796, 9.472, 9.246, 9.54, 9.456, 9.177, 9.484, 9.557,
9.493, 9.968, 9.536, 9.39, 8.922, 8.423, 8.518, 8.686,
8.771, 9.098, 9.281, 8.858, 9.027, 8.553, 8.784, 8.996,
9.379, 9.846, 9.855, 9.502, 9.608, 9.761, 9.409, 9.4,
9.332, 9.34, 9.284, 8.844, 8.722, 8.376, 8.775, 8.293,
8.144, 8.63, 8.831, 8.957, 9.18, 9.601, 9.695, 10.018,
9.841, 9.743, 9.292, 8.85, 9.316, 9.288, 9.519, 9.738,
9.289, 9.785, 9.804, 10.06, 10.188, 10.095, 9.739, 9.881,
9.7, 9.991, 10.391, 10.002],
columns=['value'])
def test_performance_stats(self):
"""test the function performance_statistics()
"""
pass
def test_fv(self):
print(f'test with test data and empty DataFrame')
self.assertAlmostEqual(eval_fv(self.test_data1), 6.39245474)
self.assertAlmostEqual(eval_fv(self.test_data2), 10.05126375)
self.assertAlmostEqual(eval_fv(self.test_data3), 6.95068113)
self.assertAlmostEqual(eval_fv(self.test_data4), 8.86508591)
self.assertAlmostEqual(eval_fv(self.test_data5), 4.58627048)
self.assertAlmostEqual(eval_fv(self.test_data6), 4.10346795)
self.assertAlmostEqual(eval_fv(self.test_data7), 2.92532313)
self.assertAlmostEqual(eval_fv(pd.DataFrame()), -np.inf)
print(f'Error testing')
self.assertRaises(AssertionError, eval_fv, 15)
self.assertRaises(KeyError,
eval_fv,
pd.DataFrame([1, 2, 3], columns=['non_value']))
def test_max_drawdown(self):
print(f'test with test data and empty DataFrame')
self.assertAlmostEqual(eval_max_drawdown(self.test_data1)[0], 0.264274308)
self.assertEqual(eval_max_drawdown(self.test_data1)[1], 53)
self.assertEqual(eval_max_drawdown(self.test_data1)[2], 86)
self.assertTrue(np.isnan(eval_max_drawdown(self.test_data1)[3]))
self.assertAlmostEqual(eval_max_drawdown(self.test_data2)[0], 0.334690849)
self.assertEqual(eval_max_drawdown(self.test_data2)[1], 0)
self.assertEqual(eval_max_drawdown(self.test_data2)[2], 10)
self.assertEqual(eval_max_drawdown(self.test_data2)[3], 19)
self.assertAlmostEqual(eval_max_drawdown(self.test_data3)[0], 0.244452899)
self.assertEqual(eval_max_drawdown(self.test_data3)[1], 90)
self.assertEqual(eval_max_drawdown(self.test_data3)[2], 99)
self.assertTrue(np.isnan(eval_max_drawdown(self.test_data3)[3]))
self.assertAlmostEqual(eval_max_drawdown(self.test_data4)[0], 0.201849684)
self.assertEqual(eval_max_drawdown(self.test_data4)[1], 14)
self.assertEqual(eval_max_drawdown(self.test_data4)[2], 50)
self.assertEqual(eval_max_drawdown(self.test_data4)[3], 54)
self.assertAlmostEqual(eval_max_drawdown(self.test_data5)[0], 0.534206456)
self.assertEqual(eval_max_drawdown(self.test_data5)[1], 21)
self.assertEqual(eval_max_drawdown(self.test_data5)[2], 60)
self.assertTrue(np.isnan(eval_max_drawdown(self.test_data5)[3]))
self.assertAlmostEqual(eval_max_drawdown(self.test_data6)[0], 0.670062689)
self.assertEqual(eval_max_drawdown(self.test_data6)[1], 0)
self.assertEqual(eval_max_drawdown(self.test_data6)[2], 70)
self.assertTrue(np.isnan(eval_max_drawdown(self.test_data6)[3]))
self.assertAlmostEqual(eval_max_drawdown(self.test_data7)[0], 0.783577449)
self.assertEqual(eval_max_drawdown(self.test_data7)[1], 17)
self.assertEqual(eval_max_drawdown(self.test_data7)[2], 51)
self.assertTrue(np.isnan(eval_max_drawdown(self.test_data7)[3]))
self.assertEqual(eval_max_drawdown(pd.DataFrame()), -np.inf)
print(f'Error testing')
self.assertRaises(AssertionError, eval_fv, 15)
self.assertRaises(KeyError,
eval_fv,
pd.DataFrame([1, 2, 3], columns=['non_value']))
# test max drawdown == 0:
# TODO: investigate: how does divide by zero change?
self.assertAlmostEqual(eval_max_drawdown(self.test_data4 - 5)[0], 1.0770474121951792)
self.assertEqual(eval_max_drawdown(self.test_data4 - 5)[1], 14)
self.assertEqual(eval_max_drawdown(self.test_data4 - 5)[2], 50)
def test_info_ratio(self):
reference = self.test_data1
self.assertAlmostEqual(eval_info_ratio(self.test_data2, reference, 'value'), 0.075553316)
self.assertAlmostEqual(eval_info_ratio(self.test_data3, reference, 'value'), 0.018949457)
self.assertAlmostEqual(eval_info_ratio(self.test_data4, reference, 'value'), 0.056328143)
self.assertAlmostEqual(eval_info_ratio(self.test_data5, reference, 'value'), -0.004270068)
self.assertAlmostEqual(eval_info_ratio(self.test_data6, reference, 'value'), 0.009198027)
self.assertAlmostEqual(eval_info_ratio(self.test_data7, reference, 'value'), -0.000890283)
def test_volatility(self):
self.assertAlmostEqual(eval_volatility(self.test_data1), 0.748646166)
self.assertAlmostEqual(eval_volatility(self.test_data2), 0.75527442)
self.assertAlmostEqual(eval_volatility(self.test_data3), 0.654188853)
self.assertAlmostEqual(eval_volatility(self.test_data4), 0.688375814)
self.assertAlmostEqual(eval_volatility(self.test_data5), 1.089989522)
self.assertAlmostEqual(eval_volatility(self.test_data6), 1.775419308)
self.assertAlmostEqual(eval_volatility(self.test_data7), 1.962758406)
self.assertAlmostEqual(eval_volatility(self.test_data1, logarithm=False), 0.750993311)
self.assertAlmostEqual(eval_volatility(self.test_data2, logarithm=False), 0.75571473)
self.assertAlmostEqual(eval_volatility(self.test_data3, logarithm=False), 0.655331424)
self.assertAlmostEqual(eval_volatility(self.test_data4, logarithm=False), 0.692683021)
self.assertAlmostEqual(eval_volatility(self.test_data5, logarithm=False), 1.09602969)
self.assertAlmostEqual(eval_volatility(self.test_data6, logarithm=False), 1.774789504)
self.assertAlmostEqual(eval_volatility(self.test_data7, logarithm=False), 2.003329156)
self.assertEqual(eval_volatility(pd.DataFrame()), -np.inf)
self.assertRaises(AssertionError, eval_volatility, [1, 2, 3])
# 测试长数据的Volatility计算
expected_volatility = np.array([np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
0.39955371, 0.39974258, 0.40309866, 0.40486593, 0.4055514,
0.40710639, 0.40708157, 0.40609006, 0.4073625, 0.40835305,
0.41155304, 0.41218193, 0.41207489, 0.41300276, 0.41308415,
0.41292392, 0.41207645, 0.41238397, 0.41229291, 0.41164056,
0.41316317, 0.41348842, 0.41462249, 0.41474574, 0.41652625,
0.41649176, 0.41701556, 0.4166593, 0.41684221, 0.41491689,
0.41435209, 0.41549087, 0.41849338, 0.41998049, 0.41959106,
0.41907311, 0.41916103, 0.42120773, 0.42052391, 0.42111225,
0.42124589, 0.42356445, 0.42214672, 0.42324022, 0.42476639,
0.42621689, 0.42549439, 0.42533678, 0.42539414, 0.42545038,
0.42593637, 0.42652095, 0.42665489, 0.42699563, 0.42798159,
0.42784512, 0.42898006, 0.42868781, 0.42874188, 0.42789631,
0.4277768, 0.42776827, 0.42685216, 0.42660989, 0.42563155,
0.42618281, 0.42606281, 0.42505222, 0.42653242, 0.42555378,
0.42500842, 0.42561939, 0.42442059, 0.42395414, 0.42384356,
0.42319135, 0.42397497, 0.42488579, 0.42449729, 0.42508766,
0.42509878, 0.42456616, 0.42535577, 0.42681884, 0.42688552,
0.42779918, 0.42706058, 0.42792887, 0.42762114, 0.42894045,
0.42977398, 0.42919859, 0.42829041, 0.42780946, 0.42825318,
0.42858952, 0.42858315, 0.42805601, 0.42764751, 0.42744107,
0.42775518, 0.42707283, 0.4258592, 0.42615335, 0.42526286,
0.4248906, 0.42368986, 0.4232565, 0.42265079, 0.42263954,
0.42153046, 0.42132051, 0.41995353, 0.41916605, 0.41914271,
0.41876945, 0.41740175, 0.41583884, 0.41614026, 0.41457908,
0.41472411, 0.41310876, 0.41261041, 0.41212369, 0.41211677,
0.4100645, 0.40852504, 0.40860297, 0.40745338, 0.40698661,
0.40644546, 0.40591375, 0.40640744, 0.40620663, 0.40656649,
0.40727154, 0.40797605, 0.40807137, 0.40808913, 0.40809676,
0.40711767, 0.40724628, 0.40713077, 0.40772698, 0.40765157,
0.40658297, 0.4065991, 0.405011, 0.40537645, 0.40432626,
0.40390177, 0.40237701, 0.40291623, 0.40301797, 0.40324145,
0.40312864, 0.40328316, 0.40190955, 0.40246506, 0.40237663,
0.40198407, 0.401969, 0.40185623, 0.40198313, 0.40005643,
0.39940743, 0.39850438, 0.39845398, 0.39695093, 0.39697295,
0.39663201, 0.39675444, 0.39538699, 0.39331959, 0.39326074,
0.39193287, 0.39157266, 0.39021327, 0.39062591, 0.38917591,
0.38976991, 0.38864187, 0.38872158, 0.38868096, 0.38868377,
0.38842057, 0.38654784, 0.38649517, 0.38600464, 0.38408115,
0.38323049, 0.38260215, 0.38207663, 0.38142669, 0.38003262,
0.37969367, 0.37768092, 0.37732108, 0.37741991, 0.37617779,
0.37698504, 0.37606784, 0.37499276, 0.37533731, 0.37350437,
0.37375172, 0.37385382, 0.37384003, 0.37338938, 0.37212288,
0.37273075, 0.370559, 0.37038506, 0.37062153, 0.36964661,
0.36818564, 0.3656634, 0.36539259, 0.36428672, 0.36502487,
0.3647148, 0.36551435, 0.36409919, 0.36348181, 0.36254383,
0.36166601, 0.36142665, 0.35954942, 0.35846915, 0.35886759,
0.35813867, 0.35642888, 0.35375231, 0.35061783, 0.35078463,
0.34995508, 0.34688918, 0.34548257, 0.34633158, 0.34622833,
0.34652111, 0.34622774, 0.34540951, 0.34418809, 0.34276593,
0.34160916, 0.33811193, 0.33822709, 0.3391685, 0.33883381])
test_volatility = eval_volatility(self.long_data)
test_volatility_roll = self.long_data['volatility'].values
self.assertAlmostEqual(test_volatility, np.nanmean(expected_volatility))
self.assertTrue(np.allclose(expected_volatility, test_volatility_roll, equal_nan=True))
def test_sharp(self):
self.assertAlmostEqual(eval_sharp(self.test_data1, 5, 0), 0.06135557)
self.assertAlmostEqual(eval_sharp(self.test_data2, 5, 0), 0.167858667)
self.assertAlmostEqual(eval_sharp(self.test_data3, 5, 0), 0.09950547)
self.assertAlmostEqual(eval_sharp(self.test_data4, 5, 0), 0.154928241)
self.assertAlmostEqual(eval_sharp(self.test_data5, 5, 0.002), 0.007868673)
self.assertAlmostEqual(eval_sharp(self.test_data6, 5, 0.002), 0.018306537)
self.assertAlmostEqual(eval_sharp(self.test_data7, 5, 0.002), 0.006259971)
# 测试长数据的sharp率计算
expected_sharp = np.array([np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
-0.02346815, -0.02618783, -0.03763912, -0.03296276, -0.03085698,
-0.02851101, -0.02375842, -0.02016746, -0.01107885, -0.01426613,
-0.00787204, -0.01135784, -0.01164232, -0.01003481, -0.00022512,
-0.00046792, -0.01209378, -0.01278892, -0.01298135, -0.01938214,
-0.01671044, -0.02120509, -0.0244281, -0.02416067, -0.02763238,
-0.027579, -0.02372774, -0.02215294, -0.02467094, -0.02091266,
-0.02590194, -0.03049876, -0.02077131, -0.01483653, -0.02488144,
-0.02671638, -0.02561547, -0.01957986, -0.02479803, -0.02703162,
-0.02658087, -0.01641755, -0.01946472, -0.01647757, -0.01280889,
-0.00893643, -0.00643275, -0.00698457, -0.00549962, -0.00654677,
-0.00494757, -0.0035633, -0.00109037, 0.00750654, 0.00451208,
0.00625502, 0.01221367, 0.01326454, 0.01535037, 0.02269538,
0.02028715, 0.02127712, 0.02333264, 0.02273159, 0.01670643,
0.01376513, 0.01265342, 0.02211647, 0.01612449, 0.00856706,
-0.00077147, -0.00268848, 0.00210993, -0.00443934, -0.00411912,
-0.0018756, -0.00867461, -0.00581601, -0.00660835, -0.00861137,
-0.00678614, -0.01188408, -0.00589617, -0.00244323, -0.00201891,
-0.01042846, -0.01471016, -0.02167034, -0.02258554, -0.01306809,
-0.00909086, -0.01233746, -0.00595166, -0.00184208, 0.00750497,
0.01481886, 0.01761972, 0.01562886, 0.01446414, 0.01285826,
0.01357719, 0.00967613, 0.01636272, 0.01458437, 0.02280183,
0.02151903, 0.01700276, 0.01597368, 0.02114336, 0.02233297,
0.02585631, 0.02768459, 0.03519235, 0.04204535, 0.04328161,
0.04672855, 0.05046191, 0.04619848, 0.04525853, 0.05381529,
0.04598861, 0.03947394, 0.04665006, 0.05586077, 0.05617728,
0.06495018, 0.06205172, 0.05665466, 0.06500615, 0.0632062,
0.06084328, 0.05851466, 0.05659229, 0.05159347, 0.0432977,
0.0474047, 0.04231723, 0.03613176, 0.03618391, 0.03591012,
0.03885674, 0.0402686, 0.03846423, 0.04534014, 0.04721458,
0.05130912, 0.05026281, 0.05394312, 0.05529349, 0.05949243,
0.05463304, 0.06195165, 0.06767606, 0.06880985, 0.07048996,
0.07078815, 0.07420767, 0.06773439, 0.0658441, 0.06470875,
0.06302349, 0.06456876, 0.06411282, 0.06216669, 0.067094,
0.07055075, 0.07254976, 0.07119253, 0.06173308, 0.05393352,
0.05681246, 0.05250643, 0.06099845, 0.0655544, 0.06977334,
0.06636514, 0.06177949, 0.06869908, 0.06719767, 0.06178738,
0.05915714, 0.06882277, 0.06756821, 0.06507994, 0.06489791,
0.06553941, 0.073123, 0.07576757, 0.06805446, 0.06063571,
0.05033801, 0.05206971, 0.05540306, 0.05249118, 0.05755587,
0.0586174, 0.05051288, 0.0564852, 0.05757284, 0.06358355,
0.06130082, 0.04925482, 0.03834472, 0.04163981, 0.04648316,
0.04457858, 0.04324626, 0.04328791, 0.04156207, 0.04818652,
0.04972634, 0.06024123, 0.06489556, 0.06255485, 0.06069815,
0.06466389, 0.07081163, 0.07895358, 0.0881782, 0.09374151,
0.08336506, 0.08764795, 0.09080174, 0.08808926, 0.08641158,
0.07811943, 0.06885318, 0.06479503, 0.06851185, 0.07382819,
0.07047903, 0.06658251, 0.07638379, 0.08667974, 0.08867918,
0.08245323, 0.08961866, 0.09905298, 0.0961908, 0.08562706,
0.0839014, 0.0849072, 0.08338395, 0.08783487, 0.09463609,
0.10332336, 0.11806497, 0.11220297, 0.11589097, 0.11678405])
test_sharp = eval_sharp(self.long_data, 5, 0.00035)
self.assertAlmostEqual(np.nanmean(expected_sharp), test_sharp)
self.assertTrue(np.allclose(self.long_data['sharp'].values, expected_sharp, equal_nan=True))
def test_beta(self):
reference = self.test_data1
self.assertAlmostEqual(eval_beta(self.test_data2, reference, 'value'), -0.017148939)
self.assertAlmostEqual(eval_beta(self.test_data3, reference, 'value'), -0.042204233)
self.assertAlmostEqual(eval_beta(self.test_data4, reference, 'value'), -0.15652986)
self.assertAlmostEqual(eval_beta(self.test_data5, reference, 'value'), -0.049195532)
self.assertAlmostEqual(eval_beta(self.test_data6, reference, 'value'), -0.026995082)
self.assertAlmostEqual(eval_beta(self.test_data7, reference, 'value'), -0.01147809)
self.assertRaises(TypeError, eval_beta, [1, 2, 3], reference, 'value')
self.assertRaises(TypeError, eval_beta, self.test_data3, [1, 2, 3], 'value')
self.assertRaises(KeyError, eval_beta, self.test_data3, reference, 'not_found_value')
# 测试长数据的beta计算
expected_beta = np.array([np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
-0.04988841, -0.05127618, -0.04692104, -0.04272652, -0.04080598,
-0.0493347, -0.0460858, -0.0416761, -0.03691527, -0.03724924,
-0.03678865, -0.03987324, -0.03488321, -0.02567672, -0.02690303,
-0.03010128, -0.02437967, -0.02571932, -0.02455681, -0.02839811,
-0.03358653, -0.03396697, -0.03466321, -0.03050966, -0.0247583,
-0.01629325, -0.01880895, -0.01480403, -0.01348783, -0.00544294,
-0.00648176, -0.00467036, -0.01135331, -0.0156841, -0.02340763,
-0.02615705, -0.02730771, -0.02906174, -0.02860664, -0.02412914,
-0.02066416, -0.01744816, -0.02185133, -0.02145285, -0.02681765,
-0.02827694, -0.02394581, -0.02744096, -0.02778825, -0.02703065,
-0.03160023, -0.03615371, -0.03681072, -0.04265126, -0.04344738,
-0.04232421, -0.04705272, -0.04533344, -0.04605934, -0.05272737,
-0.05156463, -0.05134196, -0.04730733, -0.04425352, -0.03869831,
-0.04159571, -0.04223998, -0.04346747, -0.04229844, -0.04740093,
-0.04992507, -0.04621232, -0.04477644, -0.0486915, -0.04598224,
-0.04943463, -0.05006391, -0.05362256, -0.04994067, -0.05464769,
-0.05443275, -0.05513493, -0.05173594, -0.04500994, -0.04662891,
-0.03903505, -0.0419592, -0.04307773, -0.03925718, -0.03711574,
-0.03992631, -0.0433058, -0.04533641, -0.0461183, -0.05600344,
-0.05758377, -0.05959874, -0.05605942, -0.06002859, -0.06253002,
-0.06747014, -0.06427915, -0.05931947, -0.05769974, -0.04791515,
-0.05175088, -0.05748039, -0.05385232, -0.05072975, -0.05052637,
-0.05125567, -0.05005785, -0.05325104, -0.04977727, -0.04947867,
-0.05148544, -0.05739156, -0.05742069, -0.06047279, -0.0558414,
-0.06086126, -0.06265151, -0.06411129, -0.06828052, -0.06781762,
-0.07083409, -0.07211207, -0.06799162, -0.06913295, -0.06775162,
-0.0696265, -0.06678248, -0.06867502, -0.06581961, -0.07055823,
-0.06448184, -0.06097973, -0.05795587, -0.0618383, -0.06130145,
-0.06050652, -0.05936661, -0.05749424, -0.0499, -0.05050495,
-0.04962687, -0.05033439, -0.05070116, -0.05422009, -0.05369759,
-0.05548943, -0.05907353, -0.05933035, -0.05927918, -0.06227663,
-0.06011455, -0.05650432, -0.05828134, -0.05620949, -0.05715323,
-0.05482478, -0.05387113, -0.05095559, -0.05377999, -0.05334267,
-0.05220438, -0.04001521, -0.03892434, -0.03660782, -0.04282708,
-0.04324623, -0.04127048, -0.04227559, -0.04275226, -0.04347049,
-0.04125853, -0.03806295, -0.0330632, -0.03155531, -0.03277152,
-0.03304518, -0.03878731, -0.03830672, -0.03727434, -0.0370571,
-0.04509224, -0.04207632, -0.04116198, -0.04545179, -0.04584584,
-0.05287341, -0.05417433, -0.05175836, -0.05005509, -0.04268674,
-0.03442321, -0.03457309, -0.03613426, -0.03524391, -0.03629479,
-0.04361312, -0.02626705, -0.02406115, -0.03046384, -0.03181044,
-0.03375164, -0.03661673, -0.04520779, -0.04926951, -0.05726738,
-0.0584486, -0.06220608, -0.06800563, -0.06797431, -0.07562211,
-0.07481996, -0.07731229, -0.08413381, -0.09031826, -0.09691925,
-0.11018071, -0.11952675, -0.10826026, -0.11173895, -0.10756359,
-0.10775916, -0.11664559, -0.10505051, -0.10606547, -0.09855355,
-0.10004159, -0.10857084, -0.12209301, -0.11605758, -0.11105113,
-0.1155195, -0.11569505, -0.10513348, -0.09611072, -0.10719791,
-0.10843965, -0.11025856, -0.10247839, -0.10554044, -0.10927647,
-0.10645088, -0.09982498, -0.10542734, -0.09631372, -0.08229695])
test_beta_mean = eval_beta(self.long_data, self.long_bench, 'value')
test_beta_roll = self.long_data['beta'].values
self.assertAlmostEqual(test_beta_mean, np.nanmean(expected_beta))
self.assertTrue(np.allclose(test_beta_roll, expected_beta, equal_nan=True))
def test_alpha(self):
reference = self.test_data1
self.assertAlmostEqual(eval_alpha(self.test_data2, 5, reference, 'value', 0.5), 11.63072977)
self.assertAlmostEqual(eval_alpha(self.test_data3, 5, reference, 'value', 0.5), 1.886590071)
self.assertAlmostEqual(eval_alpha(self.test_data4, 5, reference, 'value', 0.5), 6.827021872)
self.assertAlmostEqual(eval_alpha(self.test_data5, 5, reference, 'value', 0.92), -1.192265168)
self.assertAlmostEqual(eval_alpha(self.test_data6, 5, reference, 'value', 0.92), -1.437142359)
self.assertAlmostEqual(eval_alpha(self.test_data7, 5, reference, 'value', 0.92), -1.781311545)
# 测试长数据的alpha计算
expected_alpha = np.array([np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan, np.nan,
-0.09418119, -0.11188463, -0.17938358, -0.15588172, -0.1462678,
-0.13089586, -0.10780125, -0.09102891, -0.03987585, -0.06075686,
-0.02459503, -0.04104284, -0.0444565, -0.04074585, 0.02191275,
0.02255955, -0.05583375, -0.05875539, -0.06055551, -0.09648245,
-0.07913737, -0.10627829, -0.12320965, -0.12368335, -0.1506743,
-0.15768033, -0.13638829, -0.13065298, -0.14537834, -0.127428,
-0.15504529, -0.18184636, -0.12652146, -0.09190138, -0.14847221,
-0.15840648, -0.1525789, -0.11859418, -0.14700954, -0.16295761,
-0.16051645, -0.10364859, -0.11961134, -0.10258267, -0.08090148,
-0.05727746, -0.0429945, -0.04672356, -0.03581408, -0.0439215,
-0.03429495, -0.0260362, -0.01075022, 0.04931808, 0.02779388,
0.03984083, 0.08311951, 0.08995566, 0.10522428, 0.16159058,
0.14238174, 0.14759783, 0.16257712, 0.158908, 0.11302115,
0.0909566, 0.08272888, 0.15261884, 0.10546376, 0.04990313,
-0.01284111, -0.02720704, 0.00454725, -0.03965491, -0.03818265,
-0.02186992, -0.06574751, -0.04846454, -0.05204211, -0.06316498,
-0.05095099, -0.08502656, -0.04681162, -0.02362027, -0.02205091,
-0.07706374, -0.10371841, -0.14434688, -0.14797935, -0.09055402,
-0.06739549, -0.08824959, -0.04855888, -0.02291244, 0.04027138,
0.09370505, 0.11472939, 0.10243593, 0.0921445, 0.07662648,
0.07946651, 0.05450718, 0.10497677, 0.09068334, 0.15462924,
0.14231034, 0.10544952, 0.09980256, 0.14035223, 0.14942974,
0.17624102, 0.19035477, 0.2500807, 0.30724652, 0.31768915,
0.35007521, 0.38412975, 0.34356521, 0.33614463, 0.41206165,
0.33999177, 0.28045963, 0.34076789, 0.42220356, 0.42314636,
0.50790423, 0.47713348, 0.42520169, 0.50488411, 0.48705211,
0.46252601, 0.44325578, 0.42640573, 0.37986783, 0.30652822,
0.34503393, 0.2999069, 0.24928617, 0.24730218, 0.24326897,
0.26657905, 0.27861168, 0.26392824, 0.32552649, 0.34177792,
0.37837011, 0.37025267, 0.4030612, 0.41339361, 0.45076809,
0.40383354, 0.47093422, 0.52505036, 0.53614256, 0.5500943,
0.55319293, 0.59021451, 0.52358459, 0.50605947, 0.49359168,
0.47895956, 0.49320243, 0.4908336, 0.47310767, 0.51821564,
0.55105932, 0.57291504, 0.5599809, 0.46868842, 0.39620087,
0.42086934, 0.38317217, 0.45934108, 0.50048866, 0.53941991,
0.50676751, 0.46500915, 0.52993663, 0.51668366, 0.46405428,
0.44100603, 0.52726147, 0.51565458, 0.49186248, 0.49001081,
0.49367648, 0.56422294, 0.58882785, 0.51334664, 0.44386256,
0.35056709, 0.36490029, 0.39205071, 0.3677061, 0.41134736,
0.42315067, 0.35356394, 0.40324562, 0.41340007, 0.46503322,
0.44355762, 0.34854314, 0.26412842, 0.28633753, 0.32335224,
0.30761141, 0.29709569, 0.29570487, 0.28000063, 0.32802547,
0.33967726, 0.42511212, 0.46252357, 0.44244974, 0.42152907,
0.45436727, 0.50482359, 0.57339198, 0.6573356, 0.70912003,
0.60328917, 0.6395092, 0.67015805, 0.64241557, 0.62779142,
0.55028063, 0.46448736, 0.43709245, 0.46777983, 0.51789439,
0.48594916, 0.4456216, 0.52008189, 0.60548684, 0.62792473,
0.56645031, 0.62766439, 0.71829315, 0.69481356, 0.59550329,
0.58133754, 0.59014148, 0.58026655, 0.61719273, 0.67373203,
0.75573056, 0.89501633, 0.8347253, 0.87964685, 0.89015835])
test_alpha_mean = eval_alpha(self.long_data, 100, self.long_bench, 'value')
test_alpha_roll = self.long_data['alpha'].values
self.assertAlmostEqual(test_alpha_mean, np.nanmean(expected_alpha))
self.assertTrue(np.allclose(test_alpha_roll, expected_alpha, equal_nan=True))
def test_calmar(self):
"""test evaluate function eval_calmar()"""
pass
def test_benchmark(self):
reference = self.test_data1
tr, yr = eval_benchmark(self.test_data2, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
tr, yr = eval_benchmark(self.test_data3, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
tr, yr = eval_benchmark(self.test_data4, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
tr, yr = eval_benchmark(self.test_data5, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
tr, yr = eval_benchmark(self.test_data6, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
tr, yr = eval_benchmark(self.test_data7, reference, 'value')
self.assertAlmostEqual(tr, 0.19509091)
self.assertAlmostEqual(yr, 0.929154957)
def test_evaluate(self):
pass
class TestLoop(unittest.TestCase):
"""通过一个假设但精心设计的例子来测试loop_step以及loop方法的正确性"""
def setUp(self):
# 精心设计的模拟股票名称、交易日期、以及股票价格
self.shares = ['share1', 'share2', 'share3', 'share4', 'share5', 'share6', 'share7']
self.dates = ['2016/07/01', '2016/07/04', '2016/07/05', '2016/07/06', '2016/07/07',
'2016/07/08', '2016/07/11', '2016/07/12', '2016/07/13', '2016/07/14',
'2016/07/15', '2016/07/18', '2016/07/19', '2016/07/20', '2016/07/21',
'2016/07/22', '2016/07/25', '2016/07/26', '2016/07/27', '2016/07/28',
'2016/07/29', '2016/08/01', '2016/08/02', '2016/08/03', '2016/08/04',
'2016/08/05', '2016/08/08', '2016/08/09', '2016/08/10', '2016/08/11',
'2016/08/12', '2016/08/15', '2016/08/16', '2016/08/17', '2016/08/18',
'2016/08/19', '2016/08/22', '2016/08/23', '2016/08/24', '2016/08/25',
'2016/08/26', '2016/08/29', '2016/08/30', '2016/08/31', '2016/09/01',
'2016/09/02', '2016/09/05', '2016/09/06', '2016/09/07', '2016/09/08',
'2016/09/09', '2016/09/12', '2016/09/13', '2016/09/14', '2016/09/15',
'2016/09/16', '2016/09/19', '2016/09/20', '2016/09/21', '2016/09/22',
'2016/09/23', '2016/09/26', '2016/09/27', '2016/09/28', '2016/09/29',
'2016/09/30', '2016/10/10', '2016/10/11', '2016/10/12', '2016/10/13',
'2016/10/14', '2016/10/17', '2016/10/18', '2016/10/19', '2016/10/20',
'2016/10/21', '2016/10/23', '2016/10/24', '2016/10/25', '2016/10/26',
'2016/10/27', '2016/10/29', '2016/10/30', '2016/10/31', '2016/11/01',
'2016/11/02', '2016/11/05', '2016/11/06', '2016/11/07', '2016/11/08',
'2016/11/09', '2016/11/12', '2016/11/13', '2016/11/14', '2016/11/15',
'2016/11/16', '2016/11/19', '2016/11/20', '2016/11/21', '2016/11/22']
self.dates = [pd.Timestamp(date_text) for date_text in self.dates]
self.prices = np.array([[5.35, 5.09, 5.03, 4.98, 4.50, 5.09, 4.75],
[5.66, 4.84, 5.21, 5.44, 4.35, 5.06, 4.48],
[5.79, 4.60, 5.02, 5.45, 4.07, 4.76, 4.56],
[5.56, 4.63, 5.50, 5.74, 3.88, 4.62, 4.62],
[5.88, 4.64, 5.07, 5.46, 3.74, 4.63, 4.62],
[6.25, 4.51, 5.11, 5.45, 3.98, 4.25, 4.59],
[5.93, 4.96, 5.15, 5.24, 4.08, 4.13, 4.33],
[6.39, 4.65, 5.02, 5.47, 4.00, 3.91, 3.88],
[6.31, 4.26, 5.10, 5.58, 4.28, 3.77, 3.47],
[5.86, 3.77, 5.24, 5.36, 4.01, 3.43, 3.51],
[5.61, 3.39, 4.93, 5.38, 4.14, 3.68, 3.83],
[5.31, 3.76, 4.96, 5.30, 4.49, 3.63, 3.67],
[5.40, 4.06, 5.40, 5.77, 4.49, 3.94, 3.79],
[5.03, 3.87, 5.74, 5.75, 4.46, 4.40, 4.18],
[5.38, 3.91, 5.53, 6.15, 4.13, 4.03, 4.02],
[5.79, 4.13, 5.79, 6.04, 3.79, 3.93, 4.41],
[6.27, 4.27, 5.68, 6.01, 4.23, 3.50, 4.65],
[6.59, 4.57, 5.90, 5.71, 4.57, 3.39, 4.89],
[6.91, 5.04, 5.75, 5.23, 4.92, 3.30, 4.41],
[6.71, 5.31, 6.11, 5.47, 5.28, 3.25, 4.66],
[6.33, 5.40, 5.77, 5.79, 5.67, 2.94, 4.37],
[6.07, 5.21, 5.85, 5.82, 6.00, 2.71, 4.58],
[5.98, 5.06, 5.61, 5.61, 5.89, 2.55, 4.76],
[6.46, 4.69, 5.75, 5.31, 5.55, 2.21, 4.37],
[6.95, 5.12, 5.50, 5.24, 5.39, 2.29, 4.16],
[6.77, 5.27, 5.14, 5.41, 5.26, 2.21, 4.02],
[6.70, 5.72, 5.31, 5.60, 5.31, 2.04, 3.77],
[6.28, 6.10, 5.68, 5.28, 5.22, 2.39, 3.38],
[6.61, 6.27, 5.73, 4.99, 4.90, 2.30, 3.07],
[6.25, 6.49, 6.04, 5.09, 4.57, 2.41, 2.90],
[6.47, 6.16, 6.27, 5.39, 4.96, 2.40, 2.50],
[6.45, 6.26, 6.60, 5.58, 4.82, 2.79, 2.76],
[6.88, 6.39, 6.10, 5.33, 4.39, 2.67, 2.29],
[7.00, 6.58, 6.25, 5.48, 4.63, 2.27, 2.17],
[6.59, 6.20, 6.73, 5.10, 5.05, 2.09, 1.84],
[6.59, 5.70, 6.91, 5.39, 4.68, 2.55, 1.83],
[6.64, 5.20, 7.01, 5.30, 5.02, 2.22, 2.21],
[6.38, 5.37, 7.36, 5.04, 4.84, 2.59, 2.00],
[6.10, 5.40, 7.72, 5.51, 4.60, 2.59, 1.76],
[6.35, 5.22, 7.68, 5.43, 4.66, 2.95, 1.27],
[6.52, 5.38, 7.62, 5.23, 4.41, 2.69, 1.40],
[6.87, 5.53, 7.74, 4.99, 4.87, 2.20, 1.11],
[6.84, 6.03, 7.53, 5.43, 4.42, 2.69, 1.60],
[7.09, 5.77, 7.46, 5.40, 4.08, 2.65, 1.23],
[6.88, 5.66, 7.84, 5.60, 4.16, 2.63, 1.59],
[6.84, 6.08, 8.11, 5.66, 4.10, 2.14, 1.50],
[6.98, 5.62, 8.04, 6.01, 4.43, 2.39, 1.80],
[7.02, 5.63, 7.65, 5.64, 4.07, 1.95, 1.55],
[7.13, 6.11, 7.52, 5.67, 3.97, 2.32, 1.35],
[7.59, 6.03, 7.67, 5.30, 4.16, 2.69, 1.51],
[7.61, 6.27, 7.47, 4.91, 4.12, 2.51, 1.08],
[7.21, 6.28, 7.44, 5.37, 4.04, 2.62, 1.06],
[7.48, 6.52, 7.59, 5.75, 3.84, 2.16, 1.43],
[7.66, 7.00, 7.94, 6.08, 3.46, 2.35, 1.43],
[7.51, 7.34, 8.25, 6.58, 3.18, 2.31, 1.74],
[7.12, 7.34, 7.77, 6.78, 3.10, 1.96, 1.44],
[6.97, 7.68, 8.03, 7.20, 3.55, 2.35, 1.83],
[6.67, 8.09, 7.87, 7.65, 3.66, 2.58, 1.71],
[6.20, 7.68, 7.58, 8.00, 3.66, 2.40, 2.12],
[6.34, 7.58, 7.33, 7.92, 3.29, 2.20, 2.45],
[6.22, 7.46, 7.22, 8.30, 2.80, 2.31, 2.85],
[5.98, 7.59, 6.86, 8.46, 2.88, 2.16, 2.79],
[6.37, 7.19, 7.18, 7.99, 3.04, 2.16, 2.91],
[6.56, 7.40, 7.54, 8.19, 3.45, 2.20, 3.26],
[6.26, 7.48, 7.24, 8.61, 3.88, 1.73, 3.14],
[6.69, 7.93, 6.85, 8.66, 3.58, 1.93, 3.53],
[7.13, 8.23, 6.60, 8.91, 3.60, 2.25, 3.65],
[6.83, 8.35, 6.65, 9.08, 3.97, 2.69, 3.69],
[7.31, 8.44, 6.74, 9.34, 4.05, 2.59, 3.50],
[7.43, 8.35, 7.19, 8.96, 4.40, 2.14, 3.25],
[7.54, 8.58, 7.14, 8.98, 4.06, 1.68, 3.64],
[7.18, 8.82, 6.88, 8.50, 3.60, 1.98, 4.00],
[7.21, 9.09, 7.14, 8.65, 3.61, 2.14, 3.63],
[7.45, 9.02, 7.30, 8.94, 4.10, 1.89, 3.78],
[7.37, 8.87, 6.95, 8.63, 3.74, 1.97, 3.42],
[6.88, 9.22, 7.02, 8.65, 4.02, 1.99, 3.76],
[7.08, 9.04, 7.38, 8.40, 3.95, 2.37, 3.62],
[6.75, 8.60, 7.50, 8.38, 3.81, 2.14, 3.67],
[6.60, 8.48, 7.60, 8.23, 3.71, 2.35, 3.61],
[6.21, 8.71, 7.15, 8.04, 3.94, 1.86, 3.39],
[6.36, 8.79, 7.30, 7.91, 4.43, 2.14, 3.43],
[6.82, 8.93, 7.80, 7.57, 4.07, 2.39, 3.33],
[6.45, 9.36, 8.15, 7.73, 4.04, 2.53, 3.03],
[6.85, 9.68, 8.40, 7.74, 4.34, 2.47, 3.28],
[6.48, 10.16, 8.87, 8.07, 4.80, 2.93, 3.46],
[6.10, 10.56, 8.53, 7.99, 5.18, 3.09, 3.25],
[5.64, 10.63, 8.94, 7.92, 4.90, 2.93, 2.95],
[6.01, 10.55, 8.52, 8.40, 5.40, 3.22, 2.87],
[6.21, 10.65, 8.80, 8.80, 5.73, 3.06, 2.63],
[6.61, 10.55, 8.92, 8.47, 5.62, 2.90, 2.40],
[7.02, 10.19, 9.20, 8.07, 5.20, 2.68, 2.53],
[7.04, 10.48, 8.71, 7.87, 4.85, 2.46, 2.96],
[6.77, 10.36, 8.25, 8.02, 5.18, 2.41, 3.26],
[7.09, 10.03, 8.19, 8.39, 4.72, 2.74, 2.97],
[6.65, 10.24, 7.80, 8.69, 4.62, 3.15, 3.16],
[7.07, 10.01, 7.69, 8.81, 4.55, 3.40, 3.58],
[6.80, 10.14, 7.23, 8.99, 4.37, 3.82, 3.23],
[6.79, 10.31, 6.98, 9.10, 4.26, 4.02, 3.62],
[6.48, 9.88, 7.07, 8.90, 4.25, 3.76, 3.13],
[6.39, 10.05, 6.95, 8.87, 4.59, 4.10, 2.93]])
# 精心设计的模拟PT持股仓位目标信号：
self.pt_signals = np.array([[0.000, 0.000, 0.000, 0.000, 0.250, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.250, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.250, 0.100, 0.150],
[0.200, 0.200, 0.000, 0.000, 0.250, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.250, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.200, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.100, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.050, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.050, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.050, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.050, 0.000, 0.062, 0.100, 0.150],
[0.133, 0.200, 0.050, 0.000, 0.062, 0.100, 0.000],
[0.133, 0.200, 0.050, 0.000, 0.262, 0.100, 0.000],
[0.133, 0.200, 0.050, 0.000, 0.262, 0.100, 0.000],
[0.133, 0.200, 0.050, 0.000, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.050, 0.150, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.050, 0.150, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.050, 0.150, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.050, 0.150, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.050, 0.150, 0.262, 0.100, 0.000],
[0.066, 0.200, 0.250, 0.150, 0.000, 0.300, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.386, 0.136, 0.170, 0.102, 0.000, 0.204, 0.000],
[0.460, 0.119, 0.149, 0.089, 0.000, 0.179, 0.000],
[0.460, 0.119, 0.149, 0.089, 0.000, 0.179, 0.000],
[0.460, 0.119, 0.149, 0.089, 0.000, 0.179, 0.000],
[0.446, 0.116, 0.145, 0.087, 0.000, 0.087, 0.116],
[0.446, 0.116, 0.145, 0.087, 0.000, 0.087, 0.116],
[0.446, 0.116, 0.145, 0.087, 0.000, 0.087, 0.116],
[0.446, 0.116, 0.145, 0.087, 0.000, 0.087, 0.116],
[0.446, 0.116, 0.145, 0.087, 0.000, 0.087, 0.116],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.400, 0.208, 0.130, 0.078, 0.000, 0.078, 0.104],
[0.370, 0.193, 0.120, 0.072, 0.072, 0.072, 0.096],
[0.000, 0.222, 0.138, 0.222, 0.083, 0.222, 0.111],
[0.000, 0.222, 0.138, 0.222, 0.083, 0.222, 0.111],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.121, 0.195, 0.121, 0.195, 0.073, 0.195, 0.097],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.200, 0.320, 0.200, 0.000, 0.120, 0.000, 0.160],
[0.047, 0.380, 0.238, 0.000, 0.142, 0.000, 0.190],
[0.047, 0.380, 0.238, 0.000, 0.142, 0.000, 0.190],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.043, 0.434, 0.217, 0.000, 0.130, 0.000, 0.173],
[0.045, 0.454, 0.227, 0.000, 0.000, 0.000, 0.272],
[0.045, 0.454, 0.227, 0.000, 0.000, 0.000, 0.272],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.050, 0.000, 0.250, 0.000, 0.000, 0.000, 0.300],
[0.000, 0.000, 0.400, 0.000, 0.000, 0.000, 0.300],
[0.000, 0.000, 0.400, 0.000, 0.000, 0.000, 0.300],
[0.000, 0.000, 0.400, 0.000, 0.000, 0.000, 0.300]])
# 精心设计的模拟PS比例交易信号，与模拟PT信号高度相似
self.ps_signals = np.array([[0.000, 0.000, 0.000, 0.000, 0.250, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.100, 0.150],
[0.200, 0.200, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.100, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, -0.750, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[-0.333, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, -0.500, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, -1.000],
[0.000, 0.000, 0.000, 0.000, 0.200, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[-0.500, 0.000, 0.000, 0.150, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.200, 0.000, -1.000, 0.200, 0.000],
[0.500, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.200, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, -0.500, 0.200],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.200, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.150, 0.000, 0.000],
[-1.000, 0.000, 0.000, 0.250, 0.000, 0.250, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.250, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, -1.000, 0.000, -1.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[-0.800, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.100, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, -1.000, 0.000, 0.100],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, -1.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[-1.000, 0.000, 0.150, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000]])
# 精心设计的模拟VS股票交易信号，与模拟PS信号类似
self.vs_signals = np.array([[000, 000, 000, 000, 500, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 300, 300],
[400, 400, 000, 000, 000, 000, 000],
[000, 000, 250, 000, 000, 000, 000],
[000, 000, 000, 000, -400, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[-200, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, -200, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, -300],
[000, 000, 000, 000, 500, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[-200, 000, 000, 300, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 400, 000, -300, 600, 000],
[500, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[600, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, -400, 600],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 500, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 300, 000, 000],
[-500, 000, 000, 500, 000, 200, 000],
[000, 000, 000, 000, 000, 000, 000],
[500, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, -700, 000, -600, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[-400, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 300, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, -600, 000, 300],
[000, 000, 000, 000, 000, 000, 000],
[000, -300, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[-200, 000, 700, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000],
[000, 000, 000, 000, 000, 000, 000]])
# 精心设计的模拟多价格交易信号，模拟50个交易日对三只股票的操作
self.multi_shares = ['000010', '000030', '000039']
self.multi_dates = ['2016/07/01', '2016/07/04', '2016/07/05', '2016/07/06', '2016/07/07',
'2016/07/08', '2016/07/11', '2016/07/12', '2016/07/13', '2016/07/14',
'2016/07/15', '2016/07/18', '2016/07/19', '2016/07/20', '2016/07/21',
'2016/07/22', '2016/07/25', '2016/07/26', '2016/07/27', '2016/07/28',
'2016/07/29', '2016/08/01', '2016/08/02', '2016/08/03', '2016/08/04',
'2016/08/05', '2016/08/08', '2016/08/09', '2016/08/10', '2016/08/11',
'2016/08/12', '2016/08/15', '2016/08/16', '2016/08/17', '2016/08/18',
'2016/08/19', '2016/08/22', '2016/08/23', '2016/08/24', '2016/08/25',
'2016/08/26', '2016/08/29', '2016/08/30', '2016/08/31', '2016/09/01',
'2016/09/02', '2016/09/05', '2016/09/06', '2016/09/07', '2016/09/08']
self.multi_dates = [pd.Timestamp(date_text) for date_text in self.multi_dates]
# 操作的交易价格包括开盘价、最高价和收盘价
self.multi_prices_open = np.array([[10.02, 9.88, 7.26],
[10.00, 9.88, 7.00],
[9.98, 9.89, 6.88],
[9.97, 9.75, 6.91],
[9.99, 9.74, np.nan],
[10.01, 9.80, 6.81],
[10.04, 9.62, 6.63],
[10.06, 9.65, 6.45],
[10.06, 9.58, 6.16],
[10.11, 9.67, 6.24],
[10.11, 9.81, 5.96],
[10.07, 9.80, 5.97],
[10.06, 10.00, 5.96],
[10.09, 9.95, 6.20],
[10.03, 10.10, 6.35],
[10.02, 10.06, 6.11],
[10.06, 10.14, 6.37],
[10.08, 9.90, 5.58],
[9.99, 10.20, 5.65],
[10.00, 10.29, 5.65],
[10.03, 9.86, 5.19],
[10.02, 9.48, 5.42],
[10.06, 10.01, 6.30],
[10.03, 10.24, 6.15],
[9.97, 10.26, 6.05],
[9.94, 10.24, 5.89],
[9.83, 10.12, 5.22],
[9.78, 10.65, 5.20],
[9.77, 10.64, 5.07],
[9.91, 10.56, 6.04],
[9.92, 10.42, 6.12],
[9.97, 10.43, 5.85],
[9.91, 10.29, 5.67],
[9.90, 10.30, 6.02],
[9.88, 10.44, 6.04],
[9.91, 10.60, 7.07],
[9.63, 10.67, 7.64],
[9.64, 10.46, 7.99],
[9.57, 10.39, 7.59],
[9.55, 10.90, 8.73],
[9.58, 11.01, 8.72],
[9.61, 11.01, 8.97],
[9.62, np.nan, 8.58],
[9.55, np.nan, 8.71],
[9.57, 10.82, 8.77],
[9.61, 11.02, 8.40],
[9.63, 10.96, 7.95],
[9.64, 11.55, 7.76],
[9.61, 11.74, 8.25],
[9.56, 11.80, 7.51]])
self.multi_prices_high = np.array([[10.07, 9.91, 7.41],
[10.00, 10.04, 7.31],
[10.00, 9.93, 7.14],
[10.00, 10.04, 7.00],
[10.03, 9.84, np.nan],
[10.03, 9.88, 6.82],
[10.04, 9.99, 6.96],
[10.09, 9.70, 6.85],
[10.10, 9.67, 6.50],
[10.14, 9.71, 6.34],
[10.11, 9.85, 6.04],
[10.10, 9.90, 6.02],
[10.09, 10.00, 6.12],
[10.09, 10.20, 6.38],
[10.10, 10.11, 6.43],
[10.05, 10.18, 6.46],
[10.07, 10.21, 6.43],
[10.09, 10.26, 6.27],
[10.10, 10.38, 5.77],
[10.00, 10.47, 6.01],
[10.04, 10.42, 5.67],
[10.04, 10.07, 5.67],
[10.06, 10.24, 6.35],
[10.09, 10.27, 6.32],
[10.05, 10.38, 6.43],
[9.97, 10.43, 6.36],
[9.96, 10.39, 5.79],
[9.86, 10.65, 5.47],
[9.77, 10.84, 5.65],
[9.92, 10.65, 6.04],
[9.94, 10.73, 6.14],
[9.97, 10.63, 6.23],
[9.97, 10.51, 5.83],
[9.92, 10.35, 6.25],
[9.92, 10.46, 6.27],
[9.92, 10.63, 7.12],
[9.93, 10.74, 7.82],
[9.64, 10.76, 8.14],
[9.58, 10.54, 8.27],
[9.60, 11.02, 8.92],
[9.58, 11.12, 8.76],
[9.62, 11.17, 9.15],
[9.62, np.nan, 8.90],
[9.64, np.nan, 9.01],
[9.59, 10.92, 9.16],
[9.62, 11.15, 9.00],
[9.63, 11.11, 8.27],
[9.70, 11.55, 7.99],
[9.66, 11.95, 8.33],
[9.64, 11.93, 8.25]])
self.multi_prices_close = np.array([[10.04, 9.68, 6.64],
[10.00, 9.87, 7.26],
[10.00, 9.86, 7.03],
[9.99, 9.87, 6.87],
[9.97, 9.79, np.nan],
[9.99, 9.82, 6.64],
[10.03, 9.80, 6.85],
[10.03, 9.66, 6.70],
[10.06, 9.62, 6.39],
[10.06, 9.58, 6.22],
[10.11, 9.69, 5.92],
[10.09, 9.78, 5.91],
[10.07, 9.75, 6.11],
[10.06, 9.96, 5.91],
[10.09, 9.90, 6.23],
[10.03, 10.04, 6.28],
[10.03, 10.06, 6.28],
[10.06, 10.08, 6.27],
[10.08, 10.24, 5.70],
[10.00, 10.24, 5.56],
[9.99, 10.24, 5.67],
[10.03, 9.86, 5.16],
[10.03, 10.13, 5.69],
[10.06, 10.12, 6.32],
[10.03, 10.10, 6.14],
[9.97, 10.25, 6.25],
[9.94, 10.24, 5.79],
[9.83, 10.22, 5.26],
[9.77, 10.75, 5.05],
[9.84, 10.64, 5.45],
[9.91, 10.56, 6.06],
[9.93, 10.60, 6.21],
[9.96, 10.42, 5.69],
[9.91, 10.25, 5.46],
[9.91, 10.24, 6.02],
[9.88, 10.49, 6.69],
[9.91, 10.57, 7.43],
[9.64, 10.63, 7.72],
[9.56, 10.48, 8.16],
[9.57, 10.37, 7.83],
[9.55, 10.96, 8.70],
[9.57, 11.02, 8.71],
[9.61, np.nan, 8.88],
[9.61, np.nan, 8.54],
[9.55, 10.88, 8.87],
[9.57, 10.87, 8.87],
[9.63, 11.01, 8.18],
[9.64, 11.01, 7.80],
[9.65, 11.58, 7.97],
[9.62, 11.80, 8.25]])
# 交易信号包括三组，分别作用与开盘价、最高价和收盘价
# 此时的关键是股票交割期的处理，交割期不为0时，以交易日为单位交割
self.multi_signals = []
# multisignal的第一组信号为开盘价信号
self.multi_signals.append(
pd.DataFrame(np.array([[0.000, 0.000, 0.000],
[0.000, -0.500, 0.000],
[0.000, -0.500, 0.000],
[0.000, 0.000, 0.000],
[0.150, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.300, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.300],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.350, 0.250],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.100, 0.000, 0.350],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.200, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.050, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000]]),
columns=self.multi_shares,
index=self.multi_dates
)
)
# 第二组信号为最高价信号
self.multi_signals.append(
pd.DataFrame(np.array([[0.000, 0.150, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, -0.200, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.200],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000]]),
columns=self.multi_shares,
index=self.multi_dates
)
)
# 第三组信号为收盘价信号
self.multi_signals.append(
pd.DataFrame(np.array([[0.000, 0.200, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[-0.500, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, -0.800],
[0.000, 0.000, 0.000],
[0.000, -1.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[-0.750, 0.000, 0.000],
[0.000, 0.000, -0.850],
[0.000, 0.000, 0.000],
[0.000, -0.700, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, -1.000],
[0.000, 0.000, 0.000],
[0.000, 0.000, 0.000],
[-1.000, 0.000, 0.000],
[0.000, -1.000, 0.000],
[0.000, 0.000, 0.000]]),
columns=self.multi_shares,
index=self.multi_dates
)
)
# 交易回测所需的价格也有三组，分别是开盘价、最高价和收盘价
self.multi_histories = []
# multisignal的第一组信号为开盘价信号
self.multi_histories.append(
pd.DataFrame(self.multi_prices_open,
columns=self.multi_shares,
index=self.multi_dates
)
)
# 第二组信号为最高价信号
self.multi_histories.append(
pd.DataFrame(self.multi_prices_high,
columns=self.multi_shares,
index=self.multi_dates
)
)
# 第三组信号为收盘价信号
self.multi_histories.append(
pd.DataFrame(self.multi_prices_close,
columns=self.multi_shares,
index=self.multi_dates
)
)
# 设置回测参数
self.cash = qt.CashPlan(['2016/07/01', '2016/08/12', '2016/09/23'], [10000, 10000, 10000])
self.rate = qt.Cost(buy_fix=0,
sell_fix=0,
buy_rate=0,
sell_rate=0,
buy_min=0,
sell_min=0,
slipage=0)
self.rate2 = qt.Cost(buy_fix=0,
sell_fix=0,
buy_rate=0,
sell_rate=0,
buy_min=10,
sell_min=5,
slipage=0)
self.pt_signal_hp = dataframe_to_hp(
pd.DataFrame(self.pt_signals, index=self.dates, columns=self.shares),
htypes='close'
)
self.ps_signal_hp = dataframe_to_hp(
pd.DataFrame(self.ps_signals, index=self.dates, columns=self.shares),
htypes='close'
)
self.vs_signal_hp = dataframe_to_hp(
pd.DataFrame(self.vs_signals, index=self.dates, columns=self.shares),
htypes='close'
)
self.multi_signal_hp = stack_dataframes(
self.multi_signals,
stack_along='htypes',
htypes='open, high, close'
)
self.history_list = dataframe_to_hp(
pd.DataFrame(self.prices, index=self.dates, columns=self.shares),
htypes='close'
)
self.multi_history_list = stack_dataframes(
self.multi_histories,
stack_along='htypes',
htypes='open, high, close'
)
# 模拟PT信号回测结果
# PT信号，先卖后买，交割期为0
self.pt_res_sb00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 10000.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 9916.6667],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 6035.8333, 0.0000, 9761.1111],
[348.0151, 417.9188, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 2165.9050, 0.0000, 9674.8209],
[348.0151, 417.9188, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 2165.9050, 0.0000, 9712.5872],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9910.7240],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9919.3782],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9793.0692],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9513.8217],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9123.5935],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9000.5995],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9053.4865],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9248.7142],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9161.1372],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9197.3369],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9504.6981],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9875.2461],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10241.5400],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10449.2398],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10628.3269],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10500.7893],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 0.0000, 5233.1396, 0.0000, 10449.2776],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10338.2857],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10194.3474],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10471.0008],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10411.2629],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10670.0618],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10652.4799],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10526.1488],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10458.6614],
[101.4983, 417.9188, 821.7315, 288.6672, 0.0000, 2576.1284, 0.0000, 4487.0722, 0.0000, 20609.0270],
[1216.3282, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21979.4972],
[1216.3282, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21880.9628],
[1216.3282, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21630.0454],
[1216.3282, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 20968.0007],
[1216.3282, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21729.9339],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 21107.6400],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 21561.1745],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 21553.0916],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 22316.9366],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 22084.2862],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 21777.3543],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 22756.8225],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 22843.4697],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 0.0000, 2172.0393, 0.0000, 22762.1766],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 22257.0973],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 23136.5259],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 21813.7852],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 22395.3204],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 23717.6858],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 1607.1030, 1448.0262, 0.0000, 0.0000, 22715.4263],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 22498.3254],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 23341.1733],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24162.3941],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24847.1508],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 23515.9755],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24555.8997],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24390.6372],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24073.3309],
[1216.3282, 417.9188, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 2455.7405, 0.0000, 24394.6500],
[2076.3314, 903.0334, 511.8829, 288.6672, 0.0000, 669.7975, 1448.0262, 3487.5655, 0.0000, 34904.8150],
[0.0000, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 4608.8037, 0.0000, 34198.4475],
[0.0000, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 4608.8037, 0.0000, 33753.0190],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 34953.8178],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 33230.2498],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 35026.7819],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 36976.2649],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 38673.8147],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 38717.3429],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 36659.0854],
[644.7274, 903.0334, 511.8829, 897.4061, 0.0000, 3514.8404, 1448.0262, 379.3918, 0.0000, 35877.9607],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 36874.4840],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 37010.2695],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 38062.3510],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 36471.1357],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 37534.9927],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 37520.2569],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 36747.7952],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 36387.9409],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 35925.9715],
[644.7274, 1337.8498, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 2853.5665, 0.0000, 36950.7028],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 37383.2463],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 37761.2724],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 39548.2653],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 41435.1291],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 41651.6261],
[644.7274, 1657.3981, 1071.9327, 0.0000, 1229.1495, 0.0000, 1448.0262, 0.0000, 0.0000, 41131.9920],
[644.7274, 1657.3981, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 0.0000, 0.0000, 41286.4702],
[644.7274, 1657.3981, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 0.0000, 0.0000, 40978.7259],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 40334.5453],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 41387.9172],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 42492.6707],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 42953.7188],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 42005.1092],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 42017.9106],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 43750.2824],
[644.7274, 0.0000, 1071.9327, 0.0000, 0.0000, 0.0000, 3760.7116, 17485.5497, 0.0000, 41766.8679],
[0.0000, 0.0000, 2461.8404, 0.0000, 0.0000, 0.0000, 3760.7116, 12161.6930, 0.0000, 42959.1150],
[0.0000, 0.0000, 2461.8404, 0.0000, 0.0000, 0.0000, 3760.7116, 12161.6930, 0.0000, 41337.9320],
[0.0000, 0.0000, 2461.8404, 0.0000, 0.0000, 0.0000, 3760.7116, 12161.6930, 0.0000, 40290.3688]])
# PT信号，先买后卖，交割期为0
self.pt_res_bs00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 10000.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 9916.6667],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 6035.8333, 0.0000, 9761.1111],
[348.0151, 417.9188, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 2165.9050, 0.0000, 9674.8209],
[348.0151, 417.9188, 0.0000, 0.0000, 555.5556, 0.0000, 321.0892, 2165.9050, 0.0000, 9712.5872],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9910.7240],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9919.3782],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9793.0692],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9513.8217],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9123.5935],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9000.5995],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9053.4865],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9248.7142],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9161.1372],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9197.3369],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9504.6981],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 9875.2461],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10241.5400],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10449.2398],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10628.3269],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 321.0892, 3762.5512, 0.0000, 10500.7893],
[348.0151, 417.9188, 0.0000, 0.0000, 154.3882, 0.0000, 0.0000, 5233.1396, 0.0000, 10449.2776],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10338.2857],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10194.3474],
[348.0151, 417.9188, 0.0000, 0.0000, 459.8694, 0.0000, 0.0000, 3433.8551, 0.0000, 10471.0008],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10411.2629],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10670.0618],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10652.4799],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10526.1488],
[101.4983, 417.9188, 0.0000, 288.6672, 459.8694, 0.0000, 0.0000, 3541.0848, 0.0000, 10458.6614],
[101.4983, 417.9188, 821.7315, 288.6672, 0.0000, 2576.1284, 0.0000, 4487.0722, 0.0000, 20609.0270],
[797.1684, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 2703.5808, 0.0000, 21979.4972],
[1190.1307, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21700.7241],
[1190.1307, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21446.6630],
[1190.1307, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 20795.3593],
[1190.1307, 417.9188, 821.7315, 288.6672, 0.0000, 1607.1030, 0.0000, 0.0000, 0.0000, 21557.2924],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 20933.6887],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 21392.5581],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 21390.2918],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 22147.7562],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 21910.9053],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 21594.2980],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 22575.4380],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 22655.8312],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 0.0000, 2201.6110, 0.0000, 22578.4365],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 1467.7407, 0.0000, 0.0000, 22073.2661],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 1467.7407, 0.0000, 0.0000, 22955.2367],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 1467.7407, 0.0000, 0.0000, 21628.1647],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 1467.7407, 0.0000, 0.0000, 22203.4237],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 1607.1030, 1467.7407, 0.0000, 0.0000, 23516.2598],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 22505.8428],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 22199.1042],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 23027.9302],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 23848.5806],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 24540.8871],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 23205.6838],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 24267.6685],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 24115.3796],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 23814.3667],
[1190.1307, 417.9188, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 2278.3728, 0.0000, 24133.6611],
[2061.6837, 896.6628, 507.6643, 288.6672, 0.0000, 699.3848, 1467.7407, 3285.8830, 0.0000, 34658.5742],
[0.0000, 896.6628, 507.6643, 466.6033, 0.0000, 1523.7106, 1467.7407, 12328.8684, 0.0000, 33950.7917],
[0.0000, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 4380.3797, 0.0000, 33711.4045],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 34922.0959],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 33237.1081],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 35031.8071],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 36976.3376],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 38658.5245],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 38712.2854],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 36655.3125],
[644.1423, 896.6628, 507.6643, 936.6623, 0.0000, 3464.7832, 1467.7407, 154.8061, 0.0000, 35904.3692],
[644.1423, 902.2617, 514.8253, 0.0000, 15.5990, 0.0000, 1467.7407, 14821.9004, 0.0000, 36873.9080],
[644.1423, 902.2617, 514.8253, 0.0000, 1220.8683, 0.0000, 1467.7407, 10470.8781, 0.0000, 36727.7895],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 37719.9840],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 36138.1277],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 37204.0760],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 37173.1201],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 36398.2298],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 36034.2178],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 35583.6399],
[644.1423, 1338.1812, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 2753.1120, 0.0000, 36599.2645],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 37013.3408],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 37367.7449],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 39143.8273],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 41007.3074],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 41225.4657],
[644.1423, 1646.4805, 1033.4242, 0.0000, 1220.8683, 0.0000, 1467.7407, 0.0000, 0.0000, 40685.9525],
[644.1423, 1646.4805, 1033.4242, 0.0000, 0.0000, 0.0000, 1467.7407, 6592.6891, 0.0000, 40851.5435],
[644.1423, 1646.4805, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 0.0000, 0.0000, 41082.1210],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 40385.0135],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 41455.1513],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 42670.6769],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 43213.7233],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 42205.2480],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 42273.9386],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 44100.0777],
[644.1423, 0.0000, 1033.4242, 0.0000, 0.0000, 0.0000, 3974.4666, 17370.3689, 0.0000, 42059.7208],
[0.0000, 0.0000, 2483.9522, 0.0000, 0.0000, 0.0000, 3974.4666, 11619.4102, 0.0000, 43344.9653],
[0.0000, 0.0000, 2483.9522, 0.0000, 0.0000, 0.0000, 3974.4666, 11619.4102, 0.0000, 41621.0324],
[0.0000, 0.0000, 2483.9522, 0.0000, 0.0000, 0.0000, 3974.4666, 11619.4102, 0.0000, 40528.0648]])
# PT信号，先卖后买，交割期为2天（股票）0天（现金）以便利用先卖的现金继续买入
self.pt_res_sb20 = np.array(
[[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 9916.667],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 321.089, 6035.833, 0.000, 9761.111],
[348.015, 417.919, 0.000, 0.000, 555.556, 0.000, 321.089, 2165.905, 0.000, 9674.821],
[348.015, 417.919, 0.000, 0.000, 555.556, 0.000, 321.089, 2165.905, 0.000, 9712.587],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9910.724],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9919.378],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9793.069],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9513.822],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9123.593],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9000.600],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9053.487],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9248.714],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9161.137],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9197.337],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9504.698],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9875.246],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10241.540],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10449.240],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10628.327],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10500.789],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 0.000, 5233.140, 0.000, 10449.278],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10338.286],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10194.347],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10471.001],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10411.263],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10670.062],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10652.480],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10526.149],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10458.661],
[101.498, 417.919, 821.732, 288.667, 0.000, 2576.128, 0.000, 4487.072, 0.000, 20609.027],
[797.168, 417.919, 821.732, 288.667, 0.000, 2576.128, 0.000, 0.000, 0.000, 21979.497],
[1156.912, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21584.441],
[1156.912, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21309.576],
[1156.912, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 20664.323],
[1156.912, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21445.597],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 20806.458],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 21288.441],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 21294.365],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 22058.784],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 21805.540],
[1156.912, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 2223.240, 0.000, 21456.333],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22459.720],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22611.602],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22470.912],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21932.634],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22425.864],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21460.103],
[1481.947, 417.919, 504.579, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22376.968],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 23604.295],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 22704.826],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 22286.293],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 23204.755],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 24089.017],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 24768.185],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 23265.196],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 24350.540],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 24112.706],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 23709.076],
[1481.947, 417.919, 504.579, 288.667, 0.000, 763.410, 1577.904, 0.000, 0.000, 24093.545],
[2060.275, 896.050, 504.579, 288.667, 0.000, 763.410, 1577.904, 2835.944, 0.000, 34634.888],
[578.327, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 732.036, 0.000, 33912.261],
[0.000, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 4415.981, 0.000, 33711.951],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 34951.433],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 33224.596],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 35065.209],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 37018.699],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 38706.035],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 38724.569],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 36647.268],
[644.683, 896.050, 504.579, 889.896, 0.000, 3485.427, 1577.904, 186.858, 0.000, 35928.930],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 36967.229],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 37056.598],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 38129.862],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 36489.333],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 37599.602],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 37566.823],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 36799.280],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 36431.196],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 35940.942],
[644.683, 1341.215, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 2367.759, 0.000, 36973.050],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 37393.292],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 37711.276],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 39515.991],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 41404.440],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 41573.523],
[644.683, 1606.361, 1074.629, 0.000, 1232.241, 0.000, 1577.904, 0.000, 0.000, 41011.613],
[644.683, 1606.361, 1074.629, 0.000, 0.000, 0.000, 3896.406, 0.000, 0.000, 41160.181],
[644.683, 1606.361, 1074.629, 0.000, 0.000, 0.000, 3896.406, 0.000, 0.000, 40815.512],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 40145.531],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 41217.281],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 42379.061],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 42879.589],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 41891.452],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 41929.003],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 43718.052],
[644.683, 0.000, 1074.629, 0.000, 0.000, 0.000, 3896.406, 16947.110, 0.000, 41685.916],
[0.000, 0.000, 2460.195, 0.000, 0.000, 0.000, 3896.406, 11653.255, 0.000, 42930.410],
[0.000, 0.000, 2460.195, 0.000, 0.000, 0.000, 3896.406, 11653.255, 0.000, 41242.589],
[0.000, 0.000, 2460.195, 0.000, 0.000, 0.000, 3896.406, 11653.255, 0.000, 40168.084]])
# PT信号，先买后卖，交割期为2天（股票）1天（现金）
self.pt_res_bs21 = np.array([
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 9916.667],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 321.089, 6035.833, 0.000, 9761.111],
[348.015, 417.919, 0.000, 0.000, 555.556, 0.000, 321.089, 2165.905, 0.000, 9674.821],
[348.015, 417.919, 0.000, 0.000, 555.556, 0.000, 321.089, 2165.905, 0.000, 9712.587],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9910.724],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9919.378],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9793.069],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9513.822],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9123.593],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9000.600],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9053.487],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9248.714],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9161.137],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9197.337],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9504.698],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 9875.246],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10241.540],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10449.240],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10628.327],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 321.089, 3762.551, 0.000, 10500.789],
[348.015, 417.919, 0.000, 0.000, 154.388, 0.000, 0.000, 5233.140, 0.000, 10449.278],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10338.286],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10194.347],
[348.015, 417.919, 0.000, 0.000, 459.869, 0.000, 0.000, 3433.855, 0.000, 10471.001],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10411.263],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10670.062],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10652.480],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10526.149],
[101.498, 417.919, 0.000, 288.667, 459.869, 0.000, 0.000, 3541.085, 0.000, 10458.661],
[101.498, 417.919, 821.732, 288.667, 0.000, 2576.128, 0.000, 4487.072, 0.000, 20609.027],
[797.168, 417.919, 821.732, 288.667, 0.000, 2576.128, 0.000, 0.000, 0.000, 21979.497],
[797.168, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 2475.037, 0.000, 21584.441],
[1150.745, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21266.406],
[1150.745, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 20623.683],
[1150.745, 417.919, 821.732, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21404.957],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 20765.509],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 21248.748],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 21256.041],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 22018.958],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 21764.725],
[1150.745, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 2230.202, 0.000, 21413.241],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22417.021],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22567.685],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22427.699],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21889.359],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22381.938],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 21416.358],
[1476.798, 417.919, 503.586, 288.667, 0.000, 1649.148, 0.000, 0.000, 0.000, 22332.786],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 0.000, 2386.698, 0.000, 23557.595],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 23336.992],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 22907.742],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 24059.201],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 24941.902],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 25817.514],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 24127.939],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 25459.688],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 25147.370],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 2209.906, 0.000, 0.000, 25005.842],
[1476.798, 417.919, 503.586, 288.667, 0.000, 761.900, 1086.639, 2752.004, 0.000, 25598.700],
[2138.154, 929.921, 503.586, 288.667, 0.000, 761.900, 1086.639, 4818.835, 0.000, 35944.098],
[661.356, 929.921, 503.586, 553.843, 0.000, 1954.237, 1086.639, 8831.252, 0.000, 35237.243],
[0.000, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 9460.955, 0.000, 35154.442],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 36166.632],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 34293.883],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 35976.901],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 37848.552],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 39512.574],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 39538.024],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 37652.984],
[667.098, 929.921, 503.586, 553.843, 0.000, 3613.095, 1086.639, 5084.792, 0.000, 36687.909],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 37749.277],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 37865.518],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 38481.190],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 37425.087],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 38051.341],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 38065.478],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 37429.495],
[667.098, 1108.871, 745.260, 0.000, 512.148, 0.000, 1086.639, 11861.593, 0.000, 37154.479],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 36692.717],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 37327.055],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 37937.630],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 38298.645],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 39689.369],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 40992.397],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 41092.265],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 1086.639, 7576.628, 0.000, 40733.622],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 3726.579, 0.000, 0.000, 40708.515],
[667.098, 1600.830, 745.260, 0.000, 512.148, 0.000, 3726.579, 0.000, 0.000, 40485.321],
[667.098, 0.000, 745.260, 0.000, 512.148, 0.000, 3726.579, 16888.760, 0.000, 39768.059],
[667.098, 0.000, 745.260, 0.000, 512.148, 0.000, 3726.579, 16888.760, 0.000, 40519.595],
[667.098, 0.000, 745.260, 0.000, 512.148, 0.000, 3726.579, 16888.760, 0.000, 41590.937],
[667.098, 0.000, 1283.484, 0.000, 512.148, 0.000, 3726.579, 12448.413, 0.000, 42354.983],
[667.098, 0.000, 1283.484, 0.000, 512.148, 0.000, 3726.579, 12448.413, 0.000, 41175.149],
[667.098, 0.000, 1283.484, 0.000, 512.148, 0.000, 3726.579, 12448.413, 0.000, 41037.902],
[667.098, 0.000, 1283.484, 0.000, 512.148, 0.000, 3726.579, 12448.413, 0.000, 42706.213],
[667.098, 0.000, 1283.484, 0.000, 512.148, 0.000, 3726.579, 12448.413, 0.000, 40539.205],
[0.000, 0.000, 2384.452, 0.000, 512.148, 0.000, 3726.579, 9293.252, 0.000, 41608.692],
[0.000, 0.000, 2384.452, 0.000, 512.148, 0.000, 3726.579, 9293.252, 0.000, 39992.148],
[0.000, 0.000, 2384.452, 0.000, 512.148, 0.000, 3726.579, 9293.252, 0.000, 39134.828]])
# 模拟PS信号回测结果
# PS信号，先卖后买，交割期为0
self.ps_res_sb00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 10000.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 9916.6667],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 205.0654, 321.0892, 5059.7222, 0.0000, 9761.1111],
[346.9824, 416.6787, 0.0000, 0.0000, 555.5556, 205.0654, 321.0892, 1201.2775, 0.0000, 9646.1118],
[346.9824, 416.6787, 191.0372, 0.0000, 555.5556, 205.0654, 321.0892, 232.7189, 0.0000, 9685.5858],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9813.2184],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9803.1288],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9608.0198],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9311.5727],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8883.6246],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8751.3900],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8794.1811],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9136.5704],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9209.3588],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9093.8294],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9387.5537],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9585.9589],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 9928.7771],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10060.3806],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10281.0021],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10095.5613],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 0.0000, 4506.3926, 0.0000, 10029.9571],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9875.6133],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9614.9463],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9824.1722],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9732.5743],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9968.3391],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 10056.1579],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9921.4925],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9894.1621],
[115.7186, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 6179.7742, 0.0000, 20067.9370],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21133.5080],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20988.8485],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20596.7429],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 19910.7730],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20776.7070],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20051.7969],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20725.3884],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20828.8795],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21647.1811],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21310.1687],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20852.0993],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21912.3952],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21937.8282],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21962.4576],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 21389.4018],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22027.4535],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 20939.9992],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 21250.0636],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22282.7812],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 21407.0658],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 21160.2373],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 21826.7682],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22744.9403],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 23466.1185],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22017.8821],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 23191.4662],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 23099.0822],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22684.7671],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 1339.2073, 0.0000, 0.0000, 22842.1346],
[1073.8232, 416.6787, 735.6442, 269.8496, 1785.2055, 938.6967, 1339.2073, 5001.4246, 0.0000,
33323.8359],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 32820.2901],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 32891.2308],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 34776.5296],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 33909.0325],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 34560.1906],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 36080.4552],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 38618.4454],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 38497.9230],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 37110.0991],
[0.0000, 416.6787, 735.6442, 944.9611, 1785.2055, 3582.8836, 1339.2073, 0.0000, 0.0000, 35455.2467],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35646.1860],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35472.3020],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 36636.4694],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35191.7035],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 36344.2242],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 36221.6005],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35943.5708],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35708.2608],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 35589.0286],
[0.0000, 416.6787, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 15126.2788, 0.0000, 36661.0285],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 36310.5909],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 36466.7637],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 37784.4918],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 39587.6766],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 40064.0191],
[0.0000, 823.2923, 735.6442, 0.0000, 1785.2055, 0.0000, 1339.2073, 11495.2197, 0.0000, 39521.6439],
[0.0000, 823.2923, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 17142.1018, 0.0000, 39932.2761],
[0.0000, 823.2923, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 17142.1018, 0.0000, 39565.2475],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 38943.1632],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 39504.1184],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 40317.8004],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 40798.5768],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 39962.5711],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 40194.4793],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 41260.4003],
[0.0000, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 2730.5758, 25827.8351, 0.0000, 39966.3024],
[0.0000, 0.0000, 1613.4518, 0.0000, 0.0000, 0.0000, 2730.5758, 19700.7377, 0.0000, 40847.3160],
[0.0000, 0.0000, 1613.4518, 0.0000, 0.0000, 0.0000, 2730.5758, 19700.7377, 0.0000, 39654.5445],
[0.0000, 0.0000, 1613.4518, 0.0000, 0.0000, 0.0000, 2730.5758, 19700.7377, 0.0000, 38914.8151]])
# PS信号，先买后卖，交割期为0
self.ps_res_bs00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 10000.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 0.0000, 0.0000, 7500.0000, 0.0000, 9916.6667],
[0.0000, 0.0000, 0.0000, 0.0000, 555.5556, 205.0654, 321.0892, 5059.7222, 0.0000, 9761.1111],
[346.9824, 416.6787, 0.0000, 0.0000, 555.5556, 205.0654, 321.0892, 1201.2775, 0.0000, 9646.1118],
[346.9824, 416.6787, 191.0372, 0.0000, 555.5556, 205.0654, 321.0892, 232.7189, 0.0000, 9685.5858],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9813.2184],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9803.1288],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9608.0198],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9311.5727],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8883.6246],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8751.3900],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 8794.1811],
[346.9824, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 1891.0523, 0.0000, 9136.5704],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9209.3588],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9093.8294],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9387.5537],
[231.4373, 416.6787, 191.0372, 0.0000, 138.8889, 205.0654, 321.0892, 2472.2444, 0.0000, 9585.9589],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 9928.7771],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10060.3806],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10281.0021],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 321.0892, 3035.8041, 0.0000, 10095.5613],
[231.4373, 416.6787, 95.5186, 0.0000, 138.8889, 205.0654, 0.0000, 4506.3926, 0.0000, 10029.9571],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9875.6133],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9614.9463],
[231.4373, 416.6787, 95.5186, 0.0000, 474.2238, 205.0654, 0.0000, 2531.2699, 0.0000, 9824.1722],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9732.5743],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9968.3391],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 10056.1579],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9921.4925],
[115.7186, 416.6787, 95.5186, 269.8496, 474.2238, 205.0654, 0.0000, 1854.7990, 0.0000, 9894.1621],
[115.7186, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 6179.7742, 0.0000, 20067.9370],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21133.5080],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20988.8485],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20596.7429],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 19910.7730],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20776.7070],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20051.7969],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20725.3884],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20828.8795],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21647.1811],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21310.1687],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 20852.0993],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21912.3952],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21937.8282],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 1877.3934, 0.0000, 0.0000, 0.0000, 21962.4576],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 2008.8110, 0.0000, 21389.4018],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 2008.8110, 0.0000, 21625.6913],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 2008.8110, 0.0000, 20873.0389],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 2008.8110, 0.0000, 21450.9447],
[1073.8232, 416.6787, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 2008.8110, 0.0000, 22269.3892],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 21969.5329],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 21752.6924],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 22000.6088],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 23072.5655],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 23487.5201],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 22441.0460],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 23201.2700],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 23400.9485],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 22306.2008],
[1073.8232, 737.0632, 735.6442, 269.8496, 0.0000, 938.6967, 0.0000, 0.0000, 0.0000, 21989.5913],
[1073.8232, 737.0632, 735.6442, 269.8496, 1708.7766, 938.6967, 0.0000, 5215.4255, 0.0000, 31897.1636],
[0.0000, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 6421.4626, 0.0000, 31509.5059],
[0.0000, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 6421.4626, 0.0000, 31451.7888],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 32773.4592],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 32287.0318],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 32698.1938],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 34031.5183],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 35537.8336],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 36212.6487],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 36007.5294],
[978.8815, 737.0632, 735.6442, 578.0898, 1708.7766, 2145.9711, 0.0000, 0.0000, 0.0000, 34691.3797],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 33904.8810],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 34341.6098],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 35479.9505],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 34418.4455],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 34726.7182],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 34935.0407],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 34136.7505],
[978.8815, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 9162.7865, 0.0000, 33804.1575],
[195.7763, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 14025.8697, 0.0000, 33653.8970],
[195.7763, 737.0632, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 14025.8697, 0.0000, 34689.8757],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 34635.7841],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 35253.2755],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 36388.1051],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 37987.4204],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 38762.2103],
[195.7763, 1124.9219, 735.6442, 0.0000, 1708.7766, 0.0000, 0.0000, 10562.2913, 0.0000, 38574.0544],
[195.7763, 1124.9219, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 15879.4935, 0.0000, 39101.9156],
[195.7763, 1124.9219, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 15879.4935, 0.0000, 39132.5587],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 38873.2941],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39336.6594],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39565.9568],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39583.4317],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39206.8350],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39092.6551],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 39666.1834],
[195.7763, 0.0000, 735.6442, 0.0000, 0.0000, 0.0000, 1362.4361, 27747.4200, 0.0000, 38798.0749],
[0.0000, 0.0000, 1576.8381, 0.0000, 0.0000, 0.0000, 1362.4361, 23205.2077, 0.0000, 39143.5561],
[0.0000, 0.0000, 1576.8381, 0.0000, 0.0000, 0.0000, 1362.4361, 23205.2077, 0.0000, 38617.8779],
[0.0000, 0.0000, 1576.8381, 0.0000, 0.0000, 0.0000, 1362.4361, 23205.2077, 0.0000, 38156.1701]])
# PS信号，先卖后买，交割期为2天（股票）1天（现金）
self.ps_res_sb20 = np.array(
[[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 9916.667],
[0.000, 0.000, 0.000, 0.000, 555.556, 205.065, 321.089, 5059.722, 0.000, 9761.111],
[346.982, 416.679, 0.000, 0.000, 555.556, 205.065, 321.089, 1201.278, 0.000, 9646.112],
[346.982, 416.679, 191.037, 0.000, 555.556, 205.065, 321.089, 232.719, 0.000, 9685.586],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 9813.218],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 9803.129],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 9608.020],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 9311.573],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 8883.625],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 8751.390],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 8794.181],
[346.982, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 1891.052, 0.000, 9136.570],
[231.437, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 2472.244, 0.000, 9209.359],
[231.437, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 2472.244, 0.000, 9093.829],
[231.437, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 2472.244, 0.000, 9387.554],
[231.437, 416.679, 191.037, 0.000, 138.889, 205.065, 321.089, 2472.244, 0.000, 9585.959],
[231.437, 416.679, 95.519, 0.000, 138.889, 205.065, 321.089, 3035.804, 0.000, 9928.777],
[231.437, 416.679, 95.519, 0.000, 138.889, 205.065, 321.089, 3035.804, 0.000, 10060.381],
[231.437, 416.679, 95.519, 0.000, 138.889, 205.065, 321.089, 3035.804, 0.000, 10281.002],
[231.437, 416.679, 95.519, 0.000, 138.889, 205.065, 321.089, 3035.804, 0.000, 10095.561],
[231.437, 416.679, 95.519, 0.000, 138.889, 205.065, 0.000, 4506.393, 0.000, 10029.957],
[231.437, 416.679, 95.519, 0.000, 474.224, 205.065, 0.000, 2531.270, 0.000, 9875.613],
[231.437, 416.679, 95.519, 0.000, 474.224, 205.065, 0.000, 2531.270, 0.000, 9614.946],
[231.437, 416.679, 95.519, 0.000, 474.224, 205.065, 0.000, 2531.270, 0.000, 9824.172],
[115.719, 416.679, 95.519, 269.850, 474.224, 205.065, 0.000, 1854.799, 0.000, 9732.574],
[115.719, 416.679, 95.519, 269.850, 474.224, 205.065, 0.000, 1854.799, 0.000, 9968.339],
[115.719, 416.679, 95.519, 269.850, 474.224, 205.065, 0.000, 1854.799, 0.000, 10056.158],
[115.719, 416.679, 95.519, 269.850, 474.224, 205.065, 0.000, 1854.799, 0.000, 9921.492],
[115.719, 416.679, 95.519, 269.850, 474.224, 205.065, 0.000, 1854.799, 0.000, 9894.162],
[115.719, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 6179.774, 0.000, 20067.937],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21133.508],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20988.848],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20596.743],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 19910.773],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20776.707],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20051.797],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20725.388],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20828.880],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21647.181],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21310.169],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 20852.099],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21912.395],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21937.828],
[1073.823, 416.679, 735.644, 269.850, 0.000, 1877.393, 0.000, 0.000, 0.000, 21962.458],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 21389.402],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22027.453],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 20939.999],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 21250.064],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22282.781],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 21407.066],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 21160.237],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 21826.768],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22744.940],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 23466.118],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22017.882],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 23191.466],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 23099.082],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22684.767],
[1073.823, 416.679, 735.644, 269.850, 0.000, 938.697, 1339.207, 0.000, 0.000, 22842.135],
[1073.823, 416.679, 735.644, 269.850, 1785.205, 938.697, 1339.207, 5001.425, 0.000, 33323.836],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 32820.290],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 32891.231],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 34776.530],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 33909.032],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 34560.191],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 36080.455],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 38618.445],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 38497.923],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 37110.099],
[0.000, 416.679, 735.644, 944.961, 1785.205, 3582.884, 1339.207, 0.000, 0.000, 35455.247],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35646.186],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35472.302],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 36636.469],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35191.704],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 36344.224],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 36221.601],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35943.571],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35708.261],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 35589.029],
[0.000, 416.679, 735.644, 0.000, 1785.205, 0.000, 1339.207, 15126.279, 0.000, 36661.029],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 36310.591],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 36466.764],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 37784.492],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 39587.677],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 40064.019],
[0.000, 823.292, 735.644, 0.000, 1785.205, 0.000, 1339.207, 11495.220, 0.000, 39521.644],
[0.000, 823.292, 735.644, 0.000, 0.000, 0.000, 2730.576, 17142.102, 0.000, 39932.276],
[0.000, 823.292, 735.644, 0.000, 0.000, 0.000, 2730.576, 17142.102, 0.000, 39565.248],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 38943.163],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 39504.118],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 40317.800],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 40798.577],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 39962.571],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 40194.479],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 41260.400],
[0.000, 0.000, 735.644, 0.000, 0.000, 0.000, 2730.576, 25827.835, 0.000, 39966.302],
[0.000, 0.000, 1613.452, 0.000, 0.000, 0.000, 2730.576, 19700.738, 0.000, 40847.316],
[0.000, 0.000, 1613.452, 0.000, 0.000, 0.000, 2730.576, 19700.738, 0.000, 39654.544],
[0.000, 0.000, 1613.452, 0.000, 0.000, 0.000, 2730.576, 19700.738, 0.000, 38914.815]])
# PS信号，先买后卖，交割期为2天（股票）1天（现金）
self.ps_res_bs21 = np.array(
[[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 555.556, 0.000, 0.000, 7500.000, 0.000, 9916.667],
[0.000, 0.000, 0.000, 0.000, 555.556, 208.333, 326.206, 5020.833, 0.000, 9761.111],
[351.119, 421.646, 0.000, 0.000, 555.556, 208.333, 326.206, 1116.389, 0.000, 9645.961],
[351.119, 421.646, 190.256, 0.000, 555.556, 208.333, 326.206, 151.793, 0.000, 9686.841],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 9813.932],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 9803.000],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 9605.334],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 9304.001],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 8870.741],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 8738.282],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 8780.664],
[351.119, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 1810.126, 0.000, 9126.199],
[234.196, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 2398.247, 0.000, 9199.746],
[234.196, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 2398.247, 0.000, 9083.518],
[234.196, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 2398.247, 0.000, 9380.932],
[234.196, 421.646, 190.256, 0.000, 138.889, 208.333, 326.206, 2398.247, 0.000, 9581.266],
[234.196, 421.646, 95.128, 0.000, 138.889, 208.333, 326.206, 2959.501, 0.000, 9927.154],
[234.196, 421.646, 95.128, 0.000, 138.889, 208.333, 326.206, 2959.501, 0.000, 10059.283],
[234.196, 421.646, 95.128, 0.000, 138.889, 208.333, 326.206, 2959.501, 0.000, 10281.669],
[234.196, 421.646, 95.128, 0.000, 138.889, 208.333, 326.206, 2959.501, 0.000, 10093.263],
[234.196, 421.646, 95.128, 0.000, 138.889, 208.333, 0.000, 4453.525, 0.000, 10026.289],
[234.196, 421.646, 95.128, 0.000, 479.340, 208.333, 0.000, 2448.268, 0.000, 9870.523],
[234.196, 421.646, 95.128, 0.000, 479.340, 208.333, 0.000, 2448.268, 0.000, 9606.437],
[234.196, 421.646, 95.128, 0.000, 479.340, 208.333, 0.000, 2448.268, 0.000, 9818.691],
[117.098, 421.646, 95.128, 272.237, 479.340, 208.333, 0.000, 1768.219, 0.000, 9726.556],
[117.098, 421.646, 95.128, 272.237, 479.340, 208.333, 0.000, 1768.219, 0.000, 9964.547],
[117.098, 421.646, 95.128, 272.237, 479.340, 208.333, 0.000, 1768.219, 0.000, 10053.449],
[117.098, 421.646, 95.128, 272.237, 479.340, 208.333, 0.000, 1768.219, 0.000, 9917.440],
[117.098, 421.646, 95.128, 272.237, 479.340, 208.333, 0.000, 1768.219, 0.000, 9889.495],
[117.098, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 6189.948, 0.000, 20064.523],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 21124.484],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20827.077],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20396.124],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 19856.445],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20714.156],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 19971.485],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20733.948],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20938.903],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 21660.772],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 21265.298],
[708.171, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 2377.527, 0.000, 20684.378],
[1055.763, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 0.000, 0.000, 21754.770],
[1055.763, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 0.000, 0.000, 21775.215],
[1055.763, 421.646, 729.561, 272.237, 0.000, 1865.791, 0.000, 0.000, 0.000, 21801.488],
[1055.763, 421.646, 729.561, 272.237, 0.000, 932.896, 0.000, 1996.397, 0.000, 21235.427],
[1055.763, 421.646, 729.561, 272.237, 0.000, 932.896, 0.000, 1996.397, 0.000, 21466.714],
[1055.763, 421.646, 729.561, 272.237, 0.000, 932.896, 0.000, 1996.397, 0.000, 20717.431],
[1055.763, 421.646, 729.561, 272.237, 0.000, 932.896, 0.000, 1996.397, 0.000, 21294.450],
[1055.763, 421.646, 729.561, 272.237, 0.000, 932.896, 0.000, 1996.397, 0.000, 22100.247],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 21802.552],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 21593.608],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 21840.028],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 22907.725],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 23325.945],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 22291.942],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 23053.050],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 23260.084],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 22176.244],
[1055.763, 740.051, 729.561, 272.237, 0.000, 932.896, 0.000, 0.000, 0.000, 21859.297],
[1055.763, 740.051, 729.561, 272.237, 1706.748, 932.896, 0.000, 5221.105, 0.000, 31769.617],
[0.000, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 6313.462, 0.000, 31389.961],
[0.000, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 6313.462, 0.000, 31327.498],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 32647.140],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 32170.095],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 32577.742],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 33905.444],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 35414.492],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 36082.120],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 35872.293],
[962.418, 740.051, 729.561, 580.813, 1706.748, 2141.485, 0.000, 0.000, 0.000, 34558.132],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 33778.138],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 34213.578],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 35345.791],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 34288.014],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 34604.406],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 34806.850],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 34012.232],
[962.418, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 9177.053, 0.000, 33681.345],
[192.484, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 13958.345, 0.000, 33540.463],
[192.484, 740.051, 729.561, 0.000, 1706.748, 0.000, 0.000, 13958.345, 0.000, 34574.280],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 34516.781],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 35134.412],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 36266.530],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 37864.376],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 38642.633],
[192.484, 1127.221, 729.561, 0.000, 1706.748, 0.000, 0.000, 10500.917, 0.000, 38454.227],
[192.484, 1127.221, 729.561, 0.000, 0.000, 0.000, 1339.869, 15871.934, 0.000, 38982.227],
[192.484, 1127.221, 729.561, 0.000, 0.000, 0.000, 1339.869, 15871.934, 0.000, 39016.154],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 38759.803],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 39217.182],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 39439.690],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 39454.081],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 39083.341],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 38968.694],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 39532.030],
[192.484, 0.000, 729.561, 0.000, 0.000, 0.000, 1339.869, 27764.114, 0.000, 38675.507],
[0.000, 0.000, 1560.697, 0.000, 0.000, 0.000, 1339.869, 23269.751, 0.000, 39013.741],
[0.000, 0.000, 1560.697, 0.000, 0.000, 0.000, 1339.869, 23269.751, 0.000, 38497.668],
[0.000, 0.000, 1560.697, 0.000, 0.000, 0.000, 1339.869, 23269.751, 0.000, 38042.410]])
# 模拟VS信号回测结果
# VS信号，先卖后买，交割期为0
self.vs_res_sb00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 0.0000, 0.0000, 7750.0000, 0.0000, 10000.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 0.0000, 0.0000, 7750.0000, 0.0000, 9925.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 300.0000, 300.0000, 4954.0000, 0.0000, 9785.0000],
[400.0000, 400.0000, 0.0000, 0.0000, 500.0000, 300.0000, 300.0000, 878.0000, 0.0000, 9666.0000],
[400.0000, 400.0000, 173.1755, 0.0000, 500.0000, 300.0000, 300.0000, 0.0000, 0.0000, 9731.0000],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 9830.9270],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 9785.8540],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 9614.3412],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 9303.1953],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 8834.4398],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 8712.7554],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 8717.9507],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592.0000, 0.0000, 9079.1479],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598.0000, 0.0000, 9166.0276],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598.0000, 0.0000, 9023.6607],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598.0000, 0.0000, 9291.6864],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598.0000, 0.0000, 9411.6371],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9706.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9822.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9986.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9805.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 0.0000, 4993.7357, 0.0000, 9704.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9567.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9209.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9407.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9329.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9545.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9652.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9414.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9367.7357],
[0.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 9319.7357, 0.0000, 19556.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 20094.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19849.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19802.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19487.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19749.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19392.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19671.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19756.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 20111.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19867.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19775.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20314.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20310.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20253.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20044.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20495.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 19798.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20103.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20864.7357],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 20425.7357],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 20137.8405],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 20711.3567],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21470.3891],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21902.9538],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 20962.9538],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21833.5184],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21941.8169],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21278.5184],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0.0000, 0.0000, 21224.4700],
[1100.0000, 710.4842, 400.0000, 300.0000, 600.0000, 500.0000, 600.0000, 9160.0000, 0.0000, 31225.2119],
[600.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 7488.0000, 0.0000, 30894.5748],
[600.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 7488.0000, 0.0000, 30764.3811],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 31815.5828],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 31615.4215],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 32486.1394],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 33591.2847],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 34056.5428],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 34756.4863],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 34445.5428],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208.0000, 0.0000, 34433.9541],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
33870.4703],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
34014.3010],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
34680.5671],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
33890.9945],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
34004.6640],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
34127.7768],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
33421.1638],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346.0000, 0.0000,
33120.9057],
[700.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 13830.0000, 0.0000, 32613.3171],
[700.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 13830.0000, 0.0000, 33168.1558],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
33504.6236],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
33652.1318],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
34680.4867],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
35557.5191],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
35669.7128],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151.0000, 0.0000,
35211.4466],
[700.0000, 1010.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13530.0000, 0.0000, 35550.6079],
[700.0000, 1010.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13530.0000, 0.0000, 35711.6563],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 35682.6079],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 35880.8336],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 36249.8740],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 36071.6159],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 35846.1562],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 35773.3578],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 36274.9465],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695.0000, 0.0000, 35739.3094],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167.0000, 0.0000, 36135.0917],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167.0000, 0.0000, 35286.5835],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167.0000, 0.0000, 35081.3658]])
# VS信号，先买后卖，交割期为0
self.vs_res_bs00 = np.array(
[[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 0.0000, 0.0000, 7750, 0.0000, 10000],
[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 0.0000, 0.0000, 7750, 0.0000, 9925],
[0.0000, 0.0000, 0.0000, 0.0000, 500.0000, 300.0000, 300.0000, 4954, 0.0000, 9785],
[400.0000, 400.0000, 0.0000, 0.0000, 500.0000, 300.0000, 300.0000, 878, 0.0000, 9666],
[400.0000, 400.0000, 173.1755, 0.0000, 500.0000, 300.0000, 300.0000, 0, 0.0000, 9731],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 9830.927022],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 9785.854043],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 9614.341223],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 9303.195266],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 8834.439842],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 8712.755424],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 8717.95069],
[400.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 1592, 0.0000, 9079.147929],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598, 0.0000, 9166.027613],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598, 0.0000, 9023.66075],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598, 0.0000, 9291.686391],
[200.0000, 400.0000, 173.1755, 0.0000, 100.0000, 300.0000, 300.0000, 2598, 0.0000, 9411.637081],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9706.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9822.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9986.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 300.0000, 3619.7357, 0.0000, 9805.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 100.0000, 300.0000, 0.0000, 4993.7357, 0.0000, 9704.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9567.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9209.7357],
[200.0000, 400.0000, 0.0000, 0.0000, 600.0000, 300.0000, 0.0000, 2048.7357, 0.0000, 9407.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9329.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9545.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9652.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9414.7357],
[0.0000, 400.0000, 0.0000, 300.0000, 600.0000, 300.0000, 0.0000, 1779.7357, 0.0000, 9367.7357],
[0.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 9319.7357, 0.0000, 19556.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 20094.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19849.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19802.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19487.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19749.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19392.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19671.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19756.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 20111.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19867.7357],
[500.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 6094.7357, 0.0000, 19775.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20314.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20310.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 900.0000, 0.0000, 1990.7357, 0.0000, 20253.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20044.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20495.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 19798.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20103.7357],
[1100.0000, 400.0000, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 1946.7357, 0.0000, 20864.7357],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 20425.7357],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 20137.84054],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 20711.35674],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21470.38914],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21902.95375],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 20962.95375],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21833.51837],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21941.81688],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21278.51837],
[1100.0000, 710.4842, 400.0000, 300.0000, 300.0000, 500.0000, 600.0000, 0, 0.0000, 21224.46995],
[1100.0000, 710.4842, 400.0000, 300.0000, 600.0000, 500.0000, 600.0000, 9160, 0.0000, 31225.21185],
[600.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 7488, 0.0000, 30894.57479],
[600.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 7488, 0.0000, 30764.38113],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 31815.5828],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 31615.42154],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 32486.13941],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 33591.28466],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 34056.54276],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 34756.48633],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 34445.54276],
[1100.0000, 710.4842, 400.0000, 800.0000, 600.0000, 700.0000, 600.0000, 4208, 0.0000, 34433.95412],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 33870.47032],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 34014.30104],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 34680.56715],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 33890.99452],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 34004.66398],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 34127.77683],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 33421.1638],
[1100.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11346, 0.0000, 33120.9057],
[700.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 13830, 0.0000, 32613.31706],
[700.0000, 710.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 13830, 0.0000, 33168.15579],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 33504.62357],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 33652.13176],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 34680.4867],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 35557.51909],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 35669.71276],
[700.0000, 1010.4842, 400.0000, 100.0000, 600.0000, 100.0000, 600.0000, 11151, 0.0000, 35211.44665],
[700.0000, 1010.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13530, 0.0000, 35550.60792],
[700.0000, 1010.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13530, 0.0000, 35711.65633],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 35682.60792],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 35880.83362],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 36249.87403],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 36071.61593],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 35846.15615],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 35773.35783],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 36274.94647],
[700.0000, 710.4842, 400.0000, 100.0000, 0.0000, 100.0000, 900.0000, 16695, 0.0000, 35739.30941],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167, 0.0000, 36135.09172],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167, 0.0000, 35286.58353],
[500.0000, 710.4842, 1100.0000, 100.0000, 0.0000, 100.0000, 900.0000, 13167, 0.0000, 35081.36584]])
# VS信号，先卖后买，交割期为2天（股票）1天（现金）
self.vs_res_sb20 = np.array(
[[0.000, 0.000, 0.000, 0.000, 500.000, 0.000, 0.000, 7750.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 500.000, 0.000, 0.000, 7750.000, 0.000, 9925.000],
[0.000, 0.000, 0.000, 0.000, 500.000, 300.000, 300.000, 4954.000, 0.000, 9785.000],
[400.000, 400.000, 0.000, 0.000, 500.000, 300.000, 300.000, 878.000, 0.000, 9666.000],
[400.000, 400.000, 173.176, 0.000, 500.000, 300.000, 300.000, 0.000, 0.000, 9731.000],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9830.927],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9785.854],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9614.341],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9303.195],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8834.440],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8712.755],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8717.951],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9079.148],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9166.028],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9023.661],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9291.686],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9411.637],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9706.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9822.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9986.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9805.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 0.000, 4993.736, 0.000, 9704.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9567.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9209.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9407.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9329.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9545.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9652.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9414.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9367.736],
[0.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 9319.736, 0.000, 19556.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 20094.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19849.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19802.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19487.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19749.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19392.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19671.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19756.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 20111.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19867.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19775.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20314.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20310.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20253.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20044.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20495.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 19798.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20103.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20864.736],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20425.736],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20137.841],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20711.357],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21470.389],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21902.954],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20962.954],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21833.518],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21941.817],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21278.518],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21224.470],
[1100.000, 710.484, 400.000, 300.000, 600.000, 500.000, 600.000, 9160.000, 0.000, 31225.212],
[600.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 7488.000, 0.000, 30894.575],
[600.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 7488.000, 0.000, 30764.381],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 31815.583],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 31615.422],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 32486.139],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 33591.285],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34056.543],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34756.486],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34445.543],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34433.954],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33870.470],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34014.301],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34680.567],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33890.995],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34004.664],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34127.777],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33421.164],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33120.906],
[700.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 13830.000, 0.000, 32613.317],
[700.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 13830.000, 0.000, 33168.156],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 33504.624],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 33652.132],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 34680.487],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35557.519],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35669.713],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35211.447],
[700.000, 1010.484, 400.000, 100.000, 0.000, 100.000, 900.000, 13530.000, 0.000, 35550.608],
[700.000, 1010.484, 400.000, 100.000, 0.000, 100.000, 900.000, 13530.000, 0.000, 35711.656],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35682.608],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35880.834],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36249.874],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36071.616],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35846.156],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35773.358],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36274.946],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35739.309],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 36135.092],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 35286.584],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 35081.366]])
# VS信号，先买后卖，交割期为2天（股票）1天（现金）
self.vs_res_bs21 = np.array(
[[0.000, 0.000, 0.000, 0.000, 500.000, 0.000, 0.000, 7750.000, 0.000, 10000.000],
[0.000, 0.000, 0.000, 0.000, 500.000, 0.000, 0.000, 7750.000, 0.000, 9925.000],
[0.000, 0.000, 0.000, 0.000, 500.000, 300.000, 300.000, 4954.000, 0.000, 9785.000],
[400.000, 400.000, 0.000, 0.000, 500.000, 300.000, 300.000, 878.000, 0.000, 9666.000],
[400.000, 400.000, 173.176, 0.000, 500.000, 300.000, 300.000, 0.000, 0.000, 9731.000],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9830.927],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9785.854],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9614.341],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9303.195],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8834.440],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8712.755],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 8717.951],
[400.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 1592.000, 0.000, 9079.148],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9166.028],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9023.661],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9291.686],
[200.000, 400.000, 173.176, 0.000, 100.000, 300.000, 300.000, 2598.000, 0.000, 9411.637],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9706.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9822.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9986.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 300.000, 3619.736, 0.000, 9805.736],
[200.000, 400.000, 0.000, 0.000, 100.000, 300.000, 0.000, 4993.736, 0.000, 9704.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9567.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9209.736],
[200.000, 400.000, 0.000, 0.000, 600.000, 300.000, 0.000, 2048.736, 0.000, 9407.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9329.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9545.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9652.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9414.736],
[0.000, 400.000, 0.000, 300.000, 600.000, 300.000, 0.000, 1779.736, 0.000, 9367.736],
[0.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 9319.736, 0.000, 19556.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 20094.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19849.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19802.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19487.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19749.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19392.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19671.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19756.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 20111.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19867.736],
[500.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 6094.736, 0.000, 19775.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20314.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20310.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 900.000, 0.000, 1990.736, 0.000, 20253.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20044.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20495.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 19798.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20103.736],
[1100.000, 400.000, 400.000, 300.000, 300.000, 500.000, 600.000, 1946.736, 0.000, 20864.736],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20425.736],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20137.841],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20711.357],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21470.389],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21902.954],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 20962.954],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21833.518],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21941.817],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21278.518],
[1100.000, 710.484, 400.000, 300.000, 300.000, 500.000, 600.000, 0.000, 0.000, 21224.470],
[1100.000, 710.484, 400.000, 300.000, 600.000, 500.000, 600.000, 9160.000, 0.000, 31225.212],
[600.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 7488.000, 0.000, 30894.575],
[600.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 7488.000, 0.000, 30764.381],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 31815.583],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 31615.422],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 32486.139],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 33591.285],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34056.543],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34756.486],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34445.543],
[1100.000, 710.484, 400.000, 800.000, 600.000, 700.000, 600.000, 4208.000, 0.000, 34433.954],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33870.470],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34014.301],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34680.567],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33890.995],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34004.664],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 34127.777],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33421.164],
[1100.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11346.000, 0.000, 33120.906],
[700.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 13830.000, 0.000, 32613.317],
[700.000, 710.484, 400.000, 100.000, 600.000, 100.000, 600.000, 13830.000, 0.000, 33168.156],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 33504.624],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 33652.132],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 34680.487],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35557.519],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35669.713],
[700.000, 1010.484, 400.000, 100.000, 600.000, 100.000, 600.000, 11151.000, 0.000, 35211.447],
[700.000, 1010.484, 400.000, 100.000, 0.000, 100.000, 900.000, 13530.000, 0.000, 35550.608],
[700.000, 1010.484, 400.000, 100.000, 0.000, 100.000, 900.000, 13530.000, 0.000, 35711.656],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35682.608],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35880.834],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36249.874],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36071.616],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35846.156],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35773.358],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 36274.946],
[700.000, 710.484, 400.000, 100.000, 0.000, 100.000, 900.000, 16695.000, 0.000, 35739.309],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 36135.092],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 35286.584],
[500.000, 710.484, 1100.000, 100.000, 0.000, 100.000, 900.000, 13167.000, 0.000, 35081.366]])
# Multi信号处理结果，先卖后买，使用卖出的现金买进，交割期为2天（股票）0天（现金）
self.multi_res = np.array(
[[0.0000, 357.2545, 0.0000, 6506.9627, 0.0000, 9965.1867],
[0.0000, 357.2545, 0.0000, 6506.9627, 0.0000, 10033.0650],
[0.0000, 178.6273, 0.0000, 8273.5864, 0.0000, 10034.8513],
[0.0000, 178.6273, 0.0000, 8273.5864, 0.0000, 10036.6376],
[150.3516, 178.6273, 0.0000, 6771.5740, 0.0000, 10019.3404],
[150.3516, 178.6273, 0.0000, 6771.5740, 0.0000, 10027.7062],
[150.3516, 178.6273, 0.0000, 6771.5740, 0.0000, 10030.1477],
[150.3516, 178.6273, 0.0000, 6771.5740, 0.0000, 10005.1399],
[150.3516, 178.6273, 0.0000, 6771.5740, 0.0000, 10002.5054],
[150.3516, 489.4532, 0.0000, 3765.8877, 0.0000, 9967.3860],
[75.1758, 391.5625, 0.0000, 5490.1377, 0.0000, 10044.4059],
[75.1758, 391.5625, 0.0000, 5490.1377, 0.0000, 10078.1430],
[75.1758, 391.5625, 846.3525, 392.3025, 0.0000, 10138.2709],
[75.1758, 391.5625, 846.3525, 392.3025, 0.0000, 10050.4768],
[75.1758, 391.5625, 846.3525, 392.3025, 0.0000, 10300.0711],
[75.1758, 391.5625, 846.3525, 392.3025, 0.0000, 10392.6970],
[75.1758, 391.5625, 169.2705, 4644.3773, 0.0000, 10400.5282],
[75.1758, 391.5625, 169.2705, 4644.3773, 0.0000, 10408.9220],
[75.1758, 0.0000, 169.2705, 8653.9776, 0.0000, 10376.5914],
[75.1758, 0.0000, 169.2705, 8653.9776, 0.0000, 10346.8794],
[75.1758, 0.0000, 169.2705, 8653.9776, 0.0000, 10364.7474],
[75.1758, 381.1856, 645.5014, 2459.1665, 0.0000, 10302.4570],
[18.7939, 381.1856, 645.5014, 3024.6764, 0.0000, 10747.4929],
[18.7939, 381.1856, 96.8252, 6492.3097, 0.0000, 11150.9107],
[18.7939, 381.1856, 96.8252, 6492.3097, 0.0000, 11125.2946],
[18.7939, 114.3557, 96.8252, 9227.3166, 0.0000, 11191.9956],
[18.7939, 114.3557, 96.8252, 9227.3166, 0.0000, 11145.7486],
[18.7939, 114.3557, 96.8252, 9227.3166, 0.0000, 11090.0768],
[132.5972, 114.3557, 864.3802, 4223.9548, 0.0000, 11113.8733],
[132.5972, 114.3557, 864.3802, 4223.9548, 0.0000, 11456.3281],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 21983.7333],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 22120.6165],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 21654.5327],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 21429.6550],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 21912.5643],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 22516.3100],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 23169.0777],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 23390.8080],
[132.5972, 114.3557, 864.3802, 14223.9548, 0.0000, 23743.3742],
[132.5972, 559.9112, 864.3802, 9367.3999, 0.0000, 23210.7311],
[132.5972, 559.9112, 864.3802, 9367.3999, 0.0000, 24290.4375],
[132.5972, 559.9112, 864.3802, 9367.3999, 0.0000, 24335.3279],
[132.5972, 559.9112, 864.3802, 9367.3999, 0.0000, 18317.3553],
[132.5972, 559.9112, 864.3802, 9367.3999, 0.0000, 18023.4660],
[259.4270, 559.9112, 0.0000, 15820.6915, 0.0000, 24390.0527],
[259.4270, 559.9112, 0.0000, 15820.6915, 0.0000, 24389.6421],
[259.4270, 559.9112, 0.0000, 15820.6915, 0.0000, 24483.5953],
[0.0000, 559.9112, 0.0000, 18321.5674, 0.0000, 24486.1895],
[0.0000, 0.0000, 0.0000, 24805.3389, 0.0000, 24805.3389],
[0.0000, 0.0000, 0.0000, 24805.3389, 0.0000, 24805.3389]])
def test_loop_step_pt_sb00(self):
""" test loop step PT-signal, sell first"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.pt_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7500)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 555.5555556, 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_sb00[2][7],
own_amounts=self.pt_res_sb00[2][0:7],
available_cash=self.pt_res_sb00[2][7],
available_amounts=self.pt_res_sb00[2][0:7],
op=self.pt_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_sb00[2][7] + c_g + c_s
amounts = self.pt_res_sb00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_sb00[30][7],
own_amounts=self.pt_res_sb00[30][0:7],
available_cash=self.pt_res_sb00[30][7],
available_amounts=self.pt_res_sb00[30][0:7],
op=self.pt_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_sb00[30][7] + c_g + c_s
amounts = self.pt_res_sb00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_sb00[59][7] + 10000,
own_amounts=self.pt_res_sb00[59][0:7],
available_cash=self.pt_res_sb00[59][7] + 10000,
available_amounts=self.pt_res_sb00[59][0:7],
op=self.pt_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_sb00[59][7] + c_g + c_s + 10000
amounts = self.pt_res_sb00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.pt_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_sb00[95][7],
own_amounts=self.pt_res_sb00[95][0:7],
available_cash=self.pt_res_sb00[95][7],
available_amounts=self.pt_res_sb00[95][0:7],
op=self.pt_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_sb00[96][7] + c_g + c_s
amounts = self.pt_res_sb00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.pt_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_sb00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_sb00[97][0:7]))
def test_loop_step_pt_bs00(self):
""" test loop step PT-signal, buy first"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.pt_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7500)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 555.5555556, 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_bs00[2][7],
own_amounts=self.pt_res_bs00[2][0:7],
available_cash=self.pt_res_bs00[2][7],
available_amounts=self.pt_res_bs00[2][0:7],
op=self.pt_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_bs00[2][7] + c_g + c_s
amounts = self.pt_res_bs00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_bs00[30][7],
own_amounts=self.pt_res_bs00[30][0:7],
available_cash=self.pt_res_bs00[30][7],
available_amounts=self.pt_res_bs00[30][0:7],
op=self.pt_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_bs00[30][7] + c_g + c_s
amounts = self.pt_res_bs00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_bs00[59][7] + 10000,
own_amounts=self.pt_res_bs00[59][0:7],
available_cash=self.pt_res_bs00[59][7] + 10000,
available_amounts=self.pt_res_bs00[59][0:7],
op=self.pt_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_bs00[59][7] + c_g + c_s + 10000
amounts = self.pt_res_bs00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.pt_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=self.pt_res_bs00[95][7],
own_amounts=self.pt_res_bs00[95][0:7],
available_cash=self.pt_res_bs00[95][7],
available_amounts=self.pt_res_bs00[95][0:7],
op=self.pt_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.pt_res_bs00[96][7] + c_g + c_s
amounts = self.pt_res_bs00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=0,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.pt_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.pt_res_bs00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.pt_res_bs00[97][0:7]))
def test_loop_step_ps_sb00(self):
""" test loop step PS-signal, sell first"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.ps_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7500)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 555.5555556, 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_sb00[2][7],
own_amounts=self.ps_res_sb00[2][0:7],
available_cash=self.ps_res_sb00[2][7],
available_amounts=self.ps_res_sb00[2][0:7],
op=self.ps_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_sb00[2][7] + c_g + c_s
amounts = self.ps_res_sb00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_sb00[30][7],
own_amounts=self.ps_res_sb00[30][0:7],
available_cash=self.ps_res_sb00[30][7],
available_amounts=self.ps_res_sb00[30][0:7],
op=self.ps_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_sb00[30][7] + c_g + c_s
amounts = self.ps_res_sb00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_sb00[59][7] + 10000,
own_amounts=self.ps_res_sb00[59][0:7],
available_cash=self.ps_res_sb00[59][7] + 10000,
available_amounts=self.ps_res_sb00[59][0:7],
op=self.ps_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_sb00[59][7] + c_g + c_s + 10000
amounts = self.ps_res_sb00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.ps_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_sb00[95][7],
own_amounts=self.ps_res_sb00[95][0:7],
available_cash=self.ps_res_sb00[95][7],
available_amounts=self.ps_res_sb00[95][0:7],
op=self.ps_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_sb00[96][7] + c_g + c_s
amounts = self.ps_res_sb00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.ps_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_sb00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_sb00[97][0:7]))
def test_loop_step_ps_bs00(self):
""" test loop step PS-signal, buy first"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.ps_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7500)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 555.5555556, 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_bs00[2][7],
own_amounts=self.ps_res_sb00[2][0:7],
available_cash=self.ps_res_bs00[2][7],
available_amounts=self.ps_res_bs00[2][0:7],
op=self.ps_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_bs00[2][7] + c_g + c_s
amounts = self.ps_res_bs00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_bs00[30][7],
own_amounts=self.ps_res_sb00[30][0:7],
available_cash=self.ps_res_bs00[30][7],
available_amounts=self.ps_res_bs00[30][0:7],
op=self.ps_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_bs00[30][7] + c_g + c_s
amounts = self.ps_res_bs00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_bs00[59][7] + 10000,
own_amounts=self.ps_res_bs00[59][0:7],
available_cash=self.ps_res_bs00[59][7] + 10000,
available_amounts=self.ps_res_bs00[59][0:7],
op=self.ps_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_bs00[59][7] + c_g + c_s + 10000
amounts = self.ps_res_bs00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.ps_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=self.ps_res_bs00[95][7],
own_amounts=self.ps_res_bs00[95][0:7],
available_cash=self.ps_res_bs00[95][7],
available_amounts=self.ps_res_bs00[95][0:7],
op=self.ps_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.ps_res_bs00[96][7] + c_g + c_s
amounts = self.ps_res_bs00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=1,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.ps_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.ps_res_bs00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.ps_res_bs00[97][0:7]))
def test_loop_step_vs_sb00(self):
"""test loop step of Volume Signal type of signals"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.vs_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7750)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 500., 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_sb00[2][7],
own_amounts=self.vs_res_sb00[2][0:7],
available_cash=self.vs_res_sb00[2][7],
available_amounts=self.vs_res_sb00[2][0:7],
op=self.vs_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_sb00[2][7] + c_g + c_s
amounts = self.vs_res_sb00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_sb00[30][7],
own_amounts=self.vs_res_sb00[30][0:7],
available_cash=self.vs_res_sb00[30][7],
available_amounts=self.vs_res_sb00[30][0:7],
op=self.vs_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_sb00[30][7] + c_g + c_s
amounts = self.vs_res_sb00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_sb00[59][7] + 10000,
own_amounts=self.vs_res_sb00[59][0:7],
available_cash=self.vs_res_sb00[59][7] + 10000,
available_amounts=self.vs_res_sb00[59][0:7],
op=self.vs_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_sb00[59][7] + c_g + c_s + 10000
amounts = self.vs_res_sb00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.vs_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_sb00[95][7],
own_amounts=self.vs_res_sb00[95][0:7],
available_cash=self.vs_res_sb00[95][7],
available_amounts=self.vs_res_sb00[95][0:7],
op=self.vs_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_sb00[96][7] + c_g + c_s
amounts = self.vs_res_sb00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.vs_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=True,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_sb00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_sb00[97][0:7]))
def test_loop_step_vs_bs00(self):
"""test loop step of Volume Signal type of signals"""
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=10000,
own_amounts=np.zeros(7, dtype='float'),
available_cash=10000,
available_amounts=np.zeros(7, dtype='float'),
op=self.vs_signals[0],
prices=self.prices[0],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 1 result in complete looping: \n'
f'cash_change: +{c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = 10000 + c_g + c_s
amounts = np.zeros(7, dtype='float') + a_p + a_s
self.assertAlmostEqual(cash, 7750)
self.assertTrue(np.allclose(amounts, np.array([0, 0, 0, 0, 500., 0, 0])))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_bs00[2][7],
own_amounts=self.vs_res_bs00[2][0:7],
available_cash=self.vs_res_bs00[2][7],
available_amounts=self.vs_res_bs00[2][0:7],
op=self.vs_signals[3],
prices=self.prices[3],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 4 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_bs00[2][7] + c_g + c_s
amounts = self.vs_res_bs00[2][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[3][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[3][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_bs00[30][7],
own_amounts=self.vs_res_bs00[30][0:7],
available_cash=self.vs_res_bs00[30][7],
available_amounts=self.vs_res_bs00[30][0:7],
op=self.vs_signals[31],
prices=self.prices[31],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 32 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_bs00[30][7] + c_g + c_s
amounts = self.vs_res_bs00[30][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[31][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[31][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_bs00[59][7] + 10000,
own_amounts=self.vs_res_bs00[59][0:7],
available_cash=self.vs_res_bs00[59][7] + 10000,
available_amounts=self.vs_res_bs00[59][0:7],
op=self.vs_signals[60],
prices=self.prices[60],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 61 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_bs00[59][7] + c_g + c_s + 10000
amounts = self.vs_res_bs00[59][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[60][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[60][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.vs_signals[61],
prices=self.prices[61],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 62 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[61][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[61][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=self.vs_res_bs00[95][7],
own_amounts=self.vs_res_bs00[95][0:7],
available_cash=self.vs_res_bs00[95][7],
available_amounts=self.vs_res_bs00[95][0:7],
op=self.vs_signals[96],
prices=self.prices[96],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 97 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = self.vs_res_bs00[96][7] + c_g + c_s
amounts = self.vs_res_bs00[96][0:7] + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[96][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[96][0:7]))
c_g, c_s, a_p, a_s, fee = qt.core._loop_step(signal_type=2,
own_cash=cash,
own_amounts=amounts,
available_cash=cash,
available_amounts=amounts,
op=self.vs_signals[97],
prices=self.prices[97],
rate=self.rate,
pt_buy_threshold=0.1,
pt_sell_threshold=0.1,
maximize_cash_usage=False,
allow_sell_short=False,
moq_buy=0,
moq_sell=0,
print_log=True)
print(f'day 98 result in complete looping: \n'
f'cash_change: + {c_g:.2f} / {c_s:.2f}\n'
f'amount_changed: \npurchased: {np.round(a_p, 2)}\nsold:{np.round(a_s, 2)}\n'
f'----------------------------------\n')
cash = cash + c_g + c_s
amounts = amounts + a_p + a_s
self.assertAlmostEqual(cash, self.vs_res_bs00[97][7], 2)
self.assertTrue(np.allclose(amounts, self.vs_res_bs00[97][0:7]))
def test_loop_pt(self):
""" Test looping of PT proportion target signals, with
stock delivery delay = 0 days
cash delivery delay = 0 day
buy-sell sequence = sell first
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 0 days \n'
'cash delivery delay = 0 day \n'
'buy-sell sequence = sell first')
res = apply_loop(op_type=0,
op_list=self.pt_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
# print(f'in test_loop:\nresult of loop test is \n{res}')
self.assertTrue(np.allclose(res, self.pt_res_bs00, 2))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(op_type=0,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
# print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_pt_with_delay(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 1 day
use_sell_cash = False
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize_cash = False (buy and sell at the same time)')
res = apply_loop(
op_type=0,
op_list=self.pt_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
cash_delivery_period=1,
stock_delivery_period=2,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.pt_res_bs21[i]))
print()
self.assertTrue(np.allclose(res, self.pt_res_bs21, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_pt_with_delay_use_cash(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 0 day
use sell cash = True (sell stock first to use cash when possible
(not possible when cash delivery period != 0))
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize cash usage = True \n'
'but not applicable because cash delivery period == 1')
res = apply_loop(
op_type=0,
op_list=self.pt_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
cash_delivery_period=0,
stock_delivery_period=2,
inflation_rate=0,
max_cash_usage=True,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.pt_res_sb20[i]))
print()
self.assertTrue(np.allclose(res, self.pt_res_sb20, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
cash_delivery_period=1,
stock_delivery_period=2,
inflation_rate=0,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_ps(self):
""" Test looping of PS Proportion Signal type of signals
"""
res = apply_loop(op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
self.assertTrue(np.allclose(res, self.ps_res_bs00, 5))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_ps_with_delay(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 1 day
use_sell_cash = False
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize_cash = False (buy and sell at the same time)')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
cash_delivery_period=1,
stock_delivery_period=2,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.ps_res_bs21[i]))
print()
self.assertTrue(np.allclose(res, self.ps_res_bs21, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_ps_with_delay_use_cash(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 0 day
use sell cash = True (sell stock first to use cash when possible
(not possible when cash delivery period != 0))
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize cash usage = True \n'
'but not applicable because cash delivery period == 1')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
cash_delivery_period=0,
stock_delivery_period=2,
inflation_rate=0,
max_cash_usage=True,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.ps_res_sb20[i]))
print()
self.assertTrue(np.allclose(res, self.ps_res_sb20, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.ps_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
cash_delivery_period=1,
stock_delivery_period=2,
inflation_rate=0,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_vs(self):
""" Test looping of VS Volume Signal type of signals
"""
res = apply_loop(op_type=2,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
self.assertTrue(np.allclose(res, self.vs_res_bs00, 5))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(op_type=2,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_vs_with_delay(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 1 day
use_sell_cash = False
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize_cash = False (buy and sell at the same time)')
res = apply_loop(
op_type=2,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
inflation_rate=0,
cash_delivery_period=1,
stock_delivery_period=2,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.vs_res_bs21[i]))
print()
self.assertTrue(np.allclose(res, self.vs_res_bs21, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.vs_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.vs_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_vs_with_delay_use_cash(self):
""" Test looping of PT proportion target signals, with:
stock delivery delay = 2 days
cash delivery delay = 0 day
use sell cash = True (sell stock first to use cash when possible
(not possible when cash delivery period != 0))
"""
print('Test looping of PT proportion target signals, with:\n'
'stock delivery delay = 2 days \n'
'cash delivery delay = 1 day \n'
'maximize cash usage = True \n'
'but not applicable because cash delivery period == 1')
res = apply_loop(
op_type=2,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
cash_delivery_period=0,
stock_delivery_period=2,
inflation_rate=0,
max_cash_usage=True,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.vs_res_sb20[i]))
print()
self.assertTrue(np.allclose(res, self.vs_res_sb20, 3))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.vs_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.vs_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(
op_type=1,
op_list=self.vs_signal_hp,
history_list=self.history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
cash_delivery_period=1,
stock_delivery_period=2,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
def test_loop_multiple_signal(self):
""" Test looping of PS Proportion Signal type of signals
"""
res = apply_loop(op_type=1,
op_list=self.multi_signal_hp,
history_list=self.multi_history_list,
cash_plan=self.cash,
cost_rate=self.rate,
moq_buy=0,
moq_sell=0,
cash_delivery_period=0,
stock_delivery_period=2,
max_cash_usage=True,
inflation_rate=0,
print_log=False)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}\n'
f'result comparison line by line:')
for i in range(len(res)):
print(np.around(res.values[i]))
print(np.around(self.multi_res[i]))
print()
self.assertTrue(np.allclose(res, self.multi_res, 5))
print(f'test assertion errors in apply_loop: detect moqs that are not compatible')
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
0, 1,
0,
False)
self.assertRaises(AssertionError,
apply_loop,
0,
self.ps_signal_hp,
self.history_list,
self.cash,
self.rate,
1, 5,
0,
False)
print(f'test loop results with moq equal to 100')
res = apply_loop(op_type=1,
op_list=self.multi_signal_hp,
history_list=self.multi_history_list,
cash_plan=self.cash,
cost_rate=self.rate2,
moq_buy=100,
moq_sell=1,
cash_delivery_period=0,
stock_delivery_period=2,
max_cash_usage=False,
inflation_rate=0,
print_log=True)
self.assertIsInstance(res, pd.DataFrame)
print(f'in test_loop:\nresult of loop test is \n{res}')
class TestStrategy(unittest.TestCase):
""" test all properties and methods of strategy base class"""
def setUp(self) -> None:
pass
class TestLSStrategy(RollingTiming):
"""用于test测试的简单多空蒙板生成策略。基于RollingTiming滚动择时方法生成
该策略有两个参数，N与Price
N用于计算OHLC价格平均值的N日简单移动平均，判断，当移动平均值大于等于Price时，状态为看多，否则为看空
"""
def __init__(self):
super().__init__(stg_name='test_LS',
stg_text='test long/short strategy',
par_count=2,
par_types='discr, conti',
par_bounds_or_enums=([1, 5], [2, 10]),
data_types='close, open, high, low',
data_freq='d',
window_length=5)
pass
def _realize(self, hist_data: np.ndarray, params: tuple):
n, price = params
h = hist_data.T
avg = (h[0] + h[1] + h[2] + h[3]) / 4
ma = sma(avg, n)
if ma[-1] < price:
return 0
else:
return 1
class TestSelStrategy(SimpleSelecting):
"""用于Test测试的简单选股策略，基于Selecting策略生成
策略没有参数，选股周期为5D
在每个选股周期内，从股票池的三只股票中选出今日变化率 = (今收-昨收)/平均股价（OHLC平均股价）最高的两支，放入中选池，否则落选。
选股比例为平均分配
"""
def __init__(self):
super().__init__(stg_name='test_SEL',
stg_text='test portfolio selection strategy',
par_count=0,
par_types='',
par_bounds_or_enums=(),
data_types='high, low, close',
data_freq='d',
sample_freq='10d',
window_length=5)
pass
def _realize(self, hist_data: np.ndarray, params: tuple):
avg = np.nanmean(hist_data, axis=(1, 2))
dif = (hist_data[:, :, 2] - np.roll(hist_data[:, :, 2], 1, 1))
dif_no_nan = np.array([arr[~np.isnan(arr)][-1] for arr in dif])
difper = dif_no_nan / avg
large2 = difper.argsort()[1:]
chosen = np.zeros_like(avg)
chosen[large2] = 0.5
return chosen
class TestSelStrategyDiffTime(SimpleSelecting):
"""用于Test测试的简单选股策略，基于Selecting策略生成
策略没有参数，选股周期为5D
在每个选股周期内，从股票池的三只股票中选出今日变化率 = (今收-昨收)/平均股价（OHLC平均股价）最高的两支，放入中选池，否则落选。
选股比例为平均分配
"""
# TODO: This strategy is not working, find out why and improve
def __init__(self):
super().__init__(stg_name='test_SEL',
stg_text='test portfolio selection strategy',
par_count=0,
par_types='',
par_bounds_or_enums=(),
data_types='close, low, open',
data_freq='d',
sample_freq='w',
window_length=2)
pass
def _realize(self, hist_data: np.ndarray, params: tuple):
avg = hist_data.mean(axis=1).squeeze()
difper = (hist_data[:, :, 0] - np.roll(hist_data[:, :, 0], 1))[:, -1] / avg
large2 = difper.argsort()[0:2]
chosen = np.zeros_like(avg)
chosen[large2] = 0.5
return chosen
class TestSigStrategy(SimpleTiming):
"""用于Test测试的简单信号生成策略，基于SimpleTiming策略生成
策略有三个参数，第一个参数为ratio，另外两个参数为price1以及price2
ratio是k线形状比例的阈值，定义为abs((C-O)/(H-L))。当这个比值小于ratio阈值时，判断该K线为十字交叉（其实还有丁字等多种情形，但这里做了
简化处理。
信号生成的规则如下：
1，当某个K线出现十字交叉，且昨收与今收之差大于price1时，买入信号
2，当某个K线出现十字交叉，且昨收与今收之差小于price2时，卖出信号
"""
def __init__(self):
super().__init__(stg_name='test_SIG',
stg_text='test signal creation strategy',
par_count=3,
par_types='conti, conti, conti',
par_bounds_or_enums=([2, 10], [0, 3], [0, 3]),
data_types='close, open, high, low',
window_length=2)
pass
def _realize(self, hist_data: np.ndarray, params: tuple):
r, price1, price2 = params
h = hist_data.T
ratio = np.abs((h[0] - h[1]) / (h[3] - h[2]))
diff = h[0] - np.roll(h[0], 1)
sig = np.where((ratio < r) & (diff > price1),
1,
np.where((ratio < r) & (diff < price2), -1, 0))
return sig
class MyStg(qt.RollingTiming):
"""自定义双均线择时策略策略"""
def __init__(self):
"""这个均线择时策略只有三个参数：
- SMA 慢速均线，所选择的股票
- FMA 快速均线
- M 边界值
策略的其他说明
"""
"""
必须初始化的关键策略参数清单：
"""
super().__init__(
pars=(20, 100, 0.01),
par_count=3,
par_types=['discr', 'discr', 'conti'],
par_bounds_or_enums=[(10, 250), (10, 250), (0.0, 0.5)],
stg_name='CUSTOM ROLLING TIMING STRATEGY',
stg_text='Customized Rolling Timing Strategy for Testing',
data_types='close',
window_length=100,
)
print(f'=====================\n====================\n'
f'custom strategy initialized, \npars: {self.pars}\npar_count:{self.par_count}\npar_types:'
f'{self.par_types}\n'
f'{self.info()}')
# 策略的具体实现代码写在策略的_realize()函数中
# 这个函数固定接受两个参数： hist_price代表特定组合的历史数据， params代表具体的策略参数
def _realize(self, hist_price, params):
"""策略的具体实现代码：
s：短均线计算日期；l：长均线计算日期；m：均线边界宽度；hesitate：均线跨越类型"""
f, s, m = params
# 临时处理措施，在策略实现层对传入的数据切片，后续应该在策略实现层以外事先对数据切片，保证传入的数据符合data_types参数即可
h = hist_price.T
# 计算长短均线的当前值
s_ma = qt.sma(h[0], s)[-1]
f_ma = qt.sma(h[0], f)[-1]
# 计算慢均线的停止边界，当快均线在停止边界范围内时，平仓，不发出买卖信号
s_ma_u = s_ma * (1 + m)
s_ma_l = s_ma * (1 - m)
# 根据观望模式在不同的点位产生Long/short/empty标记
if f_ma > s_ma_u: # 当快均线在慢均线停止范围以上时，持有多头头寸
return 1
elif s_ma_l < f_ma < s_ma_u: # 当均线在停止边界以内时，平仓
return 0
else: # f_ma < s_ma_l 当快均线在慢均线停止范围以下时，持有空头头寸
return -1
class TestOperator(unittest.TestCase):
"""全面测试Operator对象的所有功能。包括：
1, Strategy 参数的设置
2, 历史数据的获取与分配提取
3, 策略优化参数的批量设置和优化空间的获取
4, 策略输出值的正确性验证
5, 策略结果的混合结果确认
"""
def setUp(self):
"""prepare data for Operator test"""
print('start testing HistoryPanel object\n')
# build up test data: a 4-type, 3-share, 50-day matrix of prices that contains nan values in some days
# for some share_pool
# for share1:
data_rows = 50
share1_close = [10.04, 10, 10, 9.99, 9.97, 9.99, 10.03, 10.03, 10.06, 10.06, 10.11,
10.09, 10.07, 10.06, 10.09, 10.03, 10.03, 10.06, 10.08, 10, 9.99,
10.03, 10.03, 10.06, 10.03, 9.97, 9.94, 9.83, 9.77, 9.84, 9.91, 9.93,
9.96, 9.91, 9.91, 9.88, 9.91, 9.64, 9.56, 9.57, 9.55, 9.57, 9.61, 9.61,
9.55, 9.57, 9.63, 9.64, 9.65, 9.62]
share1_open = [10.02, 10, 9.98, 9.97, 9.99, 10.01, 10.04, 10.06, 10.06, 10.11,
10.11, 10.07, 10.06, 10.09, 10.03, 10.02, 10.06, 10.08, 9.99, 10,
10.03, 10.02, 10.06, 10.03, 9.97, 9.94, 9.83, 9.78, 9.77, 9.91, 9.92,
9.97, 9.91, 9.9, 9.88, 9.91, 9.63, 9.64, 9.57, 9.55, 9.58, 9.61, 9.62,
9.55, 9.57, 9.61, 9.63, 9.64, 9.61, 9.56]
share1_high = [10.07, 10, 10, 10, 10.03, 10.03, 10.04, 10.09, 10.1, 10.14, 10.11, 10.1,
10.09, 10.09, 10.1, 10.05, 10.07, 10.09, 10.1, 10, 10.04, 10.04, 10.06,
10.09, 10.05, 9.97, 9.96, 9.86, 9.77, 9.92, 9.94, 9.97, 9.97, 9.92, 9.92,
9.92, 9.93, 9.64, 9.58, 9.6, 9.58, 9.62, 9.62, 9.64, 9.59, 9.62, 9.63,
9.7, 9.66, 9.64]
share1_low = [9.99, 10, 9.97, 9.97, 9.97, 9.98, 9.99, 10.03, 10.03, 10.04, 10.11, 10.07,
10.05, 10.03, 10.03, 10.01, 9.99, 10.03, 9.95, 10, 9.95, 10, 10.01, 9.99,
9.96, 9.89, 9.83, 9.77, 9.77, 9.8, 9.9, 9.91, 9.89, 9.89, 9.87, 9.85, 9.6,
9.64, 9.53, 9.55, 9.54, 9.55, 9.58, 9.54, 9.53, 9.53, 9.63, 9.64, 9.59, 9.56]
# for share2:
share2_close = [9.68, 9.87, 9.86, 9.87, 9.79, 9.82, 9.8, 9.66, 9.62, 9.58, 9.69, 9.78, 9.75,
9.96, 9.9, 10.04, 10.06, 10.08, 10.24, 10.24, 10.24, 9.86, 10.13, 10.12,
10.1, 10.25, 10.24, 10.22, 10.75, 10.64, 10.56, 10.6, 10.42, 10.25, 10.24,
10.49, 10.57, 10.63, 10.48, 10.37, 10.96, 11.02, np.nan, np.nan, 10.88, 10.87, 11.01,
11.01, 11.58, 11.8]
share2_open = [9.88, 9.88, 9.89, 9.75, 9.74, 9.8, 9.62, 9.65, 9.58, 9.67, 9.81, 9.8, 10,
9.95, 10.1, 10.06, 10.14, 9.9, 10.2, 10.29, 9.86, 9.48, 10.01, 10.24, 10.26,
10.24, 10.12, 10.65, 10.64, 10.56, 10.42, 10.43, 10.29, 10.3, 10.44, 10.6,
10.67, 10.46, 10.39, 10.9, 11.01, 11.01, np.nan, np.nan, 10.82, 11.02, 10.96,
11.55, 11.74, 11.8]
share2_high = [9.91, 10.04, 9.93, 10.04, 9.84, 9.88, 9.99, 9.7, 9.67, 9.71, 9.85, 9.9, 10,
10.2, 10.11, 10.18, 10.21, 10.26, 10.38, 10.47, 10.42, 10.07, 10.24, 10.27,
10.38, 10.43, 10.39, 10.65, 10.84, 10.65, 10.73, 10.63, 10.51, 10.35, 10.46,
10.63, 10.74, 10.76, 10.54, 11.02, 11.12, 11.17, np.nan, np.nan, 10.92, 11.15,
11.11, 11.55, 11.95, 11.93]
share2_low = [9.63, 9.84, 9.81, 9.74, 9.67, 9.72, 9.57, 9.54, 9.51, 9.47, 9.68, 9.63, 9.75,
9.65, 9.9, 9.93, 10.03, 9.8, 10.14, 10.09, 9.78, 9.21, 9.11, 9.68, 10.05,
10.12, 9.89, 9.89, 10.59, 10.43, 10.34, 10.32, 10.21, 10.2, 10.18, 10.36,
10.51, 10.41, 10.32, 10.37, 10.87, 10.95, np.nan, np.nan, 10.65, 10.71, 10.75,
10.91, 11.31, 11.58]
# for share3:
share3_close = [6.64, 7.26, 7.03, 6.87, np.nan, 6.64, 6.85, 6.7, 6.39, 6.22, 5.92, 5.91, 6.11,
5.91, 6.23, 6.28, 6.28, 6.27, np.nan, 5.56, 5.67, 5.16, 5.69, 6.32, 6.14, 6.25,
5.79, 5.26, 5.05, 5.45, 6.06, 6.21, 5.69, 5.46, 6.02, 6.69, 7.43, 7.72, 8.16,
7.83, 8.7, 8.71, 8.88, 8.54, 8.87, 8.87, 8.18, 7.8, 7.97, 8.25]
share3_open = [7.26, 7, 6.88, 6.91, np.nan, 6.81, 6.63, 6.45, 6.16, 6.24, 5.96, 5.97, 5.96,
6.2, 6.35, 6.11, 6.37, 5.58, np.nan, 5.65, 5.19, 5.42, 6.3, 6.15, 6.05, 5.89,
5.22, 5.2, 5.07, 6.04, 6.12, 5.85, 5.67, 6.02, 6.04, 7.07, 7.64, 7.99, 7.59,
8.73, 8.72, 8.97, 8.58, 8.71, 8.77, 8.4, 7.95, 7.76, 8.25, 7.51]
share3_high = [7.41, 7.31, 7.14, 7, np.nan, 6.82, 6.96, 6.85, 6.5, 6.34, 6.04, 6.02, 6.12, 6.38,
6.43, 6.46, 6.43, 6.27, np.nan, 6.01, 5.67, 5.67, 6.35, 6.32, 6.43, 6.36, 5.79,
5.47, 5.65, 6.04, 6.14, 6.23, 5.83, 6.25, 6.27, 7.12, 7.82, 8.14, 8.27, 8.92,
8.76, 9.15, 8.9, 9.01, 9.16, 9, 8.27, 7.99, 8.33, 8.25]
share3_low = [6.53, 6.87, 6.83, 6.7, np.nan, 6.63, 6.57, 6.41, 6.15, 6.07, 5.89, 5.82, 5.73, 5.81,
6.1, 6.06, 6.16, 5.57, np.nan, 5.51, 5.19, 5.12, 5.69, 6.01, 5.97, 5.86, 5.18, 5.19,
4.96, 5.45, 5.84, 5.85, 5.28, 5.42, 6.02, 6.69, 7.28, 7.64, 7.25, 7.83, 8.41, 8.66,
8.53, 8.54, 8.73, 8.27, 7.95, 7.67, 7.8, 7.51]
# for sel_finance test
shares_eps = np.array([[np.nan, np.nan, np.nan],
[0.1, np.nan, np.nan],
[np.nan, 0.2, np.nan],
[np.nan, np.nan, 0.3],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, 0.2],
[0.1, np.nan, np.nan],
[np.nan, 0.3, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[0.3, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, 0.3, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, 0.3],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, 0, 0.2],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[0.1, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, 0.2],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[0.15, np.nan, np.nan],
[np.nan, 0.1, np.nan],
[np.nan, np.nan, np.nan],
[0.1, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, 0.3],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[np.nan, np.nan, np.nan],
[0.2, np.nan, np.nan],
[np.nan, 0.5, np.nan],
[0.4, np.nan, 0.3],
[np.nan, np.nan, np.nan],
[np.nan, 0.3, np.nan],
[0.9, np.nan, np.nan],
[np.nan, np.nan, 0.1]])
self.date_indices = ['2016-07-01', '2016-07-04', '2016-07-05', '2016-07-06',
'2016-07-07', '2016-07-08', '2016-07-11', '2016-07-12',
'2016-07-13', '2016-07-14', '2016-07-15', '2016-07-18',
'2016-07-19', '2016-07-20', '2016-07-21', '2016-07-22',
'2016-07-25', '2016-07-26', '2016-07-27', '2016-07-28',
'2016-07-29', '2016-08-01', '2016-08-02', '2016-08-03',
'2016-08-04', '2016-08-05', '2016-08-08', '2016-08-09',
'2016-08-10', '2016-08-11', '2016-08-12', '2016-08-15',
'2016-08-16', '2016-08-17', '2016-08-18', '2016-08-19',
'2016-08-22', '2016-08-23', '2016-08-24', '2016-08-25',
'2016-08-26', '2016-08-29', '2016-08-30', '2016-08-31',
'2016-09-01', '2016-09-02', '2016-09-05', '2016-09-06',
'2016-09-07', '2016-09-08']
self.shares = ['000010', '000030', '000039']
self.types = ['close', 'open', 'high', 'low']
self.sel_finance_tyeps = ['eps']
self.test_data_3D = np.zeros((3, data_rows, 4))
self.test_data_2D = np.zeros((data_rows, 3))
self.test_data_2D2 = np.zeros((data_rows, 4))
self.test_data_sel_finance = np.empty((3, data_rows, 1))
# Build up 3D data
self.test_data_3D[0, :, 0] = share1_close
self.test_data_3D[0, :, 1] = share1_open
self.test_data_3D[0, :, 2] = share1_high
self.test_data_3D[0, :, 3] = share1_low
self.test_data_3D[1, :, 0] = share2_close
self.test_data_3D[1, :, 1] = share2_open
self.test_data_3D[1, :, 2] = share2_high
self.test_data_3D[1, :, 3] = share2_low
self.test_data_3D[2, :, 0] = share3_close
self.test_data_3D[2, :, 1] = share3_open
self.test_data_3D[2, :, 2] = share3_high
self.test_data_3D[2, :, 3] = share3_low
self.test_data_sel_finance[:, :, 0] = shares_eps.T
self.hp1 = qt.HistoryPanel(values=self.test_data_3D,
levels=self.shares,
columns=self.types,
rows=self.date_indices)
print(f'in test Operator, history panel is created for timing test')
self.hp1.info()
self.hp2 = qt.HistoryPanel(values=self.test_data_sel_finance,
levels=self.shares,
columns=self.sel_finance_tyeps,
rows=self.date_indices)
print(f'in test_Operator, history panel is created for selection finance test:')
self.hp2.info()
self.op = qt.Operator(strategies='dma', signal_type='PS')
self.op2 = qt.Operator(strategies='dma, macd, trix')
def test_init(self):
""" test initialization of Operator class"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.signal_type, 'pt')
self.assertIsInstance(op.strategies, list)
self.assertEqual(len(op.strategies), 0)
op = qt.Operator('dma')
self.assertIsInstance(op, qt.Operator)
self.assertIsInstance(op.strategies, list)
self.assertIsInstance(op.strategies[0], TimingDMA)
op = qt.Operator('dma, macd')
self.assertIsInstance(op, qt.Operator)
op = qt.Operator(['dma', 'macd'])
self.assertIsInstance(op, qt.Operator)
def test_repr(self):
""" test basic representation of Opeartor class"""
op = qt.Operator()
self.assertEqual(op.__repr__(), 'Operator()')
op = qt.Operator('macd, dma, trix, random, avg_low')
self.assertEqual(op.__repr__(), 'Operator(macd, dma, trix, random, avg_low)')
self.assertEqual(op['dma'].__repr__(), 'Q-TIMING(DMA)')
self.assertEqual(op['macd'].__repr__(), 'R-TIMING(MACD)')
self.assertEqual(op['trix'].__repr__(), 'R-TIMING(TRIX)')
self.assertEqual(op['random'].__repr__(), 'SELECT(RANDOM)')
self.assertEqual(op['avg_low'].__repr__(), 'FACTOR(AVG LOW)')
def test_info(self):
"""Test information output of Operator"""
print(f'test printing information of operator object')
self.op.info()
def test_get_strategy_by_id(self):
""" test get_strategy_by_id()"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
self.assertEqual(op.strategy_ids, ['macd', 'dma', 'trix'])
self.assertIs(op.get_strategy_by_id('macd'), op.strategies[0])
self.assertIs(op.get_strategy_by_id(1), op.strategies[1])
self.assertIs(op.get_strategy_by_id('trix'), op.strategies[2])
def test_get_items(self):
""" test method __getitem__(), it should be the same as geting strategies by id"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
self.assertEqual(op.strategy_ids, ['macd', 'dma', 'trix'])
self.assertIs(op['macd'], op.strategies[0])
self.assertIs(op['trix'], op.strategies[2])
self.assertIs(op[1], op.strategies[1])
self.assertIs(op[3], op.strategies[2])
def test_get_strategies_by_price_type(self):
""" test get_strategies_by_price_type"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
op.set_parameter('macd', price_type='open')
op.set_parameter('dma', price_type='close')
op.set_parameter('trix', price_type='open')
stg_close = op.get_strategies_by_price_type('close')
stg_open = op.get_strategies_by_price_type('open')
stg_high = op.get_strategies_by_price_type('high')
self.assertIsInstance(stg_close, list)
self.assertIsInstance(stg_open, list)
self.assertIsInstance(stg_high, list)
self.assertEqual(stg_close, [op.strategies[1]])
self.assertEqual(stg_open, [op.strategies[0], op.strategies[2]])
self.assertEqual(stg_high, [])
stg_wrong = op.get_strategies_by_price_type(123)
self.assertIsInstance(stg_wrong, list)
self.assertEqual(stg_wrong, [])
def test_get_strategy_count_by_price_type(self):
""" test get_strategy_count_by_price_type"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
op.set_parameter('macd', price_type='open')
op.set_parameter('dma', price_type='close')
op.set_parameter('trix', price_type='open')
stg_close = op.get_strategy_count_by_price_type('close')
stg_open = op.get_strategy_count_by_price_type('open')
stg_high = op.get_strategy_count_by_price_type('high')
self.assertIsInstance(stg_close, int)
self.assertIsInstance(stg_open, int)
self.assertIsInstance(stg_high, int)
self.assertEqual(stg_close, 1)
self.assertEqual(stg_open, 2)
self.assertEqual(stg_high, 0)
stg_wrong = op.get_strategy_count_by_price_type(123)
self.assertIsInstance(stg_wrong, int)
self.assertEqual(stg_wrong, 0)
def test_get_strategy_names_by_price_type(self):
""" test get_strategy_names_by_price_type"""
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
op.set_parameter('macd', price_type='open')
op.set_parameter('dma', price_type='close')
op.set_parameter('trix', price_type='open')
stg_close = op.get_strategy_names_by_price_type('close')
stg_open = op.get_strategy_names_by_price_type('open')
stg_high = op.get_strategy_names_by_price_type('high')
self.assertIsInstance(stg_close, list)
self.assertIsInstance(stg_open, list)
self.assertIsInstance(stg_high, list)
self.assertEqual(stg_close, ['DMA'])
self.assertEqual(stg_open, ['MACD', 'TRIX'])
self.assertEqual(stg_high, [])
stg_wrong = op.get_strategy_names_by_price_type(123)
self.assertIsInstance(stg_wrong, list)
self.assertEqual(stg_wrong, [])
def test_get_strategy_id_by_price_type(self):
""" test get_strategy_IDs_by_price_type"""
print('-----Test get strategy IDs by price type------\n')
op = qt.Operator()
self.assertIsInstance(op, qt.Operator)
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op = qt.Operator('macd, dma, trix')
op.set_parameter('macd', price_type='open')
op.set_parameter('dma', price_type='close')
op.set_parameter('trix', price_type='open')
stg_close = op.get_strategy_id_by_price_type('close')
stg_open = op.get_strategy_id_by_price_type('open')
stg_high = op.get_strategy_id_by_price_type('high')
self.assertIsInstance(stg_close, list)
self.assertIsInstance(stg_open, list)
self.assertIsInstance(stg_high, list)
self.assertEqual(stg_close, ['dma'])
self.assertEqual(stg_open, ['macd', 'trix'])
self.assertEqual(stg_high, [])
op.add_strategies('dma, macd')
op.set_parameter('dma_1', price_type='open')
op.set_parameter('macd', price_type='open')
op.set_parameter('macd_1', price_type='high')
op.set_parameter('trix', price_type='close')
print(f'Operator strategy id:\n'
f'{op.strategies} on memory pos:\n'
f'{[id(stg) for stg in op.strategies]}')
stg_close = op.get_strategy_id_by_price_type('close')
stg_open = op.get_strategy_id_by_price_type('open')
stg_high = op.get_strategy_id_by_price_type('high')
stg_all = op.get_strategy_id_by_price_type()
print(f'All IDs of strategies:\n'
f'{stg_all}\n'
f'All price types of strategies:\n'
f'{[stg.price_type for stg in op.strategies]}')
self.assertEqual(stg_close, ['dma', 'trix'])
self.assertEqual(stg_open, ['macd', 'dma_1'])
self.assertEqual(stg_high, ['macd_1'])
stg_wrong = op.get_strategy_id_by_price_type(123)
self.assertIsInstance(stg_wrong, list)
self.assertEqual(stg_wrong, [])
def test_property_strategies(self):
""" test property strategies"""
print(f'created a new simple Operator with only one strategy: DMA')
op = qt.Operator('dma')
strategies = op.strategies
self.assertIsInstance(strategies, list)
op.info()
print(f'created the second simple Operator with three strategies')
self.assertIsInstance(strategies[0], TimingDMA)
op = qt.Operator('dma, macd, cdl')
strategies = op.strategies
op.info()
self.assertIsInstance(strategies, list)
self.assertIsInstance(strategies[0], TimingDMA)
self.assertIsInstance(strategies[1], TimingMACD)
self.assertIsInstance(strategies[2], TimingCDL)
def test_property_strategy_count(self):
""" test Property strategy_count, and the method get_strategy_count_by_price_type()"""
self.assertEqual(self.op.strategy_count, 1)
self.assertEqual(self.op2.strategy_count, 3)
self.assertEqual(self.op.get_strategy_count_by_price_type(), 1)
self.assertEqual(self.op2.get_strategy_count_by_price_type(), 3)
self.assertEqual(self.op.get_strategy_count_by_price_type('close'), 1)
self.assertEqual(self.op.get_strategy_count_by_price_type('high'), 0)
self.assertEqual(self.op2.get_strategy_count_by_price_type('close'), 3)
self.assertEqual(self.op2.get_strategy_count_by_price_type('open'), 0)
def test_property_strategy_names(self):
""" test property strategy_ids"""
op = qt.Operator('dma')
self.assertIsInstance(op.strategy_ids, list)
names = op.strategy_ids[0]
print(f'names are {names}')
self.assertEqual(names, 'dma')
op = qt.Operator('dma, macd, trix, cdl')
self.assertIsInstance(op.strategy_ids, list)
self.assertEqual(op.strategy_ids[0], 'dma')
self.assertEqual(op.strategy_ids[1], 'macd')
self.assertEqual(op.strategy_ids[2], 'trix')
self.assertEqual(op.strategy_ids[3], 'cdl')
op = qt.Operator('dma, macd, trix, dma, dma')
self.assertIsInstance(op.strategy_ids, list)
self.assertEqual(op.strategy_ids[0], 'dma')
self.assertEqual(op.strategy_ids[1], 'macd')
self.assertEqual(op.strategy_ids[2], 'trix')
self.assertEqual(op.strategy_ids[3], 'dma_1')
self.assertEqual(op.strategy_ids[4], 'dma_2')
def test_property_strategy_blenders(self):
""" test property strategy blenders including property setter,
and test the method get_blender()"""
print(f'------- Test property strategy blenders ---------')
op = qt.Operator()
self.assertIsInstance(op.strategy_blenders, dict)
self.assertIsInstance(op.signal_type, str)
self.assertEqual(op.strategy_blenders, {})
self.assertEqual(op.signal_type, 'pt')
# test adding blender to empty operator
op.strategy_blenders = '1 + 2'
op.signal_type = 'proportion signal'
self.assertEqual(op.strategy_blenders, {})
self.assertEqual(op.signal_type, 'ps')
op.add_strategy('dma')
op.strategy_blenders = '1+2'
self.assertEqual(op.strategy_blenders, {'close': ['+', '2', '1']})
op.clear_strategies()
self.assertEqual(op.strategy_blenders, {})
op.add_strategies('dma, trix, macd, dma')
op.set_parameter('dma', price_type='open')
op.set_parameter('trix', price_type='high')
op.set_blender('open', '1+2')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, ['+', '2', '1'])
self.assertEqual(blender_close, None)
self.assertEqual(blender_high, None)
op.set_blender('open', '1+2+3')
op.set_blender('abc', '1+2+3')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
blender_abc = op.get_blender('abc')
self.assertEqual(op.strategy_blenders, {'open': ['+', '3', '+', '2', '1']})
self.assertEqual(blender_open, ['+', '3', '+', '2', '1'])
self.assertEqual(blender_close, None)
self.assertEqual(blender_high, None)
self.assertEqual(blender_abc, None)
op.set_blender('open', 123)
blender_open = op.get_blender('open')
self.assertEqual(blender_open, [])
op.set_blender(None, '1+1')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(op.bt_price_types, ['close', 'high', 'open'])
self.assertEqual(op.get_blender(), {'close': ['+', '1', '1'],
'open': ['+', '1', '1'],
'high': ['+', '1', '1']})
self.assertEqual(blender_open, ['+', '1', '1'])
self.assertEqual(blender_close, ['+', '1', '1'])
self.assertEqual(blender_high, ['+', '1', '1'])
op.set_blender(None, ['1+1', '3+4'])
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, ['+', '4', '3'])
self.assertEqual(blender_close, ['+', '1', '1'])
self.assertEqual(blender_high, ['+', '4', '3'])
self.assertEqual(op.view_blender('open'), '3+4')
self.assertEqual(op.view_blender('close'), '1+1')
self.assertEqual(op.view_blender('high'), '3+4')
op.strategy_blenders = (['1+2', '2*3', '1+4'])
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, ['+', '4', '1'])
self.assertEqual(blender_close, ['+', '2', '1'])
self.assertEqual(blender_high, ['*', '3', '2'])
self.assertEqual(op.view_blender('open'), '1+4')
self.assertEqual(op.view_blender('close'), '1+2')
self.assertEqual(op.view_blender('high'), '2*3')
# test error inputs:
# wrong type of price_type
self.assertRaises(TypeError, op.set_blender, 1, '1+3')
# price_type not found, no change is made
op.set_blender('volume', '1+3')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, ['+', '4', '1'])
self.assertEqual(blender_close, ['+', '2', '1'])
self.assertEqual(blender_high, ['*', '3', '2'])
# price_type not valid, no change is made
op.set_blender('closee', '1+2')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, ['+', '4', '1'])
self.assertEqual(blender_close, ['+', '2', '1'])
self.assertEqual(blender_high, ['*', '3', '2'])
# wrong type of blender, set to empty list
op.set_blender('open', 55)
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, [])
self.assertEqual(blender_close, ['+', '2', '1'])
self.assertEqual(blender_high, ['*', '3', '2'])
# wrong type of blender, set to empty list
op.set_blender('close', ['1+2'])
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, [])
self.assertEqual(blender_close, [])
self.assertEqual(blender_high, ['*', '3', '2'])
# can't parse blender, set to empty list
op.set_blender('high', 'a+bc')
blender_open = op.get_blender('open')
blender_close = op.get_blender('close')
blender_high = op.get_blender('high')
self.assertEqual(blender_open, [])
self.assertEqual(blender_close, [])
self.assertEqual(blender_high, [])
def test_property_singal_type(self):
""" test property signal_type"""
op = qt.Operator()
self.assertIsInstance(op.signal_type, str)
self.assertEqual(op.signal_type, 'pt')
op = qt.Operator(signal_type='ps')
self.assertIsInstance(op.signal_type, str)
self.assertEqual(op.signal_type, 'ps')
op = qt.Operator(signal_type='PS')
self.assertEqual(op.signal_type, 'ps')
op = qt.Operator(signal_type='proportion signal')
self.assertEqual(op.signal_type, 'ps')
print(f'"pt" will be the default type if wrong value is given')
op = qt.Operator(signal_type='wrong value')
self.assertEqual(op.signal_type, 'pt')
print(f'test signal_type.setter')
op.signal_type = 'ps'
self.assertEqual(op.signal_type, 'ps')
print(f'test error raising')
self.assertRaises(TypeError, setattr, op, 'signal_type', 123)
self.assertRaises(ValueError, setattr, op, 'signal_type', 'wrong value')
def test_property_op_data_types(self):
""" test property op_data_types"""
op = qt.Operator()
self.assertIsInstance(op.op_data_types, list)
self.assertEqual(op.op_data_types, [])
op = qt.Operator('macd, dma, trix')
dt = op.op_data_types
self.assertEqual(dt[0], 'close')
op = qt.Operator('macd, cdl')
dt = op.op_data_types
self.assertEqual(dt[0], 'close')
self.assertEqual(dt[1], 'high')
self.assertEqual(dt[2], 'low')
self.assertEqual(dt[3], 'open')
self.assertEqual(dt, ['close', 'high', 'low', 'open'])
op.add_strategy('dma')
dt = op.op_data_types
self.assertEqual(dt[0], 'close')
self.assertEqual(dt[1], 'high')
self.assertEqual(dt[2], 'low')
self.assertEqual(dt[3], 'open')
self.assertEqual(dt, ['close', 'high', 'low', 'open'])
def test_property_op_data_type_count(self):
""" test property op_data_type_count"""
op = qt.Operator()
self.assertIsInstance(op.op_data_type_count, int)
self.assertEqual(op.op_data_type_count, 0)
op = qt.Operator('macd, dma, trix')
dtn = op.op_data_type_count
self.assertEqual(dtn, 1)
op = qt.Operator('macd, cdl')
dtn = op.op_data_type_count
self.assertEqual(dtn, 4)
op.add_strategy('dma')
dtn = op.op_data_type_count
self.assertEqual(dtn, 4)
def test_property_op_data_freq(self):
""" test property op_data_freq"""
op = qt.Operator()
self.assertIsInstance(op.op_data_freq, str)
self.assertEqual(len(op.op_data_freq), 0)
self.assertEqual(op.op_data_freq, '')
op = qt.Operator('macd, dma, trix')
dtf = op.op_data_freq
self.assertIsInstance(dtf, str)
self.assertEqual(dtf[0], 'd')
op.set_parameter('macd', data_freq='m')
dtf = op.op_data_freq
self.assertIsInstance(dtf, list)
self.assertEqual(len(dtf), 2)
self.assertEqual(dtf[0], 'd')
self.assertEqual(dtf[1], 'm')
def test_property_bt_price_types(self):
""" test property bt_price_types"""
print('------test property bt_price_tyeps-------')
op = qt.Operator()
self.assertIsInstance(op.bt_price_types, list)
self.assertEqual(len(op.bt_price_types), 0)
self.assertEqual(op.bt_price_types, [])
op = qt.Operator('macd, dma, trix')
btp = op.bt_price_types
self.assertIsInstance(btp, list)
self.assertEqual(btp[0], 'close')
op.set_parameter('macd', price_type='open')
btp = op.bt_price_types
btpc = op.bt_price_type_count
print(f'price_types are \n{btp}')
self.assertIsInstance(btp, list)
self.assertEqual(len(btp), 2)
self.assertEqual(btp[0], 'close')
self.assertEqual(btp[1], 'open')
self.assertEqual(btpc, 2)
op.add_strategies(['dma', 'macd'])
op.set_parameter('dma_1', price_type='high')
btp = op.bt_price_types
btpc = op.bt_price_type_count
self.assertEqual(btp[0], 'close')
self.assertEqual(btp[1], 'high')
self.assertEqual(btp[2], 'open')
self.assertEqual(btpc, 3)
op.remove_strategy('dma_1')
btp = op.bt_price_types
btpc = op.bt_price_type_count
self.assertEqual(btp[0], 'close')
self.assertEqual(btp[1], 'open')
self.assertEqual(btpc, 2)
op.remove_strategy('macd_1')
btp = op.bt_price_types
btpc = op.bt_price_type_count
self.assertEqual(btp[0], 'close')
self.assertEqual(btp[1], 'open')
self.assertEqual(btpc, 2)
def test_property_op_data_type_list(self):
""" test property op_data_type_list"""
op = qt.Operator()
self.assertIsInstance(op.op_data_type_list, list)
self.assertEqual(len(op.op_data_type_list), 0)
self.assertEqual(op.op_data_type_list, [])
op = qt.Operator('macd, dma, trix, cdl')
ohd = op.op_data_type_list
print(f'ohd is {ohd}')
self.assertIsInstance(ohd, list)
self.assertEqual(ohd[0], ['close'])
op.set_parameter('macd', data_types='open, close')
ohd = op.op_data_type_list
print(f'ohd is {ohd}')
self.assertIsInstance(ohd, list)
self.assertEqual(len(ohd), 4)
self.assertEqual(ohd[0], ['open', 'close'])
self.assertEqual(ohd[1], ['close'])
self.assertEqual(ohd[2], ['close'])
self.assertEqual(ohd[3], ['open', 'high', 'low', 'close'])
def test_property_op_history_data(self):
""" Test this important function to get operation history data that shall be used in
signal generation
these data are stored in list of nd-arrays, each ndarray represents the data
that is needed for each and every strategy
"""
print(f'------- Test getting operation history data ---------')
op = qt.Operator()
self.assertIsInstance(op.strategy_blenders, dict)
self.assertIsInstance(op.signal_type, str)
self.assertEqual(op.strategy_blenders, {})
self.assertEqual(op.op_history_data, {})
self.assertEqual(op.signal_type, 'pt')
def test_property_opt_space_par(self):
""" test property opt_space_par"""
print(f'-----test property opt_space_par--------:\n')
op = qt.Operator()
self.assertIsInstance(op.opt_space_par, tuple)
self.assertIsInstance(op.opt_space_par[0], list)
self.assertIsInstance(op.opt_space_par[1], list)
self.assertEqual(len(op.opt_space_par), 2)
self.assertEqual(op.opt_space_par, ([], []))
op = qt.Operator('macd, dma, trix, cdl')
osp = op.opt_space_par
print(f'before setting opt_tags opt_space_par is empty:\n'
f'osp is {osp}\n')
self.assertIsInstance(osp, tuple)
self.assertEqual(osp[0], [])
self.assertEqual(osp[1], [])
op.set_parameter('macd', opt_tag=1)
op.set_parameter('dma', opt_tag=1)
osp = op.opt_space_par
print(f'after setting opt_tags opt_space_par is not empty:\n'
f'osp is {osp}\n')
self.assertIsInstance(osp, tuple)
self.assertEqual(len(osp), 2)
self.assertIsInstance(osp[0], list)
self.assertIsInstance(osp[1], list)
self.assertEqual(len(osp[0]), 6)
self.assertEqual(len(osp[1]), 6)
self.assertEqual(osp[0], [(10, 250), (10, 250), (10, 250), (10, 250), (10, 250), (10, 250)])
self.assertEqual(osp[1], ['discr', 'discr', 'discr', 'discr', 'discr', 'discr'])
def test_property_opt_types(self):
""" test property opt_tags"""
print(f'-----test property opt_tags--------:\n')
op = qt.Operator()
self.assertIsInstance(op.opt_tags, list)
self.assertEqual(len(op.opt_tags), 0)
self.assertEqual(op.opt_tags, [])
op = qt.Operator('macd, dma, trix, cdl')
otp = op.opt_tags
print(f'before setting opt_tags opt_space_par is empty:\n'
f'otp is {otp}\n')
self.assertIsInstance(otp, list)
self.assertEqual(otp, [0, 0, 0, 0])
op.set_parameter('macd', opt_tag=1)
op.set_parameter('dma', opt_tag=1)
otp = op.opt_tags
print(f'after setting opt_tags opt_space_par is not empty:\n'
f'otp is {otp}\n')
self.assertIsInstance(otp, list)
self.assertEqual(len(otp), 4)
self.assertEqual(otp, [1, 1, 0, 0])
def test_property_max_window_length(self):
""" test property max_window_length"""
print(f'-----test property max window length--------:\n')
op = qt.Operator()
self.assertIsInstance(op.max_window_length, int)
self.assertEqual(op.max_window_length, 0)
op = qt.Operator('macd, dma, trix, cdl')
mwl = op.max_window_length
print(f'before setting window_length the value is 270:\n'
f'mwl is {mwl}\n')
self.assertIsInstance(mwl, int)
self.assertEqual(mwl, 270)
op.set_parameter('macd', window_length=300)
op.set_parameter('dma', window_length=350)
mwl = op.max_window_length
print(f'after setting window_length the value is new set value:\n'
f'mwl is {mwl}\n')
self.assertIsInstance(mwl, int)
self.assertEqual(mwl, 350)
def test_property_bt_price_type_count(self):
""" test property bt_price_type_count"""
print(f'-----test property bt_price_type_count--------:\n')
op = qt.Operator()
self.assertIsInstance(op.bt_price_type_count, int)
self.assertEqual(op.bt_price_type_count, 0)
op = qt.Operator('macd, dma, trix, cdl')
otp = op.bt_price_type_count
print(f'before setting price_type the price count is 1:\n'
f'otp is {otp}\n')
self.assertIsInstance(otp, int)
self.assertEqual(otp, 1)
op.set_parameter('macd', price_type='open')
op.set_parameter('dma', price_type='open')
otp = op.bt_price_type_count
print(f'after setting price_type the price type count is 2:\n'
f'otp is {otp}\n')
self.assertIsInstance(otp, int)
self.assertEqual(otp, 2)
def test_property_set(self):
""" test all property setters:
setting following properties:
- strategy_blenders
- signal_type
other properties can not be set"""
print(f'------- Test setting properties ---------')
op = qt.Operator()
self.assertIsInstance(op.strategy_blenders, dict)
self.assertIsInstance(op.signal_type, str)
self.assertEqual(op.strategy_blenders, {})
self.assertEqual(op.signal_type, 'pt')
op.strategy_blenders = '1 + 2'
op.signal_type = 'proportion signal'
self.assertEqual(op.strategy_blenders, {})
self.assertEqual(op.signal_type, 'ps')
op = qt.Operator('macd, dma, trix, cdl')
# TODO: 修改set_parameter()，使下面的用法成立
# a_to_sell.set_parameter('dma, cdl', price_type='open')
op.set_parameter('dma', price_type='open')
op.set_parameter('cdl', price_type='open')
sb = op.strategy_blenders
st = op.signal_type
self.assertIsInstance(sb, dict)
print(f'before setting: strategy_blenders={sb}')
self.assertEqual(sb, {})
op.strategy_blenders = '1+2 * 3'
sb = op.strategy_blenders
print(f'after setting strategy_blender={sb}')
self.assertEqual(sb, {'close': ['+', '*', '3', '2', '1'],
'open': ['+', '*', '3', '2', '1']})
op.strategy_blenders = ['1+2', '3-4']
sb = op.strategy_blenders
print(f'after setting strategy_blender={sb}')
self.assertEqual(sb, {'close': ['+', '2', '1'],
'open': ['-', '4', '3']})
def test_operator_ready(self):
"""test the method ready of Operator"""
op = qt.Operator()
print(f'operator is ready? "{op.ready}"')
def test_operator_add_strategy(self):
"""test adding strategies to Operator"""
op = qt.Operator('dma, all, urgent')
self.assertIsInstance(op, qt.Operator)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[1], qt.SelectingAll)
self.assertIsInstance(op.strategies[2], qt.RiconUrgent)
self.assertIsInstance(op[0], qt.TimingDMA)
self.assertIsInstance(op[1], qt.SelectingAll)
self.assertIsInstance(op[2], qt.RiconUrgent)
self.assertIsInstance(op['dma'], qt.TimingDMA)
self.assertIsInstance(op['all'], qt.SelectingAll)
self.assertIsInstance(op['urgent'], qt.RiconUrgent)
self.assertEqual(op.strategy_count, 3)
print(f'test adding strategies into existing op')
print('test adding strategy by string')
op.add_strategy('macd')
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[3], qt.TimingMACD)
self.assertEqual(op.strategy_count, 4)
op.add_strategy('random')
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[4], qt.SelectingRandom)
self.assertEqual(op.strategy_count, 5)
test_ls = TestLSStrategy()
op.add_strategy(test_ls)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[5], TestLSStrategy)
self.assertEqual(op.strategy_count, 6)
print(f'Test different instance of objects are added to operator')
op.add_strategy('dma')
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[6], qt.TimingDMA)
self.assertIsNot(op.strategies[0], op.strategies[6])
def test_operator_add_strategies(self):
""" etst adding multiple strategies to Operator"""
op = qt.Operator('dma, all, urgent')
self.assertEqual(op.strategy_count, 3)
print('test adding multiple strategies -- adding strategy by list of strings')
op.add_strategies(['dma', 'macd'])
self.assertEqual(op.strategy_count, 5)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[3], qt.TimingDMA)
self.assertIsInstance(op.strategies[4], qt.TimingMACD)
print('test adding multiple strategies -- adding strategy by comma separated strings')
op.add_strategies('dma, macd')
self.assertEqual(op.strategy_count, 7)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[5], qt.TimingDMA)
self.assertIsInstance(op.strategies[6], qt.TimingMACD)
print('test adding multiple strategies -- adding strategy by list of strategies')
op.add_strategies([qt.TimingDMA(), qt.TimingMACD()])
self.assertEqual(op.strategy_count, 9)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[7], qt.TimingDMA)
self.assertIsInstance(op.strategies[8], qt.TimingMACD)
print('test adding multiple strategies -- adding strategy by list of strategy and str')
op.add_strategies(['DMA', qt.TimingMACD()])
self.assertEqual(op.strategy_count, 11)
self.assertIsInstance(op.strategies[0], qt.TimingDMA)
self.assertIsInstance(op.strategies[9], qt.TimingDMA)
self.assertIsInstance(op.strategies[10], qt.TimingMACD)
self.assertIsNot(op.strategies[0], op.strategies[9])
self.assertIs(type(op.strategies[0]), type(op.strategies[9]))
print('test adding fault data')
self.assertRaises(AssertionError, op.add_strategies, 123)
self.assertRaises(AssertionError, op.add_strategies, None)
def test_opeartor_remove_strategy(self):
""" test method remove strategy"""
op = qt.Operator('dma, all, urgent')
op.add_strategies(['dma', 'macd'])
op.add_strategies(['DMA', TestLSStrategy()])
self.assertEqual(op.strategy_count, 7)
print('test removing strategies from Operator')
op.remove_strategy('dma')
self.assertEqual(op.strategy_count, 6)
self.assertEqual(op.strategy_ids, ['all', 'urgent', 'dma_1', 'macd', 'dma_2', 'custom'])
self.assertEqual(op.strategies[0], op['all'])
self.assertEqual(op.strategies[1], op['urgent'])
self.assertEqual(op.strategies[2], op['dma_1'])
self.assertEqual(op.strategies[3], op['macd'])
self.assertEqual(op.strategies[4], op['dma_2'])
self.assertEqual(op.strategies[5], op['custom'])
op.remove_strategy('dma_1')
self.assertEqual(op.strategy_count, 5)
self.assertEqual(op.strategy_ids, ['all', 'urgent', 'macd', 'dma_2', 'custom'])
self.assertEqual(op.strategies[0], op['all'])
self.assertEqual(op.strategies[1], op['urgent'])
self.assertEqual(op.strategies[2], op['macd'])
self.assertEqual(op.strategies[3], op['dma_2'])
self.assertEqual(op.strategies[4], op['custom'])
def test_opeartor_clear_strategies(self):
""" test operator clear strategies"""
op = qt.Operator('dma, all, urgent')
op.add_strategies(['dma', 'macd'])
op.add_strategies(['DMA', TestLSStrategy()])
self.assertEqual(op.strategy_count, 7)
print('test removing strategies from Operator')
op.clear_strategies()
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
op.add_strategy('dma', pars=(12, 123, 25))
self.assertEqual(op.strategy_count, 1)
self.assertEqual(op.strategy_ids, ['dma'])
self.assertEqual(type(op.strategies[0]), TimingDMA)
self.assertEqual(op.strategies[0].pars, (12, 123, 25))
op.clear_strategies()
self.assertEqual(op.strategy_count, 0)
self.assertEqual(op.strategy_ids, [])
def test_operator_prepare_data(self):
"""test processes that related to prepare data"""
test_ls = TestLSStrategy()
test_sel = TestSelStrategy()
test_sig = TestSigStrategy()
self.op = qt.Operator(strategies=[test_ls, test_sel, test_sig])
too_early_cash = qt.CashPlan(dates='2016-01-01', amounts=10000)
early_cash = qt.CashPlan(dates='2016-07-01', amounts=10000)
on_spot_cash = qt.CashPlan(dates='2016-07-08', amounts=10000)
no_trade_cash = qt.CashPlan(dates='2016-07-08, 2016-07-30, 2016-08-11, 2016-09-03',
amounts=[10000, 10000, 10000, 10000])
# 在所有策略的参数都设置好之前调用prepare_data会发生assertion Error
self.assertRaises(AssertionError,
self.op.prepare_data,
hist_data=self.hp1,
cash_plan=qt.CashPlan(dates='2016-07-08', amounts=10000))
late_cash = qt.CashPlan(dates='2016-12-31', amounts=10000)
multi_cash = qt.CashPlan(dates='2016-07-08, 2016-08-08', amounts=[10000, 10000])
self.op.set_parameter(stg_id='custom',
pars={'000300': (5, 10.),
'000400': (5, 10.),
'000500': (5, 6.)})
self.assertEqual(self.op.strategies[0].pars, {'000300': (5, 10.),
'000400': (5, 10.),
'000500': (5, 6.)})
self.op.set_parameter(stg_id='custom_1',
pars=())
self.assertEqual(self.op.strategies[1].pars, ()),
self.op.set_parameter(stg_id='custom_2',
pars=(0.2, 0.02, -0.02))
self.assertEqual(self.op.strategies[2].pars, (0.2, 0.02, -0.02)),
self.op.prepare_data(hist_data=self.hp1,
cash_plan=on_spot_cash)
self.assertIsInstance(self.op._op_history_data, dict)
self.assertEqual(len(self.op._op_history_data), 3)
# test if automatic strategy blenders are set
self.assertEqual(self.op.strategy_blenders,
{'close': ['+', '2', '+', '1', '0']})
tim_hist_data = self.op._op_history_data['custom']
sel_hist_data = self.op._op_history_data['custom_1']
ric_hist_data = self.op._op_history_data['custom_2']
print(f'in test_prepare_data in TestOperator:')
print('selecting history data:\n', sel_hist_data)
print('originally passed data in correct sequence:\n', self.test_data_3D[:, 3:, [2, 3, 0]])
print('difference is \n', sel_hist_data - self.test_data_3D[:, :, [2, 3, 0]])
self.assertTrue(np.allclose(sel_hist_data, self.test_data_3D[:, :, [2, 3, 0]], equal_nan=True))
self.assertTrue(np.allclose(tim_hist_data, self.test_data_3D, equal_nan=True))
self.assertTrue(np.allclose(ric_hist_data, self.test_data_3D[:, 3:, :], equal_nan=True))
# raises Value Error if empty history panel is given
empty_hp = qt.HistoryPanel()
correct_hp = qt.HistoryPanel(values=np.random.randint(10, size=(3, 50, 4)),
columns=self.types,
levels=self.shares,
rows=self.date_indices)
too_many_shares = qt.HistoryPanel(values=np.random.randint(10, size=(5, 50, 4)))
too_many_types = qt.HistoryPanel(values=np.random.randint(10, size=(3, 50, 5)))
# raises Error when history panel is empty
self.assertRaises(ValueError,
self.op.prepare_data,
empty_hp,
on_spot_cash)
# raises Error when first investment date is too early
self.assertRaises(AssertionError,
self.op.prepare_data,
correct_hp,
early_cash)
# raises Error when last investment date is too late
self.assertRaises(AssertionError,
self.op.prepare_data,
correct_hp,
late_cash)
# raises Error when some of the investment dates are on no-trade-days
self.assertRaises(ValueError,
self.op.prepare_data,
correct_hp,
no_trade_cash)
# raises Error when number of shares in history data does not fit
self.assertRaises(AssertionError,
self.op.prepare_data,
too_many_shares,
on_spot_cash)
# raises Error when too early cash investment date
self.assertRaises(AssertionError,
self.op.prepare_data,
correct_hp,
too_early_cash)
# raises Error when number of d_types in history data does not fit
self.assertRaises(AssertionError,
self.op.prepare_data,
too_many_types,
on_spot_cash)
# test the effect of data type sequence in strategy definition
def test_operator_generate(self):
""" Test signal generation process of operator objects
:return:
"""
# 使用test模块的自定义策略生成三种交易策略
test_ls = TestLSStrategy()
test_sel = TestSelStrategy()
test_sel2 = TestSelStrategyDiffTime()
test_sig = TestSigStrategy()
print('--Test PT type signal generation--')
# 测试PT类型的信号生成：
# 创建一个Operator对象，信号类型为PT（比例目标信号）
# 这个Operator对象包含两个策略，分别为LS-Strategy以及Sel-Strategy，代表择时和选股策略
# 两个策略分别生成PT信号后混合成一个信号输出
self.op = qt.Operator(strategies=[test_ls, test_sel])
self.op.set_parameter(stg_id='custom',
pars={'000010': (5, 10.),
'000030': (5, 10.),
'000039': (5, 6.)})
self.op.set_parameter(stg_id=1,
pars=())
# self.a_to_sell.set_blender(blender='0+1+2')
self.op.prepare_data(hist_data=self.hp1,
cash_plan=qt.CashPlan(dates='2016-07-08', amounts=10000))
print('--test operator information in normal mode--')
self.op.info()
self.assertEqual(self.op.strategy_blenders,
{'close': ['+', '1', '0']})
self.op.set_blender(None, '0*1')
self.assertEqual(self.op.strategy_blenders,
{'close': ['*', '1', '0']})
print('--test operation signal created in Proportional Target (PT) Mode--')
op_list = self.op.create_signal(hist_data=self.hp1)
self.assertTrue(isinstance(op_list, HistoryPanel))
backtest_price_types = op_list.htypes
self.assertEqual(backtest_price_types[0], 'close')
self.assertEqual(op_list.shape, (3, 45, 1))
reduced_op_list = op_list.values.squeeze().T
print(f'op_list created, it is a 3 share/45 days/1 htype array, to make comparison happen, \n'
f'it will be squeezed to a 2-d array to compare on share-wise:\n'
f'{reduced_op_list}')
target_op_values = np.array([[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0]])
self.assertTrue(np.allclose(target_op_values, reduced_op_list, equal_nan=True))
print('--Test two separate signal generation for different price types--')
# 测试两组PT类型的信号生成：
# 在Operator对象中增加两个SigStrategy策略，策略类型相同但是策略的参数不同，回测价格类型为"OPEN"
# Opeartor应该生成两组交易信号，分别用于"close"和"open"两中不同的价格类型
# 这里需要重新生成两个新的交易策略对象，否则在op的strategies列表中产生重复的对象引用，从而引起错误
test_ls = TestLSStrategy()
test_sel = TestSelStrategy()
self.op.add_strategies([test_ls, test_sel])
self.op.set_parameter(stg_id='custom_2',
price_type='open')
self.op.set_parameter(stg_id='custom_3',
price_type='open')
self.assertEqual(self.op['custom'].price_type, 'close')
self.assertEqual(self.op['custom_2'].price_type, 'open')
self.op.set_parameter(stg_id='custom_2',
pars={'000010': (5, 10.),
'000030': (5, 10.),
'000039': (5, 6.)})
self.op.set_parameter(stg_id='custom_3',
pars=())
self.op.set_blender(blender='0 or 1', price_type='open')
self.op.prepare_data(hist_data=self.hp1,
cash_plan=qt.CashPlan(dates='2016-07-08', amounts=10000))
print('--test how operator information is printed out--')
self.op.info()
self.assertEqual(self.op.strategy_blenders,
{'close': ['*', '1', '0'],
'open': ['or', '1', '0']})
print('--test opeartion signal created in Proportional Target (PT) Mode--')
op_list = self.op.create_signal(hist_data=self.hp1)
self.assertTrue(isinstance(op_list, HistoryPanel))
signal_close = op_list['close'].squeeze().T
signal_open = op_list['open'].squeeze().T
self.assertEqual(signal_close.shape, (45, 3))
self.assertEqual(signal_open.shape, (45, 3))
target_op_close = np.array([[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.0, 0.0],
[0.5, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0],
[0.0, 0.5, 0.0]])
target_op_open = np.array([[0.5, 0.5, 1.0],
[0.5, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 0.5, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 0.0],
[1.0, 1.0, 0.0],
[1.0, 1.0, 0.0],
[1.0, 0.5, 0.0],
[1.0, 0.5, 0.0],
[1.0, 1.0, 0.0],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.0, 1.0, 0.5],
[0.5, 1.0, 0.0],
[0.5, 1.0, 0.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0],
[0.5, 1.0, 1.0]])
signal_pairs = [[list(sig1), list(sig2), sig1 == sig2]
for sig1, sig2
in zip(list(target_op_close), list(signal_close))]
print(f'signals side by side:\n'
f'{signal_pairs}')
self.assertTrue(np.allclose(target_op_close, signal_close, equal_nan=True))
signal_pairs = [[list(sig1), list(sig2), sig1 == sig2]
for sig1, sig2
in zip(list(target_op_open), list(signal_open))]
print(f'signals side by side:\n'
f'{signal_pairs}')
self.assertTrue(np.allclose(target_op_open, signal_open, equal_nan=True))
print('--Test two separate signal generation for different price types--')
# 更多测试集合
def test_stg_parameter_setting(self):
""" test setting parameters of strategies
test the method set_parameters
:return:
"""
op = qt.Operator(strategies='dma, all, urgent')
print(op.strategies, '\n', [qt.TimingDMA, qt.SelectingAll, qt.RiconUrgent])
print(f'info of Timing strategy in new op: \n{op.strategies[0].info()}')
# TODO: allow set_parameters to a list of strategies or str-listed strategies
# TODO: allow set_parameters to all strategies of specific bt price type
print(f'Set up strategy parameters by strategy id')
op.set_parameter('dma',
pars=(5, 10, 5),
opt_tag=1,
par_boes=((5, 10), (5, 15), (10, 15)),
window_length=10,
data_types=['close', 'open', 'high'])
op.set_parameter('all',
window_length=20)
op.set_parameter('all', price_type='high')
print(f'Can also set up strategy parameters by strategy index')
op.set_parameter(2, price_type='open')
op.set_parameter(2,
opt_tag=1,
pars=(9, -0.09),
window_length=10)
self.assertEqual(op.strategies[0].pars, (5, 10, 5))
self.assertEqual(op.strategies[0].par_boes, ((5, 10), (5, 15), (10, 15)))
self.assertEqual(op.strategies[2].pars, (9, -0.09))
self.assertEqual(op.op_data_freq, 'd')
self.assertEqual(op.op_data_types, ['close', 'high', 'open'])
self.assertEqual(op.opt_space_par,
([(5, 10), (5, 15), (10, 15), (1, 40), (-0.5, 0.5)],
['discr', 'discr', 'discr', 'discr', 'conti']))
self.assertEqual(op.max_window_length, 20)
print(f'KeyError will be raised if wrong strategy id is given')
self.assertRaises(KeyError, op.set_parameter, stg_id='t-1', pars=(1, 2))
self.assertRaises(KeyError, op.set_parameter, stg_id='wrong_input', pars=(1, 2))
print(f'ValueError will be raised if parameter can be set')
self.assertRaises(ValueError, op.set_parameter, stg_id=0, pars=('wrong input', 'wrong input'))
# test blenders of different price types
# test setting blenders to different price types
# TODO: to allow operands like "and", "or", "not", "xor"
# a_to_sell.set_blender('close', '0 and 1 or 2')
# self.assertEqual(a_to_sell.get_blender('close'), 'str-1.2')
self.assertEqual(op.bt_price_types, ['close', 'high', 'open'])
op.set_blender('open', '0 & 1 | 2')
self.assertEqual(op.get_blender('open'), ['|', '2', '&', '1', '0'])
op.set_blender('high', '(0|1) & 2')
self.assertEqual(op.get_blender('high'), ['&', '2', '|', '1', '0'])
op.set_blender('close', '0 & 1 | 2')
self.assertEqual(op.get_blender(), {'close': ['|', '2', '&', '1', '0'],
'high': ['&', '2', '|', '1', '0'],
'open': ['|', '2', '&', '1', '0']})
self.assertEqual(op.opt_space_par,
([(5, 10), (5, 15), (10, 15), (1, 40), (-0.5, 0.5)],
['discr', 'discr', 'discr', 'discr', 'conti']))
self.assertEqual(op.opt_tags, [1, 0, 1])
def test_signal_blend(self):
self.assertEqual(blender_parser('0 & 1'), ['&', '1', '0'])
self.assertEqual(blender_parser('0 or 1'), ['or', '1', '0'])
self.assertEqual(blender_parser('0 & 1 | 2'), ['|', '2', '&', '1', '0'])
blender = blender_parser('0 & 1 | 2')
self.assertEqual(signal_blend([1, 1, 1], blender), 1)
self.assertEqual(signal_blend([1, 0, 1], blender), 1)
self.assertEqual(signal_blend([1, 1, 0], blender), 1)
self.assertEqual(signal_blend([0, 1, 1], blender), 1)
self.assertEqual(signal_blend([0, 0, 1], blender), 1)
self.assertEqual(signal_blend([1, 0, 0], blender), 0)
self.assertEqual(signal_blend([0, 1, 0], blender), 0)
self.assertEqual(signal_blend([0, 0, 0], blender), 0)
# parse: '0 & ( 1 | 2 )'
self.assertEqual(blender_parser('0 & ( 1 | 2 )'), ['&', '|', '2', '1', '0'])
blender = blender_parser('0 & ( 1 | 2 )')
self.assertEqual(signal_blend([1, 1, 1], blender), 1)
self.assertEqual(signal_blend([1, 0, 1], blender), 1)
self.assertEqual(signal_blend([1, 1, 0], blender), 1)
self.assertEqual(signal_blend([0, 1, 1], blender), 0)
self.assertEqual(signal_blend([0, 0, 1], blender), 0)
self.assertEqual(signal_blend([1, 0, 0], blender), 0)
self.assertEqual(signal_blend([0, 1, 0], blender), 0)
self.assertEqual(signal_blend([0, 0, 0], blender), 0)
# parse: '(1-2)/3 + 0'
self.assertEqual(blender_parser('(1-2)/3 + 0'), ['+', '0', '/', '3', '-', '2', '1'])
blender = blender_parser('(1-2)/3 + 0')
self.assertEqual(signal_blend([5, 9, 1, 4], blender), 7)
# pars: '(0*1/2*(3+4))+5*(6+7)-8'
self.assertEqual(blender_parser('(0*1/2*(3+4))+5*(6+7)-8'), ['-', '8', '+', '*', '+', '7', '6', '5', '*',
'+', '4', '3', '/', '2', '*', '1', '0'])
blender = blender_parser('(0*1/2*(3+4))+5*(6+7)-8')
self.assertEqual(signal_blend([1, 1, 1, 1, 1, 1, 1, 1, 1], blender), 3)
self.assertEqual(signal_blend([2, 1, 4, 3, 5, 5, 2, 2, 10], blender), 14)
# parse: '0/max(2,1,3 + 5)+4'
self.assertEqual(blender_parser('0/max(2,1,3 + 5)+4'), ['+', '4', '/', 'max(3)', '+', '5', '3', '1', '2', '0'])
blender = blender_parser('0/max(2,1,3 + 5)+4')
self.assertEqual(signal_blend([8.0, 4, 3, 5.0, 0.125, 5], blender), 0.925)
self.assertEqual(signal_blend([2, 1, 4, 3, 5, 5, 2, 2, 10], blender), 5.25)
print('speed test')
import time
st = time.time()
blender = blender_parser('0+max(1,2,(3+4)*5, max(6, (7+8)*9), 10-11) * (12+13)')
res = []
for i in range(10000):
res = signal_blend([1, 1, 2, 3, 4, 5, 3, 4, 5, 6, 7, 8, 2, 3], blender)
et = time.time()
print(f'total time for RPN processing: {et - st}, got result: {res}')
blender = blender_parser("0 + 1 * 2")
self.assertEqual(signal_blend([1, 2, 3], blender), 7)
blender = blender_parser("(0 + 1) * 2")
self.assertEqual(signal_blend([1, 2, 3], blender), 9)
blender = blender_parser("(0+1) * 2")
self.assertEqual(signal_blend([1, 2, 3], blender), 9)
blender = blender_parser("(0 + 1) * 2")
self.assertEqual(signal_blend([1, 2, 3], blender), 9)
# TODO: 目前对于-(1+2)这样的表达式还无法处理
# self.a_to_sell.set_blender('selecting', "-(0 + 1) * 2")
# self.assertEqual(self.a_to_sell.signal_blend([1, 2, 3]), -9)
blender = blender_parser("(0-1)/2 + 3")
print(f'RPN of notation: "(0-1)/2 + 3" is:\n'
f'{" ".join(blender[::-1])}')
self.assertAlmostEqual(signal_blend([1, 2, 3, 0.0], blender), -0.33333333)
blender = blender_parser("0 + 1 / 2")
print(f'RPN of notation: "0 + 1 / 2" is:\n'
f'{" ".join(blender[::-1])}')
self.assertAlmostEqual(signal_blend([1, math.pi, 4], blender), 1.78539816)
blender = blender_parser("(0 + 1) / 2")
print(f'RPN of notation: "(0 + 1) / 2" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(signal_blend([1, 2, 3], blender), 1)
blender = blender_parser("(0 + 1 * 2) / 3")
print(f'RPN of notation: "(0 + 1 * 2) / 3" is:\n'
f'{" ".join(blender[::-1])}')
self.assertAlmostEqual(signal_blend([3, math.e, 10, 10], blender), 3.0182818284590454)
blender = blender_parser("0 / 1 * 2")
print(f'RPN of notation: "0 / 1 * 2" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(signal_blend([1, 3, 6], blender), 2)
blender = blender_parser("(0 - 1 + 2) * 4")
print(f'RPN of notation: "(0 - 1 + 2) * 4" is:\n'
f'{" ".join(blender[::-1])}')
self.assertAlmostEqual(signal_blend([1, 1, -1, np.nan, math.pi], blender), -3.141592653589793)
blender = blender_parser("0 * 1")
print(f'RPN of notation: "0 * 1" is:\n'
f'{" ".join(blender[::-1])}')
self.assertAlmostEqual(signal_blend([math.pi, math.e], blender), 8.539734222673566)
blender = blender_parser('abs(3-sqrt(2) / cos(1))')
print(f'RPN of notation: "abs(3-sqrt(2) / cos(1))" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(blender, ['abs(1)', '-', '/', 'cos(1)', '1', 'sqrt(1)', '2', '3'])
blender = blender_parser('0/max(2,1,3 + 5)+4')
print(f'RPN of notation: "0/max(2,1,3 + 5)+4" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(blender, ['+', '4', '/', 'max(3)', '+', '5', '3', '1', '2', '0'])
blender = blender_parser('1 + sum(1,2,3+3, sum(1, 2) + 3) *5')
print(f'RPN of notation: "1 + sum(1,2,3+3, sum(1, 2) + 3) *5" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(blender, ['+', '*', '5', 'sum(4)', '+', '3', 'sum(2)', '2', '1',
'+', '3', '3', '2', '1', '1'])
blender = blender_parser('1+sum(1,2,(3+5)*4, sum(3, (4+5)*6), 7-8) * (2+3)')
print(f'RPN of notation: "1+sum(1,2,(3+5)*4, sum(3, (4+5)*6), 7-8) * (2+3)" is:\n'
f'{" ".join(blender[::-1])}')
self.assertEqual(blender, ['+', '*', '+', '3', '2', 'sum(5)', '-', '8', '7',
'sum(2)', '*', '6', '+', '5', '4', '3', '*', '4',
'+', '5', '3', '2', '1', '1'])
# TODO: ndarray type of signals to be tested:
def test_set_opt_par(self):
""" test setting opt pars in batch"""
print(f'--------- Testing setting Opt Pars: set_opt_par -------')
op = qt.Operator('dma, random, crossline')
op.set_parameter('dma',
pars=(5, 10, 5),
opt_tag=1,
par_boes=((5, 10), (5, 15), (10, 15)),
window_length=10,
data_types=['close', 'open', 'high'])
self.assertEqual(op.strategies[0].pars, (5, 10, 5))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (35, 120, 10, 'buy'))
self.assertEqual(op.opt_tags, [1, 0, 0])
op.set_opt_par((5, 12, 9))
self.assertEqual(op.strategies[0].pars, (5, 12, 9))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (35, 120, 10, 'buy'))
op.set_parameter('crossline',
pars=(5, 10, 5, 'sell'),
opt_tag=1,
par_boes=((5, 10), (5, 15), (10, 15), ('buy', 'sell', 'none')),
window_length=10,
data_types=['close', 'open', 'high'])
self.assertEqual(op.opt_tags, [1, 0, 1])
op.set_opt_par((5, 12, 9, 8, 26, 9, 'buy'))
self.assertEqual(op.strategies[0].pars, (5, 12, 9))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (8, 26, 9, 'buy'))
op.set_opt_par((9, 200, 155, 8, 26, 9, 'buy', 5, 12, 9))
self.assertEqual(op.strategies[0].pars, (9, 200, 155))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (8, 26, 9, 'buy'))
# test set_opt_par when opt_tag is set to be 2 (enumerate type of parameters)
op.set_parameter('crossline',
pars=(5, 10, 5, 'sell'),
opt_tag=2,
par_boes=((5, 10), (5, 15), (10, 15), ('buy', 'sell', 'none')),
window_length=10,
data_types=['close', 'open', 'high'])
self.assertEqual(op.opt_tags, [1, 0, 2])
self.assertEqual(op.strategies[0].pars, (9, 200, 155))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (5, 10, 5, 'sell'))
op.set_opt_par((5, 12, 9, (8, 26, 9, 'buy')))
self.assertEqual(op.strategies[0].pars, (5, 12, 9))
self.assertEqual(op.strategies[1].pars, (0.5,))
self.assertEqual(op.strategies[2].pars, (8, 26, 9, 'buy'))
# Test Errors
# Not enough values for parameter
op.set_parameter('crossline', opt_tag=1)
self.assertRaises(ValueError, op.set_opt_par, (5, 12, 9, 8))
# wrong type of input
self.assertRaises(AssertionError, op.set_opt_par, [5, 12, 9, 7, 15, 12, 'sell'])
def test_stg_attribute_get_and_set(self):
self.stg = qt.TimingCrossline()
self.stg_type = 'R-TIMING'
self.stg_name = "CROSSLINE"
self.stg_text = 'Moving average crossline strategy, determine long/short position according to the cross ' \
'point' \
' of long and short term moving average prices '
self.pars = (35, 120, 10, 'buy')
self.par_boes = [(10, 250), (10, 250), (1, 100), ('buy', 'sell', 'none')]
self.par_count = 4
self.par_types = ['discr', 'discr', 'conti', 'enum']
self.opt_tag = 0
self.data_types = ['close']
self.data_freq = 'd'
self.sample_freq = 'd'
self.window_length = 270
self.assertEqual(self.stg.stg_type, self.stg_type)
self.assertEqual(self.stg.stg_name, self.stg_name)
self.assertEqual(self.stg.stg_text, self.stg_text)
self.assertEqual(self.stg.pars, self.pars)
self.assertEqual(self.stg.par_types, self.par_types)
self.assertEqual(self.stg.par_boes, self.par_boes)
self.assertEqual(self.stg.par_count, self.par_count)
self.assertEqual(self.stg.opt_tag, self.opt_tag)
self.assertEqual(self.stg.data_freq, self.data_freq)
self.assertEqual(self.stg.sample_freq, self.sample_freq)
self.assertEqual(self.stg.data_types, self.data_types)
self.assertEqual(self.stg.window_length, self.window_length)
self.stg.stg_name = 'NEW NAME'
self.stg.stg_text = 'NEW TEXT'
self.assertEqual(self.stg.stg_name, 'NEW NAME')
self.assertEqual(self.stg.stg_text, 'NEW TEXT')
self.stg.pars = (1, 2, 3, 4)
self.assertEqual(self.stg.pars, (1, 2, 3, 4))
self.stg.par_count = 3
self.assertEqual(self.stg.par_count, 3)
self.stg.par_boes = [(1, 10), (1, 10), (1, 10), (1, 10)]
self.assertEqual(self.stg.par_boes, [(1, 10), (1, 10), (1, 10), (1, 10)])
self.stg.par_types = ['conti', 'conti', 'discr', 'enum']
self.assertEqual(self.stg.par_types, ['conti', 'conti', 'discr', 'enum'])
self.stg.par_types = 'conti, conti, discr, conti'
self.assertEqual(self.stg.par_types, ['conti', 'conti', 'discr', 'conti'])
self.stg.data_types = 'close, open'
self.assertEqual(self.stg.data_types, ['close', 'open'])
self.stg.data_types = ['close', 'high', 'low']
self.assertEqual(self.stg.data_types, ['close', 'high', 'low'])
self.stg.data_freq = 'w'
self.assertEqual(self.stg.data_freq, 'w')
self.stg.window_length = 300
self.assertEqual(self.stg.window_length, 300)
def test_rolling_timing(self):
stg = TestLSStrategy()
stg_pars = {'000100': (5, 10),
'000200': (5, 10),
'000300': (5, 6)}
stg.set_pars(stg_pars)
history_data = self.hp1.values
output = stg.generate(hist_data=history_data)
self.assertIsInstance(output, np.ndarray)
self.assertEqual(output.shape, (45, 3))
lsmask = np.array([[0., 0., 1.],
[0., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 0., 1.],
[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.],
[1., 1., 0.],
[1., 1., 0.],
[1., 1., 0.],
[1., 0., 0.],
[1., 0., 0.],
[1., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 0.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.],
[0., 1., 1.]])
# TODO: Issue to be solved: the np.nan value are converted to 0 in the lsmask，这样做可能会有意想不到的后果
# TODO: 需要解决nan值的问题
self.assertEqual(output.shape, lsmask.shape)
self.assertTrue(np.allclose(output, lsmask, equal_nan=True))
def test_sel_timing(self):
stg = TestSelStrategy()
stg_pars = ()
stg.set_pars(stg_pars)
history_data = self.hp1['high, low, close', :, :]
seg_pos, seg_length, seg_count = stg._seg_periods(dates=self.hp1.hdates, freq=stg.sample_freq)
self.assertEqual(list(seg_pos), [0, 5, 11, 19, 26, 33, 41, 47, 49])
self.assertEqual(list(seg_length), [5, 6, 8, 7, 7, 8, 6, 2])
self.assertEqual(seg_count, 8)
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
self.assertIsInstance(output, np.ndarray)
self.assertEqual(output.shape, (45, 3))
selmask = np.array([[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask))
def test_simple_timing(self):
stg = TestSigStrategy()
stg_pars = (0.2, 0.02, -0.02)
stg.set_pars(stg_pars)
history_data = self.hp1['close, open, high, low', :, 3:50]
output = stg.generate(hist_data=history_data, shares=self.shares, dates=self.date_indices)
self.assertIsInstance(output, np.ndarray)
self.assertEqual(output.shape, (45, 3))
sigmatrix = np.array([[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[-1.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 1.0],
[0.0, 1.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0]])
side_by_side_array = np.array([[i, out_line, sig_line]
for
i, out_line, sig_line
in zip(range(len(output)), output, sigmatrix)])
print(f'output and signal matrix lined up side by side is \n'
f'{side_by_side_array}')
self.assertEqual(sigmatrix.shape, output.shape)
self.assertTrue(np.allclose(output, sigmatrix))
def test_sel_finance(self):
"""Test selecting_finance strategy, test all built-in strategy parameters"""
stg = SelectingFinanceIndicator()
stg_pars = (False, 'even', 'greater', 0, 0, 0.67)
stg.set_pars(stg_pars)
stg.window_length = 5
stg.data_freq = 'd'
stg.sample_freq = '10d'
stg.sort_ascending = False
stg.condition = 'greater'
stg.lbound = 0
stg.ubound = 0
stg._poq = 0.67
history_data = self.hp2.values
print(f'Start to test financial selection parameter {stg_pars}')
seg_pos, seg_length, seg_count = stg._seg_periods(dates=self.hp1.hdates, freq=stg.sample_freq)
self.assertEqual(list(seg_pos), [0, 5, 11, 19, 26, 33, 41, 47, 49])
self.assertEqual(list(seg_length), [5, 6, 8, 7, 7, 8, 6, 2])
self.assertEqual(seg_count, 8)
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
self.assertIsInstance(output, np.ndarray)
self.assertEqual(output.shape, (45, 3))
selmask = np.array([[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask))
# test single factor, get mininum factor
stg_pars = (True, 'even', 'less', 1, 1, 0.67)
stg.sort_ascending = True
stg.condition = 'less'
stg.lbound = 1
stg.ubound = 1
stg.set_pars(stg_pars)
print(f'Start to test financial selection parameter {stg_pars}')
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
selmask = np.array([[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.0, 0.5]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask))
# test single factor, get max factor in linear weight
stg_pars = (False, 'linear', 'greater', 0, 0, 0.67)
stg.sort_ascending = False
stg.weighting = 'linear'
stg.condition = 'greater'
stg.lbound = 0
stg.ubound = 0
stg.set_pars(stg_pars)
print(f'Start to test financial selection parameter {stg_pars}')
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
selmask = np.array([[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.66667, 0.33333],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.00000, 0.33333, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.00000, 0.66667],
[0.33333, 0.66667, 0.00000],
[0.33333, 0.66667, 0.00000],
[0.33333, 0.66667, 0.00000]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask))
# test single factor, get max factor in linear weight
stg_pars = (False, 'proportion', 'greater', 0, 0, 0.67)
stg.sort_ascending = False
stg.weighting = 'proportion'
stg.condition = 'greater'
stg.lbound = 0
stg.ubound = 0
stg.set_pars(stg_pars)
print(f'Start to test financial selection parameter {stg_pars}')
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
selmask = np.array([[0.00000, 0.08333, 0.91667],
[0.00000, 0.08333, 0.91667],
[0.00000, 0.08333, 0.91667],
[0.00000, 0.08333, 0.91667],
[0.00000, 0.08333, 0.91667],
[0.00000, 0.08333, 0.91667],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.91667, 0.08333],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.00000, 0.50000, 0.50000],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.00000, 0.00000, 1.00000],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.00000, 0.91667],
[0.08333, 0.91667, 0.00000],
[0.08333, 0.91667, 0.00000],
[0.08333, 0.91667, 0.00000]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask, 0.001))
# test single factor, get max factor in linear weight, threshold 0.2
stg_pars = (False, 'even', 'greater', 0.2, 0.2, 0.67)
stg.sort_ascending = False
stg.weighting = 'even'
stg.condition = 'greater'
stg.lbound = 0.2
stg.ubound = 0.2
stg.set_pars(stg_pars)
print(f'Start to test financial selection parameter {stg_pars}')
output = stg.generate(hist_data=history_data, shares=self.hp1.shares, dates=self.hp1.hdates)
selmask = np.array([[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.5, 0.5],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0],
[0.5, 0.5, 0.0]])
self.assertEqual(output.shape, selmask.shape)
self.assertTrue(np.allclose(output, selmask, 0.001))
def test_tokenizer(self):
self.assertListEqual(_exp_to_token('1+1'),
['1', '+', '1'])
print(_exp_to_token('1+1'))
self.assertListEqual(_exp_to_token('1 & 1'),
['1', '&', '1'])
print(_exp_to_token('1&1'))
self.assertListEqual(_exp_to_token('1 and 1'),
['1', 'and', '1'])
print(_exp_to_token('1 and 1'))
self.assertListEqual(_exp_to_token('1 or 1'),
['1', 'or', '1'])
print(_exp_to_token('1 or 1'))
self.assertListEqual(_exp_to_token('(1 - 1 + -1) * pi'),
['(', '1', '-', '1', '+', '-1', ')', '*', 'pi'])
print(_exp_to_token('(1 - 1 + -1) * pi'))
self.assertListEqual(_exp_to_token('abs(5-sqrt(2) / cos(pi))'),
['abs(', '5', '-', 'sqrt(', '2', ')', '/', 'cos(', 'pi', ')', ')'])
print(_exp_to_token('abs(5-sqrt(2) / cos(pi))'))
self.assertListEqual(_exp_to_token('sin(pi) + 2.14'),
['sin(', 'pi', ')', '+', '2.14'])
print(_exp_to_token('sin(pi) + 2.14'))
self.assertListEqual(_exp_to_token('(1-2)/3.0 + 0.0000'),
['(', '1', '-', '2', ')', '/', '3.0', '+', '0.0000'])
print(_exp_to_token('(1-2)/3.0 + 0.0000'))
self.assertListEqual(_exp_to_token('-(1. + .2) * max(1, 3, 5)'),
['-', '(', '1.', '+', '.2', ')', '*', 'max(', '1', ',', '3', ',', '5', ')'])
print(_exp_to_token('-(1. + .2) * max(1, 3, 5)'))
self.assertListEqual(_exp_to_token('(x + e * 10) / 10'),
['(', 'x', '+', 'e', '*', '10', ')', '/', '10'])
print(_exp_to_token('(x + e * 10) / 10'))
self.assertListEqual(_exp_to_token('8.2/((-.1+abs3(3,4,5))*0.12)'),
['8.2', '/', '(', '(', '-.1', '+', 'abs3(', '3', ',', '4', ',', '5', ')', ')', '*', '0.12',
')'])
print(_exp_to_token('8.2/((-.1+abs3(3,4,5))*0.12)'))
self.assertListEqual(_exp_to_token('8.2/abs3(3,4,25.34 + 5)*0.12'),
['8.2', '/', 'abs3(', '3', ',', '4', ',', '25.34', '+', '5', ')', '*', '0.12'])
print(_exp_to_token('8.2/abs3(3,4,25.34 + 5)*0.12'))
class TestLog(unittest.TestCase):
def test_init(self):
pass
class TestConfig(unittest.TestCase):
"""测试Config对象以及QT_CONFIG变量的设置和获取值"""
def test_init(self):
pass
def test_invest(self):
pass
def test_pars_string_to_type(self):
_parse_string_kwargs('000300', 'asset_pool', _valid_qt_kwargs())
class TestHistoryPanel(unittest.TestCase):
def setUp(self):
print('start testing HistoryPanel object\n')
self.data = np.random.randint(10, size=(5, 10, 4))
self.index = pd.date_range(start='20200101', freq='d', periods=10)
self.index2 = ['2016-07-01', '2016-07-04', '2016-07-05', '2016-07-06',
'2016-07-07', '2016-07-08', '2016-07-11', '2016-07-12',
'2016-07-13', '2016-07-14']
self.index3 = '2016-07-01, 2016-07-04, 2016-07-05, 2016-07-06, 2016-07-07, ' \
'2016-07-08, 2016-07-11, 2016-07-12, 2016-07-13, 2016-07-14'
self.shares = '000100,000101,000102,000103,000104'
self.htypes = 'close,open,high,low'
self.data2 = np.random.randint(10, size=(10, 5))
self.data3 = np.random.randint(10, size=(10, 4))
self.data4 = np.random.randint(10, size=(10))
self.hp = qt.HistoryPanel(values=self.data, levels=self.shares, columns=self.htypes, rows=self.index)
self.hp2 = qt.HistoryPanel(values=self.data2, levels=self.shares, columns='close', rows=self.index)
self.hp3 = qt.HistoryPanel(values=self.data3, levels='000100', columns=self.htypes, rows=self.index2)
self.hp4 = qt.HistoryPanel(values=self.data4, levels='000100', columns='close', rows=self.index3)
self.hp5 = qt.HistoryPanel(values=self.data)
self.hp6 = qt.HistoryPanel(values=self.data, levels=self.shares, rows=self.index3)
def test_properties(self):
""" test all properties of HistoryPanel
"""
self.assertFalse(self.hp.is_empty)
self.assertEqual(self.hp.row_count, 10)
self.assertEqual(self.hp.column_count, 4)
self.assertEqual(self.hp.level_count, 5)
self.assertEqual(self.hp.shape, (5, 10, 4))
self.assertSequenceEqual(self.hp.htypes, ['close', 'open', 'high', 'low'])
self.assertSequenceEqual(self.hp.shares, ['000100', '000101', '000102', '000103', '000104'])
self.assertSequenceEqual(list(self.hp.hdates), list(self.index))
self.assertDictEqual(self.hp.columns, {'close': 0, 'open': 1, 'high': 2, 'low': 3})
self.assertDictEqual(self.hp.levels, {'000100': 0, '000101': 1, '000102': 2, '000103': 3, '000104': 4})
row_dict = {Timestamp('2020-01-01 00:00:00', freq='D'): 0,
Timestamp('2020-01-02 00:00:00', freq='D'): 1,
Timestamp('2020-01-03 00:00:00', freq='D'): 2,
Timestamp('2020-01-04 00:00:00', freq='D'): 3,
Timestamp('2020-01-05 00:00:00', freq='D'): 4,
Timestamp('2020-01-06 00:00:00', freq='D'): 5,
Timestamp('2020-01-07 00:00:00', freq='D'): 6,
Timestamp('2020-01-08 00:00:00', freq='D'): 7,
Timestamp('2020-01-09 00:00:00', freq='D'): 8,
Timestamp('2020-01-10 00:00:00', freq='D'): 9}
self.assertDictEqual(self.hp.rows, row_dict)
def test_len(self):
""" test the function len(HistoryPanel)
:return:
"""
self.assertEqual(len(self.hp), 10)
def test_empty_history_panel(self):
"""测试空HP或者特殊HP如维度标签为纯数字的HP"""
test_hp = qt.HistoryPanel(self.data)
self.assertFalse(test_hp.is_empty)
self.assertIsInstance(test_hp, qt.HistoryPanel)
self.assertEqual(test_hp.shape[0], 5)
self.assertEqual(test_hp.shape[1], 10)
self.assertEqual(test_hp.shape[2], 4)
self.assertEqual(test_hp.level_count, 5)
self.assertEqual(test_hp.row_count, 10)
self.assertEqual(test_hp.column_count, 4)
self.assertEqual(test_hp.shares, list(range(5)))
self.assertEqual(test_hp.hdates, list(pd.date_range(start='20200730', periods=10, freq='d')))
self.assertEqual(test_hp.htypes, list(range(4)))
self.assertTrue(np.allclose(test_hp.values, self.data))
print(f'shares: {test_hp.shares}\nhtypes: {test_hp.htypes}')
print(test_hp)
# HistoryPanel should be empty if no value is given
empty_hp = qt.HistoryPanel()
self.assertTrue(empty_hp.is_empty)
self.assertIsInstance(empty_hp, qt.HistoryPanel)
self.assertEqual(empty_hp.shape[0], 0)
self.assertEqual(empty_hp.shape[1], 0)
self.assertEqual(empty_hp.shape[2], 0)
self.assertEqual(empty_hp.level_count, 0)
self.assertEqual(empty_hp.row_count, 0)
self.assertEqual(empty_hp.column_count, 0)
# HistoryPanel should also be empty if empty value (np.array([])) is given
empty_hp = qt.HistoryPanel(np.empty((5, 0, 4)), levels=self.shares, columns=self.htypes)
self.assertTrue(empty_hp.is_empty)
self.assertIsInstance(empty_hp, qt.HistoryPanel)
self.assertEqual(empty_hp.shape[0], 0)
self.assertEqual(empty_hp.shape[1], 0)
self.assertEqual(empty_hp.shape[2], 0)
self.assertEqual(empty_hp.level_count, 0)
self.assertEqual(empty_hp.row_count, 0)
self.assertEqual(empty_hp.column_count, 0)
def test_create_history_panel(self):
""" test the creation of a HistoryPanel object by passing all data explicitly
"""
self.assertIsInstance(self.hp, qt.HistoryPanel)
self.assertEqual(self.hp.shape[0], 5)
self.assertEqual(self.hp.shape[1], 10)
self.assertEqual(self.hp.shape[2], 4)
self.assertEqual(self.hp.level_count, 5)
self.assertEqual(self.hp.row_count, 10)
self.assertEqual(self.hp.column_count, 4)
self.assertEqual(list(self.hp.levels.keys()), self.shares.split(','))
self.assertEqual(list(self.hp.columns.keys()), self.htypes.split(','))
self.assertEqual(list(self.hp.rows.keys())[0], pd.Timestamp('20200101'))
self.assertIsInstance(self.hp2, qt.HistoryPanel)
self.assertEqual(self.hp2.shape[0], 5)
self.assertEqual(self.hp2.shape[1], 10)
self.assertEqual(self.hp2.shape[2], 1)
self.assertEqual(self.hp2.level_count, 5)
self.assertEqual(self.hp2.row_count, 10)
self.assertEqual(self.hp2.column_count, 1)
self.assertEqual(list(self.hp2.levels.keys()), self.shares.split(','))
self.assertEqual(list(self.hp2.columns.keys()), ['close'])
self.assertEqual(list(self.hp2.rows.keys())[0], pd.Timestamp('20200101'))
self.assertIsInstance(self.hp3, qt.HistoryPanel)
self.assertEqual(self.hp3.shape[0], 1)
self.assertEqual(self.hp3.shape[1], 10)
self.assertEqual(self.hp3.shape[2], 4)
self.assertEqual(self.hp3.level_count, 1)
self.assertEqual(self.hp3.row_count, 10)
self.assertEqual(self.hp3.column_count, 4)
self.assertEqual(list(self.hp3.levels.keys()), ['000100'])
self.assertEqual(list(self.hp3.columns.keys()), self.htypes.split(','))
self.assertEqual(list(self.hp3.rows.keys())[0], pd.Timestamp('2016-07-01'))
self.assertIsInstance(self.hp4, qt.HistoryPanel)
self.assertEqual(self.hp4.shape[0], 1)
self.assertEqual(self.hp4.shape[1], 10)
self.assertEqual(self.hp4.shape[2], 1)
self.assertEqual(self.hp4.level_count, 1)
self.assertEqual(self.hp4.row_count, 10)
self.assertEqual(self.hp4.column_count, 1)
self.assertEqual(list(self.hp4.levels.keys()), ['000100'])
self.assertEqual(list(self.hp4.columns.keys()), ['close'])
self.assertEqual(list(self.hp4.rows.keys())[0], pd.Timestamp('2016-07-01'))
self.hp5.info()
self.assertIsInstance(self.hp5, qt.HistoryPanel)
self.assertTrue(np.allclose(self.hp5.values, self.data))
self.assertEqual(self.hp5.shape[0], 5)
self.assertEqual(self.hp5.shape[1], 10)
self.assertEqual(self.hp5.shape[2], 4)
self.assertEqual(self.hp5.level_count, 5)
self.assertEqual(self.hp5.row_count, 10)
self.assertEqual(self.hp5.column_count, 4)
self.assertEqual(list(self.hp5.levels.keys()), [0, 1, 2, 3, 4])
self.assertEqual(list(self.hp5.columns.keys()), [0, 1, 2, 3])
self.assertEqual(list(self.hp5.rows.keys())[0], pd.Timestamp('2020-07-30'))
self.hp6.info()
self.assertIsInstance(self.hp6, qt.HistoryPanel)
self.assertTrue(np.allclose(self.hp6.values, self.data))
self.assertEqual(self.hp6.shape[0], 5)
self.assertEqual(self.hp6.shape[1], 10)
self.assertEqual(self.hp6.shape[2], 4)
self.assertEqual(self.hp6.level_count, 5)
self.assertEqual(self.hp6.row_count, 10)
self.assertEqual(self.hp6.column_count, 4)
self.assertEqual(list(self.hp6.levels.keys()), ['000100', '000101', '000102', '000103', '000104'])
self.assertEqual(list(self.hp6.columns.keys()), [0, 1, 2, 3])
self.assertEqual(list(self.hp6.rows.keys())[0], pd.Timestamp('2016-07-01'))
print('test creating HistoryPanel with very limited data')
print('test creating HistoryPanel with 2D data')
temp_data = | np.random.randint(10, size=(7, 3)) | numpy.random.randint |
import cv2 as cv
import argparse
import os
import numpy as np
def nearest_resize(pic, scale):
"""
nearest resize
:param pic: img
:param scale: scale >0
:return: resized img
"""
h,w,c = pic.shape # height,width,channel
th, tw = int(h * scale), int(w * scale)
# avoid the out of bounds from the original img
pic = np.pad(pic, ((0, 1), (0, 1), (0, 0)), 'reflect')
emptyImage = np.zeros((th, tw,c ), np.uint8)
h_scale = h/th
w_scale = w/tw
for i in range(th):
for j in range(tw):
# 首先找到在原图中对应的点的(X, Y)坐标
#first, find the location from the original img
corr_x = (i + 0.5)*h_scale - 0.5
corr_y = (j + 0.5)*w_scale - 0.5
emptyImage[i, j, :] = pic[int(corr_x), int(corr_y), :]
return emptyImage
def conv2D(img,kernel,padding,stride):
"""
convlution 2D
:param img: img with size [h,w,c]
:param kernel: with size [kh,kw,c] or [kh,kw]
:param padding: padding number
:param stride: stride
:return: filted img
"""
h,w,c = img.shape # height,width,channel
if kernel.ndim==2:
kernel = np.expand_dims(kernel, axis=-1)
kh,kw,kc = kernel.shape #kernel h, kernel w, kernel channel,
assert kc == 1 or kc == c
oh = int((h-kh+2*padding)/stride)+1 #out height
ow = int((w-kw+2*padding)/stride)+1 #out width
#out
emptyImage = np.zeros((oh, ow, c), np.float)
img = np.pad(img,((padding, padding), (padding, padding), (0, 0)), 'constant')
for i in range(oh):
for j in range(ow):
i_idx = i*stride
j_idx = j*stride
tmp_out = img[i_idx:i_idx+kh,j_idx:j_idx+kw,:]*kernel
for cc in range(c):
emptyImage[i,j,cc] = | np.sum(tmp_out[:,:,cc]) | numpy.sum |
import numpy as np
from fidimag.common import CuboidMesh
from fidimag.micro import TimeZeeman
def time_fun(t, frequency):
return 10*np.cos(frequency*t)
def fixture_setup(nx, ny, nz):
"""
Fixtures for the tests
"""
dx = 10.0/nx
spin = np.zeros(3*nx*ny*nz)
Ms = np.zeros(nx*ny*nz)
Ms_inv = | np.zeros(nx*ny*nz) | numpy.zeros |
from stuff import *
# Get weekday pattern from case data in order to identify exact date on SGTF graph
# 0 mod 7 is Thursday in daytodate notation (being 1970-01-01)
nc={}
with open('SAcases','r') as fp:
for x in fp:
y=x.split()
nc[datetoday(y[0])]=int(y[1])
minday=min(nc)
maxday=max(nc)
c0=[0]*7
c1=[0]*7
for d in range(minday+3,maxday-3):
ex=[nc[r] for r in range(d-3,d+4)]
if min(ex)>=50:
i=d%7
c0[i]+=1
c1[i]+=nc[d]*7/sum(ex)
#for i in range(7):
# print(i,c1[i]/c0[i])
# Thur 1.184
# Fri 1.170
# Sat 1.122
# Sun 0.913
# Mon 0.655
# Tue 0.766
# Wed 1.158
if 0:
infile='OmicronSGTF.png'
dateorigin=datetoday('2021-10-01')-564
row0,row1=23,359
col0,col1=81,614
y0=(0,358);y1=(50,43)
z0=(0,357);z1=(1600,126)
if 1:
infile='OmicronSGTF_frompdf.png'
dateorigin=datetoday('2021-10-01')-564
row0,row1=11,345
col0,col1=81,614
y0=(0,344.5);y1=(50,32)
z0=(0,344.5);z1=(2000,57.5)
# SGTF image from slide 12 of https://sacoronavirus.co.za/2021/11/25/sars-cov-2-sequencing-new-variant-update-25-november-2021/
# resized down by a factor of 2/3 in order to get 1 horizontal pixel = 1 day.
from PIL import Image
import numpy as np
im_frame = Image.open(infile)
cc = np.array(im_frame,dtype=int)
im_frame.close()
# Top-leftian, row before column
r=cc.shape[0]
c=cc.shape[1]
# Get blueness
bb=cc[:,:,2]*2-(cc[:,:,0]+cc[:,:,1])
def process(bb,name):
bb1=bb[row0:row1,:]
mm=row0+np.argmax(bb1,axis=0)
im=Image.fromarray(((bb-bb.min())/(bb.max()-bb.min())*255.999+0.0005).astype(np.dtype('uint8')))
im.save(name+'_filtered.png')
oo=cc.astype(np.dtype('uint8'))
for x in range(col0,col1): oo[mm[x],x]=[255,0,0]
im=Image.fromarray(oo)
im.save(name+'_sgtf.png')
sgtf={}
for x in range(col0,col1):
sgtf[daytodate(dateorigin+x)]=(mm[x]-y1[1])/(y0[1]-y1[1])*(y0[0]-y1[0])+y1[0]
with open(name+'_sgtf','w') as fp:
for date in sorted(list(sgtf)):
print(date,"%6.2f"%sgtf[date],file=fp)
return mm,sgtf
process(bb,'simple')
lrantialias=bb-np.maximum(np.roll(bb,1,1),np.roll(bb,-1,1))
process(lrantialias,'LRantialias')
# Hybrid because deantialiasing method is likely to work well for the vertical spike, but not when derivative is low.
spike=605
hybrid=np.concatenate([bb[:,:spike],lrantialias[:,spike:]],axis=1)
mm,sgtf=process(hybrid,'hybrid')
dd=cc[:,:,0]-np.maximum(cc[:,:,1],cc[:,:,2])
oo=(dd>3).astype(np.dtype('uint8'))*255
im=Image.fromarray(oo)
im.save('temp.png')
ee=(dd>3)*1000+np.tile( | np.arange(r-1,-1,-1) | numpy.arange |
# -*- coding: utf-8 -*-
# Created on Tue Dec 18 16:49:20 2019
# @author: arthurd
"""
HexGrid Module.
Generate Hexagonal grid. Cartesian-Hexagonal coordinates interaction.
"""
import numpy as np
import math
import matplotlib.pyplot as plt
from pyproj import Proj, Transformer
def hexbin_grid(bbox, side_length=1, proj_init=None, proj_out=None):
"""
Create a grid of hexagons.
See http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
Parameters
----------
bbox : Tuple
Box of the area to generate the hexagons.
Format : Lower X, Lower Y, Upper X, Upper Y.
side_length : float, optional
Side length of the hexagons. The default is 1.
proj_init : String, optional
If working with coordinates and the hexagons need to be calculated in another
coordinates system, proj_init refers to the starting coordinates system.
The default is None.
proj_out : String, optional
If working with coordinates and the hexagons need to be calculated in another
coordinates system, proj_out refers to the ending coordinates system.
The default is None.
Example
-------
If the bbox is in geographic coordinates, but the hexgrid should be computed
on the web mercator system.
Then,
>>> proj_init="epsg:4326"
>>> proj_out="epsg:3857"
Returns
-------
polygons : List
List of hexagons. An hexagons is a list of coordinates (tuple, Lat, Lon).
"""
startx = bbox[0]
starty = bbox[1]
endx = bbox[2]
endy = bbox[3]
proj = proj_init != proj_out
if proj:
transformer = Transformer.from_proj(Proj(init=proj_init), Proj(init=proj_out))
startx, starty = transformer.transform(startx, starty)
endx, endy = transformer.transform(endx, endy)
# calculate coordinates of the hexagon points
p = side_length * 0.5
b = side_length * math.cos(math.radians(30))
w = b * 2
h = 2 * side_length
# offset start and end coordinates by hex widths and heights to guarantee coverage
startx = startx - w
starty = starty - h/2
endx = endx
endy = endy
origx = startx
# offsets for moving along and up rows
xoffset = b
yoffset = 3 * p
P1 = np.empty((0, 2))
P2 = np.empty((0, 2))
P3 = np.empty((0, 2))
P4 = np.empty((0, 2))
P5 = np.empty((0, 2))
P6 = np.empty((0, 2))
row = 0
while starty < endy:
if row % 2 == 0:
startx = origx + xoffset
else:
startx = origx + w
while startx <= endx:
p1 = [startx, starty + p]
p2 = [startx, starty + (3 * p)]
p3 = [startx + b, starty + h]
p4 = [startx + w, starty + (3 * p)]
p5 = [startx + w, starty + p]
p6 = [startx + b, starty]
P1 = np.vstack((P1, p1))
P2 = np.vstack((P2, p2))
P3 = np.vstack((P3, p3))
P4 = np.vstack((P4, p4))
P5 = | np.vstack((P5, p5)) | numpy.vstack |
"""
Visualize Genetic Algorithm to find the shortest path for travel sales problem.
Visit my tutorial website for more: https://mofanpy.com/tutorials/
"""
import matplotlib.pyplot as plt
import numpy as np
N_CITIES = 20 # DNA size
CROSS_RATE = 0.1
MUTATE_RATE = 0.02
POP_SIZE = 500
N_GENERATIONS = 500
class GA(object):
def __init__(self, DNA_size, cross_rate, mutation_rate, pop_size, ):
self.DNA_size = DNA_size
self.cross_rate = cross_rate
self.mutate_rate = mutation_rate
self.pop_size = pop_size
self.pop = np.vstack([np.random.permutation(DNA_size) for _ in range(pop_size)])
def translateDNA(self, DNA, city_position): # get cities' coord in order
line_x = np.empty_like(DNA, dtype=np.float64)
line_y = np.empty_like(DNA, dtype=np.float64)
for i, d in enumerate(DNA):
city_coord = city_position[d]
line_x[i, :] = city_coord[:, 0]
line_y[i, :] = city_coord[:, 1]
return line_x, line_y
def get_fitness(self, line_x, line_y):
total_distance = np.empty((line_x.shape[0],), dtype=np.float64)
for i, (xs, ys) in enumerate(zip(line_x, line_y)):
total_distance[i] = np.sum(np.sqrt(np.square(np.diff(xs)) + np.square(np.diff(ys))))
fitness = np.exp(self.DNA_size * 2 / total_distance)
return fitness, total_distance
def select(self, fitness):
idx = np.random.choice(np.arange(self.pop_size), size=self.pop_size, replace=True, p=fitness / fitness.sum())
return self.pop[idx]
def crossover(self, parent, pop):
if np.random.rand() < self.cross_rate:
i_ = np.random.randint(0, self.pop_size, size=1) # select another individual from pop
cross_points = | np.random.randint(0, 2, self.DNA_size) | numpy.random.randint |
# -*- coding: utf-8 -*-
from __future__ import print_function
from __future__ import absolute_import
import os
import sys
import tempfile
import warnings
import numpy
from numpy import testing as npt
import tables
from tables import Atom, ClosedNodeError, NoSuchNodeError
from tables.utils import byteorders
from tables.tests import common
from tables.tests.common import allequal
from tables.tests.common import unittest, test_filename
from tables.tests.common import PyTablesTestCase as TestCase
from six.moves import range
#warnings.resetwarnings()
class BasicTestCase(TestCase):
"""Basic test for all the supported typecodes present in numpy.
All of them are included on pytables.
"""
endiancheck = False
def write_read(self, testarray):
a = testarray
if common.verbose:
print('\n', '-=' * 30)
print("Running test for array with type '%s'" % a.dtype.type,
end=' ')
print("for class check:", self.title)
# Create an instance of HDF5 file
filename = tempfile.mktemp(".h5")
try:
with tables.open_file(filename, mode="w") as fileh:
root = fileh.root
# Create the array under root and name 'somearray'
if self.endiancheck and a.dtype.kind != "S":
b = a.byteswap()
b.dtype = a.dtype.newbyteorder()
a = b
fileh.create_array(root, 'somearray', a, "Some array")
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
root = fileh.root
# Read the saved array
b = root.somearray.read()
# Compare them. They should be equal.
if common.verbose and not allequal(a, b):
print("Write and read arrays differ!")
# print("Array written:", a)
print("Array written shape:", a.shape)
print("Array written itemsize:", a.itemsize)
print("Array written type:", a.dtype.type)
# print("Array read:", b)
print("Array read shape:", b.shape)
print("Array read itemsize:", b.itemsize)
print("Array read type:", b.dtype.type)
if a.dtype.kind != "S":
print("Array written byteorder:", a.dtype.byteorder)
print("Array read byteorder:", b.dtype.byteorder)
# Check strictly the array equality
self.assertEqual(a.shape, b.shape)
self.assertEqual(a.shape, root.somearray.shape)
if a.dtype.kind == "S":
self.assertEqual(root.somearray.atom.type, "string")
else:
self.assertEqual(a.dtype.type, b.dtype.type)
self.assertEqual(a.dtype.type,
root.somearray.atom.dtype.type)
abo = byteorders[a.dtype.byteorder]
bbo = byteorders[b.dtype.byteorder]
if abo != "irrelevant":
self.assertEqual(abo, root.somearray.byteorder)
self.assertEqual(bbo, sys.byteorder)
if self.endiancheck:
self.assertNotEqual(bbo, abo)
obj = root.somearray
self.assertEqual(obj.flavor, 'numpy')
self.assertEqual(obj.shape, a.shape)
self.assertEqual(obj.ndim, a.ndim)
self.assertEqual(obj.chunkshape, None)
if a.shape:
nrows = a.shape[0]
else:
# scalar
nrows = 1
self.assertEqual(obj.nrows, nrows)
self.assertTrue(allequal(a, b))
finally:
# Then, delete the file
os.remove(filename)
def write_read_out_arg(self, testarray):
a = testarray
if common.verbose:
print('\n', '-=' * 30)
print("Running test for array with type '%s'" % a.dtype.type,
end=' ')
print("for class check:", self.title)
# Create an instance of HDF5 file
filename = tempfile.mktemp(".h5")
try:
with tables.open_file(filename, mode="w") as fileh:
root = fileh.root
# Create the array under root and name 'somearray'
if self.endiancheck and a.dtype.kind != "S":
b = a.byteswap()
b.dtype = a.dtype.newbyteorder()
a = b
fileh.create_array(root, 'somearray', a, "Some array")
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
root = fileh.root
# Read the saved array
b = numpy.empty_like(a, dtype=a.dtype)
root.somearray.read(out=b)
# Check strictly the array equality
self.assertEqual(a.shape, b.shape)
self.assertEqual(a.shape, root.somearray.shape)
if a.dtype.kind == "S":
self.assertEqual(root.somearray.atom.type, "string")
else:
self.assertEqual(a.dtype.type, b.dtype.type)
self.assertEqual(a.dtype.type,
root.somearray.atom.dtype.type)
abo = byteorders[a.dtype.byteorder]
bbo = byteorders[b.dtype.byteorder]
if abo != "irrelevant":
self.assertEqual(abo, root.somearray.byteorder)
self.assertEqual(abo, bbo)
if self.endiancheck:
self.assertNotEqual(bbo, sys.byteorder)
self.assertTrue(allequal(a, b))
finally:
# Then, delete the file
os.remove(filename)
def write_read_atom_shape_args(self, testarray):
a = testarray
atom = Atom.from_dtype(a.dtype)
shape = a.shape
byteorder = None
if common.verbose:
print('\n', '-=' * 30)
print("Running test for array with type '%s'" % a.dtype.type,
end=' ')
print("for class check:", self.title)
# Create an instance of HDF5 file
filename = tempfile.mktemp(".h5")
try:
with tables.open_file(filename, mode="w") as fileh:
root = fileh.root
# Create the array under root and name 'somearray'
if self.endiancheck and a.dtype.kind != "S":
b = a.byteswap()
b.dtype = a.dtype.newbyteorder()
if b.dtype.byteorder in ('>', '<'):
byteorder = byteorders[b.dtype.byteorder]
a = b
ptarr = fileh.create_array(root, 'somearray',
atom=atom, shape=shape,
title="Some array",
# specify the byteorder explicitly
# since there is no way to deduce
# it in this case
byteorder=byteorder)
self.assertEqual(shape, ptarr.shape)
self.assertEqual(atom, ptarr.atom)
ptarr[...] = a
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
root = fileh.root
# Read the saved array
b = root.somearray.read()
# Compare them. They should be equal.
if common.verbose and not allequal(a, b):
print("Write and read arrays differ!")
# print("Array written:", a)
print("Array written shape:", a.shape)
print("Array written itemsize:", a.itemsize)
print("Array written type:", a.dtype.type)
# print("Array read:", b)
print("Array read shape:", b.shape)
print("Array read itemsize:", b.itemsize)
print("Array read type:", b.dtype.type)
if a.dtype.kind != "S":
print("Array written byteorder:", a.dtype.byteorder)
print("Array read byteorder:", b.dtype.byteorder)
# Check strictly the array equality
self.assertEqual(a.shape, b.shape)
self.assertEqual(a.shape, root.somearray.shape)
if a.dtype.kind == "S":
self.assertEqual(root.somearray.atom.type, "string")
else:
self.assertEqual(a.dtype.type, b.dtype.type)
self.assertEqual(a.dtype.type,
root.somearray.atom.dtype.type)
abo = byteorders[a.dtype.byteorder]
bbo = byteorders[b.dtype.byteorder]
if abo != "irrelevant":
self.assertEqual(abo, root.somearray.byteorder)
self.assertEqual(bbo, sys.byteorder)
if self.endiancheck:
self.assertNotEqual(bbo, abo)
obj = root.somearray
self.assertEqual(obj.flavor, 'numpy')
self.assertEqual(obj.shape, a.shape)
self.assertEqual(obj.ndim, a.ndim)
self.assertEqual(obj.chunkshape, None)
if a.shape:
nrows = a.shape[0]
else:
# scalar
nrows = 1
self.assertEqual(obj.nrows, nrows)
self.assertTrue(allequal(a, b))
finally:
# Then, delete the file
os.remove(filename)
def setup00_char(self):
"""Data integrity during recovery (character objects)"""
if not isinstance(self.tupleChar, numpy.ndarray):
a = numpy.array(self.tupleChar, dtype="S")
else:
a = self.tupleChar
return a
def test00_char(self):
a = self.setup00_char()
self.write_read(a)
def test00_char_out_arg(self):
a = self.setup00_char()
self.write_read_out_arg(a)
def test00_char_atom_shape_args(self):
a = self.setup00_char()
self.write_read_atom_shape_args(a)
def test00b_char(self):
"""Data integrity during recovery (string objects)"""
a = self.tupleChar
filename = tempfile.mktemp(".h5")
try:
# Create an instance of HDF5 file
with tables.open_file(filename, mode="w") as fileh:
fileh.create_array(fileh.root, 'somearray', a, "Some array")
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
# Read the saved array
b = fileh.root.somearray.read()
if isinstance(a, bytes):
self.assertEqual(type(b), bytes)
self.assertEqual(a, b)
else:
# If a is not a python string, then it should be a list
# or ndarray
self.assertTrue(type(b) in [list, numpy.ndarray])
finally:
# Then, delete the file
os.remove(filename)
def test00b_char_out_arg(self):
"""Data integrity during recovery (string objects)"""
a = self.tupleChar
filename = tempfile.mktemp(".h5")
try:
# Create an instance of HDF5 file
with tables.open_file(filename, mode="w") as fileh:
fileh.create_array(fileh.root, 'somearray', a, "Some array")
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
# Read the saved array
b = numpy.empty_like(a)
if fileh.root.somearray.flavor != 'numpy':
self.assertRaises(TypeError,
lambda: fileh.root.somearray.read(out=b))
else:
fileh.root.somearray.read(out=b)
self.assertTrue(type(b), numpy.ndarray)
finally:
# Then, delete the file
os.remove(filename)
def test00b_char_atom_shape_args(self):
"""Data integrity during recovery (string objects)"""
a = self.tupleChar
filename = tempfile.mktemp(".h5")
try:
# Create an instance of HDF5 file
with tables.open_file(filename, mode="w") as fileh:
nparr = numpy.asarray(a)
atom = Atom.from_dtype(nparr.dtype)
shape = nparr.shape
if nparr.dtype.byteorder in ('>', '<'):
byteorder = byteorders[nparr.dtype.byteorder]
else:
byteorder = None
ptarr = fileh.create_array(fileh.root, 'somearray',
atom=atom, shape=shape,
byteorder=byteorder,
title="Some array")
self.assertEqual(shape, ptarr.shape)
self.assertEqual(atom, ptarr.atom)
ptarr[...] = a
# Re-open the file in read-only mode
with tables.open_file(filename, mode="r") as fileh:
# Read the saved array
b = numpy.empty_like(a)
if fileh.root.somearray.flavor != 'numpy':
self.assertRaises(TypeError,
lambda: fileh.root.somearray.read(out=b))
else:
fileh.root.somearray.read(out=b)
self.assertTrue(type(b), numpy.ndarray)
finally:
# Then, delete the file
os.remove(filename)
def setup01_char_nc(self):
"""Data integrity during recovery (non-contiguous character objects)"""
if not isinstance(self.tupleChar, numpy.ndarray):
a = numpy.array(self.tupleChar, dtype="S")
else:
a = self.tupleChar
if a.ndim == 0:
b = a.copy()
else:
b = a[::2]
# Ensure that this numpy string is non-contiguous
if len(b) > 1:
self.assertEqual(b.flags.contiguous, False)
return b
def test01_char_nc(self):
b = self.setup01_char_nc()
self.write_read(b)
def test01_char_nc_out_arg(self):
b = self.setup01_char_nc()
self.write_read_out_arg(b)
def test01_char_nc_atom_shape_args(self):
b = self.setup01_char_nc()
self.write_read_atom_shape_args(b)
def test02_types(self):
"""Data integrity during recovery (numerical types)"""
typecodes = ['int8', 'int16', 'int32', 'int64',
'uint8', 'uint16', 'uint32', 'uint64',
'float32', 'float64',
'complex64', 'complex128']
for name in ('float16', 'float96', 'float128',
'complex192', 'complex256'):
atomname = name.capitalize() + 'Atom'
if hasattr(tables, atomname):
typecodes.append(name)
for typecode in typecodes:
a = numpy.array(self.tupleInt, typecode)
self.write_read(a)
b = numpy.array(self.tupleInt, typecode)
self.write_read_out_arg(b)
c = numpy.array(self.tupleInt, typecode)
self.write_read_atom_shape_args(c)
def test03_types_nc(self):
"""Data integrity during recovery (non-contiguous numerical types)"""
typecodes = ['int8', 'int16', 'int32', 'int64',
'uint8', 'uint16', 'uint32', 'uint64',
'float32', 'float64',
'complex64', 'complex128', ]
for name in ('float16', 'float96', 'float128',
'complex192', 'complex256'):
atomname = name.capitalize() + 'Atom'
if hasattr(tables, atomname):
typecodes.append(name)
for typecode in typecodes:
a = numpy.array(self.tupleInt, typecode)
if a.ndim == 0:
b1 = a.copy()
b2 = a.copy()
b3 = a.copy()
else:
b1 = a[::2]
b2 = a[::2]
b3 = a[::2]
# Ensure that this array is non-contiguous
if len(b1) > 1:
self.assertEqual(b1.flags.contiguous, False)
if len(b2) > 1:
self.assertEqual(b2.flags.contiguous, False)
if len(b3) > 1:
self.assertEqual(b3.flags.contiguous, False)
self.write_read(b1)
self.write_read_out_arg(b2)
self.write_read_atom_shape_args(b3)
class Basic0DOneTestCase(BasicTestCase):
# Scalar case
title = "Rank-0 case 1"
tupleInt = 3
tupleChar = b"3"
endiancheck = True
class Basic0DTwoTestCase(BasicTestCase):
# Scalar case
title = "Rank-0 case 2"
tupleInt = 33
tupleChar = b"33"
endiancheck = True
class Basic1DZeroTestCase(BasicTestCase):
# This test case is not supported by PyTables (HDF5 limitations)
# 1D case
title = "Rank-1 case 0"
tupleInt = ()
tupleChar = ()
endiancheck = False
class Basic1DOneTestCase(BasicTestCase):
# 1D case
title = "Rank-1 case 1"
tupleInt = (3,)
tupleChar = (b"a",)
endiancheck = True
class Basic1DTwoTestCase(BasicTestCase):
# 1D case
title = "Rank-1 case 2"
tupleInt = (3, 4)
tupleChar = (b"aaa",)
endiancheck = True
class Basic1DThreeTestCase(BasicTestCase):
# 1D case
title = "Rank-1 case 3"
tupleInt = (3, 4, 5)
tupleChar = (b"aaa", b"bbb",)
endiancheck = True
class Basic2DOneTestCase(BasicTestCase):
# 2D case
title = "Rank-2 case 1"
tupleInt = numpy.array(numpy.arange((4)**2))
tupleInt.shape = (4,)*2
tupleChar = numpy.array(["abc"]*3**2, dtype="S3")
tupleChar.shape = (3,)*2
endiancheck = True
class Basic2DTwoTestCase(BasicTestCase):
# 2D case, with a multidimensional dtype
title = "Rank-2 case 2"
tupleInt = numpy.array(numpy.arange((4)), dtype=(numpy.int_, (4,)))
tupleChar = numpy.array(["abc"]*3, dtype=("S3", (3,)))
endiancheck = True
class Basic10DTestCase(BasicTestCase):
# 10D case
title = "Rank-10 test"
tupleInt = numpy.array(numpy.arange((2)**10))
tupleInt.shape = (2,)*10
tupleChar = numpy.array(
["abc"]*2**10, dtype="S3")
tupleChar.shape = (2,)*10
endiancheck = True
class Basic32DTestCase(BasicTestCase):
# 32D case (maximum)
title = "Rank-32 test"
tupleInt = numpy.array((32,))
tupleInt.shape = (1,)*32
tupleChar = numpy.array(["121"], dtype="S3")
tupleChar.shape = (1,)*32
class ReadOutArgumentTests(common.TempFileMixin, TestCase):
def setUp(self):
super(ReadOutArgumentTests, self).setUp()
self.size = 1000
def create_array(self):
array = numpy.arange(self.size, dtype='f8')
disk_array = self.h5file.create_array('/', 'array', array)
return array, disk_array
def test_read_entire_array(self):
array, disk_array = self.create_array()
out_buffer = numpy.empty((self.size, ), 'f8')
disk_array.read(out=out_buffer)
numpy.testing.assert_equal(out_buffer, array)
def test_read_contiguous_slice1(self):
array, disk_array = self.create_array()
out_buffer = numpy.arange(self.size, dtype='f8')
out_buffer = numpy.random.permutation(out_buffer)
out_buffer_orig = out_buffer.copy()
start = self.size // 2
disk_array.read(start=start, stop=self.size, out=out_buffer[start:])
numpy.testing.assert_equal(out_buffer[start:], array[start:])
numpy.testing.assert_equal(out_buffer[:start], out_buffer_orig[:start])
def test_read_contiguous_slice2(self):
array, disk_array = self.create_array()
out_buffer = numpy.arange(self.size, dtype='f8')
out_buffer = numpy.random.permutation(out_buffer)
out_buffer_orig = out_buffer.copy()
start = self.size // 4
stop = self.size - start
disk_array.read(start=start, stop=stop, out=out_buffer[start:stop])
numpy.testing.assert_equal(out_buffer[start:stop], array[start:stop])
numpy.testing.assert_equal(out_buffer[:start], out_buffer_orig[:start])
numpy.testing.assert_equal(out_buffer[stop:], out_buffer_orig[stop:])
def test_read_non_contiguous_slice_contiguous_buffer(self):
array, disk_array = self.create_array()
out_buffer = numpy.empty((self.size // 2, ), dtype='f8')
disk_array.read(start=0, stop=self.size, step=2, out=out_buffer)
numpy.testing.assert_equal(out_buffer, array[0:self.size:2])
def test_read_non_contiguous_buffer(self):
array, disk_array = self.create_array()
out_buffer = numpy.empty((self.size, ), 'f8')
out_buffer_slice = out_buffer[0:self.size:2]
# once Python 2.6 support is dropped, this could change
# to assertRaisesRegexp to check exception type and message at once
self.assertRaises(ValueError, disk_array.read, 0, self.size, 2,
out_buffer_slice)
try:
disk_array.read(0, self.size, 2, out_buffer_slice)
except ValueError as exc:
self.assertEqual('output array not C contiguous', str(exc))
def test_buffer_too_small(self):
array, disk_array = self.create_array()
out_buffer = numpy.empty((self.size // 2, ), 'f8')
self.assertRaises(ValueError, disk_array.read, 0, self.size, 1,
out_buffer)
try:
disk_array.read(0, self.size, 1, out_buffer)
except ValueError as exc:
self.assertTrue('output array size invalid, got' in str(exc))
def test_buffer_too_large(self):
array, disk_array = self.create_array()
out_buffer = numpy.empty((self.size + 1, ), 'f8')
self.assertRaises(ValueError, disk_array.read, 0, self.size, 1,
out_buffer)
try:
disk_array.read(0, self.size, 1, out_buffer)
except ValueError as exc:
self.assertTrue('output array size invalid, got' in str(exc))
class SizeOnDiskInMemoryPropertyTestCase(common.TempFileMixin, TestCase):
def setUp(self):
super(SizeOnDiskInMemoryPropertyTestCase, self).setUp()
self.array_size = (10, 10)
self.array = self.h5file.create_array(
'/', 'somearray', numpy.zeros(self.array_size, 'i4'))
def test_all_zeros(self):
self.assertEqual(self.array.size_on_disk, 10 * 10 * 4)
self.assertEqual(self.array.size_in_memory, 10 * 10 * 4)
class UnalignedAndComplexTestCase(common.TempFileMixin, TestCase):
"""Basic test for all the supported typecodes present in numpy.
Most of them are included on PyTables.
"""
def setUp(self):
super(UnalignedAndComplexTestCase, self).setUp()
self.root = self.h5file.root
def write_read(self, testArray):
if common.verbose:
print('\n', '-=' * 30)
print("\nRunning test for array with type '%s'" %
testArray.dtype.type)
# Create the array under root and name 'somearray'
a = testArray
if self.endiancheck:
byteorder = {"little": "big", "big": "little"}[sys.byteorder]
else:
byteorder = sys.byteorder
self.h5file.create_array(self.root, 'somearray', a, "Some array",
byteorder=byteorder)
if self.reopen:
self._reopen()
self.root = self.h5file.root
# Read the saved array
b = self.root.somearray.read()
# Get an array to be compared in the correct byteorder
c = a.newbyteorder(byteorder)
# Compare them. They should be equal.
if not allequal(c, b) and common.verbose:
print("Write and read arrays differ!")
print("Array written:", a)
print("Array written shape:", a.shape)
print("Array written itemsize:", a.itemsize)
print("Array written type:", a.dtype.type)
print("Array read:", b)
print("Array read shape:", b.shape)
print("Array read itemsize:", b.itemsize)
print("Array read type:", b.dtype.type)
# Check strictly the array equality
self.assertEqual(a.shape, b.shape)
self.assertEqual(a.shape, self.root.somearray.shape)
if a.dtype.byteorder != "|":
self.assertEqual(a.dtype, b.dtype)
self.assertEqual(a.dtype, self.root.somearray.atom.dtype)
self.assertEqual(byteorders[b.dtype.byteorder], sys.byteorder)
self.assertEqual(self.root.somearray.byteorder, byteorder)
self.assertTrue(allequal(c, b))
def test01_signedShort_unaligned(self):
"""Checking an unaligned signed short integer array"""
r = numpy.rec.array(b'a'*200, formats='i1,f4,i2', shape=10)
a = r["f2"]
# Ensure that this array is non-aligned
self.assertEqual(a.flags.aligned, False)
self.assertEqual(a.dtype.type, numpy.int16)
self.write_read(a)
def test02_float_unaligned(self):
"""Checking an unaligned single precision array"""
r = numpy.rec.array(b'a'*200, formats='i1,f4,i2', shape=10)
a = r["f1"]
# Ensure that this array is non-aligned
self.assertEqual(a.flags.aligned, 0)
self.assertEqual(a.dtype.type, numpy.float32)
self.write_read(a)
def test03_byte_offset(self):
"""Checking an offsetted byte array"""
r = | numpy.arange(100, dtype=numpy.int8) | numpy.arange |
"""Tests for the policies in the hbaselines/goal_conditioned subdirectory."""
import unittest
import numpy as np
import tensorflow as tf
from gym.spaces import Box
from hbaselines.utils.tf_util import get_trainable_vars
from hbaselines.goal_conditioned.td3 import GoalConditionedPolicy as \
TD3GoalConditionedPolicy
from hbaselines.goal_conditioned.sac import GoalConditionedPolicy as \
SACGoalConditionedPolicy
from hbaselines.algorithms.off_policy import SAC_PARAMS, TD3_PARAMS
from hbaselines.algorithms.off_policy import GOAL_CONDITIONED_PARAMS
class TestBaseGoalConditionedPolicy(unittest.TestCase):
"""Test GoalConditionedPolicy in hbaselines/goal_conditioned/base.py."""
def setUp(self):
self.policy_params = {
'sess': tf.compat.v1.Session(),
'ac_space': Box(low=-1, high=1, shape=(1,)),
'ob_space': Box(low=-2, high=2, shape=(2,)),
'co_space': Box(low=-3, high=3, shape=(2,)),
'verbose': 0,
}
self.policy_params.update(TD3_PARAMS.copy())
self.policy_params.update(GOAL_CONDITIONED_PARAMS.copy())
def tearDown(self):
self.policy_params['sess'].close()
del self.policy_params
# Clear the graph.
tf.compat.v1.reset_default_graph()
def test_store_transition(self):
"""Check the functionality of the store_transition() method.
This method is tested for the following cases:
1. hindsight = False, relative_goals = False
2. hindsight = False, relative_goals = True
3. hindsight = True, relative_goals = False
4. hindsight = True, relative_goals = True
"""
# =================================================================== #
# test case 1 #
# =================================================================== #
policy_params = self.policy_params.copy()
policy_params['relative_goals'] = False
policy_params['hindsight'] = False
policy_params['subgoal_testing_rate'] = 1
policy_params['meta_period'] = 4
policy_params['batch_size'] = 2
policy = TD3GoalConditionedPolicy(**policy_params)
# Initialize the variables of the policy.
policy.sess.run(tf.compat.v1.global_variables_initializer())
# Run the initialize method.
policy.initialize()
policy._meta_action = [np.array([5, 5])]
for i in range(4):
obs0 = np.array([i for _ in range(2)])
context0 = np.array([i for _ in range(3)])
action = np.array([i for _ in range(1)])
reward = i
obs1 = np.array([i+1 for _ in range(2)])
context1 = np.array([i for _ in range(3)])
done, is_final_step, evaluate = False, False, False
policy.store_transition(
obs0=obs0,
context0=context0,
action=action,
reward=reward,
obs1=obs1,
context1=context1,
done=done,
is_final_step=is_final_step,
evaluate=evaluate,
env_num=0,
)
obs_t = policy.replay_buffer._obs_t[0]
action_t = policy.replay_buffer._action_t[0]
reward = policy.replay_buffer._reward_t[0]
done = policy.replay_buffer._done_t[0]
# check the various attributes
self.assertTrue(
all(all(obs_t[i] ==
[np.array([0, 0]),
np.array([1, 1]),
np.array([2, 2]),
np.array([3, 3]),
np.array([4, 4])][i])
for i in range(len(obs_t)))
)
for i in range(len(action_t)):
self.assertTrue(
all(all(action_t[i][j] ==
[[np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5])],
[np.array([0]),
np.array([1]),
np.array([2]),
np.array([3])]][i][j])
for j in range(len(action_t[i])))
)
self.assertEqual(reward,
[[6], [-5.656854249501219, -4.24264068713107,
-2.8284271247638677, -1.4142135624084504]])
self.assertEqual(done,
[False, False, False, False])
def test_store_transition_2(self):
policy_params = self.policy_params.copy()
policy_params['relative_goals'] = True
policy_params['hindsight'] = False
policy_params['subgoal_testing_rate'] = 1
policy_params['meta_period'] = 4
policy_params['batch_size'] = 2
policy = TD3GoalConditionedPolicy(**policy_params)
# Initialize the variables of the policy.
policy.sess.run(tf.compat.v1.global_variables_initializer())
# Run the initialize method.
policy.initialize()
policy._meta_action = [np.array([5, 5])]
for i in range(4):
obs0 = np.array([i for _ in range(2)])
context0 = np.array([i for _ in range(3)])
action = np.array([i for _ in range(1)])
reward = i
obs1 = np.array([i+1 for _ in range(2)])
context1 = np.array([i for _ in range(3)])
done, is_final_step, evaluate = False, False, False
policy.store_transition(
obs0=obs0,
context0=context0,
action=action,
reward=reward,
obs1=obs1,
context1=context1,
done=done,
is_final_step=is_final_step,
evaluate=evaluate,
env_num=0,
)
obs_t = policy.replay_buffer._obs_t[0]
action_t = policy.replay_buffer._action_t[0]
reward = policy.replay_buffer._reward_t[0]
done = policy.replay_buffer._done_t[0]
# check the various attributes
self.assertTrue(
all(all(obs_t[i] ==
[np.array([0, 0]),
np.array([1, 1]),
np.array([2, 2]),
np.array([3, 3]),
np.array([4, 4])][i])
for i in range(len(obs_t)))
)
for i in range(len(action_t)):
self.assertTrue(
all(all(action_t[i][j] ==
[[np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([4, 4])],
[np.array([0]),
np.array([1]),
np.array([2]),
np.array([3])]][i][j])
for j in range(len(action_t[i])))
)
self.assertEqual(reward,
[[6], [-5.656854249501219, -5.656854249501219,
-5.656854249501219, -5.656854249501219]])
self.assertEqual(done, [False, False, False, False])
def test_store_transition_3(self):
policy_params = self.policy_params.copy()
policy_params['relative_goals'] = False
policy_params['hindsight'] = True
policy_params['subgoal_testing_rate'] = 1
policy_params['meta_period'] = 4
policy_params['batch_size'] = 2
policy = TD3GoalConditionedPolicy(**policy_params)
# Initialize the variables of the policy.
policy.sess.run(tf.compat.v1.global_variables_initializer())
# Run the initialize method.
policy.initialize()
policy._meta_action = [np.array([5, 5])]
for i in range(4):
obs0 = np.array([i for _ in range(2)])
context0 = np.array([i for _ in range(3)])
action = np.array([i for _ in range(1)])
reward = i
obs1 = np.array([i+1 for _ in range(2)])
context1 = np.array([i for _ in range(3)])
done, is_final_step, evaluate = False, False, False
policy.store_transition(
obs0=obs0,
context0=context0,
action=action,
reward=reward,
obs1=obs1,
context1=context1,
done=done,
is_final_step=is_final_step,
evaluate=evaluate,
env_num=0,
)
# unchanged sample
obs_t = policy.replay_buffer._obs_t[0]
action_t = policy.replay_buffer._action_t[0]
reward_t = policy.replay_buffer._reward_t[0]
done_t = policy.replay_buffer._done_t[0]
# check the various attributes
self.assertTrue(
all(all(obs_t[i] ==
[np.array([0, 0]),
np.array([1, 1]),
np.array([2, 2]),
np.array([3, 3]),
np.array([4, 4])][i])
for i in range(len(obs_t)))
)
for i in range(len(action_t)):
self.assertTrue(
all(all(action_t[i][j] ==
[[np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5]),
np.array([5, 5])],
[np.array([0]),
np.array([1]),
np.array([2]),
np.array([3])]][i][j])
for j in range(len(action_t[i])))
)
self.assertEqual(reward_t,
[[6], [-5.656854249501219, -4.24264068713107,
-2.8284271247638677, -1.4142135624084504]])
self.assertEqual(done_t, [False, False, False, False])
# hindsight sample
obs_t = policy.replay_buffer._obs_t[1]
action_t = policy.replay_buffer._action_t[1]
reward_t = policy.replay_buffer._reward_t[1]
done_t = policy.replay_buffer._done_t[1]
# check the various attributes
self.assertTrue(
all(all(obs_t[i] ==
[np.array([0, 0]),
np.array([1, 1]),
np.array([2, 2]),
np.array([3, 3]),
np.array([4, 4])][i])
for i in range(len(obs_t)))
)
for i in range(len(action_t)):
self.assertTrue(
all(all(action_t[i][j] ==
[[np.array([4, 4]),
np.array([4, 4]),
np.array([4, 4]),
np.array([4, 4]),
np.array([4, 4])],
[ | np.array([0]) | numpy.array |
import sys
import optparse
import logging
import time
from matplotlib.backends.backend_pdf import PdfPages
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from matplotlib.projections import PolarAxes
from matplotlib.ticker import MultipleLocator,FormatStrFormatter
import katpoint
from katpoint import rad2deg, deg2rad
# from katsdpscripts.RTS import git_info,get_git_path
def angle_wrap(angle, period=2.0 * np.pi):
"""Wrap angle into the interval -*period* / 2 ... *period* / 2."""
return (angle + 0.5 * period) % period - 0.5 * period
def save_pointingmodel(filebase,model):
# Save pointing model to file
outfile = file(filebase + '.csv', 'w')
outfile.write(model.description)
outfile.close()
logger.debug("Saved %d-parameter pointing model to '%s'" % (len(model.params), filebase + '.csv'))
# These fields contain strings, while the rest of the fields are assumed to contain floats
string_fields = ['dataset', 'target', 'timestamp_ut', 'data_unit']
# Create a date/time string for current time
now = time.strftime('%Y-%m-%d_%Hh%M')
def read_offsetfile(filename):
# Load data file in one shot as an array of strings
string_fields = ['dataset', 'target', 'timestamp_ut', 'data_unit']
data = np.loadtxt(filename, dtype='string', comments='#', delimiter=', ')
# Interpret first non-comment line as header
fields = data[0].tolist()
# By default, all fields are assumed to contain floats
formats = np.tile(np.float, len(fields))
# The string_fields are assumed to contain strings - use data's string type, as it is of sufficient length
formats[[fields.index(name) for name in string_fields if name in fields]] = data.dtype
# Convert to heterogeneous record array
data = np.rec.fromarrays(data[1:].transpose(), dtype=list(zip(fields, formats)))
# Load antenna description string from first line of file and construct antenna object from it
antenna = katpoint.Antenna(file(filename).readline().strip().partition('=')[2])
# Use the pointing model contained in antenna object as the old model (if not overridden by file)
# If the antenna has no model specified, a default null model will be used
return data,antenna
def referencemetrics(ant,az, el,measured_delta_az, measured_delta_el,delta_azimuth_std=0,delta_elevation_std=0,num_samples_limit=1):
"""Determine and sky RMS from pointing model."""
text = []
measured_delta_xel = measured_delta_az* np.cos(el) # scale due to sky shape
abs_sky_error = np.ma.array(data=measured_delta_xel,mask=False)
model_delta_az, model_delta_el = ant.pointing_model.offset(az, el)
residual_az = measured_delta_az - model_delta_az
residual_el = measured_delta_el - model_delta_el
residual_xel = residual_az * | np.cos(el) | numpy.cos |
from __future__ import division, print_function
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.backends.backend_pdf import PdfPages
from mpl_toolkits.axes_grid1 import make_axes_locatable
from mpl_toolkits.mplot3d import Axes3D
import streakline
#import streakline2
import myutils
import ffwd
from streams import load_stream, vcirc_potential, store_progparams, wrap_angles, progenitor_prior
#import streams
import astropy
import astropy.units as u
from astropy.constants import G
from astropy.table import Table
import astropy.coordinates as coord
import gala.coordinates as gc
import scipy.linalg as la
import scipy.interpolate
import scipy.optimize
import zscale
import itertools
import copy
import pickle
# observers
# defaults taken as in astropy v2.0 icrs
mw_observer = {'z_sun': 27.*u.pc, 'galcen_distance': 8.3*u.kpc, 'roll': 0*u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051*u.deg, dec=-28.936175*u.deg, frame='icrs')}
vsun = {'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}
vsun0 = {'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}
gc_observer = {'z_sun': 27.*u.pc, 'galcen_distance': 0.1*u.kpc, 'roll': 0*u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051*u.deg, dec=-28.936175*u.deg, frame='icrs')}
vgc = {'vcirc': 0*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}
vgc0 = {'vcirc': 0*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}
MASK = -9999
pparams_fid = [np.log10(0.5e10)*u.Msun, 0.7*u.kpc, np.log10(6.8e10)*u.Msun, 3*u.kpc, 0.28*u.kpc, 430*u.km/u.s, 30*u.kpc, 1.57*u.rad, 1*u.Unit(1), 1*u.Unit(1), 1*u.Unit(1), 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0*u.deg, 0*u.deg, 0*u.kpc, 0*u.km/u.s, 0*u.mas/u.yr, 0*u.mas/u.yr]
#pparams_fid = [0.5e-5*u.Msun, 0.7*u.kpc, 6.8e-5*u.Msun, 3*u.kpc, 0.28*u.kpc, 430*u.km/u.s, 30*u.kpc, 1.57*u.rad, 1*u.Unit(1), 1*u.Unit(1), 1*u.Unit(1), 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0*u.deg, 0*u.deg, 0*u.kpc, 0*u.km/u.s, 0*u.mas/u.yr, 0*u.mas/u.yr]
class Stream():
def __init__(self, x0=[]*u.kpc, v0=[]*u.km/u.s, progenitor={'coords': 'galactocentric', 'observer': {}, 'pm_polar': False}, potential='nfw', pparams=[], minit=2e4*u.Msun, mfinal=2e4*u.Msun, rcl=20*u.pc, dr=0.5, dv=2*u.km/u.s, dt=1*u.Myr, age=6*u.Gyr, nstars=600, integrator='lf'):
"""Initialize """
setup = {}
if progenitor['coords']=='galactocentric':
setup['x0'] = x0
setup['v0'] = v0
elif (progenitor['coords']=='equatorial') & (len(progenitor['observer'])!=0):
if progenitor['pm_polar']:
a = v0[1].value
phi = v0[2].value
v0[1] = a*np.sin(phi)*u.mas/u.yr
v0[2] = a*np.cos(phi)*u.mas/u.yr
# convert positions
xeq = coord.SkyCoord(x0[0], x0[1], x0[2], **progenitor['observer'])
xgal = xeq.transform_to(coord.Galactocentric)
setup['x0'] = [xgal.x.to(u.kpc), xgal.y.to(u.kpc), xgal.z.to(u.kpc)]*u.kpc
# convert velocities
setup['v0'] = gc.vhel_to_gal(xeq.icrs, rv=v0[0], pm=v0[1:], **vsun)
#setup['v0'] = [v.to(u.km/u.s) for v in vgal]*u.km/u.s
else:
raise ValueError('Observer position needed!')
setup['dr'] = dr
setup['dv'] = dv
setup['minit'] = minit
setup['mfinal'] = mfinal
setup['rcl'] = rcl
setup['dt'] = dt
setup['age'] = age
setup['nstars'] = nstars
setup['integrator'] = integrator
setup['potential'] = potential
setup['pparams'] = pparams
self.setup = setup
self.setup_aux = {}
self.fill_intid()
self.fill_potid()
self.st_params = self.format_input()
def fill_intid(self):
"""Assign integrator ID for a given integrator choice
Assumes setup dictionary has an 'integrator' key"""
if self.setup['integrator']=='lf':
self.setup_aux['iaux'] = 0
elif self.setup['integrator']=='rk':
self.setup_aux['iaux'] = 1
def fill_potid(self):
"""Assign potential ID for a given potential choice
Assumes d has a 'potential' key"""
if self.setup['potential']=='nfw':
self.setup_aux['paux'] = 3
elif self.setup['potential']=='log':
self.setup_aux['paux'] = 2
elif self.setup['potential']=='point':
self.setup_aux['paux'] = 0
elif self.setup['potential']=='gal':
self.setup_aux['paux'] = 4
elif self.setup['potential']=='lmc':
self.setup_aux['paux'] = 6
elif self.setup['potential']=='dipole':
self.setup_aux['paux'] = 8
elif self.setup['potential']=='quad':
self.setup_aux['paux'] = 9
elif self.setup['potential']=='octu':
self.setup_aux['paux'] = 10
def format_input(self):
"""Format input parameters for streakline.stream"""
p = [None]*12
# progenitor position
p[0] = self.setup['x0'].si.value
p[1] = self.setup['v0'].si.value
# potential parameters
p[2] = [x.si.value for x in self.setup['pparams']]
# stream smoothing offsets
p[3] = [self.setup['dr'], self.setup['dv'].si.value]
# potential and integrator choice
p[4] = self.setup_aux['paux']
p[5] = self.setup_aux['iaux']
# number of steps and stream stars
p[6] = int(self.setup['age']/self.setup['dt'])
p[7] = int(p[6]/self.setup['nstars'])
# cluster properties
p[8] = self.setup['minit'].si.value
p[9] = self.setup['mfinal'].si.value
p[10] = self.setup['rcl'].si.value
# time step
p[11] = self.setup['dt'].si.value
return p
def generate(self):
"""Create streakline model for a stream of set parameters"""
#xm1, xm2, xm3, xp1, xp2, xp3, vm1, vm2, vm3, vp1, vp2, vp3 = streakline.stream(*p)
stream = streakline.stream(*self.st_params)
self.leading = {}
self.leading['x'] = stream[:3]*u.m
self.leading['v'] = stream[6:9]*u.m/u.s
self.trailing = {}
self.trailing['x'] = stream[3:6]*u.m
self.trailing['v'] = stream[9:12]*u.m/u.s
def observe(self, mode='cartesian', wangle=0*u.deg, units=[], errors=[], nstars=-1, sequential=False, present=[], logerr=False, observer={'z_sun': 0.*u.pc, 'galcen_distance': 8.3*u.kpc, 'roll': 0*u.deg, 'galcen_ra': 300*u.deg, 'galcen_dec': 20*u.deg}, vobs={'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}, footprint='none', rotmatrix=None):
"""Observe the stream
stream.obs holds all observations
stream.err holds all errors"""
x = np.concatenate((self.leading['x'].to(u.kpc).value, self.trailing['x'].to(u.kpc).value), axis=1) * u.kpc
v = np.concatenate((self.leading['v'].to(u.km/u.s).value, self.trailing['v'].to(u.km/u.s).value), axis=1) * u.km/u.s
if mode=='cartesian':
# returns coordinates in following order
# x(x, y, z), v(vx, vy, vz)
if len(units)<2:
units.append(self.trailing['x'].unit)
units.append(self.trailing['v'].unit)
if len(errors)<2:
errors.append(0.2*u.kpc)
errors.append(2*u.km/u.s)
# positions
x = x.to(units[0])
ex = np.ones(np.shape(x))*errors[0]
ex = ex.to(units[0])
# velocities
v = v.to(units[1])
ev = np.ones(np.shape(v))*errors[1]
ev = ev.to(units[1])
self.obs = np.concatenate([x,v]).value
self.err = np.concatenate([ex,ev]).value
elif mode=='equatorial':
# assumes coordinates in the following order:
# ra, dec, distance, vrad, mualpha, mudelta
if len(units)!=6:
units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr]
if len(errors)!=6:
errors = [0.2*u.deg, 0.2*u.deg, 0.5*u.kpc, 1*u.km/u.s, 0.2*u.mas/u.yr, 0.2*u.mas/u.yr]
# define reference frame
xgal = coord.Galactocentric(x, **observer)
#frame = coord.Galactocentric(**observer)
# convert
xeq = xgal.transform_to(coord.ICRS)
veq = gc.vgal_to_hel(xeq, v, **vobs)
# store coordinates
ra, dec, dist = [xeq.ra.to(units[0]).wrap_at(wangle), xeq.dec.to(units[1]), xeq.distance.to(units[2])]
vr, mua, mud = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])]
obs = np.hstack([ra, dec, dist, vr, mua, mud]).value
obs = np.reshape(obs,(6,-1))
if footprint=='sdss':
infoot = dec > -2.5*u.deg
obs = obs[:,infoot]
if np.allclose(rotmatrix, np.eye(3))!=1:
xi, eta = myutils.rotate_angles(obs[0], obs[1], rotmatrix)
obs[0] = xi
obs[1] = eta
self.obs = obs
# store errors
err = np.ones(np.shape(self.obs))
if logerr:
for i in range(6):
err[i] *= np.exp(errors[i].to(units[i]).value)
else:
for i in range(6):
err[i] *= errors[i].to(units[i]).value
self.err = err
self.obsunit = units
self.obserror = errors
# randomly select nstars from the stream
if nstars>-1:
if sequential:
select = np.linspace(0, np.shape(self.obs)[1], nstars, endpoint=False, dtype=int)
else:
select = np.random.randint(low=0, high=np.shape(self.obs)[1], size=nstars)
self.obs = self.obs[:,select]
self.err = self.err[:,select]
# include only designated dimensions
if len(present)>0:
self.obs = self.obs[present]
self.err = self.err[present]
self.obsunit = [ self.obsunit[x] for x in present ]
self.obserror = [ self.obserror[x] for x in present ]
def prog_orbit(self):
"""Generate progenitor orbital history"""
orbit = streakline.orbit(self.st_params[0], self.st_params[1], self.st_params[2], self.st_params[4], self.st_params[5], self.st_params[6], self.st_params[11], -1)
self.orbit = {}
self.orbit['x'] = orbit[:3]*u.m
self.orbit['v'] = orbit[3:]*u.m/u.s
def project(self, name, N=1000, nbatch=-1):
"""Project the stream from observed to native coordinates"""
poly = np.loadtxt("../data/{0:s}_all.txt".format(name))
self.streak = np.poly1d(poly)
self.streak_x = np.linspace(np.min(self.obs[0])-2, np.max(self.obs[0])+2, N)
self.streak_y = np.polyval(self.streak, self.streak_x)
self.streak_b = np.zeros(N)
self.streak_l = np.zeros(N)
pdot = np.polyder(poly)
for i in range(N):
length = scipy.integrate.quad(self._delta_path, self.streak_x[0], self.streak_x[i], args=(pdot,))
self.streak_l[i] = length[0]
XB = np.transpose(np.vstack([self.streak_x, self.streak_y]))
n = np.shape(self.obs)[1]
if nbatch<0:
nstep = 0
nbatch = -1
else:
nstep = np.int(n/nbatch)
i1 = 0
i2 = nbatch
for i in range(nstep):
XA = np.transpose(np.vstack([np.array(self.obs[0][i1:i2]), np.array(self.obs[1][i1:i2])]))
self.emdist(XA, XB, i1=i1, i2=i2)
i1 += nbatch
i2 += nbatch
XA = np.transpose(np.vstack([np.array(self.catalog['ra'][i1:]), np.array(self.catalog['dec'][i1:])]))
self.emdist(XA, XB, i1=i1, i2=n)
#self.catalog.write("../data/{0:s}_footprint_catalog.txt".format(self.name), format='ascii.commented_header')
def emdist(self, XA, XB, i1=0, i2=-1):
""""""
distances = scipy.spatial.distance.cdist(XA, XB)
self.catalog['b'][i1:i2] = np.min(distances, axis=1)
imin = np.argmin(distances, axis=1)
self.catalog['b'][i1:i2][self.catalog['dec'][i1:i2]<self.streak_y[imin]] *= -1
self.catalog['l'][i1:i2] = self.streak_l[imin]
def _delta_path(self, x, pdot):
"""Return integrand for calculating length of a path along a polynomial"""
return np.sqrt(1 + np.polyval(pdot, x)**2)
def plot(self, mode='native', fig=None, color='k', **kwargs):
"""Plot stream"""
# Plotting
if fig==None:
plt.close()
plt.figure()
ax = plt.axes([0.12,0.1,0.8,0.8])
if mode=='native':
# Color setup
cindices = np.arange(self.setup['nstars']) # colors of stream particles
nor = mpl.colors.Normalize(vmin=0, vmax=self.setup['nstars']) # colormap normalization
plt.plot(self.setup['x0'][0].to(u.kpc).value, self.setup['x0'][2].to(u.kpc).value, 'wo', ms=10, mew=2, zorder=3)
plt.scatter(self.trailing['x'][0].to(u.kpc).value, self.trailing['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='winter', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1)
plt.scatter(self.leading['x'][0].to(u.kpc).value, self.leading['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='autumn', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1)
plt.xlabel("X (kpc)")
plt.ylabel("Z (kpc)")
elif mode=='observed':
plt.subplot(221)
plt.plot(self.obs[0], self.obs[1], 'o', color=color, **kwargs)
plt.xlabel("RA")
plt.ylabel("Dec")
plt.subplot(223)
plt.plot(self.obs[0], self.obs[2], 'o', color=color, **kwargs)
plt.xlabel("RA")
plt.ylabel("Distance")
plt.subplot(222)
plt.plot(self.obs[3], self.obs[4], 'o', color=color, **kwargs)
plt.xlabel("V$_r$")
plt.ylabel("$\mu\\alpha$")
plt.subplot(224)
plt.plot(self.obs[3], self.obs[5], 'o', color=color, **kwargs)
plt.xlabel("V$_r$")
plt.ylabel("$\mu\delta$")
plt.tight_layout()
#plt.minorticks_on()
def read(self, fname, units={'x': u.kpc, 'v': u.km/u.s}):
"""Read stream star positions from a file"""
t = np.loadtxt(fname).T
n = np.shape(t)[1]
ns = int((n-1)/2)
self.setup['nstars'] = ns
# progenitor
self.setup['x0'] = t[:3,0] * units['x']
self.setup['v0'] = t[3:,0] * units['v']
# leading tail
self.leading = {}
self.leading['x'] = t[:3,1:ns+1] * units['x']
self.leading['v'] = t[3:,1:ns+1] * units['v']
# trailing tail
self.trailing = {}
self.trailing['x'] = t[:3,ns+1:] * units['x']
self.trailing['v'] = t[3:,ns+1:] * units['v']
def save(self, fname):
"""Save stream star positions to a file"""
# define table
t = Table(names=('x', 'y', 'z', 'vx', 'vy', 'vz'))
# add progenitor info
t.add_row(np.ravel([self.setup['x0'].to(u.kpc).value, self.setup['v0'].to(u.km/u.s).value]))
# add leading tail infoobsmode
tt = Table(np.concatenate((self.leading['x'].to(u.kpc).value, self.leading['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz'))
t = astropy.table.vstack([t,tt])
# add trailing tail info
tt = Table(np.concatenate((self.trailing['x'].to(u.kpc).value, self.trailing['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz'))
t = astropy.table.vstack([t,tt])
# save to file
t.write(fname, format='ascii.commented_header')
# make a streakline model of a stream
def stream_model(name='gd1', pparams0=pparams_fid, dt=0.2*u.Myr, rotmatrix=np.eye(3), graph=False, graphsave=False, observer=mw_observer, vobs=vsun, footprint='', obsmode='equatorial'):
"""Create a streakline model of a stream
baryonic component as in kupper+2015: 3.4e10*u.Msun, 0.7*u.kpc, 1e11*u.Msun, 6.5*u.kpc, 0.26*u.kpc"""
# vary progenitor parameters
mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb'))
for i in range(3):
mock['x0'][i] += pparams0[26+i]
mock['v0'][i] += pparams0[29+i]
# vary potential parameters
potential = 'octu'
pparams = pparams0[:26]
#print(pparams[0])
pparams[0] = (10**pparams0[0].value)*pparams0[0].unit
pparams[2] = (10**pparams0[2].value)*pparams0[2].unit
#pparams[0] = pparams0[0]*1e15
#pparams[2] = pparams0[2]*1e15
#print(pparams[0])
# adjust circular velocity in this halo
vobs['vcirc'] = vcirc_potential(observer['galcen_distance'], pparams=pparams)
# create a model stream with these parameters
params = {'generate': {'x0': mock['x0'], 'v0': mock['v0'], 'progenitor': {'coords': 'equatorial', 'observer': mock['observer'], 'pm_polar': False}, 'potential': potential, 'pparams': pparams, 'minit': mock['mi'], 'mfinal': mock['mf'], 'rcl': 20*u.pc, 'dr': 0., 'dv': 0*u.km/u.s, 'dt': dt, 'age': mock['age'], 'nstars': 400, 'integrator': 'lf'}, 'observe': {'mode': mock['obsmode'], 'wangle': mock['wangle'], 'nstars':-1, 'sequential':True, 'errors': [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s, 0.5*u.mas/u.yr, 0.5*u.mas/u.yr], 'present': [0,1,2,3,4,5], 'observer': mock['observer'], 'vobs': mock['vobs'], 'footprint': mock['footprint'], 'rotmatrix': rotmatrix}}
stream = Stream(**params['generate'])
stream.generate()
stream.observe(**params['observe'])
################################
# Plot observed stream and model
if graph:
observed = load_stream(name)
Ndim = np.shape(observed.obs)[0]
modcol = 'k'
obscol = 'orange'
ylabel = ['Dec (deg)', 'Distance (kpc)', 'Radial velocity (km/s)']
plt.close()
fig, ax = plt.subplots(1, 3, figsize=(12,4))
for i in range(3):
plt.sca(ax[i])
plt.gca().invert_xaxis()
plt.xlabel('R.A. (deg)')
plt.ylabel(ylabel[i])
plt.plot(observed.obs[0], observed.obs[i+1], 's', color=obscol, mec='none', ms=8, label='Observed stream')
plt.plot(stream.obs[0], stream.obs[i+1], 'o', color=modcol, mec='none', ms=4, label='Fiducial model')
if i==0:
plt.legend(frameon=False, handlelength=0.5, fontsize='small')
plt.tight_layout()
if graphsave:
plt.savefig('../plots/mock_observables_{}_p{}.png'.format(name, potential), dpi=150)
return stream
def progenitor_params(n):
"""Return progenitor parameters for a given stream"""
if n==-1:
age = 1.6*u.Gyr
mi = 1e4*u.Msun
mf = 2e-1*u.Msun
x0, v0 = gd1_coordinates(observer=mw_observer)
elif n==-2:
age = 2.7*u.Gyr
mi = 1e5*u.Msun
mf = 2e4*u.Msun
x0, v0 = pal5_coordinates(observer=mw_observer, vobs=vsun0)
elif n==-3:
age = 3.5*u.Gyr
mi = 5e4*u.Msun
mf = 2e-1*u.Msun
x0, v0 = tri_coordinates(observer=mw_observer)
elif n==-4:
age = 2*u.Gyr
mi = 2e4*u.Msun
mf = 2e-1*u.Msun
x0, v0 = atlas_coordinates(observer=mw_observer)
out = {'x0': x0, 'v0': v0, 'age': age, 'mi': mi, 'mf': mf}
return out
def gal2eq(x, v, observer=mw_observer, vobs=vsun0):
""""""
# define reference frame
xgal = coord.Galactocentric(np.array(x)[:,np.newaxis]*u.kpc, **observer)
# convert
xeq = xgal.transform_to(coord.ICRS)
veq = gc.vgal_to_hel(xeq, np.array(v)[:,np.newaxis]*u.km/u.s, **vobs)
# store coordinates
units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr]
xobs = [xeq.ra.to(units[0]), xeq.dec.to(units[1]), xeq.distance.to(units[2])]
vobs = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])]
return(xobs, vobs)
def gd1_coordinates(observer=mw_observer):
"""Approximate GD-1 progenitor coordinates"""
x = coord.SkyCoord(ra=154.377*u.deg, dec=41.5309*u.deg, distance=8.2*u.kpc, **observer)
x_ = x.galactocentric
x0 = [x_.x.value, x_.y.value, x_.z.value]
v0 = [-90, -250, -120]
return (x0, v0)
def pal5_coordinates(observer=mw_observer, vobs=vsun0):
"""Pal5 coordinates"""
# sdss
ra = 229.0128*u.deg
dec = -0.1082*u.deg
# bob's rrlyrae
d = 21.7*u.kpc
# harris
#d = 23.2*u.kpc
# odenkirchen 2002
vr = -58.7*u.km/u.s
# fritz & kallivayalil 2015
mua = -2.296*u.mas/u.yr
mud = -2.257*u.mas/u.yr
d = 24*u.kpc
x = coord.SkyCoord(ra=ra, dec=dec, distance=d, **observer)
x0 = x.galactocentric
v0 = gc.vhel_to_gal(x.icrs, rv=vr, pm=[mua, mud], **vobs).to(u.km/u.s)
return ([x0.x.value, x0.y.value, x0.z.value], v0.value.tolist())
def tri_coordinates(observer=mw_observer):
"""Approximate Triangulum progenitor coordinates"""
x = coord.SkyCoord(ra=22.38*u.deg, dec=30.26*u.deg, distance=33*u.kpc, **observer)
x_ = x.galactocentric
x0 = [x_.x.value, x_.y.value, x_.z.value]
v0 = [-40, 155, 155]
return (x0, v0)
def atlas_coordinates(observer=mw_observer):
"""Approximate ATLAS progenitor coordinates"""
x = coord.SkyCoord(ra=20*u.deg, dec=-27*u.deg, distance=20*u.kpc, **observer)
x_ = x.galactocentric
x0 = [x_.x.value, x_.y.value, x_.z.value]
v0 = [40, 150, -120]
return (x0, v0)
# great circle orientation
def find_greatcircle(stream=None, name='gd1', pparams=pparams_fid, dt=0.2*u.Myr, save=True, graph=True):
"""Save rotation matrix for a stream model"""
if stream==None:
stream = stream_model(name, pparams0=pparams, dt=dt)
# find the pole
ra = np.radians(stream.obs[0])
dec = np.radians(stream.obs[1])
rx = np.cos(ra) * np.cos(dec)
ry = np.sin(ra) * np.cos(dec)
rz = np.sin(dec)
r = np.column_stack((rx, ry, rz))
# fit the plane
x0 = np.array([0, 1, 0])
lsq = scipy.optimize.minimize(wfit_plane, x0, args=(r,))
x0 = lsq.x/np.linalg.norm(lsq.x)
ra0 = np.arctan2(x0[1], x0[0])
dec0 = np.arcsin(x0[2])
ra0 += np.pi
dec0 = np.pi/2 - dec0
# euler rotations
R0 = myutils.rotmatrix(np.degrees(-ra0), 2)
R1 = myutils.rotmatrix(np.degrees(dec0), 1)
R2 = myutils.rotmatrix(0, 2)
R = np.dot(R2, np.matmul(R1, R0))
xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R)
# put xi = 50 at the beginning of the stream
xi[xi>180] -= 360
xi += 360
xi0 = np.min(xi) - 50
R2 = myutils.rotmatrix(-xi0, 2)
R = np.dot(R2, np.matmul(R1, R0))
xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R)
if save:
np.save('../data/rotmatrix_{}'.format(name), R)
f = open('../data/mock_{}.params'.format(name), 'rb')
mock = pickle.load(f)
mock['rotmatrix'] = R
f.close()
f = open('../data/mock_{}.params'.format(name), 'wb')
pickle.dump(mock, f)
f.close()
if graph:
plt.close()
fig, ax = plt.subplots(1,2,figsize=(10,5))
plt.sca(ax[0])
plt.plot(stream.obs[0], stream.obs[1], 'ko')
plt.xlabel('R.A. (deg)')
plt.ylabel('Dec (deg)')
plt.sca(ax[1])
plt.plot(xi, eta, 'ko')
plt.xlabel('$\\xi$ (deg)')
plt.ylabel('$\\eta$ (deg)')
plt.ylim(-5, 5)
plt.tight_layout()
plt.savefig('../plots/gc_orientation_{}.png'.format(name))
return R
def wfit_plane(x, r, p=None):
"""Fit a plane to a set of 3d points"""
Np = np.shape(r)[0]
if np.any(p)==None:
p = np.ones(Np)
Q = np.zeros((3,3))
for i in range(Np):
Q += p[i]**2 * np.outer(r[i], r[i])
x = x/np.linalg.norm(x)
lsq = np.inner(x, np.inner(Q, x))
return lsq
# observed streams
#def load_stream(n):
#"""Load stream observations"""
#if n==-1:
#observed = load_gd1(present=[0,1,2,3])
#elif n==-2:
#observed = load_pal5(present=[0,1,2,3])
#elif n==-3:
#observed = load_tri(present=[0,1,2,3])
#elif n==-4:
#observed = load_atlas(present=[0,1,2,3])
#return observed
def endpoints(name):
""""""
stream = load_stream(name)
# find endpoints
amin = np.argmin(stream.obs[0])
amax = np.argmax(stream.obs[0])
ra = np.array([stream.obs[0][i] for i in [amin, amax]])
dec = np.array([stream.obs[1][i] for i in [amin, amax]])
f = open('../data/mock_{}.params'.format(name), 'rb')
mock = pickle.load(f)
# rotate endpoints
R = mock['rotmatrix']
xi, eta = myutils.rotate_angles(ra, dec, R)
#xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R)
mock['ra_range'] = ra
mock['xi_range'] = xi #np.percentile(xi, [10,90])
f.close()
f = open('../data/mock_{}.params'.format(name), 'wb')
pickle.dump(mock, f)
f.close()
def load_pal5(present, nobs=50, potential='gal'):
""""""
if len(present)==2:
t = Table.read('../data/pal5_members.txt', format='ascii.commented_header')
dist = 21.7
deltadist = 0.7
np.random.seed(34)
t = t[np.random.randint(0, high=len(t), size=nobs)]
nobs = len(t)
d = np.random.randn(nobs)*deltadist + dist
obs = np.array([t['ra'], t['dec'], d])
obsunit = [u.deg, u.deg, u.kpc]
err = np.repeat( np.array([2e-4, 2e-4, 0.7]), nobs ).reshape(3, -1)
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc]
if len(present)==3:
#t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header')
t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header')
obs = np.array([t['ra'], t['dec'], t['d']])
obsunit = [u.deg, u.deg, u.kpc]
err = np.array([t['err_ra'], t['err_dec'], t['err_d']])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc]
if len(present)==4:
#t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header')
t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header')
obs = np.array([t['ra'], t['dec'], t['d'], t['vr']])
obsunit = [u.deg, u.deg, u.kpc, u.km/u.s]
err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s]
observed = Stream(potential=potential)
observed.obs = obs
observed.obsunit = obsunit
observed.err = err
observed.obserror = obserr
return observed
def load_gd1(present, nobs=50, potential='gal'):
""""""
if len(present)==3:
t = Table.read('../data/gd1_members.txt', format='ascii.commented_header')
dist = 0
deltadist = 0.5
np.random.seed(34)
t = t[np.random.randint(0, high=len(t), size=nobs)]
nobs = len(t)
d = np.random.randn(nobs)*deltadist + dist
d += t['l']*0.04836 + 9.86
obs = np.array([t['ra'], t['dec'], d])
obsunit = [u.deg, u.deg, u.kpc]
err = np.repeat( np.array([2e-4, 2e-4, 0.5]), nobs ).reshape(3, -1)
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc]
if len(present)==4:
#t = Table.read('../data/gd1_kinematic.txt', format='ascii.commented_header')
t = Table.read('../data/gd1_allmembers.txt', format='ascii.commented_header')
obs = np.array([t['ra'], t['dec'], t['d'], t['vr']])
obsunit = [u.deg, u.deg, u.kpc, u.km/u.s]
err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s]
ind = np.all(obs!=MASK, axis=0)
observed = Stream(potential=potential)
observed.obs = obs#[np.array(present)]
observed.obsunit = obsunit
observed.err = err#[np.array(present)]
observed.obserror = obserr
return observed
def load_tri(present, nobs=50, potential='gal'):
""""""
if len(present)==4:
t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header')
obs = np.array([t['ra'], t['dec'], t['d'], t['vr']])
obsunit = [u.deg, u.deg, u.kpc, u.km/u.s]
err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s]
if len(present)==3:
t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header')
obs = np.array([t['ra'], t['dec'], t['d']])
obsunit = [u.deg, u.deg, u.kpc]
err = np.array([t['err_ra'], t['err_dec'], t['err_d']])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc]
ind = np.all(obs!=MASK, axis=0)
observed = Stream(potential=potential)
observed.obs = obs
observed.obsunit = obsunit
observed.err = err
observed.obserror = obserr
return observed
def load_atlas(present, nobs=50, potential='gal'):
""""""
ra, dec = atlas_track()
n = np.size(ra)
d = np.random.randn(n)*2 + 20
obs = np.array([ra, dec, d])
obsunit = [u.deg, u.deg, u.kpc]
err = np.array([np.ones(n)*0.05, np.ones(n)*0.05, np.ones(n)*2])
obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s]
observed = Stream(potential=potential)
observed.obs = obs
observed.obsunit = obsunit
observed.err = err
observed.obserror = obserr
return observed
def atlas_track():
""""""
ra0, dec0 = np.radians(77.16), np.radians(46.92 - 90)
# euler rotations
D = np.array([[np.cos(ra0), np.sin(ra0), 0], [-np.sin(ra0), np.cos(ra0), 0], [0, 0, 1]])
C = np.array([[np.cos(dec0), 0, np.sin(dec0)], [0, 1, 0], [-np.sin(dec0), 0, np.cos(dec0)]])
B = np.diag(np.ones(3))
R = np.dot(B, np.dot(C, D))
Rinv = np.linalg.inv(R)
l0 = np.linspace(0, 2*np.pi, 500)
b0 = np.zeros(500)
xeq, yeq, zeq = myutils.eq2car(l0, b0)
eq = np.column_stack((xeq, yeq, zeq))
eq_rot = np.zeros(np.shape(eq))
for i in range(np.size(l0)):
eq_rot[i] = np.dot(Rinv, eq[i])
l0_rot, b0_rot = myutils.car2eq(eq_rot[:, 0], eq_rot[:, 1], eq_rot[:, 2])
ra_s, dec_s = np.degrees(l0_rot), np.degrees(b0_rot)
ind_s = (ra_s>17) & (ra_s<30)
ra_s = ra_s[ind_s]
dec_s = dec_s[ind_s]
return (ra_s, dec_s)
def fancy_name(n):
"""Return nicely formatted stream name"""
names = {-1: 'GD-1', -2: 'Palomar 5', -3: 'Triangulum', -4: 'ATLAS'}
return names[n]
# model parameters
def get_varied_pars(vary):
"""Return indices and steps for a preset of varied parameters, and a label for varied parameters
Parameters:
vary - string setting the parameter combination to be varied, options: 'potential', 'progenitor', 'halo', or a list thereof"""
if type(vary) is not list:
vary = [vary]
Nt = len(vary)
vlabel = '_'.join(vary)
pid = []
dp = []
for v in vary:
o1, o2 = get_varied_bytype(v)
pid += o1
dp += o2
return (pid, dp, vlabel)
def get_varied_bytype(vary):
"""Get varied parameter of a particular type"""
if vary=='potential':
pid = [5,6,8,10,11]
dp = [20*u.km/u.s, 2*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1), 0.4e11*u.Msun]
elif vary=='bary':
pid = [0,1,2,3,4]
# gd1
dp = [1e-1*u.Msun, 0.005*u.kpc, 1e-1*u.Msun, 0.002*u.kpc, 0.002*u.kpc]
## atlas & triangulum
#dp = [0.4e5*u.Msun, 0.0005*u.kpc, 0.5e6*u.Msun, 0.0002*u.kpc, 0.002*u.kpc]
# pal5
dp = [1e-2*u.Msun, 0.000005*u.kpc, 1e-2*u.Msun, 0.000002*u.kpc, 0.00002*u.kpc]
dp = [1e-7*u.Msun, 0.5*u.kpc, 1e-7*u.Msun, 0.5*u.kpc, 0.5*u.kpc]
dp = [1e-2*u.Msun, 0.5*u.kpc, 1e-2*u.Msun, 0.5*u.kpc, 0.5*u.kpc]
elif vary=='halo':
pid = [5,6,8,10]
dp = [20*u.km/u.s, 2*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1)]
dp = [35*u.km/u.s, 2.9*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1)]
elif vary=='progenitor':
pid = [26,27,28,29,30,31]
dp = [1*u.deg, 1*u.deg, 0.5*u.kpc, 20*u.km/u.s, 0.3*u.mas/u.yr, 0.3*u.mas/u.yr]
elif vary=='dipole':
pid = [11,12,13]
#dp = [1e-11*u.Unit(1), 1e-11*u.Unit(1), 1e-11*u.Unit(1)]
dp = [0.05*u.pc/u.Myr**2, 0.05*u.pc/u.Myr**2, 0.05*u.pc/u.Myr**2]
elif vary=='quad':
pid = [14,15,16,17,18]
dp = [0.5*u.Gyr**-2 for x in range(5)]
elif vary=='octu':
pid = [19,20,21,22,23,24,25]
dp = [0.001*u.Gyr**-2*u.kpc**-1 for x in range(7)]
else:
pid = []
dp = []
return (pid, dp)
def get_parlabel(pid):
"""Return label for a list of parameter ids
Parameter:
pid - list of parameter ids"""
master = ['log $M_b$', '$a_b$', 'log $M_d$', '$a_d$', '$b_d$', '$V_h$', '$R_h$', '$\phi$', '$q_x$', '$q_y$', '$q_z$', '$a_{1,-1}$', '$a_{1,0}$', '$a_{1,1}$', '$a_{2,-2}$', '$a_{2,-1}$', '$a_{2,0}$', '$a_{2,1}$', '$a_{2,2}$', '$a_{3,-3}$', '$a_{3,-2}$', '$a_{3,-1}$', '$a_{3,0}$', '$a_{3,1}$', '$a_{3,2}$', '$a_{3,3}$', '$RA_p$', '$Dec_p$', '$d_p$', '$V_{r_p}$', '$\mu_{\\alpha_p}$', '$\mu_{\delta_p}$', ]
master_units = ['dex', 'kpc', 'dex', 'kpc', 'kpc', 'km/s', 'kpc', 'rad', '', '', '', 'pc/Myr$^2$', 'pc/Myr$^2$', 'pc/Myr$^2$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'deg', 'deg', 'kpc', 'km/s', 'mas/yr', 'mas/yr', ]
if type(pid) is list:
labels = []
units = []
for i in pid:
labels += [master[i]]
units += [master_units[i]]
else:
labels = master[pid]
units = master_units[pid]
return (labels, units)
def get_steps(Nstep=50, log=False):
"""Return deltax steps in both directions
Paramerets:
Nstep - number of steps in one direction (default: 50)
log - if True, steps are logarithmically spaced (default: False)"""
if log:
step = np.logspace(-10, 1, Nstep)
else:
step = np.linspace(0.1, 10, Nstep)
step = np.concatenate([-step[::-1], step])
return (Nstep, step)
def lmc_position():
""""""
ra = 80.8939*u.deg
dec = -69.7561*u.deg
dm = 18.48
d = 10**(1 + dm/5)*u.pc
x = coord.SkyCoord(ra=ra, dec=dec, distance=d)
xgal = [x.galactocentric.x.si, x.galactocentric.y.si, x.galactocentric.z.si]
print(xgal)
def lmc_properties():
""""""
# penarrubia 2016
mass = 2.5e11*u.Msun
ra = 80.8939*u.deg
dec = -69.7561*u.deg
dm = 18.48
d = 10**(1 + dm/5)*u.pc
c1 = coord.SkyCoord(ra=ra, dec=dec, distance=d)
cgal1 = c1.transform_to(coord.Galactocentric)
xgal = np.array([cgal1.x.to(u.kpc).value, cgal1.y.to(u.kpc).value, cgal1.z.to(u.kpc).value])*u.kpc
return (mass, xgal)
# fit bspline to a stream model
def fit_bspline(n, pparams=pparams_fid, dt=0.2*u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False):
"""Fit bspline to a stream model and save to file"""
Ndim = 6
fits = [None]*(Ndim-1)
if align:
rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n))
else:
rotmatrix = None
stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
Nobs = 10
k = 3
isort = np.argsort(stream.obs[0])
ra = np.linspace(np.min(stream.obs[0])*1.05, np.max(stream.obs[0])*0.95, Nobs)
t = np.r_[(stream.obs[0][isort][0],)*(k+1), ra, (stream.obs[0][isort][-1],)*(k+1)]
for j in range(Ndim-1):
fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k)
if len(save)>0:
np.savez('../data/{:s}'.format(save), fits=fits)
if graph:
xlims, ylims = get_stream_limits(n, align)
ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)']
if align:
ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)']
if fiducial:
stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix)
fidsort = np.argsort(stream_fid.obs[0])
ra = np.linspace(np.min(stream_fid.obs[0])*1.05, np.max(stream_fid.obs[0])*0.95, Nobs)
tfid = np.r_[(stream_fid.obs[0][fidsort][0],)*(k+1), ra, (stream_fid.obs[0][fidsort][-1],)*(k+1)]
llabel = 'b-spline fit'
else:
llabel = ''
plt.close()
fig, ax = plt.subplots(2,5,figsize=(20,5), sharex=True, gridspec_kw = {'height_ratios':[3, 1]})
for i in range(Ndim-1):
plt.sca(ax[0][i])
plt.plot(stream.obs[0], stream.obs[i+1], 'ko')
plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]), 'r-', lw=2, label=llabel)
if fiducial:
fits_fid = scipy.interpolate.make_lsq_spline(stream_fid.obs[0][fidsort], stream_fid.obs[i+1][fidsort], tfid, k=k)
plt.plot(stream_fid.obs[0], stream_fid.obs[i+1], 'wo', mec='k', alpha=0.1)
plt.plot(stream_fid.obs[0][fidsort], fits_fid(stream_fid.obs[0][fidsort]), 'b-', lw=2, label='Fiducial')
plt.ylabel(ylabel[i+1])
plt.xlim(xlims[0], xlims[1])
plt.ylim(ylims[i][0], ylims[i][1])
plt.sca(ax[1][i])
if fiducial:
yref = fits_fid(stream.obs[0])
ycolor = 'b'
else:
yref = fits[i](stream.obs[0])
ycolor = 'r'
plt.axhline(0, color=ycolor, lw=2)
if fiducial: plt.plot(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], 'wo', mec='k', alpha=0.1)
plt.plot(stream.obs[0], stream.obs[i+1] - yref, 'ko')
if fiducial:
fits_diff = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], t, k=k)
plt.plot(stream.obs[0][isort], fits_diff(stream.obs[0][isort]), 'r--')
plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]) - yref[isort], 'r-', lw=2, label=llabel)
plt.xlabel(ylabel[0])
plt.ylabel('$\Delta$ {}'.format(ylabel[i+1].split(' ')[0]))
if fiducial:
plt.sca(ax[0][Ndim-2])
plt.legend(fontsize='small')
plt.tight_layout()
if len(graphsave)>0:
plt.savefig('../plots/{:s}.png'.format(graphsave))
def fitbyt_bspline(n, pparams=pparams_fid, dt=0.2*u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False):
"""Fit each tail individually"""
Ndim = 6
fits = [None]*(Ndim-1)
if align:
rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n))
else:
rotmatrix = None
stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
Nobs = 10
k = 3
isort = np.argsort(stream.obs[0])
ra = np.linspace(np.min(stream.obs[0])*1.05, np.max(stream.obs[0])*0.95, Nobs)
t = np.r_[(stream.obs[0][isort][0],)*(k+1), ra, (stream.obs[0][isort][-1],)*(k+1)]
for j in range(Ndim-1):
fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k)
if len(save)>0:
np.savez('../data/{:s}'.format(save), fits=fits)
if graph:
xlims, ylims = get_stream_limits(n, align)
ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)']
if align:
ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)']
if fiducial:
stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix)
plt.close()
fig, ax = plt.subplots(2,Ndim,figsize=(20,4), sharex=True, gridspec_kw = {'height_ratios':[3, 1]})
for i in range(Ndim):
plt.sca(ax[0][i])
Nhalf = int(0.5*np.size(stream.obs[i]))
plt.plot(stream.obs[i][:Nhalf], 'o')
plt.plot(stream.obs[i][Nhalf:], 'o')
if fiducial:
plt.plot(stream_fid.obs[i][:Nhalf], 'wo', mec='k', mew=0.2, alpha=0.5)
plt.plot(stream_fid.obs[i][Nhalf:], 'wo', mec='k', mew=0.2, alpha=0.5)
plt.ylabel(ylabel[i])
plt.sca(ax[1][i])
if fiducial:
plt.plot(stream.obs[i][:Nhalf] - stream_fid.obs[i][:Nhalf], 'o')
plt.plot(stream.obs[i][Nhalf:] - stream_fid.obs[i][Nhalf:], 'o')
if fiducial:
plt.sca(ax[0][Ndim-1])
plt.legend(fontsize='small')
plt.tight_layout()
if len(graphsave)>0:
plt.savefig('../plots/{:s}.png'.format(graphsave))
else:
return fig
def get_stream_limits(n, align=False):
"""Return lists with limiting values in different dimensions"""
if n==-1:
xlims = [260, 100]
ylims = [[-20, 70], [5, 15], [-400, 400], [-15,5], [-15, 5]]
elif n==-2:
xlims = [250, 210]
ylims = [[-20, 15], [17, 27], [-80, -20], [-5,0], [-5, 0]]
elif n==-3:
xlims = [27, 17]
ylims = [[10, 50], [34, 36], [-175, -50], [0.45, 1], [0.1, 0.7]]
elif n==-4:
xlims = [35, 10]
ylims = [[-40, -20], [15, 25], [50, 200], [-0.5,0.5], [-1.5, -0.5]]
if align:
ylims[0] = [-5, 5]
xup = [110, 110, 80, 80]
xlims = [xup[np.abs(n)-1], 40]
return (xlims, ylims)
# step sizes for derivatives
def iterate_steps(n):
"""Calculate derivatives for different parameter classes, and plot"""
for vary in ['bary', 'halo', 'progenitor']:
print(n, vary)
step_convergence(n, Nstep=10, vary=vary)
choose_step(n, Nstep=10, vary=vary)
def iterate_plotsteps(n):
"""Plot stream models for a variety of model parameters"""
for vary in ['bary', 'halo', 'progenitor']:
print(n, vary)
pid, dp, vlabel = get_varied_pars(vary)
for p in range(len(pid)):
plot_steps(n, p=p, Nstep=5, vary=vary, log=False)
def plot_steps(n, p=0, Nstep=20, log=True, dt=0.2*u.Myr, vary='halo', verbose=False, align=True, observer=mw_observer, vobs=vsun):
"""Plot stream for different values of a potential parameter"""
if align:
rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n))
else:
rotmatrix = None
pparams0 = pparams_fid
pid, dp, vlabel = get_varied_pars(vary)
plabel, punit = get_parlabel(pid[p])
Nstep, step = get_steps(Nstep=Nstep, log=log)
plt.close()
fig, ax = plt.subplots(5,5,figsize=(20,10), sharex=True, gridspec_kw = {'height_ratios':[3, 1, 1, 1, 1]})
# fiducial model
stream0 = stream_model(n, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix, observer=observer, vobs=vobs)
Nobs = 10
k = 3
isort = np.argsort(stream0.obs[0])
ra = np.linspace(np.min(stream0.obs[0])*1.05, np.max(stream0.obs[0])*0.95, Nobs)
t = np.r_[(stream0.obs[0][isort][0],)*(k+1), ra, (stream0.obs[0][isort][-1],)*(k+1)]
fits = [None]*5
for j in range(5):
fits[j] = scipy.interpolate.make_lsq_spline(stream0.obs[0][isort], stream0.obs[j+1][isort], t, k=k)
# excursions
stream_fits = [[None] * 5 for x in range(2 * Nstep)]
for i, s in enumerate(step[:]):
pparams = [x for x in pparams0]
pparams[pid[p]] = pparams[pid[p]] + s*dp[p]
stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
color = mpl.cm.RdBu(i/(2*Nstep-1))
#print(i, dp[p], pparams)
# fits
iexsort = np.argsort(stream.obs[0])
raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs)
tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)]
fits_ex = [None]*5
for j in range(5):
fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k)
stream_fits[i][j] = fits_ex[j]
plt.sca(ax[0][j])
plt.plot(stream.obs[0], stream.obs[j+1], 'o', color=color, ms=2)
plt.sca(ax[1][j])
plt.plot(stream.obs[0], stream.obs[j+1] - fits[j](stream.obs[0]), 'o', color=color, ms=2)
plt.sca(ax[2][j])
plt.plot(stream.obs[0], fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]), 'o', color=color, ms=2)
plt.sca(ax[3][j])
plt.plot(stream.obs[0], (fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]))/(s*dp[p]), 'o', color=color, ms=2)
# symmetric derivatives
ra_der = np.linspace(np.min(stream0.obs[0])*1.05, np.max(stream0.obs[0])*0.95, 100)
for i in range(Nstep):
color = mpl.cm.Greys_r(i/Nstep)
for j in range(5):
dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der)
dydx = -dy / np.abs(2*step[i]*dp[p])
plt.sca(ax[4][j])
plt.plot(ra_der, dydx, '-', color=color, lw=2, zorder=Nstep-i)
# labels, limits
xlims, ylims = get_stream_limits(n, align)
ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)']
if align:
ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)']
for j in range(5):
plt.sca(ax[0][j])
plt.ylabel(ylabel[j+1])
plt.xlim(xlims[0], xlims[1])
plt.ylim(ylims[j][0], ylims[j][1])
plt.sca(ax[1][j])
plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0]))
plt.sca(ax[2][j])
plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0]))
plt.sca(ax[3][j])
plt.ylabel('$\Delta${}/$\Delta${}'.format(ylabel[j+1].split(' ')[0], plabel))
plt.sca(ax[4][j])
plt.xlabel(ylabel[0])
plt.ylabel('$\langle$$\Delta${}/$\Delta${}$\\rangle$'.format(ylabel[j+1].split(' ')[0], plabel))
#plt.suptitle('Varying {}'.format(plabel), fontsize='small')
plt.tight_layout()
plt.savefig('../plots/observable_steps_{:d}_{:s}_p{:d}_Ns{:d}.png'.format(n, vlabel, p, Nstep))
def step_convergence(name='gd1', Nstep=20, log=True, layer=1, dt=0.2*u.Myr, vary='halo', align=True, graph=False, verbose=False, Nobs=10, k=3, ra_der=np.nan, Nra=50):
"""Check deviations in numerical derivatives for consecutive step sizes"""
mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb'))
if align:
rotmatrix = mock['rotmatrix']
xmm = mock['xi_range']
else:
rotmatrix = np.eye(3)
xmm = mock['ra_range']
# fiducial model
pparams0 = pparams_fid
stream0 = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix)
if np.any(~np.isfinite(ra_der)):
ra_der = np.linspace(xmm[0]*1.05, xmm[1]*0.95, Nra)
Nra = np.size(ra_der)
# parameters to vary
pid, dp, vlabel = get_varied_pars(vary)
Np = len(pid)
dpvec = np.array([x.value for x in dp])
Nstep, step = get_steps(Nstep=Nstep, log=log)
dydx_all = np.empty((Np, Nstep, 5, Nra))
dev_der = np.empty((Np, Nstep-2*layer))
step_der = np.empty((Np, Nstep-2*layer))
for p in range(Np):
plabel = get_parlabel(pid[p])
if verbose: print(p, plabel)
# excursions
stream_fits = [[None] * 5 for x in range(2 * Nstep)]
for i, s in enumerate(step[:]):
if verbose: print(i, s)
pparams = [x for x in pparams0]
pparams[pid[p]] = pparams[pid[p]] + s*dp[p]
stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
# fits
iexsort = np.argsort(stream.obs[0])
raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs)
tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)]
fits_ex = [None]*5
for j in range(5):
fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k)
stream_fits[i][j] = fits_ex[j]
# symmetric derivatives
dydx = np.empty((Nstep, 5, Nra))
for i in range(Nstep):
color = mpl.cm.Greys_r(i/Nstep)
for j in range(5):
dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der)
dydx[i][j] = -dy / np.abs(2*step[i]*dp[p])
dydx_all[p] = dydx
# deviations from adjacent steps
step_der[p] = -step[layer:Nstep-layer] * dp[p]
for i in range(layer, Nstep-layer):
dev_der[p][i-layer] = 0
for j in range(5):
for l in range(layer):
dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i-l-1][j])**2)
dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i+l+1][j])**2)
np.savez('../data/step_convergence_{}_{}_Ns{}_log{}_l{}'.format(name, vlabel, Nstep, log, layer), step=step_der, dev=dev_der, ders=dydx_all, steps_all=np.outer(dpvec,step[Nstep:]))
if graph:
plt.close()
fig, ax = plt.subplots(1,Np,figsize=(4*Np,4))
for p in range(Np):
plt.sca(ax[p])
plt.plot(step_der[p], dev_der[p], 'ko')
#plabel = get_parlabel(pid[p])
#plt.xlabel('$\Delta$ {}'.format(plabel))
plt.ylabel('D')
plt.gca().set_yscale('log')
plt.tight_layout()
plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer))
def choose_step(name='gd1', tolerance=2, Nstep=20, log=True, layer=1, vary='halo'):
""""""
pid, dp, vlabel = get_varied_pars(vary)
Np = len(pid)
plabels, units = get_parlabel(pid)
punits = ['({})'.format(x) if len(x) else '' for x in units]
t = np.load('../data/step_convergence_{}_{}_Ns{}_log{}_l{}.npz'.format(name, vlabel, Nstep, log, layer))
dev = t['dev']
step = t['step']
dydx = t['ders']
steps_all = t['steps_all'][:,::-1]
Nra = np.shape(dydx)[-1]
best = np.empty(Np)
# plot setup
da = 4
nrow = 2
ncol = Np
plt.close()
fig, ax = plt.subplots(nrow, ncol, figsize=(da*ncol, da*1.3), squeeze=False, sharex='col', gridspec_kw = {'height_ratios':[1.2, 3]})
for p in range(Np):
# choose step
dmin = np.min(dev[p])
dtol = tolerance * dmin
opt_step = np.min(step[p][dev[p]<dtol])
opt_id = step[p]==opt_step
best[p] = opt_step
## largest step w deviation smaller than 1e-4
#opt_step = np.max(step[p][dev[p]<1e-4])
#opt_id = step[p]==opt_step
#best[p] = opt_step
plt.sca(ax[0][p])
for i in range(5):
for j in range(10):
plt.plot(steps_all[p], np.tanh(dydx[p,:,i,np.int64(j*Nra/10)]), '-', color='{}'.format(i/5), lw=0.5, alpha=0.5)
plt.axvline(opt_step, ls='-', color='r', lw=2)
plt.ylim(-1,1)
plt.ylabel('Derivative')
plt.title('{}'.format(plabels[p])+'$_{best}$ = '+'{:2.2g}'.format(opt_step), fontsize='small')
plt.sca(ax[1][p])
plt.plot(step[p], dev[p], 'ko')
plt.axvline(opt_step, ls='-', color='r', lw=2)
plt.plot(step[p][opt_id], dev[p][opt_id], 'ro')
plt.axhline(dtol, ls='-', color='orange', lw=1)
y0, y1 = plt.gca().get_ylim()
plt.axhspan(y0, dtol, color='orange', alpha=0.3, zorder=0)
plt.gca().set_yscale('log')
plt.gca().set_xscale('log')
plt.xlabel('$\Delta$ {} {}'.format(plabels[p], punits[p]))
plt.ylabel('Derivative deviation')
np.save('../data/optimal_step_{}_{}'.format(name, vlabel), best)
plt.tight_layout(h_pad=0)
plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer))
def read_optimal_step(name, vary, equal=False):
"""Return optimal steps for a range of parameter types"""
if type(vary) is not list:
vary = [vary]
dp = np.empty(0)
for v in vary:
dp_opt = np.load('../data/optimal_step_{}_{}.npy'.format(name, v))
dp = np.concatenate([dp, dp_opt])
if equal:
dp = np.array([0.05, 0.05, 0.2, 1, 0.01, 0.01, 0.05, 0.1, 0.05, 0.1, 0.1, 10, 1, 0.01, 0.01])
return dp
def visualize_optimal_steps(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, dt=0.2*u.Myr, Nobs=50, k=3):
""""""
mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb'))
if align:
rotmatrix = mock['rotmatrix']
xmm = mock['xi_range']
else:
rotmatrix = np.eye(3)
xmm = mock['ra_range']
# varied parameters
pparams0 = pparams_fid
pid, dp_fid, vlabel = get_varied_pars(vary)
Np = len(pid)
dp_opt = read_optimal_step(name, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
fiducial = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix)
iexsort = np.argsort(fiducial.obs[0])
raex = np.linspace(np.percentile(fiducial.obs[0], 10), np.percentile(fiducial.obs[0], 90), Nobs)
tex = np.r_[(fiducial.obs[0][iexsort][0],)*(k+1), raex, (fiducial.obs[0][iexsort][-1],)*(k+1)]
fit = scipy.interpolate.make_lsq_spline(fiducial.obs[0][iexsort], fiducial.obs[1][iexsort], tex, k=k)
nrow = 2
ncol = np.int64((Np+1)/nrow)
da = 4
c = ['b', 'b', 'b', 'r', 'r', 'r']
plt.close()
fig, ax = plt.subplots(nrow, ncol, figsize=(ncol*da, nrow*da), squeeze=False)
for p in range(Np):
plt.sca(ax[p%2][int(p/2)])
for i, s in enumerate([-1.1, -1, -0.9, 0.9, 1, 1.1]):
pparams = [x for x in pparams0]
pparams[pid[p]] = pparams[pid[p]] + s*dp[p]
stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
# bspline fits to stream centerline
iexsort = np.argsort(stream.obs[0])
raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs)
tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)]
fitex = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[1][iexsort], tex, k=k)
plt.plot(raex, fitex(raex) - fit(raex), '-', color=c[i])
plt.xlabel('R.A. (deg)')
plt.ylabel('Dec (deg)')
#print(get_parlabel(p))
plt.title('$\Delta$ {} = {:.2g}'.format(get_parlabel(p)[0], dp[p]), fontsize='medium')
plt.tight_layout()
plt.savefig('../plots/{}_optimal_steps.png'.format(name), dpi=200)
# observing modes
def define_obsmodes():
"""Output a pickled dictionary with typical uncertainties and dimensionality of data for a number of observing modes"""
obsmodes = {}
obsmodes['fiducial'] = {'sig_obs': np.array([0.1, 2, 5, 0.1, 0.1]), 'Ndim': [3,4,6]}
obsmodes['binospec'] = {'sig_obs': np.array([0.1, 2, 10, 0.1, 0.1]), 'Ndim': [3,4,6]}
obsmodes['hectochelle'] = {'sig_obs': np.array([0.1, 2, 1, 0.1, 0.1]), 'Ndim': [3,4,6]}
obsmodes['desi'] = {'sig_obs': np.array([0.1, 2, 10, np.nan, np.nan]), 'Ndim': [4,]}
obsmodes['gaia'] = {'sig_obs': np.array([0.1, 0.2, 10, 0.2, 0.2]), 'Ndim': [6,]}
obsmodes['exgal'] = {'sig_obs': np.array([0.5, np.nan, 20, np.nan, np.nan]), 'Ndim': [3,]}
pickle.dump(obsmodes, open('../data/observing_modes.info','wb'))
def obsmode_name(mode):
"""Return full name of the observing mode"""
if type(mode) is not list:
mode = [mode]
full_names = {'fiducial': 'Fiducial',
'binospec': 'Binospec',
'hectochelle': 'Hectochelle',
'desi': 'DESI-like',
'gaia': 'Gaia-like',
'exgal': 'Extragalactic'}
keys = full_names.keys()
names = []
for m in mode:
if m in keys:
name = full_names[m]
else:
name = m
names += [name]
return names
# crbs using bspline
def calculate_crb(name='gd1', dt=0.2*u.Myr, vary=['progenitor', 'bary', 'halo'], ra=np.nan, dd=0.5, Nmin=15, verbose=False, align=True, scale=False, errmode='fiducial', k=3):
""""""
mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb'))
if align:
rotmatrix = mock['rotmatrix']
xmm = np.sort(mock['xi_range'])
else:
rotmatrix = np.eye(3)
xmm = np.sort(mock['ra_range'])
# typical uncertainties and data availability
obsmodes = pickle.load(open('../data/observing_modes.info', 'rb'))
if errmode not in obsmodes.keys():
errmode = 'fiducial'
sig_obs = obsmodes[errmode]['sig_obs']
data_dim = obsmodes[errmode]['Ndim']
# mock observations
if np.any(~np.isfinite(ra)):
if (np.int64((xmm[1]-xmm[0])/dd + 1) < Nmin):
dd = (xmm[1]-xmm[0])/Nmin
ra = np.arange(xmm[0], xmm[1]+dd, dd)
#ra = np.linspace(xmm[0]*1.05, xmm[1]*0.95, Nobs)
#else:
Nobs = np.size(ra)
print(name, Nobs)
err = np.tile(sig_obs, Nobs).reshape(Nobs,-1)
# varied parameters
pparams0 = pparams_fid
pid, dp_fid, vlabel = get_varied_pars(vary)
Np = len(pid)
dp_opt = read_optimal_step(name, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
fits_ex = [[[None]*5 for x in range(2)] for y in range(Np)]
if scale:
dp_unit = unity_scale(dp)
dps = [x*y for x,y in zip(dp, dp_unit)]
# calculate derivatives for all parameters
for p in range(Np):
for i, s in enumerate([-1, 1]):
pparams = [x for x in pparams0]
pparams[pid[p]] = pparams[pid[p]] + s*dp[p]
stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix)
# bspline fits to stream centerline
iexsort = np.argsort(stream.obs[0])
raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs)
tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)]
for j in range(5):
fits_ex[p][i][j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k)
# populate matrix of derivatives and calculate CRB
for Ndim in data_dim:
#for Ndim in [6,]:
Ndata = Nobs * (Ndim - 1)
cyd = np.empty(Ndata)
dydx = np.empty((Np, Ndata))
dy2 = np.empty((2, Np, Ndata))
for j in range(1, Ndim):
for p in range(Np):
dy = fits_ex[p][0][j-1](ra) - fits_ex[p][1][j-1](ra)
dy2[0][p][(j-1)*Nobs:j*Nobs] = fits_ex[p][0][j-1](ra)
dy2[1][p][(j-1)*Nobs:j*Nobs] = fits_ex[p][1][j-1](ra)
#positive = np.abs(dy)>0
#if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dy[positive])), np.max(np.abs(dy)), np.median(np.abs(dy))))
if scale:
dydx[p][(j-1)*Nobs:j*Nobs] = -dy / np.abs(2*dps[p].value)
else:
dydx[p][(j-1)*Nobs:j*Nobs] = -dy / np.abs(2*dp[p].value)
#if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dydx[p][(j-1)*Nobs:j*Nobs][positive])), np.max(np.abs(dydx[p][(j-1)*Nobs:j*Nobs])), np.median(np.abs(dydx[p][(j-1)*Nobs:j*Nobs]))))
#print(j, p, get_parlabel(pid[p])[0], dp[p], np.min(np.abs(dy)), np.max(np.abs(dy)), np.median(dydx[p][(j-1)*Nobs:j*Nobs]))
cyd[(j-1)*Nobs:j*Nobs] = err[:,j-1]**2
np.savez('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), dydx=dydx, y=dy2, cyd=cyd, dp=dp_opt)
# data component of the Fisher matrix
cy = np.diag(cyd)
cyi = np.diag(1. / cyd)
caux = np.matmul(cyi, dydx.T)
dxi = np.matmul(dydx, caux)
# component based on prior knowledge of model parameters
pxi = priors(name, vary)
# full Fisher matrix
cxi = dxi + pxi
if verbose:
cx = np.linalg.inv(cxi)
cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers
sx = np.sqrt(np.diag(cx))
print('CRB', sx)
print('condition {:g}'.format(np.linalg.cond(cxi)))
print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0])))
cx = stable_inverse(cxi)
print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0])))
np.savez('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), cxi=cxi, dxi=dxi, pxi=pxi)
def priors(name, vary):
"""Return covariance matrix with prior knowledge about parameters"""
mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb'))
cprog = mock['prog_prior']
cbary = np.array([0.1*x.value for x in pparams_fid[:5]])**-2
chalo = np.zeros(4)
cdipole = np.zeros(3)
cquad = np.zeros(5)
coctu = np.zeros(7)
priors = {'progenitor': cprog, 'bary': cbary, 'halo': chalo, 'dipole': cdipole, 'quad': cquad, 'octu': coctu}
cprior = np.empty(0)
for v in vary:
cprior = np.concatenate([cprior, priors[v]])
pxi = np.diag(cprior)
return pxi
def scale2invert(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], verbose=False, align=True, errmode='fiducial'):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
#dp = read_optimal_step(name, vary)
d = np.load('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
dydx = d['dydx']
cyd = d['cyd']
y = d['y']
dp = d['dp']
dy = (y[1,:,:] - y[0,:,:])
dydx = (y[1,:,:] - y[0,:,:]) / (2*dp[:,np.newaxis])
scaling_par = np.median(np.abs(dydx), axis=1)
dydx = dydx / scaling_par[:,np.newaxis]
dydx_ = np.reshape(dydx, (len(dp), Ndim-1, -1))
scaling_dim = np.median(np.abs(dydx_), axis=(2,0))
dydx_ = dydx_ / scaling_dim[np.newaxis,:,np.newaxis]
cyd_ = np.reshape(cyd, (Ndim-1, -1))
cyd_ = cyd_ / scaling_dim[:,np.newaxis]
cyd = np.reshape(cyd_, (-1))
dydx = np.reshape(dydx_, (len(dp), -1))
mmin = np.min(np.abs(dy), axis=0)
mmax = np.max(np.abs(dy), axis=0)
mmed = np.median(np.abs(dydx), axis=1)
dyn_range = mmax/mmin
#print(dyn_range)
print(np.min(dyn_range), np.max(dyn_range), np.std(dyn_range))
cy = np.diag(cyd)
cyi = np.diag(1. / cyd)
caux = np.matmul(cyi, dydx.T)
cxi = np.matmul(dydx, caux)
print('condition {:e}'.format(np.linalg.cond(cxi)))
cx = np.linalg.inv(cxi)
cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers
print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0])))
cx = stable_inverse(cxi, maxiter=30)
print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0])))
def unity_scale(dp):
""""""
dim_scale = 10**np.array([2, 3, 3, 2, 4, 3, 7, 7, 5, 7, 7, 4, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4])
dim_scale = 10**np.array([3, 2, 3, 4, 0, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 3])
#dim_scale = 10**np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3])
#dim_scale = 10**np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3])
dp_unit = [(dp[x].value*dim_scale[x])**-1 for x in range(len(dp))]
return dp_unit
def test_inversion(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], align=True, errmode='fiducial'):
""""""
pid, dp, vlabel = get_varied_pars(vary)
d = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
cxi = d['cxi']
N = np.shape(cxi)[0]
cx_ = np.linalg.inv(cxi)
cx = stable_inverse(cxi, verbose=True, maxiter=100)
#cx_ii = stable_inverse(cx, verbose=True, maxiter=50)
print('condition {:g}'.format(np.linalg.cond(cxi)))
print('linalg inverse', np.allclose(np.matmul(cx_,cxi), np.eye(N)))
print('stable inverse', np.allclose(np.matmul(cx,cxi), np.eye(N)))
#print(np.matmul(cx,cxi))
#print('inverse inverse', np.allclose(cx_ii, cxi))
def stable_inverse(a, maxiter=20, verbose=False):
"""Invert a matrix with a bad condition number"""
N = np.shape(a)[0]
# guess
q = np.linalg.inv(a)
qa = np.matmul(q,a)
# iterate
for i in range(maxiter):
if verbose: print(i, np.sqrt(np.sum((qa - np.eye(N))**2)), np.allclose(qa, np.eye(N)))
if np.allclose(qa, np.eye(N)):
return q
qai = np.linalg.inv(qa)
q = np.matmul(qai,q)
qa = np.matmul(q,a)
return q
def crb_triangle(n, vary, Ndim=6, align=True, plot='all', fast=False):
""""""
pid, dp, vlabel = get_varied_pars(vary)
plabels, units = get_parlabel(pid)
params = ['$\Delta$' + x + '({})'.format(y) for x,y in zip(plabels, units)]
if align:
alabel = '_align'
else:
alabel = ''
fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
cxi = fm['cxi']
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
#print(cx[0][0])
if plot=='halo':
cx = cx[:4, :4]
params = params[:4]
elif plot=='bary':
cx = cx[4:9, 4:9]
params = params[4:9]
elif plot=='progenitor':
cx = cx[9:, 9:]
params = params[9:]
Nvar = len(params)
plt.close()
dax = 2
fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(dax*Nvar, dax*Nvar), sharex='col', sharey='row')
for i in range(0,Nvar-1):
for j in range(i+1,Nvar):
plt.sca(ax[j-1][i])
cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]])
w, v = np.linalg.eig(cx_2d)
if np.all(np.isreal(v)):
theta = np.degrees(np.arccos(v[0][0]))
width = np.sqrt(w[0])*2
height = np.sqrt(w[1])*2
e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.5), lw=2)
plt.gca().add_patch(e)
plt.gca().autoscale_view()
#plt.xlim(-ylim[i],ylim[i])
#plt.ylim(-ylim[j], ylim[j])
if j==Nvar-1:
plt.xlabel(params[i])
if i==0:
plt.ylabel(params[j])
# turn off unused axes
for i in range(0,Nvar-1):
for j in range(i+1,Nvar-1):
plt.sca(ax[i][j])
plt.axis('off')
plt.tight_layout()
plt.savefig('../plots/crb_triangle_{:s}_{:d}_{:s}_{:d}_{:s}.pdf'.format(alabel, n, vlabel, Ndim, plot))
def crb_triangle_alldim(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, plot='all', fast=False, scale=False, errmode='fiducial'):
"""Show correlations in CRB between a chosen set of parameters in a triangle plot"""
pid, dp_fid, vlabel = get_varied_pars(vary)
dp_opt = read_optimal_step(name, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
plabels, units = get_parlabel(pid)
punits = [' ({})'.format(x) if len(x) else '' for x in units]
params = ['$\Delta$ {}{}'.format(x, y) for x,y in zip(plabels, punits)]
if plot=='halo':
i0 = 11
i1 = 15
elif plot=='bary':
i0 = 6
i1 = 11
elif plot=='progenitor':
i0 = 0
i1 = 6
elif plot=='dipole':
i0 = 15
i1 = len(params)
else:
i0 = 0
i1 = len(params)
Nvar = i1 - i0
params = params[i0:i1]
if scale:
dp_unit = unity_scale(dp)
#print(dp_unit)
dp_unit = dp_unit[i0:i1]
pid = pid[i0:i1]
label = ['RA, Dec, d', 'RA, Dec, d, $V_r$', 'RA, Dec, d, $V_r$, $\mu_\\alpha$, $\mu_\delta$']
plt.close()
dax = 2
fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(dax*Nvar, dax*Nvar), sharex='col', sharey='row')
for l, Ndim in enumerate([3, 4, 6]):
fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
cxi = fm['cxi']
#cxi = np.load('../data/crb/bspline_cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npy'.format(errmode, Ndim, name, align, vlabel))
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
cx = cx[i0:i1,i0:i1]
for i in range(0,Nvar-1):
for j in range(i+1,Nvar):
plt.sca(ax[j-1][i])
if scale:
cx_2d = np.array([[cx[i][i]/dp_unit[i]**2, cx[i][j]/(dp_unit[i]*dp_unit[j])], [cx[j][i]/(dp_unit[j]*dp_unit[i]), cx[j][j]/dp_unit[j]**2]])
else:
cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]])
w, v = np.linalg.eig(cx_2d)
if np.all(np.isreal(v)):
theta = np.degrees(np.arctan2(v[1][0], v[0][0]))
width = np.sqrt(w[0])*2
height = np.sqrt(w[1])*2
e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.1+l/4), lw=2, label=label[l])
plt.gca().add_patch(e)
if l==1:
plt.gca().autoscale_view()
if j==Nvar-1:
plt.xlabel(params[i])
if i==0:
plt.ylabel(params[j])
# turn off unused axes
for i in range(0,Nvar-1):
for j in range(i+1,Nvar-1):
plt.sca(ax[i][j])
plt.axis('off')
plt.sca(ax[int(Nvar/2-1)][int(Nvar/2-1)])
plt.legend(loc=2, bbox_to_anchor=(1,1))
plt.tight_layout()
plt.savefig('../plots/cxi_{:s}_{:s}_a{:1d}_{:s}_{:s}.pdf'.format(errmode, name, align, vlabel, plot))
def compare_optimal_steps():
""""""
vary = ['progenitor', 'bary', 'halo', 'dipole', 'quad']
vary = ['progenitor', 'bary', 'halo']
for name in ['gd1', 'tri']:
print(name)
print(read_optimal_step(name, vary))
def get_crb(name, Nstep=10, vary=['progenitor', 'bary', 'halo'], first=True):
""""""
if first:
store_progparams(name)
wrap_angles(name, save=True)
progenitor_prior(name)
find_greatcircle(name=name)
endpoints(name)
for v in vary:
step_convergence(name=name, Nstep=Nstep, vary=v)
choose_step(name=name, Nstep=Nstep, vary=v)
calculate_crb(name=name, vary=vary, verbose=True)
crb_triangle_alldim(name=name, vary=vary)
########################
# cartesian coordinates
# accelerations
def acc_kepler(x, p=1*u.Msun):
"""Keplerian acceleration"""
r = np.linalg.norm(x)*u.kpc
a = -G * p * 1e11 * r**-3 * x
return a.to(u.pc*u.Myr**-2)
def acc_bulge(x, p=[pparams_fid[j] for j in range(2)]):
""""""
r = np.linalg.norm(x)*u.kpc
a = -(G*p[0]*x/(r * (r + p[1])**2)).to(u.pc*u.Myr**-2)
return a
def acc_disk(x, p=[pparams_fid[j] for j in range(2,5)]):
""""""
R = np.linalg.norm(x[:2])*u.kpc
z = x[2]
a = -(G*p[0]*x * (R**2 + (p[1] + np.sqrt(z**2 + p[2]**2))**2)**-1.5).to(u.pc*u.Myr**-2)
a[2] *= (1 + p[2]/np.sqrt(z**2 + p[2]**2))
return a
def acc_nfw(x, p=[pparams_fid[j] for j in [5,6,8,10]]):
""""""
r = np.linalg.norm(x)*u.kpc
q = np.array([1*u.Unit(1), p[2], p[3]])
a = (p[0]**2 * p[1] * r**-3 * (1/(1+p[1]/r) - np.log(1+r/p[1])) * x * q**-2).to(u.pc*u.Myr**-2)
return a
def acc_dipole(x, p=[pparams_fid[j] for j in range(11,14)]):
"""Acceleration due to outside dipole perturbation"""
pv = [x.value for x in p]
a = np.sqrt(3/(4*np.pi)) * np.array([pv[2], pv[0], pv[1]])*u.pc*u.Myr**-2
return a
def acc_quad(x, p=[pparams_fid[j] for j in range(14,19)]):
"""Acceleration due to outside quadrupole perturbation"""
a = np.zeros(3)*u.pc*u.Myr**-2
f = 0.5*np.sqrt(15/np.pi)
a[0] = x[0]*(f*p[4] - f/np.sqrt(3)*p[2]) + x[1]*f*p[0] + x[2]*f*p[3]
a[1] = x[0]*f*p[0] - x[1]*(f*p[4] + f/np.sqrt(3)*p[2]) + x[2]*f*p[1]
a[2] = x[0]*f*p[3] + x[1]*f*p[1] + x[2]*2*f/np.sqrt(3)*p[2]
return a.to(u.pc*u.Myr**-2)
def acc_octu(x, p=[pparams_fid[j] for j in range(19,26)]):
"""Acceleration due to outside octupole perturbation"""
a = np.zeros(3)*u.pc*u.Myr**-2
f = np.array([0.25*np.sqrt(35/(2*np.pi)), 0.5*np.sqrt(105/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(7/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(105/np.pi), 0.25*np.sqrt(35/(2*np.pi))])
xu = x.unit
pu = p[0].unit
pvec = np.array([i.value for i in p]) * pu
dmat = np.ones((3,7)) * f * pvec * xu**2
x = np.array([i.value for i in x])
dmat[0] *= np.array([6*x[0]*x[1], x[1]*x[2], -2*x[0]*x[1], -6*x[0]*x[2], 4*x[2]**2-x[1]**2-3*x[0]**2, 2*x[0]*x[2], 3*x[0]**2-3*x[1]**2])
dmat[1] *= np.array([3*x[0]**2-3*x[1]**2, x[0]*x[2], 4*x[2]**2-x[0]**2-3*x[1]**2, -6*x[1]*x[2], -2*x[0]*x[1], -2*x[1]*x[2], -6*x[0]*x[1]])
dmat[2] *= np.array([0, x[0]*x[1], 8*x[1]*x[2], 6*x[2]**2-3*x[0]**2-3*x[1]**2, 8*x[0]*x[2], x[0]**2-x[1]**2, 0])
a = np.einsum('ij->i', dmat) * dmat.unit
return a.to(u.pc*u.Myr**-2)
# derivatives
def der_kepler(x, p=1*u.Msun):
"""Derivative of Kepler potential parameters wrt cartesian components of the acceleration"""
r = np.linalg.norm(x)*u.kpc
dmat = np.zeros((3,1)) * u.pc**-1 * u.Myr**2 * u.Msun
dmat[:,0] = (-r**3/(G*x)).to(u.pc**-1 * u.Myr**2 * u.Msun) * 1e-11
return dmat.value
def pder_kepler(x, p=1*u.Msun):
"""Derivative of cartesian components of the acceleration wrt to Kepler potential parameter"""
r = np.linalg.norm(x)*u.kpc
dmat = np.zeros((3,1)) * u.pc * u.Myr**-2 * u.Msun**-1
dmat[:,0] = (-G*x*r**-3).to(u.pc * u.Myr**-2 * u.Msun**-1) * 1e11
return dmat.value
def pder_nfw(x, pu=[pparams_fid[j] for j in [5,6,8,10]]):
"""Calculate derivatives of cartesian components of the acceleration wrt halo potential parameters"""
p = pu
q = np.array([1, p[2], p[3]])
# physical quantities
r = np.linalg.norm(x)*u.kpc
a = acc_nfw(x, p=pu)
# derivatives
dmat = np.zeros((3, 4))
# Vh
dmat[:,0] = 2*a/p[0]
# Rh
dmat[:,1] = a/p[1] + p[0]**2 * p[1] * r**-3 * (1/(p[1]+p[1]**2/r) - 1/(r*(1+p[1]/r)**2)) * x * q**-2
# qy, qz
for i in [1,2]:
dmat[i,i+1] = (-2*a[i]/q[i]).value
return dmat
def pder_bulge(x, pu=[pparams_fid[j] for j in range(2)]):
"""Calculate derivarives of cartesian components of the acceleration wrt Hernquist bulge potential parameters"""
# coordinates
r = np.linalg.norm(x)*u.kpc
# accelerations
ab = acc_bulge(x, p=pu[:2])
# derivatives
dmat = np.zeros((3, 2))
# Mb
dmat[:,0] = ab/pu[0]
# ab
dmat[:,1] = 2 * ab / (r + pu[1])
return dmat
def pder_disk(x, pu=[pparams_fid[j] for j in range(2,5)]):
"""Calculate derivarives of cartesian components of the acceleration wrt Miyamoto-Nagai disk potential parameters"""
# coordinates
R = np.linalg.norm(x[:2])*u.kpc
z = x[2]
aux = np.sqrt(z**2 + pu[2]**2)
# accelerations
ad = acc_disk(x, p=pu)
# derivatives
dmat = np.zeros((3, 3))
# Md
dmat[:,0] = ad / pu[0]
# ad
dmat[:,1] = 3 * ad * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2)
# bd
dmat[:2,2] = 3 * ad[:2] * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2) * pu[2] / aux
dmat[2,2] = (3 * ad[2] * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2) * pu[2] / aux - G * pu[0] * z * (R**2 + (pu[1] + aux)**2)**-1.5 * z**2 * (pu[2]**2 + z**2)**-1.5).value
return dmat
def der_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]):
"""Calculate derivatives of dipole potential parameters wrt (Cartesian) components of the acceleration vector a"""
# shape: 3, Npar
dmat = np.zeros((3,3))
f = np.sqrt((4*np.pi)/3)
dmat[0,2] = f
dmat[1,0] = f
dmat[2,1] = f
return dmat
def pder_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]):
"""Calculate derivatives of (Cartesian) components of the acceleration vector a wrt dipole potential parameters"""
# shape: 3, Npar
dmat = np.zeros((3,3))
f = np.sqrt(3/(4*np.pi))
dmat[0,2] = f
dmat[1,0] = f
dmat[2,1] = f
return dmat
def der_quad(x, p=[pparams_fid[j] for j in range(14,19)]):
"""Caculate derivatives of quadrupole potential parameters wrt (Cartesian) components of the acceleration vector a"""
f = 2/np.sqrt(15/np.pi)
s = np.sqrt(3)
x = [1e-3/i.value for i in x]
dmat = np.ones((3,5)) * f
dmat[0] = np.array([x[1], 0, -s*x[0], x[2], x[0]])
dmat[1] = np.array([x[0], x[2], -s*x[1], 0, -x[1]])
dmat[2] = np.array([0, x[1], 0.5*s*x[2], x[0], 0])
return dmat
def pder_quad(x, p=[pparams_fid[j] for j in range(14,19)]):
"""Caculate derivatives of (Cartesian) components of the acceleration vector a wrt quadrupole potential parameters"""
f = 0.5*np.sqrt(15/np.pi)
s = 1/np.sqrt(3)
x = [1e-3*i.value for i in x]
dmat = np.ones((3,5)) * f
dmat[0] *= np.array([x[1], 0, -s*x[0], x[2], x[0]])
dmat[1] *= np.array([x[0], x[2], -s*x[1], 0, -x[1]])
dmat[2] *= np.array([0, x[1], 2*s*x[2], x[0], 0])
return dmat
def pder_octu(x, p=[pparams_fid[j] for j in range(19,26)]):
"""Caculate derivatives of (Cartesian) components of the acceleration vector a wrt octupole potential parameters"""
f = np.array([0.25*np.sqrt(35/(2*np.pi)), 0.5*np.sqrt(105/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(7/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(105/np.pi), 0.25*np.sqrt(35/(2*np.pi))])
x = [1e-3*i.value for i in x]
dmat = np.ones((3,7)) * f
dmat[0] *= np.array([6*x[0]*x[1], x[1]*x[2], -2*x[0]*x[1], -6*x[0]*x[2], 4*x[2]**2-x[1]**2-3*x[0]**2, 2*x[0]*x[2], 3*x[0]**2-3*x[1]**2])
dmat[1] *= np.array([3*x[0]**2-3*x[1]**2, x[0]*x[2], 4*x[2]**2-x[0]**2-3*x[1]**2, -6*x[1]*x[2], -2*x[0]*x[1], -2*x[1]*x[2], -6*x[0]*x[1]])
dmat[2] *= np.array([0, x[0]*x[1], 8*x[1]*x[2], 6*x[2]**2-3*x[0]**2-3*x[1]**2, 8*x[0]*x[2], x[0]**2-x[1]**2, 0])
return dmat
def crb_ax(n, Ndim=6, vary=['halo', 'bary', 'progenitor'], align=True, fast=False):
"""Calculate CRB inverse matrix for 3D acceleration at position x in a halo potential"""
pid, dp, vlabel = get_varied_pars(vary)
if align:
alabel = '_align'
else:
alabel = ''
# read in full inverse CRB for stream modeling
cxi = np.load('../data/crb/bspline_cxi{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, n, vlabel, Ndim))
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
# subset halo parameters
Nhalo = 4
cq = cx[:Nhalo,:Nhalo]
if fast:
cqi = np.linalg.inv(cq)
else:
cqi = stable_inverse(cq)
xi = np.array([-8.3, 0.1, 0.1])*u.kpc
x0, v0 = gd1_coordinates()
#xi = np.array(x0)*u.kpc
d = 50
Nb = 20
x = np.linspace(x0[0]-d, x0[0]+d, Nb)
y = np.linspace(x0[1]-d, x0[1]+d, Nb)
x = np.linspace(-d, d, Nb)
y = np.linspace(-d, d, Nb)
xv, yv = np.meshgrid(x, y)
xf = np.ravel(xv)
yf = np.ravel(yv)
af = np.empty((Nb**2, 3))
plt.close()
fig, ax = plt.subplots(3,3,figsize=(11,10))
dimension = ['x', 'y', 'z']
xlabel = ['y', 'x', 'x']
ylabel = ['z', 'z', 'y']
for j in range(3):
if j==0:
xin = np.array([np.repeat(x0[j], Nb**2), xf, yf]).T
elif j==1:
xin = np.array([xf, np.repeat(x0[j], Nb**2), yf]).T
elif j==2:
xin = np.array([xf, yf, np.repeat(x0[j], Nb**2)]).T
for i in range(Nb**2):
#xi = np.array([xf[i], yf[i], x0[2]])*u.kpc
xi = xin[i]*u.kpc
a = acc_nfw(xi)
dqda = halo_accelerations(xi)
cai = np.matmul(dqda, np.matmul(cqi, dqda.T))
if fast:
ca = np.linalg.inv(cai)
else:
ca = stable_inverse(cai)
a_crb = (np.sqrt(np.diag(ca)) * u.km**2 * u.kpc**-1 * u.s**-2).to(u.pc*u.Myr**-2)
af[i] = np.abs(a_crb/a)
af[i] = a_crb
for i in range(3):
plt.sca(ax[j][i])
im = plt.imshow(af[:,i].reshape(Nb,Nb), extent=[-d, d, -d, d], cmap=mpl.cm.gray) #, norm=mpl.colors.LogNorm(), vmin=1e-2, vmax=0.1)
plt.xlabel(xlabel[j]+' (kpc)')
plt.ylabel(ylabel[j]+' (kpc)')
divider = make_axes_locatable(plt.gca())
cax = divider.append_axes("top", size="4%", pad=0.05)
plt.colorbar(im, cax=cax, orientation='horizontal')
plt.gca().xaxis.set_ticks_position('top')
cax.tick_params(axis='x', labelsize='xx-small')
if j==0:
plt.title('a$_{}$'.format(dimension[i]), y=4)
plt.tight_layout(rect=[0,0,1,0.95])
plt.savefig('../plots/acc_{}_{}_{}.png'.format(n, vlabel, Ndim))
def acc_cart(x, components=['bary', 'halo', 'dipole']):
""""""
acart = np.zeros(3) * u.pc*u.Myr**-2
dict_acc = {'bary': [acc_bulge, acc_disk], 'halo': [acc_nfw], 'dipole': [acc_dipole], 'quad': [acc_quad], 'octu': [acc_octu], 'point': [acc_kepler]}
accelerations = []
for c in components:
accelerations += dict_acc[c]
for acc in accelerations:
a_ = acc(x)
acart += a_
return acart
def acc_rad(x, components=['bary', 'halo', 'dipole']):
"""Return radial acceleration"""
r = np.linalg.norm(x) * x.unit
theta = np.arccos(x[2].value/r.value)
phi = np.arctan2(x[1].value, x[0].value)
trans = np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)])
a_cart = acc_cart(x, components=components)
a_rad = np.dot(a_cart, trans)
return a_rad
def ader_cart(x, components=['bary', 'halo', 'dipole']):
""""""
dacart = np.empty((3,0))
dict_der = {'bary': [der_bulge, der_disk], 'halo': [der_nfw], 'dipole': [der_dipole], 'quad': [der_quad], 'point': [der_kepler]}
derivatives = []
for c in components:
derivatives += dict_der[c]
for ader in derivatives:
da_ = ader(x)
dacart = np.hstack((dacart, da_))
return dacart
def apder_cart(x, components=['bary', 'halo', 'dipole']):
""""""
dacart = np.empty((3,0))
dict_der = {'bary': [pder_bulge, pder_disk], 'halo': [pder_nfw], 'dipole': [pder_dipole], 'quad': [pder_quad], 'octu': [pder_octu], 'point': [pder_kepler]}
derivatives = []
for c in components:
derivatives += dict_der[c]
for ader in derivatives:
da_ = ader(x)
dacart = np.hstack((dacart, da_))
return dacart
def apder_rad(x, components=['bary', 'halo', 'dipole']):
"""Return dar/dx_pot (radial acceleration/potential parameters) evaluated at vector x"""
r = np.linalg.norm(x) * x.unit
theta = np.arccos(x[2].value/r.value)
phi = np.arctan2(x[1].value, x[0].value)
trans = np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)])
dadq_cart = apder_cart(x, components=components)
dadq_rad = np.einsum('ij,i->j', dadq_cart, trans)
return dadq_rad
def crb_acart(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', align=True, d=20, Nb=50, fast=False, scale=False, relative=True, progenitor=False, errmode='fiducial'):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
if align:
alabel = '_align'
else:
alabel = ''
if relative:
vmin = 1e-2
vmax = 1
rlabel = ' / a'
else:
vmin = 3e-1
vmax = 1e1
rlabel = ' (pc Myr$^{-2}$)'
# read in full inverse CRB for stream modeling
cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim))
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
# choose the appropriate components:
Nprog, Nbary, Nhalo, Ndipole, Npoint = [6, 5, 4, 3, 1]
if 'progenitor' not in vary:
Nprog = 0
nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'all': Nprog, 'point': 0}
nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'all': np.shape(cx)[0], 'point': 1}
if 'progenitor' not in vary:
nstart['dipole'] = Npoint
nend['dipole'] = Npoint + Ndipole
if component in ['bary', 'halo', 'dipole', 'point']:
components = [component]
else:
components = [x for x in vary if x!='progenitor']
cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]]
Npot = np.shape(cq)[0]
if fast:
cqi = np.linalg.inv(cq)
else:
cqi = stable_inverse(cq)
if scale:
dp_opt = read_optimal_step(n, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]])
scale_mat = np.outer(scale_vec, scale_vec)
cqi *= scale_mat
if progenitor:
x0, v0 = gd1_coordinates()
else:
x0 = np.array([4, 4, 0])
Rp = np.linalg.norm(x0[:2])
zp = x0[2]
R = np.linspace(-d, d, Nb)
k = x0[1]/x0[0]
x = R/np.sqrt(1+k**2)
y = k * x
z = np.linspace(-d, d, Nb)
xv, zv = np.meshgrid(x, z)
yv, zv = np.meshgrid(y, z)
xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T
Npix = np.size(xv)
af = np.empty((Npix, 3))
derf = np.empty((Npix, 3, Npot))
for i in range(Npix):
xi = xin[i]*u.kpc
a = acc_cart(xi, components=components)
dadq = apder_cart(xi, components=components)
derf[i] = dadq
ca = np.matmul(dadq, np.matmul(cq, dadq.T))
a_crb = np.sqrt(np.diag(ca)) * u.pc * u.Myr**-2
if relative:
af[i] = np.abs(a_crb/a)
else:
af[i] = a_crb
#print(xi, a_crb)
# save
np.savez('../data/crb_acart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative), acc=af, x=xin, der=derf)
plt.close()
fig, ax = plt.subplots(1, 3, figsize=(15, 5))
label = ['$\Delta$ $a_X$', '$\Delta$ $a_Y$', '$\Delta$ $a_Z$']
for i in range(3):
plt.sca(ax[i])
im = plt.imshow(af[:,i].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=mpl.colors.LogNorm())
if progenitor:
plt.plot(Rp, zp, 'r*', ms=10)
plt.xlabel('R (kpc)')
plt.ylabel('Z (kpc)')
divider = make_axes_locatable(plt.gca())
cax = divider.append_axes("right", size="3%", pad=0.1)
plt.colorbar(im, cax=cax)
plt.ylabel(label[i] + rlabel)
plt.tight_layout()
plt.savefig('../plots/crb_acc_cart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative))
def crb_acart_cov(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', j=0, align=True, d=20, Nb=30, fast=False, scale=False, relative=True, progenitor=False, batch=False, errmode='fiducial'):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
if align:
alabel = '_align'
else:
alabel = ''
if relative:
vmin = 1e-2
vmax = 1
rlabel = ' / a'
else:
vmin = -0.005
vmax = 0.005
#vmin = 1e-2
#vmax = 1e0
rlabel = ' (pc Myr$^{-2}$)'
# read in full inverse CRB for stream modeling
cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim))
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
# choose the appropriate components:
Nprog, Nbary, Nhalo, Ndipole, Nquad, Npoint = [6, 5, 4, 3, 5, 1]
if 'progenitor' not in vary:
Nprog = 0
nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'quad': Nprog + Nbary + Nhalo + Ndipole, 'all': Nprog, 'point': 0}
nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'quad': Nprog + Nbary + Nhalo + Ndipole + Nquad, 'all': np.shape(cx)[0], 'point': 1}
if 'progenitor' not in vary:
nstart['dipole'] = Npoint
nend['dipole'] = Npoint + Ndipole
if component in ['bary', 'halo', 'dipole', 'quad', 'point']:
components = [component]
else:
components = [x for x in vary if x!='progenitor']
cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]]
Npot = np.shape(cq)[0]
if fast:
cqi = np.linalg.inv(cq)
else:
cqi = stable_inverse(cq)
if scale:
dp_opt = read_optimal_step(n, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]])
scale_mat = np.outer(scale_vec, scale_vec)
cqi *= scale_mat
if progenitor:
prog_coords = {-1: gd1_coordinates(), -2: pal5_coordinates(), -3: tri_coordinates(), -4: atlas_coordinates()}
x0, v0 = prog_coords[n]
print(x0)
else:
x0 = np.array([4, 4, 0])
Rp = np.linalg.norm(x0[:2])
zp = x0[2]
R = np.linspace(-d, d, Nb)
k = x0[1]/x0[0]
x = R/np.sqrt(1+k**2)
y = k * x
z = np.linspace(-d, d, Nb)
xv, zv = np.meshgrid(x, z)
yv, zv = np.meshgrid(y, z)
xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T
Npix = np.size(xv)
af = np.empty((Npix, 3))
derf = np.empty((Npix*3, Npot))
for i in range(Npix):
xi = xin[i]*u.kpc
a = acc_cart(xi, components=components)
dadq = apder_cart(xi, components=components)
derf[i*3:(i+1)*3] = dadq
ca = np.matmul(derf, np.matmul(cq, derf.T))
Nx = Npot
Nw = Npix*3
vals, vecs = la.eigh(ca, eigvals=(Nw - Nx - 2, Nw - 1))
## check orthogonality:
#for i in range(Npot-1):
#for k in range(i+1, Npot):
#print(i, k)
#print(np.dot(vecs[:,i], vecs[:,k]))
#print(np.dot(vecs[::3,i], vecs[::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k]))
# save
np.savez('../data/crb_acart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative, progenitor), x=xin, der=derf, c=ca)
plt.close()
fig, ax = plt.subplots(1, 3, figsize=(15, 5))
if j==0:
vcomb = np.sqrt(np.sum(vecs**2*vals, axis=1))
label = ['($\Sigma$ Eigval $\\times$ Eigvec$^2$ $a_{}$'.format(x)+')$^{1/2}$' for x in ['X', 'Y', 'Z']]
vmin = 1e-2
vmax = 5e0
norm = mpl.colors.LogNorm()
else:
vcomb = vecs[:,j]
label = ['Eig {} $a_{}$'.format(np.abs(j), x) for x in ['X', 'Y', 'Z']]
vmin = -0.025
vmax = 0.025
norm = None
for i in range(3):
plt.sca(ax[i])
#im = plt.imshow(vecs[i::3,j].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax)
im = plt.imshow(vcomb[i::3].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=norm)
if progenitor:
plt.plot(Rp, zp, 'r*', ms=10)
plt.xlabel('R (kpc)')
plt.ylabel('Z (kpc)')
divider = make_axes_locatable(plt.gca())
cax = divider.append_axes("right", size="3%", pad=0.1)
plt.colorbar(im, cax=cax)
plt.ylabel(label[i])
plt.tight_layout()
if batch:
return fig
else:
plt.savefig('../plots/crb_acc_cart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, np.abs(j), Ndim, d, Nb, relative, progenitor))
def a_vecfield(vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', d=20, Nb=10):
"""Plot acceleration field in R,z plane"""
if component in ['bary', 'halo', 'dipole', 'quad', 'point']:
components = [component]
else:
components = [x for x in vary if x!='progenitor']
x0 = np.array([4, 4, 0])
R = np.linspace(-d, d, Nb)
k = x0[1]/x0[0]
x = R/np.sqrt(1+k**2)
y = k * x
z = np.linspace(-d, d, Nb)
xv, zv = np.meshgrid(x, z)
yv, zv = np.meshgrid(y, z)
xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T
Rin = np.linalg.norm(xin[:,:2], axis=1) * np.sign(xin[:,0])
zin = xin[:,2]
Npix = np.size(xv)
acart_pix = np.empty((Npix, 3))
acyl_pix = np.empty((Npix, 2))
for i in range(Npix):
xi = xin[i]*u.kpc
acart = acc_cart(xi, components=components)
acart_pix[i] = acart
acyl_pix[:,0] = np.linalg.norm(acart_pix[:,:2], axis=1) * -np.sign(xin[:,0])
acyl_pix[:,1] = acart_pix[:,2]
plt.close()
plt.figure()
plt.quiver(Rin, zin, acyl_pix[:,0], acyl_pix[:,1])
plt.tight_layout()
def a_crbcov_vecfield(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], errmode='fiducial', component='all', j=0, align=True, d=20, Nb=10, fast=False, scale=True, relative=False, progenitor=False, batch=False):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
if align:
alabel = '_align'
else:
alabel = ''
if relative:
vmin = 1e-2
vmax = 1
rlabel = ' / a'
else:
vmin = -0.005
vmax = 0.005
#vmin = 1e-2
#vmax = 1e0
rlabel = ' (pc Myr$^{-2}$)'
# read in full inverse CRB for stream modeling
cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim))
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
# choose the appropriate components:
Nprog, Nbary, Nhalo, Ndipole, Nquad, Npoint = [6, 5, 4, 3, 5, 1]
if 'progenitor' not in vary:
Nprog = 0
nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'quad': Nprog + Nbary + Nhalo + Ndipole, 'all': Nprog, 'point': 0}
nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'quad': Nprog + Nbary + Nhalo + Ndipole + Nquad, 'all': np.shape(cx)[0], 'point': 1}
if 'progenitor' not in vary:
nstart['dipole'] = Npoint
nend['dipole'] = Npoint + Ndipole
if component in ['bary', 'halo', 'dipole', 'quad', 'point']:
components = [component]
else:
components = [x for x in vary if x!='progenitor']
cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]]
Npot = np.shape(cq)[0]
if fast:
cqi = np.linalg.inv(cq)
else:
cqi = stable_inverse(cq)
if scale:
dp_opt = read_optimal_step(n, vary)
dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)]
scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]])
scale_mat = np.outer(scale_vec, scale_vec)
cqi *= scale_mat
if progenitor:
x0, v0 = gd1_coordinates()
else:
x0 = np.array([4, 4, 0])
Rp = np.linalg.norm(x0[:2])
zp = x0[2]
R = np.linspace(-d, d, Nb)
k = x0[1]/x0[0]
x = R/np.sqrt(1+k**2)
y = k * x
z = np.linspace(-d, d, Nb)
xv, zv = np.meshgrid(x, z)
yv, zv = np.meshgrid(y, z)
xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T
Rin = np.linalg.norm(xin[:,:2], axis=1) * np.sign(xin[:,0])
zin = xin[:,2]
Npix = np.size(xv)
acart_pix = np.empty((Npix, 3))
acyl_pix = np.empty((Npix, 2))
vcomb_pix = np.empty((Npix, 2))
af = np.empty((Npix, 3))
derf = np.empty((Npix*3, Npot))
for i in range(Npix):
xi = xin[i]*u.kpc
a = acc_cart(xi, components=components)
acart_pix[i] = a
dadq = apder_cart(xi, components=components)
derf[i*3:(i+1)*3] = dadq
acyl_pix[:,0] = np.linalg.norm(acart_pix[:,:2], axis=1) * -np.sign(xin[:,0])
acyl_pix[:,1] = acart_pix[:,2]
ca = np.matmul(derf, np.matmul(cq, derf.T))
Nx = Npot
Nw = Npix*3
vals, vecs = la.eigh(ca, eigvals=(Nw - Nx - 2, Nw - 1))
if j==0:
vcomb = np.sqrt(np.sum(vecs**2*vals, axis=1))
label = ['($\Sigma$ Eigval $\\times$ Eigvec$^2$ $a_{}$'.format(x)+')$^{1/2}$' for x in ['X', 'Y', 'Z']]
vmin = 1e-3
vmax = 1e-1
norm = mpl.colors.LogNorm()
else:
vcomb = vecs[:,j]*np.sqrt(vals[j])
label = ['Eig {} $a_{}$'.format(np.abs(j), x) for x in ['X', 'Y', 'Z']]
vmin = -0.025
vmax = 0.025
norm = None
vcomb_pix[:,0] = np.sqrt(vcomb[0::3]**2 + vcomb[1::3]**2) * -np.sign(xin[:,0])
#vcomb_pix[:,0] = np.sqrt(vcomb[0::3]**2 + vcomb[1::3]**2) * -np.sign(vcomb[0::3])
vcomb_pix[:,1] = vcomb[2::3]
plt.close()
fig, ax = plt.subplots(1,2,figsize=(10,5))
plt.sca(ax[0])
plt.quiver(Rin, zin, acyl_pix[:,0], acyl_pix[:,1], pivot='middle')
plt.xlabel('R (kpc)')
plt.ylabel('Z (kpc)')
plt.title('Acceleration {}'.format(component), fontsize='medium')
plt.sca(ax[1])
plt.quiver(Rin, zin, vcomb_pix[:,0], vcomb_pix[:,1], pivot='middle', headwidth=0, headlength=0, headaxislength=0, scale=0.02, scale_units='xy')
plt.xlabel('R (kpc)')
plt.ylabel('Z (kpc)')
plt.title('Eigenvector {}'.format(np.abs(j)), fontsize='medium')
plt.tight_layout()
if batch:
return fig
else:
plt.savefig('../plots/afield_crbcov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, np.abs(j), Ndim, d, Nb, relative))
def summary(n, mode='scalar', vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], errmode='fiducial', component='all'):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
fn = {'scalar': crb_acart_cov, 'vector': a_crbcov_vecfield}
bins = {'scalar': 30, 'vector': 10}
Nprog, Nbary, Nhalo, Ndipole, Nquad, Npoint = [6, 5, 4, 3, 5, 1]
Npars = {'bary': Nbary, 'halo': Nhalo, 'dipole': Ndipole, 'quad': Nquad, 'point': Npoint}
if component in ['bary', 'halo', 'dipole', 'quad', 'point']:
components = [component]
else:
components = [x for x in vary if x!='progenitor']
Niter = [Npars[x] for x in components]
Niter = sum(Niter) + 1
pp = PdfPages('../plots/acceleration_{}_{}_{}_{}_{}.pdf'.format(n, errmode, vlabel, component, mode))
for i in range(Niter):
print(i, Niter)
fig = fn[mode](-1, progenitor=True, batch=True, errmode=errmode, vary=vary, component=component, j=-i, d=20, Nb=bins[mode])
pp.savefig(fig)
pp.close()
#########
# Summary
def full_names():
""""""
full = {'gd1': 'GD-1', 'atlas': 'ATLAS', 'tri': 'Triangulum', 'ps1a': 'PS1A', 'ps1b': 'PS1B', 'ps1c': 'PS1C', 'ps1d': 'PS1D', 'ps1e': 'PS1E', 'ophiuchus': 'Ophiuchus', 'hermus': 'Hermus', 'kwando': 'Kwando', 'orinoco': 'Orinoco', 'sangarius': 'Sangarius', 'scamander': 'Scamander'}
return full
def full_name(name):
""""""
full = full_names()
return full[name]
def get_done(sort_length=False):
""""""
done = ['gd1', 'tri', 'atlas', 'ps1a', 'ps1c', 'ps1e', 'ophiuchus', 'kwando', 'orinoco', 'sangarius', 'hermus', 'ps1d']
done = ['gd1', 'tri', 'atlas', 'ps1a', 'ps1c', 'ps1e', 'kwando', 'orinoco', 'sangarius', 'hermus', 'ps1d']
# length
if sort_length:
tosort = []
for name in done:
mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb'))
tosort += [np.max(mock['xi_range']) - np.min(mock['xi_range'])]
done = [x for _,x in sorted(zip(tosort,done))]
else:
tosort = []
vary = ['progenitor', 'bary', 'halo']
Ndim = 6
errmode = 'fiducial'
align = True
pid, dp_fid, vlabel = get_varied_pars(vary)
pid_vh = myutils.wherein(np.array(pid), np.array([5]))
for name in done:
fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
cxi = fm['cxi']
cx = stable_inverse(cxi)
crb = np.sqrt(np.diag(cx))
tosort += [crb[pid_vh]]
done = [x for _,x in sorted(zip(tosort,done))][::-1]
return done
def store_mocks():
""""""
done = get_done()
for name in done:
stream = stream_model(name)
np.save('../data/streams/mock_observed_{}'.format(name), stream.obs)
def period(name):
"""Return orbital period in units of stepsize and number of complete periods"""
orbit = stream_orbit(name=name)
r = np.linalg.norm(orbit['x'].to(u.kpc), axis=0)
a = np.abs(np.fft.rfft(r))
f = np.argmax(a[1:]) + 1
p = np.size(a)/f
return (p, f)
def extract_crbs(Ndim=6, vary=['progenitor', 'bary', 'halo'], component='halo', errmode='fiducial', j=0, align=True, fast=False, scale=False):
""""""
pid, dp_fid, vlabel = get_varied_pars(vary)
names = get_done()
tout = Table(names=('name', 'crb'))
pparams0 = pparams_fid
pid_comp, dp_fid2, vlabel2 = get_varied_pars(component)
Np = len(pid_comp)
pid_crb = myutils.wherein(np.array(pid), np.array(pid_comp))
plt.close()
fig, ax = plt.subplots(Np,1,figsize=(10,15), subplot_kw=dict(projection='mollweide'))
for name in names[:]:
fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel))
cxi = fm['cxi']
if fast:
cx = np.linalg.inv(cxi)
else:
cx = stable_inverse(cxi)
crb = np.sqrt(np.diag(cx))
#print([pparams0[pid_comp[i]] for i in range(Np)])
crb_frac = [crb[pid_crb[i]]/pparams0[pid_comp[i]].value for i in range(Np)]
print(name, crb_frac)
stream = stream_model(name=name)
for i in range(Np):
plt.sca(ax[i])
color_index = np.array(crb_frac[:])
color_index[color_index>0.2] = 0.2
color_index /= 0.2
color = mpl.cm.viridis(color_index[i])
plt.plot(np.radians(stream.obs[0]), | np.radians(stream.obs[1]) | numpy.radians |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = | N.array([0,0,0]) | numpy.array |
"""This module contains useful functions and classes for thermal system calculation
Symbols:
h: convection_heat_transfer_coeffient [W/m2K]
k: thermal conductivity [W/mK]
r: radius [m]
cp: specific heat capacity at constant pressure [J/kgK]
temp: temperature [degC or K]
"""
import logging
import warnings
from abc import ABC, abstractmethod
from enum import Enum, auto, unique
from functools import cached_property
from typing import Union, Tuple, NamedTuple
import numpy as np
from CoolProp.CoolProp import PropsSI
from CoolProp.HumidAirProp import HAPropsSI
import matplotlib.pyplot as plt
from scipy.optimize import root
# Define logger
logger = logging.getLogger('thermal_system_calculation')
logger.setLevel(logging.INFO)
ch = logging.StreamHandler()
ch.setLevel(logging.INFO)
formatter = logging.Formatter('%(asctime)s - %(name)s - %(levelname)s - %(message)s')
ch.setFormatter(formatter)
logger.addHandler(ch)
Numeric = Union[float, np.ndarray]
GRAVITY = 9.81
def get_heat_flux_by_conduction(
temperature_from: Numeric,
temperature_to: Numeric,
thickness: Numeric,
thermal_conductivity: Numeric,
) -> Numeric:
"""Returns heat flux [W/m2] by conduction from a section of material to another"""
return thermal_conductivity * (temperature_from - temperature_to) / thickness
def get_heat_flux_by_convection(h: Numeric, temp_from: Numeric, temp_to: Numeric) -> float:
"""Returns heat flux [W/m2] by convection from a surface of a temperature (temp_from) to the
fluid with another temperature (temp_to) for the given heat convection coefficient (alpha)"""
return h * (temp_from - temp_to)
###################################################################################################
# Exercise 2
def get_thermal_resistance_cylinder(
radius: Numeric,
wall_thickness: Numeric,
thermal_conductivity: Numeric,
length: Numeric
) -> Numeric:
"""Returns thermal resistance [m2K/W] for a cylinder"""
outer_radius = radius + wall_thickness
return np.log(outer_radius / radius) / (2 * np.pi * length * thermal_conductivity)
Numeric = Union[float, np.ndarray]
@unique
class TipBoundaryConditionForFin(Enum):
Convection = auto()
Adiabatic = auto()
Temperature = auto()
Long = auto()
class FinConfiguration(NamedTuple):
perimeter: float
area_cross_section: float
length: float
def get_heat_transfer_1D_fin_with_uniform_cross_section(
x: Numeric,
temp_base: Numeric,
temp_surr: Numeric,
fin_configuration: FinConfiguration,
h: Numeric,
k: Numeric,
boundary_condition: TipBoundaryConditionForFin,
temp_tip: Numeric = None
) -> Tuple[Numeric, Numeric]:
m = np.sqrt(h * fin_configuration.perimeter / (k * fin_configuration.area_cross_section))
h_mk = h / (m * k)
m_l_x = m * (fin_configuration.length - x)
m_l = m * fin_configuration.length
theta_b = temp_base - temp_surr
mm = np.sqrt(h * fin_configuration.perimeter * k * fin_configuration.area_cross_section) * \
theta_b
if boundary_condition == TipBoundaryConditionForFin.Convection:
denominator = (np.cosh(m_l) + h_mk * np.sinh(m_l))
theta = (np.cosh(m_l_x) + h_mk * np.sinh(m_l_x)) / denominator * theta_b
heat_transfer_rate = mm * (np.sinh(m_l) + h_mk * np.cosh(m_l)) / denominator
elif boundary_condition == TipBoundaryConditionForFin.Adiabatic:
theta = np.cosh(m_l_x) / np.cosh(m_l) * theta_b
heat_transfer_rate = mm * np.tanh(m_l)
elif boundary_condition == TipBoundaryConditionForFin.Temperature:
theta_l_b = (temp_tip - temp_surr) / theta_b
theta = (theta_l_b * np.sinh(m * x) + np.sinh(m_l_x)) / np.sinh(m_l) * theta_b
heat_transfer_rate = mm * (np.cosh(m_l) - theta_l_b) / np.sinh(m_l)
elif boundary_condition == TipBoundaryConditionForFin.Long:
theta = np.exp(-m * x) * theta_b
heat_transfer_rate = mm
else:
raise TypeError(f'Invalid boundary condition is given: {boundary_condition}')
temp = theta + temp_surr
return heat_transfer_rate, temp
# CoolProp related classes, functions
@unique
class Fluid(Enum):
WATER = auto()
AIR = auto()
AMMONIA = auto()
CO2 = auto()
H2 = auto()
NITROGEN = auto()
OXYGEN = auto()
R134A = auto()
R143A = auto()
R407C = auto()
@unique
class ThermodynamicState(Enum):
PRESSURE = 'P'
TEMPERATURE = 'T'
SATURATION = 'Q'
@unique
class Properties(Enum):
SPECIFIC_HEAT_CAPACITY_CONSTANT_PRESSURE = 'C'
SPECIFIC_HEAT_CAPACITY_CONSTANT_VOLUME = 'CVMASS'
GAS_CONSTANT_MOL = 'GAS_CONSTANT'
DENSITY = 'D'
CRITICAL_TEMPERATURE = 'Tcrit'
RELATIVE_HUMIDITY = 'R'
SPECIFIC_ENTHALPY = 'H'
SPECIFIC_ENTROPY = 'S'
SPECIFIC_INTERNAL_ENERGY = 'U'
THERMAL_CONDUCTIVITY = 'CONDUCTIVITY'
DYNAMIC_VISCOSITY = 'VISCOSITY'
EXPANSION_COEFFICIENT_ISOBARIC = 'ISOBARIC_EXPANSION_COEFFICIENT'
@unique
class NonCircularCylinderGeometry(Enum):
SQUARE_FLAT = auto()
SQUARE_OBLIQUE = auto()
HEXAGON_FLAT = auto()
HEXAGON_OBLIQUE = auto()
VERTICAL_FLAT_FRONT = auto()
VERTICAL_FLAT_BACK = auto()
@unique
class TubeBankArrangement(Enum):
Aligned = auto()
Staggered = auto()
class TubeBankConfiguration(NamedTuple):
arrangement: TubeBankArrangement
vertical_spacing: float
horizontal_spacing: float
number_rows: float
number_tubes_each_row: float
def get_maximum_velocity(self, velocity: float, diameter: float):
if self.arrangement == TubeBankArrangement.Aligned:
return self.vertical_spacing / (self.vertical_spacing - diameter) * velocity
diagonal_spacing = | np.sqrt(self.horizontal_spacing ** 2 + (self.vertical_spacing / 2) ** 2) | numpy.sqrt |
# -*- coding: utf-8 -*-
"""
Created on Thu May 30 20:03:50 2019
Finds Vg1 and Vg2 values above a threshold, determined by the ratio of the areas
of a Gaussian fit of the intensity histogram to the total area of the intensities
@author: <NAME>
"""
import numpy as np
import scipy.signal as ss
import scipy.optimize as opt
from scipy.signal import medfilt2d, savgol_filter
from scipy.ndimage import correlate
from sklearn.neighbors import KDTree
import stability as stab
def hist_data(z):
"""
Finds x and y data from histogram
:param z: input
:return: x and y
"""
data = np.histogram(z, bins='scott')
x = data[1]
x = np.array([(x[i] + x[i + 1]) / 2 for i in range(0, len(x) - 1)])
return x, np.array(data[0])
def gauss(x, *params):
return abs(params[2]) * np.exp(-(x - params[0]) ** 2 / (2 * params[1] ** 2))
def multi_gaussian(x, *params):
"""
Fits multiple Gaussian distributions, number of which determined by the number of parameters inputted
"""
y = np.zeros_like(x)
index = np.arange(0, len(params), 3)
if index.size > 1:
for i in range(0, len(params) // 3):
mu = params[i]
sig = params[i + len(params) // 3]
amp = params[i + 2 * len(params) // 3]
y = y + abs(amp) * np.exp(-(x - mu) ** 2 / (2 * sig ** 2))
else:
y = y + abs(params[2]) * np.exp(-(x - params[0]) ** 2 / (2 * params[1] ** 2))
return y
def multi_gauss_background(x, *params):
y = np.zeros_like(x)
index = np.arange(0, len(params) - 2, 3)
if index.size > 1:
y = y + params[0] * x + params[1]
for i in range(0, (len(params) - 2) // 3):
mu = params[i + 2]
sig = params[i + 2 + (len(params) - 2) // 3]
amp = params[i + 2 + 2 * (len(params) - 2) // 3]
y = y + abs(amp) * np.exp(-(x - mu) ** 2 / (2 * sig ** 2))
else:
y = y + params[0] * x + params[1] + abs(params[4]) * np.exp(-(x - params[2]) ** 2 / (2 * params[3] ** 2))
return y
def greedy_guess(guess, x, y):
n = (len(guess) - 2) // 3
m, sig, a = guess[2:n + 2], guess[n + 2:2 * n + 2], guess[2 * n + 2:]
chi = (y - multi_gauss_background(x, *guess)) / multi_gauss_background(x, *guess)
chi = savgol_filter(chi, 3, 2)
m, a = np.append(m, float(x[np.where(chi == np.max(chi))])), np.append(a, float(y[np.where(chi == np.max(chi))]))
sig = np.append(sig, sig[n - 1] / 2)
return np.append(guess[:2], np.append(m, np.append(sig, a)))
def gradient(x, y, z):
"""
Calculates gradient along x and y of intensities to reduce noise
@param x: x vales
@param y: y values
@param z: intensities
@return:
"""
m_z = np.reshape(z, (len(np.unique(y)), len(np.unique(x))))# Transform array into matrix
sg = savgol_filter(m_z, 5, 2) + savgol_filter(m_z, 5, 2, axis=0) # Savgol filter acts as a low pass band filter
signal = sg - np.mean(sg) + np.mean(m_z)
return np.reshape(signal, np.shape(x))
def gradient_exp(x, y, z):
"""
Calculates gradient along x and y of intensities to reduce noise
@param x: x vales
@param y: y values
@param z: intensities
@return:
"""
m_z = np.reshape(z, (len(np.unique(y)), len(np.unique(x))))# Transform array into matrix
diff = [[0, -1, 0], [-1, 5, -1], [0, -1, 0]]
z_diff = correlate(m_z, diff)
sg = savgol_filter(z_diff, 5, 2) + savgol_filter(z_diff, 5, 2, axis=0) # Savgol filter acts as a low pass band filter
signal = sg - np.mean(sg) + np.mean(m_z)
return np.reshape(signal, np.shape(x))
def filtering(x, y, z):
m_z = np.reshape(z, (len(np.unique(y)), len(np.unique(x)))) # Transform array into matrix
s = medfilt2d(m_z)
return np.reshape(s, (int(len(x)),))
def normalise(z):
"""
Unity-based normalisation function, such that all values range between 0 and 1
:param z: Raw data that needs normalising
:return: Normalised data
"""
return np.nan_to_num((z - np.min(z)) / (np.max(z) - np.min(z)))
def fit_gauss(z):
intensity = normalise(z)
x, y = hist_data(intensity)
guess = np.append(0, np.append(np.median(y), np.append(np.median(x[np.where(y == np.max(y))]),
np.append(np.std(x[np.where(y > np.median(y))]),
np.max(y)))))
fit_param, cov = opt.curve_fit(multi_gauss_background, x, y, guess)
if fit_param[2] > 0.5:
index = np.where(intensity<fit_param[2]-3*abs(fit_param[3]))
else:
index = np.where(intensity>fit_param[2]+3*abs(fit_param[3]))
return index
def curved_plane(x, y, param):
return param[0]*x + param[1]*x**2 + param[2]*y + param[3]*y**2 + param[4]*x*y + param[5]
def linear_plane(x, y, param):
return param[0]*x + param[1]*y + param[2]
def minimise_plane(param, x, y, z):
return np.sum((z - linear_plane(x, y, param))**2)
def linear(x, z):
return (np.median(z[np.where(x==np.min(x))])-np.median(z[np.where(x==np.max(x))]))/(np.min(x)-np.max(x))
def remove_background(x, y, z):
p = gradient_exp(x, y, z)
param = np.array((linear(x, z), linear(y,z), np.median(p)))
sol = opt.minimize(minimise_plane, param, args=(x, y, p))
p_n = normalise(p - linear_plane(x, y, sol.x))
return p_n*(np.max(z)-np.min(z)) + np.min(z)
def grad_exp(z, val_x, val_y):
val = z.reshape(val_y, val_x)
scharr = np.array([[ -3-3j, 0-10j, +3 -3j],
[-10+0j, 0+ 0j, +10 +0j],
[ -3+3j, 0+10j, +3 +3j]]) # Gx + j*Gy
grad = ss.convolve2d(val, scharr, boundary='symm', mode='same')
index = np.where(np.logical_or(abs(np.angle(grad).flatten())<=0.15, abs(np.angle(grad).flatten())>=np.pi-0.15))
z[index] = 0
return z
def get_klpq_div(p_probs, q_probs):
# Calcualtes the Kullback-Leibler divergence between pi and qi
kl_div = 0.0
for pi, qi in zip(p_probs, q_probs):
kl_div += pi*np.nan_to_num(np.log(pi/qi))
return kl_div
def D_KL(threshold, x, y):
# Finds best fit Gaussian distribution and calculates the corresponding Kullback-Leibler divergence
index = np.where(np.logical_and(x>=threshold[0], x<=threshold[1]))
xs, ys = x[index], y[index]
if np.trapz(ys)>0:
ys = ys/np.trapz(ys)
else:
return np.inf
guess = np.append(np.median(xs[np.where(ys == np.max(ys))]),
np.append(np.std(xs[np.where(ys > np.median(ys))]),
np.max(ys)))
bounds = ((np.min(x)-np.std(x), np.std(x)/10**4, np.mean(ys)), (np.max(x)+np.std(x), np.max(x)-np.min(x), 10*np.max(ys)))
fit_param, cov = opt.curve_fit(gauss, xs, ys, guess, bounds=bounds)
return get_klpq_div(ys+10**-7, gauss(xs, *fit_param)+10**-7) # Add small epsilon to ensure that we donn't devide by zero
def minimise_DKL(x, y):
# Estimate first guess and boundaries to use:
guess = np.append(np.median(x[np.where(y == np.max(y))]),
np.append(np.std(x[np.where(y > np.median(y))]),
np.max(y)))
b = ((np.min(x)-np.std(x), np.std(x)/10**4, np.mean(y)), (np.max(x)+np.std(x), np.max(x)-np.min(x), np.max(y)*10))
fit_param, cov = opt.curve_fit(gauss, x, y, guess, bounds=b)
x0 = [fit_param[0]-2*fit_param[1], fit_param[0]+2*fit_param[1]]
bound = ((np.min(x), fit_param[0]-fit_param[1]), (fit_param[0]+fit_param[1], np.max(x)))
# Find optimal bound solutions
sol = opt.minimize(D_KL, x0, jac=None, method='L-BFGS-B', options={'eps':1/len(x)}, args=(x, y), bounds=bound)
return sol.x
def threshold_DKL(z):
intensity = normalise(z)
x, y = hist_data(intensity)
y = y**0.5 # Broadens peak to allow to identify finer structure in the intensity
threshold = minimise_DKL(x, y)
if abs(np.max(z))>abs(np.min(z)):
index = np.where(intensity>=threshold[1])
else:
index = np.where(intensity<=threshold[0])
return index
def threshold(z, val):
if abs(np.max(z))>abs(np.min(z)):
v = abs(np.min(z))*0.9
else:
v = -abs(np.max(z))*0.9
val = np.append(val, v)
v = np.mean(abs(val))
m = np.where(np.logical_or(z > v, z < -v))
return m, val
def intense(z, index):
x, y = hist_data(z)
guess = np.append(np.median(x[np.where(y == np.max(y))]),
np.append(np.std(x[np.where(y > np.median(y))]),
np.max(y)))
fit_param, cov = opt.curve_fit(gauss, x, y, guess)
return z[index]-fit_param[0]
def threshold_experimental(vg1, vg2, i, q):
i_g, q_g = remove_background(vg1, vg2, i), remove_background(vg1, vg2, q)
m_i, m_q = threshold_DKL(i_g), threshold_DKL(q_g)
index = np.unique(np.append(m_i, m_q))
intensity = normalise(abs(intense(i, index)))+normalise(abs(intense(q, index)))
return vg1[index], vg2[index], intensity, i_g, q_g, index
def threshold_theoretical(vg1, vg2, i):
i_g = gradient(vg1, vg2, i)
x, y = hist_data(i_g)
x = normalise(x)
fit_param = [np.median(x[np.where(y == np.max(y))]), np.std(x[np.where(y > np.median(y))]), np.max(y)]
try:
fit_one, _ = opt.curve_fit(multi_gaussian, x, y, fit_param)
ind = np.where(x > fit_one[0] + fit_one[1])
ys = y[ind] - multi_gaussian(x[ind], *fit_one)
guess = [fit_one[0], np.median(x[ind][np.where(ys == np.max(ys))]),
fit_one[1], np.std(x[np.where(y > np.median(ys))]),
fit_one[2], np.max(ys)]
try:
fit_param, cov = opt.curve_fit(multi_gaussian, x, y, guess)
error = np.sqrt(np.diag(cov))
if error[1] * 10 > error[0]:
index = np.where(normalise(i) > fit_param[1])
else:
index = np.where(normalise(i) > 0.4)
except:
val = np.min(x[np.where(x > fit_one[0] + fit_one[1])])
index = np.where(normalise(i) > val)
except:
index = np.where(normalise(i) > 0.4)
return vg1[index], vg2[index], i[index], x, y, fit_param
def averaging_xy(x, y, intensity, leaf, n_neighbours):
"""
Uses KDTree to find n_neighbours and then calculates a weighted mean, resulting in thinning the data
:param x: threshold x values
:param y: threshold y values
:param intensity: corresponding intensities
:param leaf: determines how many neighbouring points to check, leaf > n_neighbours
:param n_neighbours: number of neighbours to average through
:return: thinned x and y values
"""
data = np.transpose(np.vstack([x, y]))
xs, ys, zs = [], [], []
tree = KDTree(data, leaf_size=leaf) # Finds relation between points
for i in range(0, len(data)):# // n_neighbours):
# Figure out which are the neighbouring points
# dist, ind = tree.query(np.reshape(data[i * n_neighbours, :], (1, -1)), k=n_neighbours)
dist, ind = tree.query(np.reshape(data[i, :], (1, -1)), k=n_neighbours)
# takes weighted average of x and y values of given point
x_m, y_m = np.average(x[ind], weights=intensity[ind]), np.average(y[ind], weights=intensity[ind])
z_m = np.average(intensity[ind])
xs, ys, zs = np.append(xs, x_m), np.append(ys, y_m), np.append(zs, z_m)
return xs, ys, zs
def thinning(Vg1, Vg2, i_g, q_g, ind):
val_x, val_y = len(np.unique(Vg1)), len(np.unique(Vg2))
# Set data points below threshold to zero
M = np.sqrt(i_g**2+q_g**2)
mask = np.ones(M.shape,dtype=bool)
mask[ind] = False
M[mask] = 0
M = grad_exp(M, val_x, val_y)
# Find peaks along x
if val_x > 100:
peaks, hight = ss.find_peaks(M, width=1, distance=val_x//100)
else:
peaks, hight = ss.find_peaks(M, width=1)
xs, ys, zs = Vg1[peaks], Vg2[peaks], M[peaks]
# Find peaks along y
xt = np.reshape(np.transpose(np.reshape(Vg1, (val_y, val_x))), np.shape(Vg1))
yt = np.reshape(np.transpose(np.reshape(Vg2, (val_y, val_x))), np.shape(Vg2))
Mt = np.reshape(np.transpose(np.reshape(M, (val_y, val_x))), np.shape(M))
if val_y > 100:
peaks, hight = ss.find_peaks(Mt, width=1, distance=val_y//100)
else:
peaks, hight = ss.find_peaks(Mt, width=1)
# add peaks from both directions
xs, ys, zs = np.append(xs, xt[peaks]), np.append(ys, yt[peaks]), np.append(zs, Mt[peaks])
# xs, ys, zs = averaging_xy(xs, ys, zs, 100, 10)
return xs, ys, zs
def thinning_IQ(vg1, vg2, z, val_x):
x, y = hist_data(z)
y = y**0.5 # Broadens peak to allow to identify finer structure in the intensity
threshold = minimise_DKL(x, y)
if abs(np.max(z))>abs( | np.min(z) | numpy.min |
#########################################################################################################
# This is a script for computing the number of voronoi edges shared by different lipids in a ternary
# mixture of DPPC/DSPC, DIPC, and CHOL in the MARTINI coarse-grained model.
#It can be used as well for atomistic simulations
#
# This script uses the (x,y) coordinates of lipid head groups to perform Voronoi tessellation
# The outputs from this script are:
# (1) counts of voronoi edges between lipids in each leaflet
# (2) tertiary (lipid1 + lipid2 + lipid3) mixing entropy and binary (lipid1 + lipid2) mixing entropy, ignoring lipid3 (CHOL)
# (3) the ratio of #CHOL-DPPC / #CHOL-DIPC Voronoi edges
#
# The selection of lipids can be changed by changing the definitions of lipid[1-3] and sel[1-3]
# The system topology and trajectory can be set by changing the definitions of top and traj
#
# Usage is: ternary_lipid_voronoi_edges.py <side>
# where <side> is "up" or "down", analyzing either the upper or lower leaflet of a MARTINI DPPC:DIPC:CHOL#
# membrane using induces of the membrane as if the system was built using the insane.py tool
#########################################################################################################
import sys
import numpy as np
from MDAnalysis import *
import MDAnalysis
import MDAnalysis.lib.distances
import time
import numpy.linalg
import scipy.stats
import matplotlib.pyplot as plt
import math
import MDAnalysis.lib.NeighborSearch as NS
from scipy.spatial import Voronoi, voronoi_plot_2d
import multiprocessing as mp
print ('Initiating Voroni Tesselation')
top = '../trajectory_every1ns_from7.5us.gro'
traj = '../trajectory_every100ns_from7.5us.xtc'
side = sys.argv[1] # "up" for upper leaflet "down" for lower leaflet
u = MDAnalysis.Universe(top,traj)
#Lipid Residue names
lipid1 ='DSPC'
lipid2 ='DLIPC'
lipid3 ='CHL'
# Atom selections
sel1 = 'resname %s and name P'%lipid1
sel2 = 'resname %s and name P'%lipid2
sel3 = 'resname %s and name O2'%lipid3
# Identify number of residues in each lipid and extract only he top residues (for now)
#Frames to be calculated
end_f = u.trajectory.n_frames
print (end_f)
start_f = 0
skip = 1
# Number of processors to use in multiprocessing
nprocs = 1
frames = np.arange(start_f, end_f)[::skip]
n_frames = len(frames)
######################################################################################
# Make empty arrays to hold contact counts
ens_Lpd1_Lpd1 = np.zeros(n_frames)
ens_Lpd2_Lpd2 = np.zeros(n_frames)
ens_Lpd3_Lpd3 = np.zeros(n_frames)
ens_Lpd1_Lpd2 = np.zeros(n_frames)
ens_Lpd1_Lpd3 = np.zeros(n_frames)
ens_Lpd2_Lpd3 = np.zeros(n_frames)
ens_sum_bonds = np.zeros(n_frames)
ens_avg_bonds = np.zeros(n_frames)
ens_mix_entropy = np.zeros(n_frames)
######################################################################################
def voronoi_tessel(ts):
# set the time step
print ('Frame %i in %i'%(ts, end_f))
u = MDAnalysis.Universe(top,traj)
u.trajectory[0]
# Select atoms within this particular frame
lpd1_atoms = u.select_atoms(sel1)
lpd2_atoms = u.select_atoms(sel2)
lpd3_atoms = u.select_atoms(sel3)
zmean = np.mean(np.concatenate([lpd1_atoms.positions[:,2], lpd2_atoms.positions[:,2], lpd3_atoms.positions[:,2]]))
num_lpd1 = lpd1_atoms.n_atoms
num_lpd2 = lpd2_atoms.n_atoms
# select atoms in the upper leaflet using positions in the first frame of simulation
# select cholesterol headgroups within 1.5 nm of lipid headgroups in the selected leaflet in the current frame
if side == 'up':
lpd1i=[]
zpos = lpd1_atoms.positions[:,2]
for i in range(num_lpd1):
if zpos[i] > zmean:
lpd1i.append(lpd1_atoms[i])
lpd1i = np.sum(np.array(lpd1i))
lpd2i=[]
zpos = lpd2_atoms.positions[:,2]
for i in range(num_lpd2):
if zpos[i] > zmean:
lpd2i.append(lpd2_atoms[i])
lpd2i = np.sum(np.array(lpd2i))
lipids = lpd1i + lpd2i
u.trajectory[ts] # now move to the frame currently being analyzed
ns_lipids = NS.AtomNeighborSearch(lpd3_atoms)
lpd3i = ns_lipids.search(lipids,20.0)
elif side == 'down':
lpd1i=[]
zpos = lpd1_atoms.positions[:,2]
for i in range(num_lpd1):
if zpos[i] < zmean:
lpd1i.append(lpd1_atoms[i])
lpd1i = np.sum(np.array(lpd1i))
lpd2i=[]
zpos = lpd2_atoms.positions[:,2]
for i in range(num_lpd2):
if zpos[i] < zmean:
lpd2i.append(lpd2_atoms[i])
lpd2i = np.sum(np.array(lpd2i))
lipids = lpd1i + lpd2i
u.trajectory[ts] # now move to the frame currently being analyzed
ns_lipids = NS.AtomNeighborSearch(lpd3_atoms)
lpd3i = ns_lipids.search(lipids,20.0)
lpd_atms = lpd1i + lpd2i + lpd3i
#Extracting the coordinates
Pxyz = lpd_atms.positions
Pxy = []
for l in range(0,len(Pxyz)) :
Pxy.append([Pxyz[l][0],Pxyz[l][1]])
#Extracting xy coordinates and residue names
atm_list = []
for a in range(0, len(Pxyz)):
atm_list.append([Pxyz[a][0],Pxyz[a][1],lpd_atms[a].resname])
#Introducing PBC
x_box = u.dimensions[0]
y_box = u.dimensions[1]
xplus = []
xminus = []
xyplus = []
xyminus = []
for atm in range(0 ,len(atm_list)):
xplus.append([atm_list[atm][0]+x_box,atm_list[atm][1],atm_list[atm][2]])
xminus.append([atm_list[atm][0]-x_box,atm_list[atm][1],atm_list[atm][2]])
atm_list_px = atm_list + xplus + xminus
for atm in range(0 ,len(atm_list_px)):
xyplus.append([atm_list_px[atm][0],atm_list_px[atm][1]+y_box,atm_list_px[atm][2]])
xyminus.append([atm_list_px[atm][0],atm_list_px[atm][1]-y_box,atm_list_px[atm][2]])
atm_list_p = atm_list_px + xyplus + xyminus
atm_xy = []
for i in range(0,len(atm_list_p)) :
atm_xy.append([atm_list_p[i][0],atm_list_p[i][1]])
vor = Voronoi(atm_xy)
vor_s = Voronoi(Pxy)
vertices = vor.vertices
ridge_points = vor.ridge_points
Lpd1_Lpd1_I = 0
Lpd2_Lpd2_I = 0
Lpd3_Lpd3_I = 0
Lpd1_Lpd2_I = 0
Lpd1_Lpd3_I = 0
Lpd2_Lpd3_I = 0
Lpd1_Lpd1_E = 0
Lpd2_Lpd2_E = 0
Lpd3_Lpd3_E = 0
Lpd1_Lpd2_E = 0
Lpd1_Lpd3_E = 0
Lpd2_Lpd3_E = 0
r_length = len(ridge_points)
for k in range (0,r_length) :
ridge_k = ridge_points[k]
Li = atm_list_p[int(ridge_k[0])]
Lj = atm_list_p[int(ridge_k[1])]
#Lipids INSIDE the box
if 0 < Li[0] < x_box and 0 < Li[1] < y_box and 0 < Lj[0] < x_box and 0 < Lj[1] < y_box :
if Li[2] == lipid1 and Lj[2] == lipid1:
Lpd1_Lpd1_I = Lpd1_Lpd1_I + 1
if Li[2] == lipid2 and Lj[2] == lipid2:
Lpd2_Lpd2_I = Lpd2_Lpd2_I + 1
if Li[2] == lipid3 and Lj[2] == lipid3:
Lpd3_Lpd3_I = Lpd3_Lpd3_I + 1
if Li[2] == lipid1 and Lj[2] == lipid2:
Lpd1_Lpd2_I = Lpd1_Lpd2_I + 1
if Li[2] == lipid2 and Lj[2] == lipid1:
Lpd1_Lpd2_I = Lpd1_Lpd2_I + 1
if Li[2] == lipid1 and Lj[2] == lipid3:
Lpd1_Lpd3_I = Lpd1_Lpd3_I + 1
if Li[2] == lipid3 and Lj[2] == lipid1:
Lpd1_Lpd3_I = Lpd1_Lpd3_I + 1
if Li[2] == lipid2 and Lj[2] == lipid3:
Lpd2_Lpd3_I = Lpd2_Lpd3_I + 1
if Li[2] == lipid3 and Lj[2] == lipid2:
Lpd2_Lpd3_I = Lpd2_Lpd3_I + 1
#Lipids at the EDGE of the box
if 0 <= Li[0] < x_box and 0 <= Li[1] < y_box or 0 <= Lj[0] < x_box and 0 <= Lj[1] < y_box :
if Li[2] == lipid1 and Lj[2] == lipid1:
Lpd1_Lpd1_E = Lpd1_Lpd1_E + 1
if Li[2] == lipid2 and Lj[2] == lipid2:
Lpd2_Lpd2_E = Lpd2_Lpd2_E + 1
if Li[2] == lipid3 and Lj[2] == lipid3:
Lpd3_Lpd3_E = Lpd3_Lpd3_E + 1
if Li[2] == lipid1 and Lj[2] == lipid2:
Lpd1_Lpd2_E = Lpd1_Lpd2_E + 1
if Li[2] == lipid2 and Lj[2] == lipid1:
Lpd1_Lpd2_E = Lpd1_Lpd2_E + 1
if Li[2] == lipid1 and Lj[2] == lipid3:
Lpd1_Lpd3_E = Lpd1_Lpd3_E + 1
if Li[2] == lipid3 and Lj[2] == lipid1:
Lpd1_Lpd3_E = Lpd1_Lpd3_E + 1
if Li[2] == lipid2 and Lj[2] == lipid3:
Lpd2_Lpd3_E = Lpd2_Lpd3_E + 1
if Li[2] == lipid3 and Lj[2] == lipid2:
Lpd2_Lpd3_E = Lpd2_Lpd3_E + 1
#Total = LipidsInside + (Lipids including EDGES - Lipids Inside)/2 -----> Correction for over counting the lipids in periodic images
Lpd1_Lpd1 = Lpd1_Lpd1_I + (Lpd1_Lpd1_E - Lpd1_Lpd1_I)/2
Lpd2_Lpd2 = Lpd2_Lpd2_I + (Lpd2_Lpd2_E - Lpd2_Lpd2_I)/2
Lpd3_Lpd3 = Lpd3_Lpd3_I + (Lpd3_Lpd3_E - Lpd3_Lpd3_I)/2
Lpd1_Lpd2 = Lpd1_Lpd2_I + (Lpd1_Lpd2_E - Lpd1_Lpd2_I)/2
Lpd1_Lpd3 = Lpd1_Lpd3_I + (Lpd1_Lpd3_E - Lpd1_Lpd3_I)/2
Lpd2_Lpd3 = Lpd2_Lpd3_I + (Lpd2_Lpd3_E - Lpd2_Lpd3_I)/2
sum_bonds = Lpd1_Lpd1 + Lpd2_Lpd2 + Lpd3_Lpd3 + Lpd1_Lpd2 + Lpd1_Lpd3 + Lpd2_Lpd3
#Considering only Similar Lipid (SL) and Dissimilar Lipid (DL) Bonds
SL = Lpd1_Lpd1 + Lpd2_Lpd2 + Lpd3_Lpd3
DL = Lpd1_Lpd2 + Lpd1_Lpd3 + Lpd2_Lpd3
#Calculating Fractions
X_SL = float(SL)/float(sum_bonds) #Similar Lipid
X_DL = float(DL)/float(sum_bonds) #Dissimilar Lipid
#Mixing Entropy
mix_entropy = -(X_SL * np.log(X_SL)) +( X_DL * np.log(X_DL))
#Calculating Averages
sum_bonds = Lpd1_Lpd1 + Lpd1_Lpd2 + Lpd2_Lpd2
avg_bonds = float(sum_bonds)/float(len(atm_list))
return Lpd1_Lpd1, Lpd2_Lpd2, Lpd3_Lpd3, Lpd1_Lpd2, Lpd1_Lpd3, Lpd2_Lpd3, sum_bonds, avg_bonds, mix_entropy
pool = mp.Pool(processes=nprocs)
print ('Initiating multiprocessing with %i processors'%nprocs)
results = pool.map(voronoi_tessel, frames)
ens_Lpd1_Lpd1_np = []
ens_Lpd2_Lpd2_np = []
ens_Lpd3_Lpd3_np = []
ens_Lpd1_Lpd2_np = []
ens_Lpd1_Lpd3_np = []
ens_Lpd2_Lpd3_np = []
ens_sum_bonds_np = []
ens_avg_bonds_np = []
ens_mix_entropy_np = []
for i in range(n_frames):
ens_Lpd1_Lpd1_np.append(results[i][0])
ens_Lpd2_Lpd2_np.append(results[i][1])
ens_Lpd3_Lpd3_np.append(results[i][2])
ens_Lpd1_Lpd2_np.append(results[i][3])
ens_Lpd1_Lpd3_np.append(results[i][4])
ens_Lpd2_Lpd3_np.append(results[i][5])
ens_sum_bonds_np.append(results[i][6])
ens_avg_bonds_np.append(results[i][7])
ens_mix_entropy_np.append(results[i][8])
ens_Lpd1_Lpd1_np = np.asarray(ens_Lpd1_Lpd1_np)
ens_Lpd2_Lpd2_np = np.asarray(ens_Lpd2_Lpd2_np)
ens_Lpd3_Lpd3_np = np.asarray(ens_Lpd3_Lpd3_np)
ens_Lpd1_Lpd2_np = np.asarray(ens_Lpd1_Lpd2_np)
ens_Lpd1_Lpd3_np = np.asarray(ens_Lpd1_Lpd3_np)
ens_Lpd2_Lpd3_np = np.asarray(ens_Lpd2_Lpd3_np)
ens_sum_bonds_np = np.asarray(ens_sum_bonds_np)
ens_avg_bonds_np = np.asarray(ens_avg_bonds_np)
ens_mix_entropy_np = np.asarray(ens_mix_entropy_np)
# Define output file names
if side == "up":
Lpd1_Lpd1_fn = 'upper_Lpd1_Lpd1.dat'
Lpd2_Lpd2_fn = 'upper_Lpd2_Lpd2.dat'
Lpd3_Lpd3_fn = 'upper_Lpd3_Lpd3.dat'
Lpd1_Lpd2_fn = 'upper_Lpd1_Lpd2.dat'
Lpd1_Lpd3_fn = 'upper_Lpd1_Lpd3.dat'
Lpd2_Lpd3_fn = 'upper_Lpd2_Lpd3.dat'
sum_bonds_fn = 'upper_sum_bonds.dat'
avg_bonds_fn = 'upper_avg_bonds.dat'
mix_entropy_fn = 'upper_mix_entropy.dat'
elif side == "down":
Lpd1_Lpd1_fn = 'lower_Lpd1_Lpd1.dat'
Lpd2_Lpd2_fn = 'lower_Lpd2_Lpd2.dat'
Lpd3_Lpd3_fn = 'lower_Lpd3_Lpd3.dat'
Lpd1_Lpd2_fn = 'lower_Lpd1_Lpd2.dat'
Lpd1_Lpd3_fn = 'lower_Lpd1_Lpd3.dat'
Lpd2_Lpd3_fn = 'lower_Lpd2_Lpd3.dat'
sum_bonds_fn = 'lower_sum_bonds.dat'
avg_bonds_fn = 'lower_avg_bonds.dat'
mix_entropy_fn = 'lower_mix_entropy.dat'
#Writing Outputs
| np.savetxt(Lpd1_Lpd1_fn,ens_Lpd1_Lpd1_np) | numpy.savetxt |
import numpy as np
import random
from abc import abstractmethod, ABC
from scipy import signal
class Task(ABC):
"""
Task class.
This allows to select various types of tasks while sharing the same base structure.
Author: <NAME>
"""
def __init__(self):
self.time_v = None
self.state_indices = {'p': 0, 'q': 1, 'r': 2, 'V': 3, 'alpha': 4, 'beta': 5,
'phi': 6, 'theta': 7, 'psi': 8, 'h': 9, 'x': 10, 'y': 11}
self.obs_indices = None
self.track_signals = None
self.track_indices = []
self.signals = {}
self.agent_catalog = self.get_agent_catalog()
return
def organize_indices(self, signals, obs_indices):
track_signals = np.zeros(self.time_v.shape[0])
track_indices = []
for state in signals:
if signals[state].shape[0] != self.time_v.shape[0]:
signals[state] = np.append(signals[state], signals[state][-1])
track_signals = np.vstack([track_signals, signals[state]])
track_indices.append(int(self.state_indices[state]))
track_signals = track_signals[1:]
obs_indices = track_indices + obs_indices
return track_signals, track_indices, obs_indices
def choose_task(self, evaluation, failure, FDD):
if failure[0] is not 'normal':
if evaluation:
if FDD:
task_fun = self.get_task_eval_FDD
else:
task_fun = self.get_task_eval_fail
else:
task_fun = self.get_task_tr_fail
else:
if evaluation:
task_fun = self.get_task_eval
else:
task_fun = self.get_task_tr
return task_fun, evaluation, FDD
@abstractmethod
def get_agent_catalog(self):
catalog = {'normal': None, 'elev_range': None, 'aileron_eff': None, 'rudder_stuck': None,
'horz_tail': None, 'vert_tail': None, 'icing': None, 'cg_shift': None}
return catalog
@abstractmethod
def get_task_tr(self):
self.time_v: np.ndarray = np.arange(0, 20, 0.01)
pass
@abstractmethod
def get_task_eval(self):
self.time_v: np.ndarray = np.arange(0, 80, 0.01)
pass
@abstractmethod
def get_task_tr_fail(self):
pass
@abstractmethod
def get_task_eval_fail(self):
self.time_v: np.ndarray = np.arange(0, 70, 0.01)
pass
@abstractmethod
def get_task_eval_FDD(self):
self.time_v: np.ndarray = np.arange(0, 120, 0.01)
pass
@abstractmethod
def return_signals(self):
pass
class BodyRateTask(Task):
def get_agent_catalog(self):
catalog = super(BodyRateTask, self).get_agent_catalog()
catalog['normal'] = 'body_rates_RG2SG4'
return catalog
def get_task_tr(self):
super(BodyRateTask, self).get_task_tr()
self.signals['p'] = np.hstack([np.zeros(int(2.5 * self.time_v.shape[0] / self.time_v[-1].round())),
5 * np.sin(self.time_v[:int(self.time_v.shape[0] * 3 / 4)] * 0.2 * np.pi * 2),
# 5 * np.sin(time_v[:int(time_v.shape[0] / 4)] * 3.5 * np.pi * 0.2),
# -5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# 5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# np.zeros(int(2.5 * time_v.shape[0] / time_v[-1].round())),
])
self.signals['q'] = np.hstack([5 * np.sin(self.time_v[:int(self.time_v.shape[0] * 3 / 4)] * 0.2 * np.pi * 2),
# 5 * np.sin(time_v[:int(time_v.shape[0] / 4)] * 3.5 * np.pi * 0.2),
# -5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# 5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(2.5 * self.time_v.shape[0] / self.time_v[-1].round())),
])
return self.return_signals()
def get_task_eval(self):
super(BodyRateTask, self).get_task_eval()
self.signals['p'] = np.hstack([np.zeros(int(2.5 * self.time_v.shape[0] / self.time_v[-1].round())),
5 * np.sin(self.time_v[:int(self.time_v.shape[0] * 3 / 4)] * 0.2 * np.pi * 2),
# 5 * np.sin(time_v[:int(time_v.shape[0] / 4)] * 3.5 * np.pi * 0.2),
# -5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# 5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# np.zeros(int(2.5 * time_v.shape[0] / time_v[-1].round())),
])
self.signals['q'] = np.hstack([5 * np.sin(self.time_v[:int(self.time_v.shape[0] * 3 / 4)] * 0.2 * np.pi * 2),
# 5 * np.sin(time_v[:int(time_v.shape[0] / 4)] * 3.5 * np.pi * 0.2),
# -5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
# 5 * np.ones(int(2.5 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(2.5 * self.time_v.shape[0] / self.time_v[-1].round())),
])
return self.return_signals()
def get_task_tr_fail(self):
raise NotImplementedError
def get_task_eval_fail(self):
raise NotImplementedError
def get_task_eval_FDD(self):
raise NotImplementedError
def return_signals(self):
self.signals['beta'] = np.zeros(int(self.time_v.shape[0]))
self.obs_indices = [self.state_indices['r']]
self.track_signals, self.track_indices, self.obs_indices = self.organize_indices(self.signals, self.obs_indices)
return self.track_signals, self.track_indices, self.obs_indices, self.time_v, 'body_rates'
couple = ['PZ5QGW', 'GT0PLE']
# couple = ['XQ2G4Q', 'GT0PLE']
# couple = ['PZ5QGW', '9VZ5VE']
class AttitudeTask(Task):
def get_agent_catalog(self):
catalog = super(AttitudeTask, self).get_agent_catalog()
catalog['normal'] = '3attitude_step_' + couple[1]
catalog['elev_range'] = '3attitude_step_Q4N8GV_de'
catalog['aileron_eff'] = '3attitude_step_E919SW_da'
catalog['rudder_stuck'] = '3attitude_step_HNAKCC_dr'
catalog['horz_tail'] = '3attitude_step_R0EV0U_ht'
catalog['vert_tail'] = '3attitude_step_2KGDYQ_vt'
catalog['icing'] = '3attitude_step_9MUWUB_ice'
catalog['cg_shift'] = '3attitude_step_5K6QFG_cg'
return catalog
def get_task_tr(self, init_alt=2000):
super(AttitudeTask, self).get_task_tr()
angle_theta = random.choice([20, 15, -20, -15])
time_v = self.time_v
self.signals['theta'] = np.hstack(
[angle_theta * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
angle_theta * np.ones(int(3.5 * time_v.shape[0] / time_v[-1].round())),
angle_theta * np.cos(time_v[:np.argwhere(time_v == 0.5)[0, 0]] * 0.33 * np.pi * 2),
angle_theta / 2 * np.ones(int(4. * time_v.shape[0] / time_v[-1].round())),
angle_theta / 2 * np.cos(time_v[:np.argwhere(time_v == 0.5)[0, 0]] * 0.47 * np.pi * 2),
-angle_theta * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.17 * np.pi * 2),
-angle_theta * np.ones(int(3.5 * time_v.shape[0] / time_v[-1].round())),
-angle_theta * np.cos(time_v[:np.argwhere(time_v == 0.5)[0, 0]] * 0.33 * np.pi * 2),
-angle_theta / 2 * np.ones(int(4.5 * time_v.shape[0] / time_v[-1].round())),
])
angle_phi = random.choice([45, 35, 25, -45, -35, -25])
self.signals['phi'] = np.hstack([np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.sin(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
angle_phi * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.cos(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * np.sin(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
-angle_phi * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * np.cos(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def get_task_eval(self, init_alt=2000):
super(AttitudeTask, self).get_task_eval()
time_v = self.time_v
self.signals['theta'] = np.hstack([20 * np.sin(time_v[:np.argwhere(time_v == 5.0)[0, 0]] * 0.05 * np.pi * 2),
20 * np.ones(int(8 * time_v.shape[0] / time_v[-1].round())),
20 * np.cos(time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.08 * np.pi * 2),
10 * np.ones(int(15 * time_v.shape[0] / time_v[-1].round())),
10 * np.cos(time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(25 * time_v.shape[0] / time_v[-1].round())),
-15 * np.sin(time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.13 * np.pi * 2),
-15 * np.ones(int(12 * time_v.shape[0] / time_v[-1].round())),
-15 * np.cos(time_v[:np.argwhere(time_v == 4)[0, 0]] * 0.06 * np.pi * 2),
0 * np.ones(int(5 * time_v.shape[0] / time_v[-1].round())),
])
sign = 1
self.signals['phi'] = np.hstack([0 * np.ones(int(5 * time_v.shape[0] / time_v[-1].round())),
sign * 45 * np.sin(
time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.13 * np.pi * 2),
sign * 45 * np.ones(int(9 * time_v.shape[0] / time_v[-1].round())),
sign * 45 * np.cos(time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
-sign * 30 * np.sin(
time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.13 * np.pi * 2),
-sign * 30 * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
-sign * 30 * np.cos(
time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(5 * time_v.shape[0] / time_v[-1].round())),
sign * 70 * np.sin(
time_v[:np.argwhere(time_v == 5.5)[0, 0]] * 0.05 * np.pi * 2),
sign * 70 * np.ones(int(8 * time_v.shape[0] / time_v[-1].round())),
sign * 70 * np.cos(
time_v[:np.argwhere(time_v == 5.5)[0, 0]] * 0.04 * np.pi * 2),
0 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-sign * 35 * np.sin(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
-sign * 35 * np.ones(int(9 * time_v.shape[0] / time_v[-1].round())),
-sign * 35 * np.cos(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(8 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def get_task_tr_fail(self, theta_angle=15, init_alt=2000):
super(AttitudeTask, self).get_task_tr()
time_v = self.time_v
angle_theta = random.choice([1, -1]) * theta_angle
self.signals['theta'] = np.hstack(
[angle_theta * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
angle_theta * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
angle_theta * np.cos(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
-angle_theta * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.17 * np.pi * 2),
-angle_theta * np.ones(int(5.5 * time_v.shape[0] / time_v[-1].round())),
-angle_theta * np.cos(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
np.zeros(int(2.5 * time_v.shape[0] / time_v[-1].round())),
])
angle_phi = random.choice([25, -25, -30])
self.signals['phi'] = np.hstack([np.zeros(int(1.5 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.sin(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
angle_phi * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.cos(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(3 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * np.sin(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
-angle_phi * np.ones(int(3.5 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * np.cos(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(4 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def get_task_eval_fail(self, theta_angle=15, init_alt=2000):
super(AttitudeTask, self).get_task_eval_fail()
time_v = self.time_v
self.signals['theta'] = np.hstack([np.zeros(int(10 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.sin(
time_v[:np.argwhere(time_v == 4.0)[0, 0]] * 0.06 * np.pi * 2),
theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.cos(
time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.sin(
time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.13 * np.pi * 2),
-theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.cos(
time_v[:np.argwhere(time_v == 4)[0, 0]] * 0.06 * np.pi * 2),
0 * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
])
self.signals['phi'] = np.hstack([np.zeros(int(16 * time_v.shape[0] / time_v[-1].round())),
-20 * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
-20 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-20 * np.cos(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(16 * time_v.shape[0] / time_v[-1].round())),
20 * np.sin(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
20 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
20 * np.cos(time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(20 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def get_task_eval_FDD(self, theta_angle=15, init_alt=2000):
super(AttitudeTask, self).get_task_eval_FDD()
time_v = self.time_v
self.signals['theta'] = np.hstack([np.zeros(int(10 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.sin(
time_v[:np.argwhere(time_v == 4.0)[0, 0]] * 0.06 * np.pi * 2),
theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.cos(
time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.sin(
time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.13 * np.pi * 2),
-theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.cos(
time_v[:np.argwhere(time_v == 4)[0, 0]] * 0.06 * np.pi * 2),
0 * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(4 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.sin(
time_v[:np.argwhere(time_v == 4.0)[0, 0]] * 0.06 * np.pi * 2),
theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
theta_angle * np.cos(
time_v[:np.argwhere(time_v == 2.0)[0, 0]] * 0.12 * np.pi * 2),
0 * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.sin(
time_v[:np.argwhere(time_v == 2)[0, 0]] * 0.13 * np.pi * 2),
-theta_angle * np.ones(int(14 * time_v.shape[0] / time_v[-1].round())),
-theta_angle * np.cos(
time_v[:np.argwhere(time_v == 4)[0, 0]] * 0.06 * np.pi * 2),
0 * np.ones(int(10 * time_v.shape[0] / time_v[-1].round())),
])
roll_angle = 20
self.signals['phi'] = np.hstack([np.zeros(int(16 * time_v.shape[0] / time_v[-1].round())),
-roll_angle * np.sin(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
-roll_angle * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-roll_angle * np.cos(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(16 * time_v.shape[0] / time_v[-1].round())),
roll_angle * np.sin(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
roll_angle * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
roll_angle * np.cos(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(10 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(10 * time_v.shape[0] / time_v[-1].round())),
-roll_angle * np.sin(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
-roll_angle * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
-roll_angle * np.cos(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(16 * time_v.shape[0] / time_v[-1].round())),
roll_angle * np.sin(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
roll_angle * np.ones(int(6 * time_v.shape[0] / time_v[-1].round())),
roll_angle * np.cos(
time_v[:np.argwhere(time_v == 1.5)[0, 0]] * 0.16 * np.pi * 2),
0 * np.ones(int(16 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def return_signals(self):
self.signals['beta'] = np.zeros(int(self.time_v.shape[0]))
self.obs_indices = [self.state_indices['p'], self.state_indices['q'], self.state_indices['r']]
self.track_signals, self.track_indices, self.obs_indices = self.organize_indices(self.signals, self.obs_indices)
return self.track_signals, self.track_indices, self.obs_indices, self.time_v, '3attitude_step'
class DisturbanceRejectionAtt(AttitudeTask):
def get_task_eval(self, init_alt=2000):
self.time_v = np.arange(0, 20, 0.01)
self.signals['theta'] = np.zeros((self.time_v.shape[0],))
self.signals['phi'] = np.zeros((self.time_v.shape[0],))
return self.return_signals()
class AltitudeTask(Task):
def get_agent_catalog(self):
catalog = super(AltitudeTask, self).get_agent_catalog()
catalog['normal'] = 'altitude_2attitude_P7V00G'
catalog['elev_range'] = 'altitude_2attitude_P7V00G'
catalog['aileron_eff'] = 'altitude_2attitude_P7V00G'
catalog['rudder_stuck'] = 'altitude_2attitude_P7V00G'
catalog['horz_tail'] = 'altitude_2attitude_P7V00G'
catalog['vert_tail'] = 'altitude_2attitude_P7V00G'
catalog['icing'] = 'altitude_2attitude_P7V00G'
catalog['cg_shift'] = 'altitude_2attitude_P7V00G'
return catalog
def get_task_tr(self, init_alt=2000):
super(AltitudeTask, self).get_task_tr()
time_v = self.time_v
self.signals['h'] = np.hstack([np.linspace(init_alt, init_alt+55, int(10 * time_v.shape[0] / time_v[-1].round())),
init_alt+55 * np.ones(int(10 * time_v.shape[0] / time_v[-1].round())),
# np.linspace(2044, 2025, int(3.75 * time_v.shape[0] / time_v[-1].round())),
# 2025 * np.ones(int(6.75 * time_v.shape[0] / time_v[-1].round())),
])
angle_phi = random.choice([45, 35, -45, -35])
self.signals['phi'] = np.hstack([np.zeros(int(1 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.sin(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
angle_phi * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
angle_phi * np.cos(time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(3 * time_v.shape[0] / time_v[-1].round())),
np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * 0.8 * np.sin(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
-angle_phi * 0.8 * np.ones(int(4 * time_v.shape[0] / time_v[-1].round())),
-angle_phi * 0.8 * np.cos(
time_v[:np.argwhere(time_v == 1)[0, 0]] * 0.25 * np.pi * 2),
np.zeros(int(2 * time_v.shape[0] / time_v[-1].round())),
])
return self.return_signals()
def get_task_eval(self, init_alt=2000):
self.time_v = time_v = | np.arange(0, 120, 0.01) | numpy.arange |
import numpy as np
import pandas as pd
from numpy import array, atleast_2d, linspace, zeros
from scipy.optimize import root
from dolo.algos.dtcscc.steady_state import find_deterministic_equilibrium
from dolo.numeric.optimize.ncpsolve import ncpsolve
from dolo.numeric.optimize.newton import newton
from dolo.numeric.serial_operations import serial_multiplication as smult
def _shocks_to_epsilons(model, shocks, T):
"""
Helper function to support input argument `shocks` being one of many
different data types. Will always return a `T, n_e` matrix.
"""
n_e = len(model.calibration['shocks'])
# if we have a DataFrame, convert it to a dict and rely on the method below
if isinstance(shocks, pd.DataFrame):
shocks = {k: shocks[k].tolist() for k in shocks.columns}
# handle case where shocks might be a dict. Be careful to handle case where
# value arrays are not the same length
if isinstance(shocks, dict):
epsilons = np.zeros((T+1, n_e))
for (i, k) in enumerate(model.symbols["shocks"]):
if k in shocks:
this_shock = shocks[k]
epsilons[:len(this_shock)-1, i] = this_shock[1:]
epsilons[(len(this_shock)-1):, i] = this_shock[-1]
else:
# otherwise set to value in calibration
epsilons[:, i] = model.calibration["shocks"][i]
return epsilons
# read from calibration if not given
if shocks is None:
shocks = model.calibration["shocks"]
# now we just assume that shocks is array-like and try using the output of
# np.asarray(shocks)
shocks = np.asarray(shocks)
shocks = shocks.reshape((-1, n_e))
# until last period, exogenous shock takes its last value
epsilons = np.zeros((T+1, n_e))
epsilons[:(shocks.shape[0]-1), :] = shocks[1:, :]
epsilons[(shocks.shape[0]-1):, :] = shocks[-1:, :]
return epsilons
def deterministic_solve(model, shocks=None, start_states=None, T=100,
ignore_constraints=False, maxit=100,
initial_guess=None, verbose=False, tol=1e-6):
"""
Computes a perfect foresight simulation using a stacked-time algorithm.
The initial state is specified either by providing a series of exogenous
shocks and assuming the model is initially in equilibrium with the first
value of the shock, or by specifying an initial value for the states.
Parameters
----------
model : NumericModel
"fg" or "fga" model to be solved
shocks : array-like, dict, or pandas.DataFrame
A specification of the shocks to the model. Can be any of the
following (note by "declaration order" below we mean the order
of `model.symbols["shocks"]`):
- A 1d numpy array-like specifying a time series for a single
shock, or all shocks stacked into a single array.
- A 2d numpy array where each column specifies the time series
for one of the shocks in declaration order. This must be an
`N` by number of shocks 2d array.
- A dict where keys are strings found in
`model.symbols["shocks"]` and values are a time series of
values for that shock. For model shocks that do not appear in
this dict, the shock is set to the calibrated value. Note
that this interface is the most flexible as it allows the user
to pass values for only a subset of the model shocks and it
allows the passed time series to be of different lengths.
- A DataFrame where columns map shock names into time series.
The same assumptions and behavior that are used in the dict
case apply here
If nothing is given here, `shocks` is set equal to the
calibrated values found in `model.calibration["shocks"]` for
all periods.
If the length of any time-series in shocks is less than `T`
(see below) it is assumed that that particular shock will
remain at the final given value for the duration of the
simulaiton.
start_states : ndarray or dict
a vector with the value of initial states, or a calibration
dictionary with the initial values of states and controls
T : int
horizon for the perfect foresight simulation
maxit : int
maximum number of iteration for the nonlinear solver
verbose : boolean
if True, the solver displays iterations
tol : float
stopping criterium for the nonlinear solver
ignore_constraints : bool
if True, complementarity constraints are ignored.
Returns
-------
pandas dataframe
a dataframe with T+1 observations of the model variables along the
simulation (states, controls, auxiliaries). The first observation is
the steady-state corresponding to the first value of the shocks. The
simulation should return to a steady-state corresponding to the last
value of the exogenous shocks.
"""
# TODO:
# if model.model_spec == 'fga':
# from dolo.compiler.converter import GModel_fg_from_fga
# model = GModel_fg_from_fga(model)
# definitions
n_s = len(model.calibration['states'])
n_x = len(model.calibration['controls'])
epsilons = _shocks_to_epsilons(model, shocks, T)
# final initial and final steady-states consistent with exogenous shocks
if start_states is None:
start_states = model.calibration
if isinstance(start_states, dict):
# at least that part is clear
start_equilibrium = start_states
start_s = start_equilibrium['states']
start_x = start_equilibrium['controls']
final_s = start_equilibrium['states']
final_x = start_equilibrium['controls']
elif isinstance(start_states, np.ndarray):
start_s = start_states
start_x = model.calibration['controls']
final_s = model.calibration['states']
final_x = model.calibration['controls']
# if start_constraints:
# # we ignore start_constraints
# start_dict.update(start_constraints)
# final_equilibrium = start_constraints.copy()
# else:
# final_eqm = find_deterministic_equilibrium(model,
# constraints=final_dict)
# final_s = final_eqm['states']
# final_x = final_eqm['controls']
#
# start_s = start_states
# start_x = final_x
# TODO: for start_x, it should be possible to use first order guess
final = np.concatenate([final_s, final_x])
start = np.concatenate([start_s, start_x])
if verbose is True:
print("Initial states : {}".format(start_s))
print("Final controls : {}".format(final_x))
p = model.calibration['parameters']
if initial_guess is None:
initial_guess = np.row_stack([start*(1-l) + final*l
for l in linspace(0.0, 1.0, T+1)])
else:
if isinstance(initial_guess, pd.DataFrame):
initial_guess = np.array(initial_guess).T.copy()
initial_guess = initial_guess[:, :n_s+n_x]
initial_guess[0, :n_s] = start_s
initial_guess[-1, n_s:] = final_x
sh = initial_guess.shape
if model.x_bounds and not ignore_constraints:
initial_states = initial_guess[:, :n_s]
[lb, ub] = [u(initial_states, p) for u in model.x_bounds]
lower_bound = initial_guess*0 - np.inf
lower_bound[:, n_s:] = lb
upper_bound = initial_guess*0 + np.inf
upper_bound[:, n_s:] = ub
test1 = max(lb.max(axis=0) - lb.min(axis=0))
test2 = max(ub.max(axis=0) - ub.min(axis=0))
if test1 > 0.00000001 or test2 > 0.00000001:
msg = "Not implemented: perfect foresight solution requires that "
msg += "controls have constant bounds."
raise Exception(msg)
else:
ignore_constraints = True
lower_bound = None
upper_bound = None
nn = sh[0]*sh[1]
def fobj(vec):
o = det_residual(model, vec.reshape(sh), start_s, final_x, epsilons)[0]
return o.ravel()
if not ignore_constraints:
def ff(vec):
return det_residual(model, vec.reshape(sh), start_s, final_x,
epsilons, jactype='sparse')
x0 = initial_guess.ravel()
sol, nit = ncpsolve(ff, lower_bound.ravel(), upper_bound.ravel(),
initial_guess.ravel(), verbose=verbose,
maxit=maxit, tol=tol, jactype='sparse')
sol = sol.reshape(sh)
else:
def ff(vec):
return det_residual(model, vec.reshape(sh), start_s, final_x,
epsilons, diff=False).ravel()
x0 = initial_guess.ravel()
sol = root(ff, x0, jac=False)
res = ff(sol.x)
sol = sol.x.reshape(sh)
if 'auxiliary' in model.functions:
colnames = (model.symbols['states'] + model.symbols['controls'] +
model.symbols['auxiliaries'])
# compute auxiliaries
y = model.functions['auxiliary'](sol[:, :n_s], sol[:, n_s:], p)
sol = np.column_stack([sol, y])
else:
colnames = model.symbols['states'] + model.symbols['controls']
sol = np.column_stack([sol, epsilons])
colnames = colnames + model.symbols['shocks']
ts = pd.DataFrame(sol, columns=colnames)
return ts
def det_residual(model, guess, start, final, shocks, diff=True,
jactype='sparse'):
'''
Computes the residuals, the derivatives of the stacked-time system.
:param model: an fga model
:param guess: the guess for the simulated values. An `(n_s.n_x) x N` array,
where n_s is the number of states,
n_x the number of controls, and `N` the length of the simulation.
:param start: initial boundary condition (initial value of the states)
:param final: final boundary condition (last value of the controls)
:param shocks: values for the exogenous shocks
:param diff: if True, the derivatives are computes
:return: a list with two elements:
- an `(n_s.n_x) x N` array with the residuals of the system
- a `(n_s.n_x) x N x (n_s.n_x) x N` array representing the jacobian of
the system
'''
# TODO: compute a sparse derivative and ensure the solvers can deal with it
n_s = len(model.symbols['states'])
n_x = len(model.symbols['controls'])
n_e = len(model.symbols['shocks'])
N = guess.shape[0]
p = model.calibration['parameters']
f = model.functions['arbitrage']
g = model.functions['transition']
vec = guess[:-1, :]
vec_f = guess[1:, :]
s = vec[:, :n_s]
x = vec[:, n_s:]
S = vec_f[:, :n_s]
X = vec_f[:, n_s:]
e = shocks[:-1, :]
E = shocks[1:, :]
if diff:
SS, SS_s, SS_x, SS_e = g(s, x, e, p, diff=True)
R, R_s, R_x, R_e, R_S, R_X = f(s, x, E, S, X, p, diff=True)
else:
SS = g(s, x, e, p)
R = f(s, x, E, S, X, p)
res_s = SS - S
res_x = R
res = | np.zeros((N, n_s+n_x)) | numpy.zeros |
from __future__ import print_function
from datetime import datetime, timedelta
import numpy as np
import pandas as pd
from pandas import (Series, Index, Int64Index, Timestamp, Period,
DatetimeIndex, PeriodIndex, TimedeltaIndex,
Timedelta, timedelta_range, date_range, Float64Index,
_np_version_under1p10)
import pandas.tslib as tslib
import pandas.tseries.period as period
import pandas.util.testing as tm
from pandas.tests.test_base import Ops
class TestDatetimeIndexOps(Ops):
tz = [None, 'UTC', 'Asia/Tokyo', 'US/Eastern', 'dateutil/Asia/Singapore',
'dateutil/US/Pacific']
def setUp(self):
super(TestDatetimeIndexOps, self).setUp()
mask = lambda x: (isinstance(x, DatetimeIndex) or
isinstance(x, PeriodIndex))
self.is_valid_objs = [o for o in self.objs if mask(o)]
self.not_valid_objs = [o for o in self.objs if not mask(o)]
def test_ops_properties(self):
self.check_ops_properties(
['year', 'month', 'day', 'hour', 'minute', 'second', 'weekofyear',
'week', 'dayofweek', 'dayofyear', 'quarter'])
self.check_ops_properties(['date', 'time', 'microsecond', 'nanosecond',
'is_month_start', 'is_month_end',
'is_quarter_start',
'is_quarter_end', 'is_year_start',
'is_year_end', 'weekday_name'],
lambda x: isinstance(x, DatetimeIndex))
def test_ops_properties_basic(self):
# sanity check that the behavior didn't change
# GH7206
for op in ['year', 'day', 'second', 'weekday']:
self.assertRaises(TypeError, lambda x: getattr(self.dt_series, op))
# attribute access should still work!
s = Series(dict(year=2000, month=1, day=10))
self.assertEqual(s.year, 2000)
self.assertEqual(s.month, 1)
self.assertEqual(s.day, 10)
self.assertRaises(AttributeError, lambda: s.weekday)
def test_asobject_tolist(self):
idx = pd.date_range(start='2013-01-01', periods=4, freq='M',
name='idx')
expected_list = [Timestamp('2013-01-31'),
Timestamp('2013-02-28'),
Timestamp('2013-03-31'),
Timestamp('2013-04-30')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
idx = pd.date_range(start='2013-01-01', periods=4, freq='M',
name='idx', tz='Asia/Tokyo')
expected_list = [Timestamp('2013-01-31', tz='Asia/Tokyo'),
Timestamp('2013-02-28', tz='Asia/Tokyo'),
Timestamp('2013-03-31', tz='Asia/Tokyo'),
Timestamp('2013-04-30', tz='Asia/Tokyo')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
idx = DatetimeIndex([datetime(2013, 1, 1), datetime(2013, 1, 2),
pd.NaT, datetime(2013, 1, 4)], name='idx')
expected_list = [Timestamp('2013-01-01'),
Timestamp('2013-01-02'), pd.NaT,
Timestamp('2013-01-04')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
def test_minmax(self):
for tz in self.tz:
# monotonic
idx1 = pd.DatetimeIndex(['2011-01-01', '2011-01-02',
'2011-01-03'], tz=tz)
self.assertTrue(idx1.is_monotonic)
# non-monotonic
idx2 = pd.DatetimeIndex(['2011-01-01', pd.NaT, '2011-01-03',
'2011-01-02', pd.NaT], tz=tz)
self.assertFalse(idx2.is_monotonic)
for idx in [idx1, idx2]:
self.assertEqual(idx.min(), Timestamp('2011-01-01', tz=tz))
self.assertEqual(idx.max(), Timestamp('2011-01-03', tz=tz))
self.assertEqual(idx.argmin(), 0)
self.assertEqual(idx.argmax(), 2)
for op in ['min', 'max']:
# Return NaT
obj = DatetimeIndex([])
self.assertTrue(pd.isnull(getattr(obj, op)()))
obj = DatetimeIndex([pd.NaT])
self.assertTrue(pd.isnull(getattr(obj, op)()))
obj = DatetimeIndex([pd.NaT, pd.NaT, pd.NaT])
self.assertTrue(pd.isnull(getattr(obj, op)()))
def test_numpy_minmax(self):
dr = pd.date_range(start='2016-01-15', end='2016-01-20')
self.assertEqual(np.min(dr),
Timestamp('2016-01-15 00:00:00', freq='D'))
self.assertEqual(np.max(dr),
Timestamp('2016-01-20 00:00:00', freq='D'))
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.min, dr, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.max, dr, out=0)
self.assertEqual(np.argmin(dr), 0)
self.assertEqual(np.argmax(dr), 5)
if not _np_version_under1p10:
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.argmin, dr, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.argmax, dr, out=0)
def test_round(self):
for tz in self.tz:
rng = pd.date_range(start='2016-01-01', periods=5,
freq='30Min', tz=tz)
elt = rng[1]
expected_rng = DatetimeIndex([
Timestamp('2016-01-01 00:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 00:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 01:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 02:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 02:00:00', tz=tz, freq='30T'),
])
expected_elt = expected_rng[1]
tm.assert_index_equal(rng.round(freq='H'), expected_rng)
self.assertEqual(elt.round(freq='H'), expected_elt)
msg = pd.tseries.frequencies._INVALID_FREQ_ERROR
with tm.assertRaisesRegexp(ValueError, msg):
rng.round(freq='foo')
with tm.assertRaisesRegexp(ValueError, msg):
elt.round(freq='foo')
msg = "<MonthEnd> is a non-fixed frequency"
tm.assertRaisesRegexp(ValueError, msg, rng.round, freq='M')
tm.assertRaisesRegexp(ValueError, msg, elt.round, freq='M')
def test_repeat_range(self):
rng = date_range('1/1/2000', '1/1/2001')
result = rng.repeat(5)
self.assertIsNone(result.freq)
self.assertEqual(len(result), 5 * len(rng))
for tz in self.tz:
index = pd.date_range('2001-01-01', periods=2, freq='D', tz=tz)
exp = pd.DatetimeIndex(['2001-01-01', '2001-01-01',
'2001-01-02', '2001-01-02'], tz=tz)
for res in [index.repeat(2), np.repeat(index, 2)]:
tm.assert_index_equal(res, exp)
self.assertIsNone(res.freq)
index = pd.date_range('2001-01-01', periods=2, freq='2D', tz=tz)
exp = pd.DatetimeIndex(['2001-01-01', '2001-01-01',
'2001-01-03', '2001-01-03'], tz=tz)
for res in [index.repeat(2), np.repeat(index, 2)]:
tm.assert_index_equal(res, exp)
self.assertIsNone(res.freq)
index = pd.DatetimeIndex(['2001-01-01', 'NaT', '2003-01-01'],
tz=tz)
exp = pd.DatetimeIndex(['2001-01-01', '2001-01-01', '2001-01-01',
'NaT', 'NaT', 'NaT',
'2003-01-01', '2003-01-01', '2003-01-01'],
tz=tz)
for res in [index.repeat(3), np.repeat(index, 3)]:
tm.assert_index_equal(res, exp)
self.assertIsNone(res.freq)
def test_repeat(self):
reps = 2
msg = "the 'axis' parameter is not supported"
for tz in self.tz:
rng = pd.date_range(start='2016-01-01', periods=2,
freq='30Min', tz=tz)
expected_rng = DatetimeIndex([
Timestamp('2016-01-01 00:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 00:00:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 00:30:00', tz=tz, freq='30T'),
Timestamp('2016-01-01 00:30:00', tz=tz, freq='30T'),
])
res = rng.repeat(reps)
tm.assert_index_equal(res, expected_rng)
self.assertIsNone(res.freq)
tm.assert_index_equal(np.repeat(rng, reps), expected_rng)
tm.assertRaisesRegexp(ValueError, msg, np.repeat,
rng, reps, axis=1)
def test_representation(self):
idx = []
idx.append(DatetimeIndex([], freq='D'))
idx.append(DatetimeIndex(['2011-01-01'], freq='D'))
idx.append(DatetimeIndex(['2011-01-01', '2011-01-02'], freq='D'))
idx.append(DatetimeIndex(
['2011-01-01', '2011-01-02', '2011-01-03'], freq='D'))
idx.append(DatetimeIndex(
['2011-01-01 09:00', '2011-01-01 10:00', '2011-01-01 11:00'
], freq='H', tz='Asia/Tokyo'))
idx.append(DatetimeIndex(
['2011-01-01 09:00', '2011-01-01 10:00', pd.NaT], tz='US/Eastern'))
idx.append(DatetimeIndex(
['2011-01-01 09:00', '2011-01-01 10:00', pd.NaT], tz='UTC'))
exp = []
exp.append("""DatetimeIndex([], dtype='datetime64[ns]', freq='D')""")
exp.append("DatetimeIndex(['2011-01-01'], dtype='datetime64[ns]', "
"freq='D')")
exp.append("DatetimeIndex(['2011-01-01', '2011-01-02'], "
"dtype='datetime64[ns]', freq='D')")
exp.append("DatetimeIndex(['2011-01-01', '2011-01-02', '2011-01-03'], "
"dtype='datetime64[ns]', freq='D')")
exp.append("DatetimeIndex(['2011-01-01 09:00:00+09:00', "
"'2011-01-01 10:00:00+09:00', '2011-01-01 11:00:00+09:00']"
", dtype='datetime64[ns, Asia/Tokyo]', freq='H')")
exp.append("DatetimeIndex(['2011-01-01 09:00:00-05:00', "
"'2011-01-01 10:00:00-05:00', 'NaT'], "
"dtype='datetime64[ns, US/Eastern]', freq=None)")
exp.append("DatetimeIndex(['2011-01-01 09:00:00+00:00', "
"'2011-01-01 10:00:00+00:00', 'NaT'], "
"dtype='datetime64[ns, UTC]', freq=None)""")
with pd.option_context('display.width', 300):
for indx, expected in zip(idx, exp):
for func in ['__repr__', '__unicode__', '__str__']:
result = getattr(indx, func)()
self.assertEqual(result, expected)
def test_representation_to_series(self):
idx1 = DatetimeIndex([], freq='D')
idx2 = DatetimeIndex(['2011-01-01'], freq='D')
idx3 = DatetimeIndex(['2011-01-01', '2011-01-02'], freq='D')
idx4 = DatetimeIndex(
['2011-01-01', '2011-01-02', '2011-01-03'], freq='D')
idx5 = DatetimeIndex(['2011-01-01 09:00', '2011-01-01 10:00',
'2011-01-01 11:00'], freq='H', tz='Asia/Tokyo')
idx6 = DatetimeIndex(['2011-01-01 09:00', '2011-01-01 10:00', pd.NaT],
tz='US/Eastern')
idx7 = DatetimeIndex(['2011-01-01 09:00', '2011-01-02 10:15'])
exp1 = """Series([], dtype: datetime64[ns])"""
exp2 = """0 2011-01-01
dtype: datetime64[ns]"""
exp3 = """0 2011-01-01
1 2011-01-02
dtype: datetime64[ns]"""
exp4 = """0 2011-01-01
1 2011-01-02
2 2011-01-03
dtype: datetime64[ns]"""
exp5 = """0 2011-01-01 09:00:00+09:00
1 2011-01-01 10:00:00+09:00
2 2011-01-01 11:00:00+09:00
dtype: datetime64[ns, Asia/Tokyo]"""
exp6 = """0 2011-01-01 09:00:00-05:00
1 2011-01-01 10:00:00-05:00
2 NaT
dtype: datetime64[ns, US/Eastern]"""
exp7 = """0 2011-01-01 09:00:00
1 2011-01-02 10:15:00
dtype: datetime64[ns]"""
with pd.option_context('display.width', 300):
for idx, expected in zip([idx1, idx2, idx3, idx4,
idx5, idx6, idx7],
[exp1, exp2, exp3, exp4,
exp5, exp6, exp7]):
result = repr(Series(idx))
self.assertEqual(result, expected)
def test_summary(self):
# GH9116
idx1 = DatetimeIndex([], freq='D')
idx2 = DatetimeIndex(['2011-01-01'], freq='D')
idx3 = DatetimeIndex(['2011-01-01', '2011-01-02'], freq='D')
idx4 = DatetimeIndex(
['2011-01-01', '2011-01-02', '2011-01-03'], freq='D')
idx5 = DatetimeIndex(['2011-01-01 09:00', '2011-01-01 10:00',
'2011-01-01 11:00'],
freq='H', tz='Asia/Tokyo')
idx6 = DatetimeIndex(['2011-01-01 09:00', '2011-01-01 10:00', pd.NaT],
tz='US/Eastern')
exp1 = """DatetimeIndex: 0 entries
Freq: D"""
exp2 = """DatetimeIndex: 1 entries, 2011-01-01 to 2011-01-01
Freq: D"""
exp3 = """DatetimeIndex: 2 entries, 2011-01-01 to 2011-01-02
Freq: D"""
exp4 = """DatetimeIndex: 3 entries, 2011-01-01 to 2011-01-03
Freq: D"""
exp5 = ("DatetimeIndex: 3 entries, 2011-01-01 09:00:00+09:00 "
"to 2011-01-01 11:00:00+09:00\n"
"Freq: H")
exp6 = """DatetimeIndex: 3 entries, 2011-01-01 09:00:00-05:00 to NaT"""
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5, idx6],
[exp1, exp2, exp3, exp4, exp5, exp6]):
result = idx.summary()
self.assertEqual(result, expected)
def test_resolution(self):
for freq, expected in zip(['A', 'Q', 'M', 'D', 'H', 'T',
'S', 'L', 'U'],
['day', 'day', 'day', 'day', 'hour',
'minute', 'second', 'millisecond',
'microsecond']):
for tz in self.tz:
idx = pd.date_range(start='2013-04-01', periods=30, freq=freq,
tz=tz)
self.assertEqual(idx.resolution, expected)
def test_union(self):
for tz in self.tz:
# union
rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
expected1 = pd.date_range('1/1/2000', freq='D', periods=10, tz=tz)
rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
expected2 = pd.date_range('1/1/2000', freq='D', periods=8, tz=tz)
rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other3 = pd.DatetimeIndex([], tz=tz)
expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
for rng, other, expected in [(rng1, other1, expected1),
(rng2, other2, expected2),
(rng3, other3, expected3)]:
result_union = rng.union(other)
tm.assert_index_equal(result_union, expected)
def test_add_iadd(self):
for tz in self.tz:
# offset
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), Timedelta(hours=2)]
for delta in offsets:
rng = pd.date_range('2000-01-01', '2000-02-01', tz=tz)
result = rng + delta
expected = pd.date_range('2000-01-01 02:00',
'2000-02-01 02:00', tz=tz)
tm.assert_index_equal(result, expected)
rng += delta
tm.assert_index_equal(rng, expected)
# int
rng = pd.date_range('2000-01-01 09:00', freq='H', periods=10,
tz=tz)
result = rng + 1
expected = pd.date_range('2000-01-01 10:00', freq='H', periods=10,
tz=tz)
tm.assert_index_equal(result, expected)
rng += 1
tm.assert_index_equal(rng, expected)
idx = DatetimeIndex(['2011-01-01', '2011-01-02'])
msg = "cannot add a datelike to a DatetimeIndex"
with tm.assertRaisesRegexp(TypeError, msg):
idx + Timestamp('2011-01-01')
with tm.assertRaisesRegexp(TypeError, msg):
Timestamp('2011-01-01') + idx
def test_add_dti_dti(self):
# previously performed setop (deprecated in 0.16.0), now raises
# TypeError (GH14164)
dti = date_range('20130101', periods=3)
dti_tz = date_range('20130101', periods=3).tz_localize('US/Eastern')
with tm.assertRaises(TypeError):
dti + dti
with tm.assertRaises(TypeError):
dti_tz + dti_tz
with tm.assertRaises(TypeError):
dti_tz + dti
with tm.assertRaises(TypeError):
dti + dti_tz
def test_difference(self):
for tz in self.tz:
# diff
rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
expected1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
expected2 = pd.date_range('1/1/2000', freq='D', periods=3, tz=tz)
rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
other3 = pd.DatetimeIndex([], tz=tz)
expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
for rng, other, expected in [(rng1, other1, expected1),
(rng2, other2, expected2),
(rng3, other3, expected3)]:
result_diff = rng.difference(other)
tm.assert_index_equal(result_diff, expected)
def test_sub_isub(self):
for tz in self.tz:
# offset
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), Timedelta(hours=2)]
for delta in offsets:
rng = pd.date_range('2000-01-01', '2000-02-01', tz=tz)
expected = pd.date_range('1999-12-31 22:00',
'2000-01-31 22:00', tz=tz)
result = rng - delta
tm.assert_index_equal(result, expected)
rng -= delta
tm.assert_index_equal(rng, expected)
# int
rng = pd.date_range('2000-01-01 09:00', freq='H', periods=10,
tz=tz)
result = rng - 1
expected = pd.date_range('2000-01-01 08:00', freq='H', periods=10,
tz=tz)
tm.assert_index_equal(result, expected)
rng -= 1
tm.assert_index_equal(rng, expected)
def test_sub_dti_dti(self):
# previously performed setop (deprecated in 0.16.0), now changed to
# return subtraction -> TimeDeltaIndex (GH ...)
dti = date_range('20130101', periods=3)
dti_tz = date_range('20130101', periods=3).tz_localize('US/Eastern')
dti_tz2 = date_range('20130101', periods=3).tz_localize('UTC')
expected = TimedeltaIndex([0, 0, 0])
result = dti - dti
tm.assert_index_equal(result, expected)
result = dti_tz - dti_tz
tm.assert_index_equal(result, expected)
with tm.assertRaises(TypeError):
dti_tz - dti
with tm.assertRaises(TypeError):
dti - dti_tz
with tm.assertRaises(TypeError):
dti_tz - dti_tz2
# isub
dti -= dti
tm.assert_index_equal(dti, expected)
# different length raises ValueError
dti1 = date_range('20130101', periods=3)
dti2 = date_range('20130101', periods=4)
with tm.assertRaises(ValueError):
dti1 - dti2
# NaN propagation
dti1 = DatetimeIndex(['2012-01-01', np.nan, '2012-01-03'])
dti2 = DatetimeIndex(['2012-01-02', '2012-01-03', np.nan])
expected = TimedeltaIndex(['1 days', np.nan, np.nan])
result = dti2 - dti1
tm.assert_index_equal(result, expected)
def test_sub_period(self):
# GH 13078
# not supported, check TypeError
p = pd.Period('2011-01-01', freq='D')
for freq in [None, 'D']:
idx = pd.DatetimeIndex(['2011-01-01', '2011-01-02'], freq=freq)
with tm.assertRaises(TypeError):
idx - p
with tm.assertRaises(TypeError):
p - idx
def test_comp_nat(self):
left = pd.DatetimeIndex([pd.Timestamp('2011-01-01'), pd.NaT,
pd.Timestamp('2011-01-03')])
right = pd.DatetimeIndex([pd.NaT, pd.NaT, pd.Timestamp('2011-01-03')])
for l, r in [(left, right), (left.asobject, right.asobject)]:
result = l == r
expected = np.array([False, False, True])
tm.assert_numpy_array_equal(result, expected)
result = l != r
expected = np.array([True, True, False])
tm.assert_numpy_array_equal(result, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l == pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT == r, expected)
expected = np.array([True, True, True])
tm.assert_numpy_array_equal(l != pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT != l, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l < pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT > l, expected)
def test_value_counts_unique(self):
# GH 7735
for tz in self.tz:
idx = pd.date_range('2011-01-01 09:00', freq='H', periods=10)
# create repeated values, 'n'th element is repeated by n+1 times
idx = DatetimeIndex(np.repeat(idx.values, range(1, len(idx) + 1)),
tz=tz)
exp_idx = pd.date_range('2011-01-01 18:00', freq='-1H', periods=10,
tz=tz)
expected = Series(range(10, 0, -1), index=exp_idx, dtype='int64')
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
expected = pd.date_range('2011-01-01 09:00', freq='H', periods=10,
tz=tz)
tm.assert_index_equal(idx.unique(), expected)
idx = DatetimeIndex(['2013-01-01 09:00', '2013-01-01 09:00',
'2013-01-01 09:00', '2013-01-01 08:00',
'2013-01-01 08:00', pd.NaT], tz=tz)
exp_idx = DatetimeIndex(['2013-01-01 09:00', '2013-01-01 08:00'],
tz=tz)
expected = Series([3, 2], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
exp_idx = DatetimeIndex(['2013-01-01 09:00', '2013-01-01 08:00',
pd.NaT], tz=tz)
expected = Series([3, 2, 1], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(dropna=False),
expected)
tm.assert_index_equal(idx.unique(), exp_idx)
def test_nonunique_contains(self):
# GH 9512
for idx in map(DatetimeIndex,
([0, 1, 0], [0, 0, -1], [0, -1, -1],
['2015', '2015', '2016'], ['2015', '2015', '2014'])):
tm.assertIn(idx[0], idx)
def test_order(self):
# with freq
idx1 = DatetimeIndex(['2011-01-01', '2011-01-02',
'2011-01-03'], freq='D', name='idx')
idx2 = DatetimeIndex(['2011-01-01 09:00', '2011-01-01 10:00',
'2011-01-01 11:00'], freq='H',
tz='Asia/Tokyo', name='tzidx')
for idx in [idx1, idx2]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, idx)
self.assertEqual(ordered.freq, idx.freq)
ordered = idx.sort_values(ascending=False)
expected = idx[::-1]
self.assert_index_equal(ordered, expected)
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq.n, -1)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, idx)
self.assert_numpy_array_equal(indexer,
np.array([0, 1, 2]),
check_dtype=False)
self.assertEqual(ordered.freq, idx.freq)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
expected = idx[::-1]
self.assert_index_equal(ordered, expected)
self.assert_numpy_array_equal(indexer,
np.array([2, 1, 0]),
check_dtype=False)
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq.n, -1)
# without freq
for tz in self.tz:
idx1 = DatetimeIndex(['2011-01-01', '2011-01-03', '2011-01-05',
'2011-01-02', '2011-01-01'],
tz=tz, name='idx1')
exp1 = DatetimeIndex(['2011-01-01', '2011-01-01', '2011-01-02',
'2011-01-03', '2011-01-05'],
tz=tz, name='idx1')
idx2 = DatetimeIndex(['2011-01-01', '2011-01-03', '2011-01-05',
'2011-01-02', '2011-01-01'],
tz=tz, name='idx2')
exp2 = DatetimeIndex(['2011-01-01', '2011-01-01', '2011-01-02',
'2011-01-03', '2011-01-05'],
tz=tz, name='idx2')
idx3 = DatetimeIndex([pd.NaT, '2011-01-03', '2011-01-05',
'2011-01-02', pd.NaT], tz=tz, name='idx3')
exp3 = DatetimeIndex([pd.NaT, pd.NaT, '2011-01-02', '2011-01-03',
'2011-01-05'], tz=tz, name='idx3')
for idx, expected in [(idx1, exp1), (idx2, exp2), (idx3, exp3)]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, expected)
self.assertIsNone(ordered.freq)
ordered = idx.sort_values(ascending=False)
self.assert_index_equal(ordered, expected[::-1])
self.assertIsNone(ordered.freq)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, expected)
exp = np.array([0, 4, 3, 1, 2])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertIsNone(ordered.freq)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, expected[::-1])
exp = np.array([2, 1, 3, 4, 0])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertIsNone(ordered.freq)
def test_getitem(self):
idx1 = pd.date_range('2011-01-01', '2011-01-31', freq='D', name='idx')
idx2 = pd.date_range('2011-01-01', '2011-01-31', freq='D',
tz='Asia/Tokyo', name='idx')
for idx in [idx1, idx2]:
result = idx[0]
self.assertEqual(result, Timestamp('2011-01-01', tz=idx.tz))
result = idx[0:5]
expected = pd.date_range('2011-01-01', '2011-01-05', freq='D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[0:10:2]
expected = pd.date_range('2011-01-01', '2011-01-09', freq='2D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[-20:-5:3]
expected = pd.date_range('2011-01-12', '2011-01-24', freq='3D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[4::-1]
expected = DatetimeIndex(['2011-01-05', '2011-01-04', '2011-01-03',
'2011-01-02', '2011-01-01'],
freq='-1D', tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
def test_drop_duplicates_metadata(self):
# GH 10115
idx = pd.date_range('2011-01-01', '2011-01-31', freq='D', name='idx')
result = idx.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertEqual(idx.freq, result.freq)
idx_dup = idx.append(idx)
self.assertIsNone(idx_dup.freq) # freq is reset
result = idx_dup.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertIsNone(result.freq)
def test_drop_duplicates(self):
# to check Index/Series compat
base = pd.date_range('2011-01-01', '2011-01-31', freq='D', name='idx')
idx = base.append(base[:5])
res = idx.drop_duplicates()
tm.assert_index_equal(res, base)
res = Series(idx).drop_duplicates()
tm.assert_series_equal(res, Series(base))
res = idx.drop_duplicates(keep='last')
exp = base[5:].append(base[:5])
tm.assert_index_equal(res, exp)
res = Series(idx).drop_duplicates(keep='last')
tm.assert_series_equal(res, Series(exp, index=np.arange(5, 36)))
res = idx.drop_duplicates(keep=False)
tm.assert_index_equal(res, base[5:])
res = Series(idx).drop_duplicates(keep=False)
tm.assert_series_equal(res, Series(base[5:], index=np.arange(5, 31)))
def test_take(self):
# GH 10295
idx1 = pd.date_range('2011-01-01', '2011-01-31', freq='D', name='idx')
idx2 = pd.date_range('2011-01-01', '2011-01-31', freq='D',
tz='Asia/Tokyo', name='idx')
for idx in [idx1, idx2]:
result = idx.take([0])
self.assertEqual(result, Timestamp('2011-01-01', tz=idx.tz))
result = idx.take([0, 1, 2])
expected = pd.date_range('2011-01-01', '2011-01-03', freq='D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([0, 2, 4])
expected = pd.date_range('2011-01-01', '2011-01-05', freq='2D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([7, 4, 1])
expected = pd.date_range('2011-01-08', '2011-01-02', freq='-3D',
tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([3, 2, 5])
expected = DatetimeIndex(['2011-01-04', '2011-01-03',
'2011-01-06'],
freq=None, tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertIsNone(result.freq)
result = idx.take([-3, 2, 5])
expected = DatetimeIndex(['2011-01-29', '2011-01-03',
'2011-01-06'],
freq=None, tz=idx.tz, name='idx')
self.assert_index_equal(result, expected)
self.assertIsNone(result.freq)
def test_take_invalid_kwargs(self):
idx = pd.date_range('2011-01-01', '2011-01-31', freq='D', name='idx')
indices = [1, 6, 5, 9, 10, 13, 15, 3]
msg = r"take\(\) got an unexpected keyword argument 'foo'"
tm.assertRaisesRegexp(TypeError, msg, idx.take,
indices, foo=2)
msg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, msg, idx.take,
indices, out=indices)
msg = "the 'mode' parameter is not supported"
tm.assertRaisesRegexp(ValueError, msg, idx.take,
indices, mode='clip')
def test_infer_freq(self):
# GH 11018
for freq in ['A', '2A', '-2A', 'Q', '-1Q', 'M', '-1M', 'D', '3D',
'-3D', 'W', '-1W', 'H', '2H', '-2H', 'T', '2T', 'S',
'-3S']:
idx = pd.date_range('2011-01-01 09:00:00', freq=freq, periods=10)
result = pd.DatetimeIndex(idx.asi8, freq='infer')
tm.assert_index_equal(idx, result)
self.assertEqual(result.freq, freq)
def test_nat_new(self):
idx = pd.date_range('2011-01-01', freq='D', periods=5, name='x')
result = idx._nat_new()
exp = pd.DatetimeIndex([pd.NaT] * 5, name='x')
tm.assert_index_equal(result, exp)
result = idx._nat_new(box=False)
exp = np.array([tslib.iNaT] * 5, dtype=np.int64)
tm.assert_numpy_array_equal(result, exp)
def test_shift(self):
# GH 9903
for tz in self.tz:
idx = pd.DatetimeIndex([], name='xxx', tz=tz)
tm.assert_index_equal(idx.shift(0, freq='H'), idx)
tm.assert_index_equal(idx.shift(3, freq='H'), idx)
idx = pd.DatetimeIndex(['2011-01-01 10:00', '2011-01-01 11:00'
'2011-01-01 12:00'], name='xxx', tz=tz)
tm.assert_index_equal(idx.shift(0, freq='H'), idx)
exp = pd.DatetimeIndex(['2011-01-01 13:00', '2011-01-01 14:00'
'2011-01-01 15:00'], name='xxx', tz=tz)
tm.assert_index_equal(idx.shift(3, freq='H'), exp)
exp = pd.DatetimeIndex(['2011-01-01 07:00', '2011-01-01 08:00'
'2011-01-01 09:00'], name='xxx', tz=tz)
tm.assert_index_equal(idx.shift(-3, freq='H'), exp)
def test_nat(self):
self.assertIs(pd.DatetimeIndex._na_value, pd.NaT)
self.assertIs(pd.DatetimeIndex([])._na_value, pd.NaT)
for tz in [None, 'US/Eastern', 'UTC']:
idx = pd.DatetimeIndex(['2011-01-01', '2011-01-02'], tz=tz)
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, False]))
self.assertFalse(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
np.array([], dtype=np.intp))
idx = pd.DatetimeIndex(['2011-01-01', 'NaT'], tz=tz)
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, True]))
self.assertTrue(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
np.array([1], dtype=np.intp))
def test_equals(self):
# GH 13107
for tz in [None, 'UTC', 'US/Eastern', 'Asia/Tokyo']:
idx = pd.DatetimeIndex(['2011-01-01', '2011-01-02', 'NaT'])
self.assertTrue(idx.equals(idx))
self.assertTrue(idx.equals(idx.copy()))
self.assertTrue(idx.equals(idx.asobject))
self.assertTrue(idx.asobject.equals(idx))
self.assertTrue(idx.asobject.equals(idx.asobject))
self.assertFalse(idx.equals(list(idx)))
self.assertFalse(idx.equals(pd.Series(idx)))
idx2 = pd.DatetimeIndex(['2011-01-01', '2011-01-02', 'NaT'],
tz='US/Pacific')
self.assertFalse(idx.equals(idx2))
self.assertFalse(idx.equals(idx2.copy()))
self.assertFalse(idx.equals(idx2.asobject))
self.assertFalse(idx.asobject.equals(idx2))
self.assertFalse(idx.equals(list(idx2)))
self.assertFalse(idx.equals(pd.Series(idx2)))
# same internal, different tz
idx3 = pd.DatetimeIndex._simple_new(idx.asi8, tz='US/Pacific')
tm.assert_numpy_array_equal(idx.asi8, idx3.asi8)
self.assertFalse(idx.equals(idx3))
self.assertFalse(idx.equals(idx3.copy()))
self.assertFalse(idx.equals(idx3.asobject))
self.assertFalse(idx.asobject.equals(idx3))
self.assertFalse(idx.equals(list(idx3)))
self.assertFalse(idx.equals(pd.Series(idx3)))
class TestTimedeltaIndexOps(Ops):
def setUp(self):
super(TestTimedeltaIndexOps, self).setUp()
mask = lambda x: isinstance(x, TimedeltaIndex)
self.is_valid_objs = [o for o in self.objs if mask(o)]
self.not_valid_objs = []
def test_ops_properties(self):
self.check_ops_properties(['days', 'hours', 'minutes', 'seconds',
'milliseconds'])
self.check_ops_properties(['microseconds', 'nanoseconds'])
def test_asobject_tolist(self):
idx = timedelta_range(start='1 days', periods=4, freq='D', name='idx')
expected_list = [Timedelta('1 days'), Timedelta('2 days'),
Timedelta('3 days'), Timedelta('4 days')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
idx = TimedeltaIndex([timedelta(days=1), timedelta(days=2), pd.NaT,
timedelta(days=4)], name='idx')
expected_list = [Timedelta('1 days'), Timedelta('2 days'), pd.NaT,
Timedelta('4 days')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
def test_minmax(self):
# monotonic
idx1 = TimedeltaIndex(['1 days', '2 days', '3 days'])
self.assertTrue(idx1.is_monotonic)
# non-monotonic
idx2 = TimedeltaIndex(['1 days', np.nan, '3 days', 'NaT'])
self.assertFalse(idx2.is_monotonic)
for idx in [idx1, idx2]:
self.assertEqual(idx.min(), Timedelta('1 days')),
self.assertEqual(idx.max(), Timedelta('3 days')),
self.assertEqual(idx.argmin(), 0)
self.assertEqual(idx.argmax(), 2)
for op in ['min', 'max']:
# Return NaT
obj = TimedeltaIndex([])
self.assertTrue(pd.isnull(getattr(obj, op)()))
obj = TimedeltaIndex([pd.NaT])
self.assertTrue(pd.isnull(getattr(obj, op)()))
obj = TimedeltaIndex([pd.NaT, pd.NaT, pd.NaT])
self.assertTrue(pd.isnull(getattr(obj, op)()))
def test_numpy_minmax(self):
dr = pd.date_range(start='2016-01-15', end='2016-01-20')
td = TimedeltaIndex(np.asarray(dr))
self.assertEqual(np.min(td), Timedelta('16815 days'))
self.assertEqual(np.max(td), Timedelta('16820 days'))
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.min, td, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.max, td, out=0)
self.assertEqual(np.argmin(td), 0)
self.assertEqual(np.argmax(td), 5)
if not _np_version_under1p10:
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.argmin, td, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.argmax, td, out=0)
def test_round(self):
td = pd.timedelta_range(start='16801 days', periods=5, freq='30Min')
elt = td[1]
expected_rng = TimedeltaIndex([
Timedelta('16801 days 00:00:00'),
Timedelta('16801 days 00:00:00'),
Timedelta('16801 days 01:00:00'),
Timedelta('16801 days 02:00:00'),
Timedelta('16801 days 02:00:00'),
])
expected_elt = expected_rng[1]
tm.assert_index_equal(td.round(freq='H'), expected_rng)
self.assertEqual(elt.round(freq='H'), expected_elt)
msg = pd.tseries.frequencies._INVALID_FREQ_ERROR
with self.assertRaisesRegexp(ValueError, msg):
td.round(freq='foo')
with tm.assertRaisesRegexp(ValueError, msg):
elt.round(freq='foo')
msg = "<MonthEnd> is a non-fixed frequency"
tm.assertRaisesRegexp(ValueError, msg, td.round, freq='M')
tm.assertRaisesRegexp(ValueError, msg, elt.round, freq='M')
def test_representation(self):
idx1 = TimedeltaIndex([], freq='D')
idx2 = TimedeltaIndex(['1 days'], freq='D')
idx3 = TimedeltaIndex(['1 days', '2 days'], freq='D')
idx4 = TimedeltaIndex(['1 days', '2 days', '3 days'], freq='D')
idx5 = TimedeltaIndex(['1 days 00:00:01', '2 days', '3 days'])
exp1 = """TimedeltaIndex([], dtype='timedelta64[ns]', freq='D')"""
exp2 = ("TimedeltaIndex(['1 days'], dtype='timedelta64[ns]', "
"freq='D')")
exp3 = ("TimedeltaIndex(['1 days', '2 days'], "
"dtype='timedelta64[ns]', freq='D')")
exp4 = ("TimedeltaIndex(['1 days', '2 days', '3 days'], "
"dtype='timedelta64[ns]', freq='D')")
exp5 = ("TimedeltaIndex(['1 days 00:00:01', '2 days 00:00:00', "
"'3 days 00:00:00'], dtype='timedelta64[ns]', freq=None)")
with pd.option_context('display.width', 300):
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5],
[exp1, exp2, exp3, exp4, exp5]):
for func in ['__repr__', '__unicode__', '__str__']:
result = getattr(idx, func)()
self.assertEqual(result, expected)
def test_representation_to_series(self):
idx1 = TimedeltaIndex([], freq='D')
idx2 = TimedeltaIndex(['1 days'], freq='D')
idx3 = TimedeltaIndex(['1 days', '2 days'], freq='D')
idx4 = TimedeltaIndex(['1 days', '2 days', '3 days'], freq='D')
idx5 = TimedeltaIndex(['1 days 00:00:01', '2 days', '3 days'])
exp1 = """Series([], dtype: timedelta64[ns])"""
exp2 = """0 1 days
dtype: timedelta64[ns]"""
exp3 = """0 1 days
1 2 days
dtype: timedelta64[ns]"""
exp4 = """0 1 days
1 2 days
2 3 days
dtype: timedelta64[ns]"""
exp5 = """0 1 days 00:00:01
1 2 days 00:00:00
2 3 days 00:00:00
dtype: timedelta64[ns]"""
with pd.option_context('display.width', 300):
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5],
[exp1, exp2, exp3, exp4, exp5]):
result = repr(pd.Series(idx))
self.assertEqual(result, expected)
def test_summary(self):
# GH9116
idx1 = TimedeltaIndex([], freq='D')
idx2 = TimedeltaIndex(['1 days'], freq='D')
idx3 = TimedeltaIndex(['1 days', '2 days'], freq='D')
idx4 = TimedeltaIndex(['1 days', '2 days', '3 days'], freq='D')
idx5 = TimedeltaIndex(['1 days 00:00:01', '2 days', '3 days'])
exp1 = """TimedeltaIndex: 0 entries
Freq: D"""
exp2 = """TimedeltaIndex: 1 entries, 1 days to 1 days
Freq: D"""
exp3 = """TimedeltaIndex: 2 entries, 1 days to 2 days
Freq: D"""
exp4 = """TimedeltaIndex: 3 entries, 1 days to 3 days
Freq: D"""
exp5 = ("TimedeltaIndex: 3 entries, 1 days 00:00:01 to 3 days "
"00:00:00")
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5],
[exp1, exp2, exp3, exp4, exp5]):
result = idx.summary()
self.assertEqual(result, expected)
def test_add_iadd(self):
# only test adding/sub offsets as + is now numeric
# offset
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), Timedelta(hours=2)]
for delta in offsets:
rng = timedelta_range('1 days', '10 days')
result = rng + delta
expected = timedelta_range('1 days 02:00:00', '10 days 02:00:00',
freq='D')
tm.assert_index_equal(result, expected)
rng += delta
tm.assert_index_equal(rng, expected)
# int
rng = timedelta_range('1 days 09:00:00', freq='H', periods=10)
result = rng + 1
expected = timedelta_range('1 days 10:00:00', freq='H', periods=10)
tm.assert_index_equal(result, expected)
rng += 1
tm.assert_index_equal(rng, expected)
def test_sub_isub(self):
# only test adding/sub offsets as - is now numeric
# offset
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), Timedelta(hours=2)]
for delta in offsets:
rng = timedelta_range('1 days', '10 days')
result = rng - delta
expected = timedelta_range('0 days 22:00:00', '9 days 22:00:00')
tm.assert_index_equal(result, expected)
rng -= delta
tm.assert_index_equal(rng, expected)
# int
rng = timedelta_range('1 days 09:00:00', freq='H', periods=10)
result = rng - 1
expected = timedelta_range('1 days 08:00:00', freq='H', periods=10)
tm.assert_index_equal(result, expected)
rng -= 1
tm.assert_index_equal(rng, expected)
idx = TimedeltaIndex(['1 day', '2 day'])
msg = "cannot subtract a datelike from a TimedeltaIndex"
with tm.assertRaisesRegexp(TypeError, msg):
idx - Timestamp('2011-01-01')
result = Timestamp('2011-01-01') + idx
expected = DatetimeIndex(['2011-01-02', '2011-01-03'])
tm.assert_index_equal(result, expected)
def test_ops_compat(self):
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), Timedelta(hours=2)]
rng = timedelta_range('1 days', '10 days', name='foo')
# multiply
for offset in offsets:
self.assertRaises(TypeError, lambda: rng * offset)
# divide
expected = Int64Index((np.arange(10) + 1) * 12, name='foo')
for offset in offsets:
result = rng / offset
tm.assert_index_equal(result, expected, exact=False)
# divide with nats
rng = TimedeltaIndex(['1 days', pd.NaT, '2 days'], name='foo')
expected = Float64Index([12, np.nan, 24], name='foo')
for offset in offsets:
result = rng / offset
tm.assert_index_equal(result, expected)
# don't allow division by NaT (make could in the future)
self.assertRaises(TypeError, lambda: rng / pd.NaT)
def test_subtraction_ops(self):
# with datetimes/timedelta and tdi/dti
tdi = TimedeltaIndex(['1 days', pd.NaT, '2 days'], name='foo')
dti = date_range('20130101', periods=3, name='bar')
td = Timedelta('1 days')
dt = Timestamp('20130101')
self.assertRaises(TypeError, lambda: tdi - dt)
self.assertRaises(TypeError, lambda: tdi - dti)
self.assertRaises(TypeError, lambda: td - dt)
self.assertRaises(TypeError, lambda: td - dti)
result = dt - dti
expected = TimedeltaIndex(['0 days', '-1 days', '-2 days'], name='bar')
tm.assert_index_equal(result, expected)
result = dti - dt
expected = TimedeltaIndex(['0 days', '1 days', '2 days'], name='bar')
tm.assert_index_equal(result, expected)
result = tdi - td
expected = TimedeltaIndex(['0 days', pd.NaT, '1 days'], name='foo')
tm.assert_index_equal(result, expected, check_names=False)
result = td - tdi
expected = TimedeltaIndex(['0 days', pd.NaT, '-1 days'], name='foo')
tm.assert_index_equal(result, expected, check_names=False)
result = dti - td
expected = DatetimeIndex(
['20121231', '20130101', '20130102'], name='bar')
tm.assert_index_equal(result, expected, check_names=False)
result = dt - tdi
expected = DatetimeIndex(['20121231', pd.NaT, '20121230'], name='foo')
tm.assert_index_equal(result, expected)
def test_subtraction_ops_with_tz(self):
# check that dt/dti subtraction ops with tz are validated
dti = date_range('20130101', periods=3)
ts = Timestamp('20130101')
dt = ts.to_pydatetime()
dti_tz = date_range('20130101', periods=3).tz_localize('US/Eastern')
ts_tz = Timestamp('20130101').tz_localize('US/Eastern')
ts_tz2 = Timestamp('20130101').tz_localize('CET')
dt_tz = ts_tz.to_pydatetime()
td = Timedelta('1 days')
def _check(result, expected):
self.assertEqual(result, expected)
self.assertIsInstance(result, Timedelta)
# scalars
result = ts - ts
expected = Timedelta('0 days')
_check(result, expected)
result = dt_tz - ts_tz
expected = Timedelta('0 days')
_check(result, expected)
result = ts_tz - dt_tz
expected = Timedelta('0 days')
_check(result, expected)
# tz mismatches
self.assertRaises(TypeError, lambda: dt_tz - ts)
self.assertRaises(TypeError, lambda: dt_tz - dt)
self.assertRaises(TypeError, lambda: dt_tz - ts_tz2)
self.assertRaises(TypeError, lambda: dt - dt_tz)
self.assertRaises(TypeError, lambda: ts - dt_tz)
self.assertRaises(TypeError, lambda: ts_tz2 - ts)
self.assertRaises(TypeError, lambda: ts_tz2 - dt)
self.assertRaises(TypeError, lambda: ts_tz - ts_tz2)
# with dti
self.assertRaises(TypeError, lambda: dti - ts_tz)
self.assertRaises(TypeError, lambda: dti_tz - ts)
self.assertRaises(TypeError, lambda: dti_tz - ts_tz2)
result = dti_tz - dt_tz
expected = TimedeltaIndex(['0 days', '1 days', '2 days'])
tm.assert_index_equal(result, expected)
result = dt_tz - dti_tz
expected = TimedeltaIndex(['0 days', '-1 days', '-2 days'])
tm.assert_index_equal(result, expected)
result = dti_tz - ts_tz
expected = TimedeltaIndex(['0 days', '1 days', '2 days'])
tm.assert_index_equal(result, expected)
result = ts_tz - dti_tz
expected = TimedeltaIndex(['0 days', '-1 days', '-2 days'])
tm.assert_index_equal(result, expected)
result = td - td
expected = Timedelta('0 days')
_check(result, expected)
result = dti_tz - td
expected = DatetimeIndex(
['20121231', '20130101', '20130102'], tz='US/Eastern')
tm.assert_index_equal(result, expected)
def test_dti_tdi_numeric_ops(self):
# These are normally union/diff set-like ops
tdi = TimedeltaIndex(['1 days', pd.NaT, '2 days'], name='foo')
dti = date_range('20130101', periods=3, name='bar')
# TODO(wesm): unused?
# td = Timedelta('1 days')
# dt = Timestamp('20130101')
result = tdi - tdi
expected = TimedeltaIndex(['0 days', pd.NaT, '0 days'], name='foo')
tm.assert_index_equal(result, expected)
result = tdi + tdi
expected = TimedeltaIndex(['2 days', pd.NaT, '4 days'], name='foo')
tm.assert_index_equal(result, expected)
result = dti - tdi # name will be reset
expected = DatetimeIndex(['20121231', pd.NaT, '20130101'])
tm.assert_index_equal(result, expected)
def test_sub_period(self):
# GH 13078
# not supported, check TypeError
p = pd.Period('2011-01-01', freq='D')
for freq in [None, 'H']:
idx = pd.TimedeltaIndex(['1 hours', '2 hours'], freq=freq)
with tm.assertRaises(TypeError):
idx - p
with tm.assertRaises(TypeError):
p - idx
def test_addition_ops(self):
# with datetimes/timedelta and tdi/dti
tdi = TimedeltaIndex(['1 days', pd.NaT, '2 days'], name='foo')
dti = date_range('20130101', periods=3, name='bar')
td = Timedelta('1 days')
dt = Timestamp('20130101')
result = tdi + dt
expected = DatetimeIndex(['20130102', pd.NaT, '20130103'], name='foo')
tm.assert_index_equal(result, expected)
result = dt + tdi
expected = DatetimeIndex(['20130102', pd.NaT, '20130103'], name='foo')
tm.assert_index_equal(result, expected)
result = td + tdi
expected = TimedeltaIndex(['2 days', pd.NaT, '3 days'], name='foo')
tm.assert_index_equal(result, expected)
result = tdi + td
expected = TimedeltaIndex(['2 days', pd.NaT, '3 days'], name='foo')
tm.assert_index_equal(result, expected)
# unequal length
self.assertRaises(ValueError, lambda: tdi + dti[0:1])
self.assertRaises(ValueError, lambda: tdi[0:1] + dti)
# random indexes
self.assertRaises(TypeError, lambda: tdi + Int64Index([1, 2, 3]))
# this is a union!
# self.assertRaises(TypeError, lambda : Int64Index([1,2,3]) + tdi)
result = tdi + dti # name will be reset
expected = DatetimeIndex(['20130102', pd.NaT, '20130105'])
tm.assert_index_equal(result, expected)
result = dti + tdi # name will be reset
expected = DatetimeIndex(['20130102', pd.NaT, '20130105'])
tm.assert_index_equal(result, expected)
result = dt + td
expected = Timestamp('20130102')
self.assertEqual(result, expected)
result = td + dt
expected = Timestamp('20130102')
self.assertEqual(result, expected)
def test_comp_nat(self):
left = pd.TimedeltaIndex([pd.Timedelta('1 days'), pd.NaT,
pd.Timedelta('3 days')])
right = pd.TimedeltaIndex([pd.NaT, pd.NaT, pd.Timedelta('3 days')])
for l, r in [(left, right), (left.asobject, right.asobject)]:
result = l == r
expected = np.array([False, False, True])
tm.assert_numpy_array_equal(result, expected)
result = l != r
expected = np.array([True, True, False])
tm.assert_numpy_array_equal(result, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l == pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT == r, expected)
expected = np.array([True, True, True])
tm.assert_numpy_array_equal(l != pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT != l, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l < pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT > l, expected)
def test_value_counts_unique(self):
# GH 7735
idx = timedelta_range('1 days 09:00:00', freq='H', periods=10)
# create repeated values, 'n'th element is repeated by n+1 times
idx = TimedeltaIndex(np.repeat(idx.values, range(1, len(idx) + 1)))
exp_idx = timedelta_range('1 days 18:00:00', freq='-1H', periods=10)
expected = Series(range(10, 0, -1), index=exp_idx, dtype='int64')
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
expected = timedelta_range('1 days 09:00:00', freq='H', periods=10)
tm.assert_index_equal(idx.unique(), expected)
idx = TimedeltaIndex(['1 days 09:00:00', '1 days 09:00:00',
'1 days 09:00:00', '1 days 08:00:00',
'1 days 08:00:00', pd.NaT])
exp_idx = TimedeltaIndex(['1 days 09:00:00', '1 days 08:00:00'])
expected = Series([3, 2], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
exp_idx = TimedeltaIndex(['1 days 09:00:00', '1 days 08:00:00',
pd.NaT])
expected = Series([3, 2, 1], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(dropna=False), expected)
tm.assert_index_equal(idx.unique(), exp_idx)
def test_nonunique_contains(self):
# GH 9512
for idx in map(TimedeltaIndex, ([0, 1, 0], [0, 0, -1], [0, -1, -1],
['00:01:00', '00:01:00', '00:02:00'],
['00:01:00', '00:01:00', '00:00:01'])):
tm.assertIn(idx[0], idx)
def test_unknown_attribute(self):
# GH 9680
tdi = pd.timedelta_range(start=0, periods=10, freq='1s')
ts = pd.Series(np.random.normal(size=10), index=tdi)
self.assertNotIn('foo', ts.__dict__.keys())
self.assertRaises(AttributeError, lambda: ts.foo)
def test_order(self):
# GH 10295
idx1 = TimedeltaIndex(['1 day', '2 day', '3 day'], freq='D',
name='idx')
idx2 = TimedeltaIndex(
['1 hour', '2 hour', '3 hour'], freq='H', name='idx')
for idx in [idx1, idx2]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, idx)
self.assertEqual(ordered.freq, idx.freq)
ordered = idx.sort_values(ascending=False)
expected = idx[::-1]
self.assert_index_equal(ordered, expected)
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq.n, -1)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, idx)
self.assert_numpy_array_equal(indexer,
np.array([0, 1, 2]),
check_dtype=False)
self.assertEqual(ordered.freq, idx.freq)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, idx[::-1])
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq.n, -1)
idx1 = TimedeltaIndex(['1 hour', '3 hour', '5 hour',
'2 hour ', '1 hour'], name='idx1')
exp1 = TimedeltaIndex(['1 hour', '1 hour', '2 hour',
'3 hour', '5 hour'], name='idx1')
idx2 = TimedeltaIndex(['1 day', '3 day', '5 day',
'2 day', '1 day'], name='idx2')
# TODO(wesm): unused?
# exp2 = TimedeltaIndex(['1 day', '1 day', '2 day',
# '3 day', '5 day'], name='idx2')
# idx3 = TimedeltaIndex([pd.NaT, '3 minute', '5 minute',
# '2 minute', pd.NaT], name='idx3')
# exp3 = TimedeltaIndex([pd.NaT, pd.NaT, '2 minute', '3 minute',
# '5 minute'], name='idx3')
for idx, expected in [(idx1, exp1), (idx1, exp1), (idx1, exp1)]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, expected)
self.assertIsNone(ordered.freq)
ordered = idx.sort_values(ascending=False)
self.assert_index_equal(ordered, expected[::-1])
self.assertIsNone(ordered.freq)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, expected)
exp = np.array([0, 4, 3, 1, 2])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertIsNone(ordered.freq)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, expected[::-1])
exp = np.array([2, 1, 3, 4, 0])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertIsNone(ordered.freq)
def test_getitem(self):
idx1 = pd.timedelta_range('1 day', '31 day', freq='D', name='idx')
for idx in [idx1]:
result = idx[0]
self.assertEqual(result, pd.Timedelta('1 day'))
result = idx[0:5]
expected = pd.timedelta_range('1 day', '5 day', freq='D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[0:10:2]
expected = pd.timedelta_range('1 day', '9 day', freq='2D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[-20:-5:3]
expected = pd.timedelta_range('12 day', '24 day', freq='3D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx[4::-1]
expected = TimedeltaIndex(['5 day', '4 day', '3 day',
'2 day', '1 day'],
freq='-1D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
def test_drop_duplicates_metadata(self):
# GH 10115
idx = pd.timedelta_range('1 day', '31 day', freq='D', name='idx')
result = idx.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertEqual(idx.freq, result.freq)
idx_dup = idx.append(idx)
self.assertIsNone(idx_dup.freq) # freq is reset
result = idx_dup.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertIsNone(result.freq)
def test_drop_duplicates(self):
# to check Index/Series compat
base = pd.timedelta_range('1 day', '31 day', freq='D', name='idx')
idx = base.append(base[:5])
res = idx.drop_duplicates()
tm.assert_index_equal(res, base)
res = Series(idx).drop_duplicates()
tm.assert_series_equal(res, Series(base))
res = idx.drop_duplicates(keep='last')
exp = base[5:].append(base[:5])
tm.assert_index_equal(res, exp)
res = Series(idx).drop_duplicates(keep='last')
tm.assert_series_equal(res, Series(exp, index=np.arange(5, 36)))
res = idx.drop_duplicates(keep=False)
tm.assert_index_equal(res, base[5:])
res = Series(idx).drop_duplicates(keep=False)
tm.assert_series_equal(res, Series(base[5:], index=np.arange(5, 31)))
def test_take(self):
# GH 10295
idx1 = pd.timedelta_range('1 day', '31 day', freq='D', name='idx')
for idx in [idx1]:
result = idx.take([0])
self.assertEqual(result, pd.Timedelta('1 day'))
result = idx.take([-1])
self.assertEqual(result, pd.Timedelta('31 day'))
result = idx.take([0, 1, 2])
expected = pd.timedelta_range('1 day', '3 day', freq='D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([0, 2, 4])
expected = pd.timedelta_range('1 day', '5 day', freq='2D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([7, 4, 1])
expected = pd.timedelta_range('8 day', '2 day', freq='-3D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
result = idx.take([3, 2, 5])
expected = TimedeltaIndex(['4 day', '3 day', '6 day'], name='idx')
self.assert_index_equal(result, expected)
self.assertIsNone(result.freq)
result = idx.take([-3, 2, 5])
expected = TimedeltaIndex(['29 day', '3 day', '6 day'], name='idx')
self.assert_index_equal(result, expected)
self.assertIsNone(result.freq)
def test_take_invalid_kwargs(self):
idx = pd.timedelta_range('1 day', '31 day', freq='D', name='idx')
indices = [1, 6, 5, 9, 10, 13, 15, 3]
msg = r"take\(\) got an unexpected keyword argument 'foo'"
tm.assertRaisesRegexp(TypeError, msg, idx.take,
indices, foo=2)
msg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, msg, idx.take,
indices, out=indices)
msg = "the 'mode' parameter is not supported"
tm.assertRaisesRegexp(ValueError, msg, idx.take,
indices, mode='clip')
def test_infer_freq(self):
# GH 11018
for freq in ['D', '3D', '-3D', 'H', '2H', '-2H', 'T', '2T', 'S', '-3S'
]:
idx = pd.timedelta_range('1', freq=freq, periods=10)
result = pd.TimedeltaIndex(idx.asi8, freq='infer')
tm.assert_index_equal(idx, result)
self.assertEqual(result.freq, freq)
def test_nat_new(self):
idx = pd.timedelta_range('1', freq='D', periods=5, name='x')
result = idx._nat_new()
exp = pd.TimedeltaIndex([pd.NaT] * 5, name='x')
tm.assert_index_equal(result, exp)
result = idx._nat_new(box=False)
exp = np.array([tslib.iNaT] * 5, dtype=np.int64)
tm.assert_numpy_array_equal(result, exp)
def test_shift(self):
# GH 9903
idx = pd.TimedeltaIndex([], name='xxx')
tm.assert_index_equal(idx.shift(0, freq='H'), idx)
tm.assert_index_equal(idx.shift(3, freq='H'), idx)
idx = pd.TimedeltaIndex(['5 hours', '6 hours', '9 hours'], name='xxx')
tm.assert_index_equal(idx.shift(0, freq='H'), idx)
exp = pd.TimedeltaIndex(['8 hours', '9 hours', '12 hours'], name='xxx')
tm.assert_index_equal(idx.shift(3, freq='H'), exp)
exp = pd.TimedeltaIndex(['2 hours', '3 hours', '6 hours'], name='xxx')
tm.assert_index_equal(idx.shift(-3, freq='H'), exp)
tm.assert_index_equal(idx.shift(0, freq='T'), idx)
exp = pd.TimedeltaIndex(['05:03:00', '06:03:00', '9:03:00'],
name='xxx')
tm.assert_index_equal(idx.shift(3, freq='T'), exp)
exp = pd.TimedeltaIndex(['04:57:00', '05:57:00', '8:57:00'],
name='xxx')
tm.assert_index_equal(idx.shift(-3, freq='T'), exp)
def test_repeat(self):
index = pd.timedelta_range('1 days', periods=2, freq='D')
exp = pd.TimedeltaIndex(['1 days', '1 days', '2 days', '2 days'])
for res in [index.repeat(2), np.repeat(index, 2)]:
tm.assert_index_equal(res, exp)
self.assertIsNone(res.freq)
index = TimedeltaIndex(['1 days', 'NaT', '3 days'])
exp = TimedeltaIndex(['1 days', '1 days', '1 days',
'NaT', 'NaT', 'NaT',
'3 days', '3 days', '3 days'])
for res in [index.repeat(3), np.repeat(index, 3)]:
tm.assert_index_equal(res, exp)
self.assertIsNone(res.freq)
def test_nat(self):
self.assertIs(pd.TimedeltaIndex._na_value, pd.NaT)
self.assertIs(pd.TimedeltaIndex([])._na_value, pd.NaT)
idx = pd.TimedeltaIndex(['1 days', '2 days'])
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, False]))
self.assertFalse(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
np.array([], dtype=np.intp))
idx = pd.TimedeltaIndex(['1 days', 'NaT'])
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, True]))
self.assertTrue(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
np.array([1], dtype=np.intp))
def test_equals(self):
# GH 13107
idx = pd.TimedeltaIndex(['1 days', '2 days', 'NaT'])
self.assertTrue(idx.equals(idx))
self.assertTrue(idx.equals(idx.copy()))
self.assertTrue(idx.equals(idx.asobject))
self.assertTrue(idx.asobject.equals(idx))
self.assertTrue(idx.asobject.equals(idx.asobject))
self.assertFalse(idx.equals(list(idx)))
self.assertFalse(idx.equals(pd.Series(idx)))
idx2 = pd.TimedeltaIndex(['2 days', '1 days', 'NaT'])
self.assertFalse(idx.equals(idx2))
self.assertFalse(idx.equals(idx2.copy()))
self.assertFalse(idx.equals(idx2.asobject))
self.assertFalse(idx.asobject.equals(idx2))
self.assertFalse(idx.asobject.equals(idx2.asobject))
self.assertFalse(idx.equals(list(idx2)))
self.assertFalse(idx.equals(pd.Series(idx2)))
class TestPeriodIndexOps(Ops):
def setUp(self):
super(TestPeriodIndexOps, self).setUp()
mask = lambda x: (isinstance(x, DatetimeIndex) or
isinstance(x, PeriodIndex))
self.is_valid_objs = [o for o in self.objs if mask(o)]
self.not_valid_objs = [o for o in self.objs if not mask(o)]
def test_ops_properties(self):
self.check_ops_properties(
['year', 'month', 'day', 'hour', 'minute', 'second', 'weekofyear',
'week', 'dayofweek', 'dayofyear', 'quarter'])
self.check_ops_properties(['qyear'],
lambda x: isinstance(x, PeriodIndex))
def test_asobject_tolist(self):
idx = pd.period_range(start='2013-01-01', periods=4, freq='M',
name='idx')
expected_list = [pd.Period('2013-01-31', freq='M'),
pd.Period('2013-02-28', freq='M'),
pd.Period('2013-03-31', freq='M'),
pd.Period('2013-04-30', freq='M')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
self.assert_index_equal(result, expected)
self.assertEqual(result.name, expected.name)
self.assertEqual(idx.tolist(), expected_list)
idx = PeriodIndex(['2013-01-01', '2013-01-02', 'NaT',
'2013-01-04'], freq='D', name='idx')
expected_list = [pd.Period('2013-01-01', freq='D'),
pd.Period('2013-01-02', freq='D'),
pd.Period('NaT', freq='D'),
pd.Period('2013-01-04', freq='D')]
expected = pd.Index(expected_list, dtype=object, name='idx')
result = idx.asobject
self.assertTrue(isinstance(result, Index))
self.assertEqual(result.dtype, object)
tm.assert_index_equal(result, expected)
for i in [0, 1, 3]:
self.assertEqual(result[i], expected[i])
self.assertIs(result[2], pd.NaT)
self.assertEqual(result.name, expected.name)
result_list = idx.tolist()
for i in [0, 1, 3]:
self.assertEqual(result_list[i], expected_list[i])
self.assertIs(result_list[2], pd.NaT)
def test_minmax(self):
# monotonic
idx1 = pd.PeriodIndex([pd.NaT, '2011-01-01', '2011-01-02',
'2011-01-03'], freq='D')
self.assertTrue(idx1.is_monotonic)
# non-monotonic
idx2 = pd.PeriodIndex(['2011-01-01', pd.NaT, '2011-01-03',
'2011-01-02', pd.NaT], freq='D')
self.assertFalse(idx2.is_monotonic)
for idx in [idx1, idx2]:
self.assertEqual(idx.min(), pd.Period('2011-01-01', freq='D'))
self.assertEqual(idx.max(), pd.Period('2011-01-03', freq='D'))
self.assertEqual(idx1.argmin(), 1)
self.assertEqual(idx2.argmin(), 0)
self.assertEqual(idx1.argmax(), 3)
self.assertEqual(idx2.argmax(), 2)
for op in ['min', 'max']:
# Return NaT
obj = PeriodIndex([], freq='M')
result = getattr(obj, op)()
self.assertIs(result, tslib.NaT)
obj = PeriodIndex([pd.NaT], freq='M')
result = getattr(obj, op)()
self.assertIs(result, tslib.NaT)
obj = PeriodIndex([pd.NaT, pd.NaT, pd.NaT], freq='M')
result = getattr(obj, op)()
self.assertIs(result, tslib.NaT)
def test_numpy_minmax(self):
pr = pd.period_range(start='2016-01-15', end='2016-01-20')
self.assertEqual(np.min(pr), Period('2016-01-15', freq='D'))
self.assertEqual(np.max(pr), Period('2016-01-20', freq='D'))
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.min, pr, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.max, pr, out=0)
self.assertEqual(np.argmin(pr), 0)
self.assertEqual(np.argmax(pr), 5)
if not _np_version_under1p10:
errmsg = "the 'out' parameter is not supported"
tm.assertRaisesRegexp(ValueError, errmsg, np.argmin, pr, out=0)
tm.assertRaisesRegexp(ValueError, errmsg, np.argmax, pr, out=0)
def test_representation(self):
# GH 7601
idx1 = PeriodIndex([], freq='D')
idx2 = PeriodIndex(['2011-01-01'], freq='D')
idx3 = PeriodIndex(['2011-01-01', '2011-01-02'], freq='D')
idx4 = PeriodIndex(['2011-01-01', '2011-01-02', '2011-01-03'],
freq='D')
idx5 = PeriodIndex(['2011', '2012', '2013'], freq='A')
idx6 = PeriodIndex(['2011-01-01 09:00', '2012-02-01 10:00',
'NaT'], freq='H')
idx7 = pd.period_range('2013Q1', periods=1, freq="Q")
idx8 = pd.period_range('2013Q1', periods=2, freq="Q")
idx9 = pd.period_range('2013Q1', periods=3, freq="Q")
idx10 = PeriodIndex(['2011-01-01', '2011-02-01'], freq='3D')
exp1 = """PeriodIndex([], dtype='period[D]', freq='D')"""
exp2 = """PeriodIndex(['2011-01-01'], dtype='period[D]', freq='D')"""
exp3 = ("PeriodIndex(['2011-01-01', '2011-01-02'], dtype='period[D]', "
"freq='D')")
exp4 = ("PeriodIndex(['2011-01-01', '2011-01-02', '2011-01-03'], "
"dtype='period[D]', freq='D')")
exp5 = ("PeriodIndex(['2011', '2012', '2013'], dtype='period[A-DEC]', "
"freq='A-DEC')")
exp6 = ("PeriodIndex(['2011-01-01 09:00', '2012-02-01 10:00', 'NaT'], "
"dtype='period[H]', freq='H')")
exp7 = ("PeriodIndex(['2013Q1'], dtype='period[Q-DEC]', "
"freq='Q-DEC')")
exp8 = ("PeriodIndex(['2013Q1', '2013Q2'], dtype='period[Q-DEC]', "
"freq='Q-DEC')")
exp9 = ("PeriodIndex(['2013Q1', '2013Q2', '2013Q3'], "
"dtype='period[Q-DEC]', freq='Q-DEC')")
exp10 = ("PeriodIndex(['2011-01-01', '2011-02-01'], "
"dtype='period[3D]', freq='3D')")
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5,
idx6, idx7, idx8, idx9, idx10],
[exp1, exp2, exp3, exp4, exp5,
exp6, exp7, exp8, exp9, exp10]):
for func in ['__repr__', '__unicode__', '__str__']:
result = getattr(idx, func)()
self.assertEqual(result, expected)
def test_representation_to_series(self):
# GH 10971
idx1 = PeriodIndex([], freq='D')
idx2 = PeriodIndex(['2011-01-01'], freq='D')
idx3 = PeriodIndex(['2011-01-01', '2011-01-02'], freq='D')
idx4 = PeriodIndex(['2011-01-01', '2011-01-02',
'2011-01-03'], freq='D')
idx5 = PeriodIndex(['2011', '2012', '2013'], freq='A')
idx6 = PeriodIndex(['2011-01-01 09:00', '2012-02-01 10:00',
'NaT'], freq='H')
idx7 = pd.period_range('2013Q1', periods=1, freq="Q")
idx8 = pd.period_range('2013Q1', periods=2, freq="Q")
idx9 = pd.period_range('2013Q1', periods=3, freq="Q")
exp1 = """Series([], dtype: object)"""
exp2 = """0 2011-01-01
dtype: object"""
exp3 = """0 2011-01-01
1 2011-01-02
dtype: object"""
exp4 = """0 2011-01-01
1 2011-01-02
2 2011-01-03
dtype: object"""
exp5 = """0 2011
1 2012
2 2013
dtype: object"""
exp6 = """0 2011-01-01 09:00
1 2012-02-01 10:00
2 NaT
dtype: object"""
exp7 = """0 2013Q1
dtype: object"""
exp8 = """0 2013Q1
1 2013Q2
dtype: object"""
exp9 = """0 2013Q1
1 2013Q2
2 2013Q3
dtype: object"""
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5,
idx6, idx7, idx8, idx9],
[exp1, exp2, exp3, exp4, exp5,
exp6, exp7, exp8, exp9]):
result = repr(pd.Series(idx))
self.assertEqual(result, expected)
def test_summary(self):
# GH9116
idx1 = PeriodIndex([], freq='D')
idx2 = PeriodIndex(['2011-01-01'], freq='D')
idx3 = PeriodIndex(['2011-01-01', '2011-01-02'], freq='D')
idx4 = PeriodIndex(
['2011-01-01', '2011-01-02', '2011-01-03'], freq='D')
idx5 = PeriodIndex(['2011', '2012', '2013'], freq='A')
idx6 = PeriodIndex(
['2011-01-01 09:00', '2012-02-01 10:00', 'NaT'], freq='H')
idx7 = pd.period_range('2013Q1', periods=1, freq="Q")
idx8 = pd.period_range('2013Q1', periods=2, freq="Q")
idx9 = pd.period_range('2013Q1', periods=3, freq="Q")
exp1 = """PeriodIndex: 0 entries
Freq: D"""
exp2 = """PeriodIndex: 1 entries, 2011-01-01 to 2011-01-01
Freq: D"""
exp3 = """PeriodIndex: 2 entries, 2011-01-01 to 2011-01-02
Freq: D"""
exp4 = """PeriodIndex: 3 entries, 2011-01-01 to 2011-01-03
Freq: D"""
exp5 = """PeriodIndex: 3 entries, 2011 to 2013
Freq: A-DEC"""
exp6 = """PeriodIndex: 3 entries, 2011-01-01 09:00 to NaT
Freq: H"""
exp7 = """PeriodIndex: 1 entries, 2013Q1 to 2013Q1
Freq: Q-DEC"""
exp8 = """PeriodIndex: 2 entries, 2013Q1 to 2013Q2
Freq: Q-DEC"""
exp9 = """PeriodIndex: 3 entries, 2013Q1 to 2013Q3
Freq: Q-DEC"""
for idx, expected in zip([idx1, idx2, idx3, idx4, idx5,
idx6, idx7, idx8, idx9],
[exp1, exp2, exp3, exp4, exp5,
exp6, exp7, exp8, exp9]):
result = idx.summary()
self.assertEqual(result, expected)
def test_resolution(self):
for freq, expected in zip(['A', 'Q', 'M', 'D', 'H',
'T', 'S', 'L', 'U'],
['day', 'day', 'day', 'day',
'hour', 'minute', 'second',
'millisecond', 'microsecond']):
idx = pd.period_range(start='2013-04-01', periods=30, freq=freq)
self.assertEqual(idx.resolution, expected)
def test_union(self):
# union
rng1 = pd.period_range('1/1/2000', freq='D', periods=5)
other1 = pd.period_range('1/6/2000', freq='D', periods=5)
expected1 = pd.period_range('1/1/2000', freq='D', periods=10)
rng2 = pd.period_range('1/1/2000', freq='D', periods=5)
other2 = pd.period_range('1/4/2000', freq='D', periods=5)
expected2 = pd.period_range('1/1/2000', freq='D', periods=8)
rng3 = pd.period_range('1/1/2000', freq='D', periods=5)
other3 = pd.PeriodIndex([], freq='D')
expected3 = pd.period_range('1/1/2000', freq='D', periods=5)
rng4 = pd.period_range('2000-01-01 09:00', freq='H', periods=5)
other4 = pd.period_range('2000-01-02 09:00', freq='H', periods=5)
expected4 = pd.PeriodIndex(['2000-01-01 09:00', '2000-01-01 10:00',
'2000-01-01 11:00', '2000-01-01 12:00',
'2000-01-01 13:00', '2000-01-02 09:00',
'2000-01-02 10:00', '2000-01-02 11:00',
'2000-01-02 12:00', '2000-01-02 13:00'],
freq='H')
rng5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
'2000-01-01 09:05'], freq='T')
other5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:05'
'2000-01-01 09:08'],
freq='T')
expected5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
'2000-01-01 09:05', '2000-01-01 09:08'],
freq='T')
rng6 = pd.period_range('2000-01-01', freq='M', periods=7)
other6 = pd.period_range('2000-04-01', freq='M', periods=7)
expected6 = pd.period_range('2000-01-01', freq='M', periods=10)
rng7 = pd.period_range('2003-01-01', freq='A', periods=5)
other7 = pd.period_range('1998-01-01', freq='A', periods=8)
expected7 = pd.period_range('1998-01-01', freq='A', periods=10)
for rng, other, expected in [(rng1, other1, expected1),
(rng2, other2, expected2),
(rng3, other3, expected3), (rng4, other4,
expected4),
(rng5, other5, expected5), (rng6, other6,
expected6),
(rng7, other7, expected7)]:
result_union = rng.union(other)
tm.assert_index_equal(result_union, expected)
def test_add_iadd(self):
rng = pd.period_range('1/1/2000', freq='D', periods=5)
other = pd.period_range('1/6/2000', freq='D', periods=5)
# previously performed setop union, now raises TypeError (GH14164)
with tm.assertRaises(TypeError):
rng + other
with tm.assertRaises(TypeError):
rng += other
# offset
# DateOffset
rng = pd.period_range('2014', '2024', freq='A')
result = rng + pd.offsets.YearEnd(5)
expected = pd.period_range('2019', '2029', freq='A')
tm.assert_index_equal(result, expected)
rng += pd.offsets.YearEnd(5)
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(365, 'D'),
timedelta(365), Timedelta(days=365)]:
msg = ('Input has different freq(=.+)? '
'from PeriodIndex\\(freq=A-DEC\\)')
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng + o
rng = pd.period_range('2014-01', '2016-12', freq='M')
result = rng + pd.offsets.MonthEnd(5)
expected = pd.period_range('2014-06', '2017-05', freq='M')
tm.assert_index_equal(result, expected)
rng += pd.offsets.MonthEnd(5)
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(365, 'D'),
timedelta(365), Timedelta(days=365)]:
rng = pd.period_range('2014-01', '2016-12', freq='M')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=M\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng + o
# Tick
offsets = [pd.offsets.Day(3), timedelta(days=3),
np.timedelta64(3, 'D'), pd.offsets.Hour(72),
timedelta(minutes=60 * 24 * 3), np.timedelta64(72, 'h'),
Timedelta('72:00:00')]
for delta in offsets:
rng = pd.period_range('2014-05-01', '2014-05-15', freq='D')
result = rng + delta
expected = pd.period_range('2014-05-04', '2014-05-18', freq='D')
tm.assert_index_equal(result, expected)
rng += delta
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(4, 'h'),
timedelta(hours=23), Timedelta('23:00:00')]:
rng = pd.period_range('2014-05-01', '2014-05-15', freq='D')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=D\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng + o
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), pd.offsets.Minute(120),
timedelta(minutes=120), np.timedelta64(120, 'm'),
Timedelta(minutes=120)]
for delta in offsets:
rng = pd.period_range('2014-01-01 10:00', '2014-01-05 10:00',
freq='H')
result = rng + delta
expected = pd.period_range('2014-01-01 12:00', '2014-01-05 12:00',
freq='H')
tm.assert_index_equal(result, expected)
rng += delta
tm.assert_index_equal(rng, expected)
for delta in [pd.offsets.YearBegin(2), timedelta(minutes=30),
np.timedelta64(30, 's'), Timedelta(seconds=30)]:
rng = pd.period_range('2014-01-01 10:00', '2014-01-05 10:00',
freq='H')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=H\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
result = rng + delta
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng += delta
# int
rng = pd.period_range('2000-01-01 09:00', freq='H', periods=10)
result = rng + 1
expected = pd.period_range('2000-01-01 10:00', freq='H', periods=10)
tm.assert_index_equal(result, expected)
rng += 1
tm.assert_index_equal(rng, expected)
def test_difference(self):
# diff
rng1 = pd.period_range('1/1/2000', freq='D', periods=5)
other1 = pd.period_range('1/6/2000', freq='D', periods=5)
expected1 = pd.period_range('1/1/2000', freq='D', periods=5)
rng2 = pd.period_range('1/1/2000', freq='D', periods=5)
other2 = pd.period_range('1/4/2000', freq='D', periods=5)
expected2 = pd.period_range('1/1/2000', freq='D', periods=3)
rng3 = pd.period_range('1/1/2000', freq='D', periods=5)
other3 = pd.PeriodIndex([], freq='D')
expected3 = pd.period_range('1/1/2000', freq='D', periods=5)
rng4 = pd.period_range('2000-01-01 09:00', freq='H', periods=5)
other4 = pd.period_range('2000-01-02 09:00', freq='H', periods=5)
expected4 = rng4
rng5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
'2000-01-01 09:05'], freq='T')
other5 = pd.PeriodIndex(
['2000-01-01 09:01', '2000-01-01 09:05'], freq='T')
expected5 = pd.PeriodIndex(['2000-01-01 09:03'], freq='T')
rng6 = pd.period_range('2000-01-01', freq='M', periods=7)
other6 = pd.period_range('2000-04-01', freq='M', periods=7)
expected6 = pd.period_range('2000-01-01', freq='M', periods=3)
rng7 = pd.period_range('2003-01-01', freq='A', periods=5)
other7 = pd.period_range('1998-01-01', freq='A', periods=8)
expected7 = pd.period_range('2006-01-01', freq='A', periods=2)
for rng, other, expected in [(rng1, other1, expected1),
(rng2, other2, expected2),
(rng3, other3, expected3),
(rng4, other4, expected4),
(rng5, other5, expected5),
(rng6, other6, expected6),
(rng7, other7, expected7), ]:
result_union = rng.difference(other)
tm.assert_index_equal(result_union, expected)
def test_sub_isub(self):
# previously performed setop, now raises TypeError (GH14164)
# TODO needs to wait on #13077 for decision on result type
rng = pd.period_range('1/1/2000', freq='D', periods=5)
other = pd.period_range('1/6/2000', freq='D', periods=5)
with tm.assertRaises(TypeError):
rng - other
with tm.assertRaises(TypeError):
rng -= other
# offset
# DateOffset
rng = pd.period_range('2014', '2024', freq='A')
result = rng - pd.offsets.YearEnd(5)
expected = pd.period_range('2009', '2019', freq='A')
tm.assert_index_equal(result, expected)
rng -= pd.offsets.YearEnd(5)
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(365, 'D'),
timedelta(365)]:
rng = pd.period_range('2014', '2024', freq='A')
msg = ('Input has different freq(=.+)? '
'from PeriodIndex\\(freq=A-DEC\\)')
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng - o
rng = pd.period_range('2014-01', '2016-12', freq='M')
result = rng - pd.offsets.MonthEnd(5)
expected = pd.period_range('2013-08', '2016-07', freq='M')
tm.assert_index_equal(result, expected)
rng -= pd.offsets.MonthEnd(5)
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(365, 'D'),
timedelta(365)]:
rng = pd.period_range('2014-01', '2016-12', freq='M')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=M\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng - o
# Tick
offsets = [pd.offsets.Day(3), timedelta(days=3),
np.timedelta64(3, 'D'), pd.offsets.Hour(72),
timedelta(minutes=60 * 24 * 3), np.timedelta64(72, 'h')]
for delta in offsets:
rng = pd.period_range('2014-05-01', '2014-05-15', freq='D')
result = rng - delta
expected = pd.period_range('2014-04-28', '2014-05-12', freq='D')
tm.assert_index_equal(result, expected)
rng -= delta
tm.assert_index_equal(rng, expected)
for o in [pd.offsets.YearBegin(2), pd.offsets.MonthBegin(1),
pd.offsets.Minute(), np.timedelta64(4, 'h'),
timedelta(hours=23)]:
rng = pd.period_range('2014-05-01', '2014-05-15', freq='D')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=D\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng - o
offsets = [pd.offsets.Hour(2), timedelta(hours=2),
np.timedelta64(2, 'h'), pd.offsets.Minute(120),
timedelta(minutes=120), np.timedelta64(120, 'm')]
for delta in offsets:
rng = pd.period_range('2014-01-01 10:00', '2014-01-05 10:00',
freq='H')
result = rng - delta
expected = pd.period_range('2014-01-01 08:00', '2014-01-05 08:00',
freq='H')
tm.assert_index_equal(result, expected)
rng -= delta
tm.assert_index_equal(rng, expected)
for delta in [pd.offsets.YearBegin(2), timedelta(minutes=30),
np.timedelta64(30, 's')]:
rng = pd.period_range('2014-01-01 10:00', '2014-01-05 10:00',
freq='H')
msg = 'Input has different freq(=.+)? from PeriodIndex\\(freq=H\\)'
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
result = rng + delta
with tm.assertRaisesRegexp(period.IncompatibleFrequency, msg):
rng += delta
# int
rng = pd.period_range('2000-01-01 09:00', freq='H', periods=10)
result = rng - 1
expected = pd.period_range('2000-01-01 08:00', freq='H', periods=10)
tm.assert_index_equal(result, expected)
rng -= 1
tm.assert_index_equal(rng, expected)
def test_comp_nat(self):
left = pd.PeriodIndex([pd.Period('2011-01-01'), pd.NaT,
pd.Period('2011-01-03')])
right = pd.PeriodIndex([pd.NaT, pd.NaT, pd.Period('2011-01-03')])
for l, r in [(left, right), (left.asobject, right.asobject)]:
result = l == r
expected = np.array([False, False, True])
tm.assert_numpy_array_equal(result, expected)
result = l != r
expected = np.array([True, True, False])
tm.assert_numpy_array_equal(result, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l == pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT == r, expected)
expected = np.array([True, True, True])
tm.assert_numpy_array_equal(l != pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT != l, expected)
expected = np.array([False, False, False])
tm.assert_numpy_array_equal(l < pd.NaT, expected)
tm.assert_numpy_array_equal(pd.NaT > l, expected)
def test_value_counts_unique(self):
# GH 7735
idx = pd.period_range('2011-01-01 09:00', freq='H', periods=10)
# create repeated values, 'n'th element is repeated by n+1 times
idx = PeriodIndex(np.repeat(idx.values, range(1, len(idx) + 1)),
freq='H')
exp_idx = PeriodIndex(['2011-01-01 18:00', '2011-01-01 17:00',
'2011-01-01 16:00', '2011-01-01 15:00',
'2011-01-01 14:00', '2011-01-01 13:00',
'2011-01-01 12:00', '2011-01-01 11:00',
'2011-01-01 10:00',
'2011-01-01 09:00'], freq='H')
expected = Series(range(10, 0, -1), index=exp_idx, dtype='int64')
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
expected = pd.period_range('2011-01-01 09:00', freq='H',
periods=10)
tm.assert_index_equal(idx.unique(), expected)
idx = PeriodIndex(['2013-01-01 09:00', '2013-01-01 09:00',
'2013-01-01 09:00', '2013-01-01 08:00',
'2013-01-01 08:00', pd.NaT], freq='H')
exp_idx = PeriodIndex(['2013-01-01 09:00', '2013-01-01 08:00'],
freq='H')
expected = Series([3, 2], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(), expected)
exp_idx = PeriodIndex(['2013-01-01 09:00', '2013-01-01 08:00',
pd.NaT], freq='H')
expected = Series([3, 2, 1], index=exp_idx)
for obj in [idx, Series(idx)]:
tm.assert_series_equal(obj.value_counts(dropna=False), expected)
tm.assert_index_equal(idx.unique(), exp_idx)
def test_drop_duplicates_metadata(self):
# GH 10115
idx = pd.period_range('2011-01-01', '2011-01-31', freq='D', name='idx')
result = idx.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertEqual(idx.freq, result.freq)
idx_dup = idx.append(idx) # freq will not be reset
result = idx_dup.drop_duplicates()
self.assert_index_equal(idx, result)
self.assertEqual(idx.freq, result.freq)
def test_drop_duplicates(self):
# to check Index/Series compat
base = pd.period_range('2011-01-01', '2011-01-31', freq='D',
name='idx')
idx = base.append(base[:5])
res = idx.drop_duplicates()
tm.assert_index_equal(res, base)
res = Series(idx).drop_duplicates()
tm.assert_series_equal(res, Series(base))
res = idx.drop_duplicates(keep='last')
exp = base[5:].append(base[:5])
tm.assert_index_equal(res, exp)
res = Series(idx).drop_duplicates(keep='last')
tm.assert_series_equal(res, Series(exp, index=np.arange(5, 36)))
res = idx.drop_duplicates(keep=False)
tm.assert_index_equal(res, base[5:])
res = Series(idx).drop_duplicates(keep=False)
tm.assert_series_equal(res, Series(base[5:], index=np.arange(5, 31)))
def test_order_compat(self):
def _check_freq(index, expected_index):
if isinstance(index, PeriodIndex):
self.assertEqual(index.freq, expected_index.freq)
pidx = PeriodIndex(['2011', '2012', '2013'], name='pidx', freq='A')
# for compatibility check
iidx = Index([2011, 2012, 2013], name='idx')
for idx in [pidx, iidx]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, idx)
_check_freq(ordered, idx)
ordered = idx.sort_values(ascending=False)
self.assert_index_equal(ordered, idx[::-1])
_check_freq(ordered, idx[::-1])
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, idx)
self.assert_numpy_array_equal(indexer,
np.array([0, 1, 2]),
check_dtype=False)
_check_freq(ordered, idx)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, idx[::-1])
self.assert_numpy_array_equal(indexer,
np.array([2, 1, 0]),
check_dtype=False)
_check_freq(ordered, idx[::-1])
pidx = PeriodIndex(['2011', '2013', '2015', '2012',
'2011'], name='pidx', freq='A')
pexpected = PeriodIndex(
['2011', '2011', '2012', '2013', '2015'], name='pidx', freq='A')
# for compatibility check
iidx = Index([2011, 2013, 2015, 2012, 2011], name='idx')
iexpected = Index([2011, 2011, 2012, 2013, 2015], name='idx')
for idx, expected in [(pidx, pexpected), (iidx, iexpected)]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, expected)
_check_freq(ordered, idx)
ordered = idx.sort_values(ascending=False)
self.assert_index_equal(ordered, expected[::-1])
_check_freq(ordered, idx)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, expected)
exp = np.array([0, 4, 3, 1, 2])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
_check_freq(ordered, idx)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, expected[::-1])
exp = np.array([2, 1, 3, 4, 0])
self.assert_numpy_array_equal(indexer, exp,
check_dtype=False)
_check_freq(ordered, idx)
pidx = PeriodIndex(['2011', '2013', 'NaT', '2011'], name='pidx',
freq='D')
result = pidx.sort_values()
expected = PeriodIndex(['NaT', '2011', '2011', '2013'],
name='pidx', freq='D')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, 'D')
result = pidx.sort_values(ascending=False)
expected = PeriodIndex(
['2013', '2011', '2011', 'NaT'], name='pidx', freq='D')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, 'D')
def test_order(self):
for freq in ['D', '2D', '4D']:
idx = PeriodIndex(['2011-01-01', '2011-01-02', '2011-01-03'],
freq=freq, name='idx')
ordered = idx.sort_values()
self.assert_index_equal(ordered, idx)
self.assertEqual(ordered.freq, idx.freq)
ordered = idx.sort_values(ascending=False)
expected = idx[::-1]
self.assert_index_equal(ordered, expected)
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq, freq)
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, idx)
self.assert_numpy_array_equal(indexer,
np.array([0, 1, 2]),
check_dtype=False)
self.assertEqual(ordered.freq, idx.freq)
self.assertEqual(ordered.freq, freq)
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
expected = idx[::-1]
self.assert_index_equal(ordered, expected)
self.assert_numpy_array_equal(indexer,
np.array([2, 1, 0]),
check_dtype=False)
self.assertEqual(ordered.freq, expected.freq)
self.assertEqual(ordered.freq, freq)
idx1 = PeriodIndex(['2011-01-01', '2011-01-03', '2011-01-05',
'2011-01-02', '2011-01-01'], freq='D', name='idx1')
exp1 = PeriodIndex(['2011-01-01', '2011-01-01', '2011-01-02',
'2011-01-03', '2011-01-05'], freq='D', name='idx1')
idx2 = PeriodIndex(['2011-01-01', '2011-01-03', '2011-01-05',
'2011-01-02', '2011-01-01'],
freq='D', name='idx2')
exp2 = PeriodIndex(['2011-01-01', '2011-01-01', '2011-01-02',
'2011-01-03', '2011-01-05'],
freq='D', name='idx2')
idx3 = PeriodIndex([pd.NaT, '2011-01-03', '2011-01-05',
'2011-01-02', pd.NaT], freq='D', name='idx3')
exp3 = PeriodIndex([pd.NaT, pd.NaT, '2011-01-02', '2011-01-03',
'2011-01-05'], freq='D', name='idx3')
for idx, expected in [(idx1, exp1), (idx2, exp2), (idx3, exp3)]:
ordered = idx.sort_values()
self.assert_index_equal(ordered, expected)
self.assertEqual(ordered.freq, 'D')
ordered = idx.sort_values(ascending=False)
self.assert_index_equal(ordered, expected[::-1])
self.assertEqual(ordered.freq, 'D')
ordered, indexer = idx.sort_values(return_indexer=True)
self.assert_index_equal(ordered, expected)
exp = np.array([0, 4, 3, 1, 2])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertEqual(ordered.freq, 'D')
ordered, indexer = idx.sort_values(return_indexer=True,
ascending=False)
self.assert_index_equal(ordered, expected[::-1])
exp = np.array([2, 1, 3, 4, 0])
self.assert_numpy_array_equal(indexer, exp, check_dtype=False)
self.assertEqual(ordered.freq, 'D')
def test_getitem(self):
idx1 = pd.period_range('2011-01-01', '2011-01-31', freq='D',
name='idx')
for idx in [idx1]:
result = idx[0]
self.assertEqual(result, pd.Period('2011-01-01', freq='D'))
result = idx[-1]
self.assertEqual(result, pd.Period('2011-01-31', freq='D'))
result = idx[0:5]
expected = pd.period_range('2011-01-01', '2011-01-05', freq='D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx[0:10:2]
expected = pd.PeriodIndex(['2011-01-01', '2011-01-03',
'2011-01-05',
'2011-01-07', '2011-01-09'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx[-20:-5:3]
expected = pd.PeriodIndex(['2011-01-12', '2011-01-15',
'2011-01-18',
'2011-01-21', '2011-01-24'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx[4::-1]
expected = PeriodIndex(['2011-01-05', '2011-01-04', '2011-01-03',
'2011-01-02', '2011-01-01'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
def test_take(self):
# GH 10295
idx1 = pd.period_range('2011-01-01', '2011-01-31', freq='D',
name='idx')
for idx in [idx1]:
result = idx.take([0])
self.assertEqual(result, pd.Period('2011-01-01', freq='D'))
result = idx.take([5])
self.assertEqual(result, pd.Period('2011-01-06', freq='D'))
result = idx.take([0, 1, 2])
expected = pd.period_range('2011-01-01', '2011-01-03', freq='D',
name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, 'D')
self.assertEqual(result.freq, expected.freq)
result = idx.take([0, 2, 4])
expected = pd.PeriodIndex(['2011-01-01', '2011-01-03',
'2011-01-05'], freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx.take([7, 4, 1])
expected = pd.PeriodIndex(['2011-01-08', '2011-01-05',
'2011-01-02'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx.take([3, 2, 5])
expected = PeriodIndex(['2011-01-04', '2011-01-03', '2011-01-06'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
result = idx.take([-3, 2, 5])
expected = PeriodIndex(['2011-01-29', '2011-01-03', '2011-01-06'],
freq='D', name='idx')
self.assert_index_equal(result, expected)
self.assertEqual(result.freq, expected.freq)
self.assertEqual(result.freq, 'D')
def test_nat_new(self):
idx = pd.period_range('2011-01', freq='M', periods=5, name='x')
result = idx._nat_new()
exp = pd.PeriodIndex([pd.NaT] * 5, freq='M', name='x')
tm.assert_index_equal(result, exp)
result = idx._nat_new(box=False)
exp = np.array([tslib.iNaT] * 5, dtype=np.int64)
tm.assert_numpy_array_equal(result, exp)
def test_shift(self):
# GH 9903
idx = pd.PeriodIndex([], name='xxx', freq='H')
with tm.assertRaises(TypeError):
# period shift doesn't accept freq
idx.shift(1, freq='H')
tm.assert_index_equal(idx.shift(0), idx)
tm.assert_index_equal(idx.shift(3), idx)
idx = pd.PeriodIndex(['2011-01-01 10:00', '2011-01-01 11:00'
'2011-01-01 12:00'], name='xxx', freq='H')
tm.assert_index_equal(idx.shift(0), idx)
exp = pd.PeriodIndex(['2011-01-01 13:00', '2011-01-01 14:00'
'2011-01-01 15:00'], name='xxx', freq='H')
tm.assert_index_equal(idx.shift(3), exp)
exp = pd.PeriodIndex(['2011-01-01 07:00', '2011-01-01 08:00'
'2011-01-01 09:00'], name='xxx', freq='H')
tm.assert_index_equal(idx.shift(-3), exp)
def test_repeat(self):
index = pd.period_range('2001-01-01', periods=2, freq='D')
exp = pd.PeriodIndex(['2001-01-01', '2001-01-01',
'2001-01-02', '2001-01-02'], freq='D')
for res in [index.repeat(2), np.repeat(index, 2)]:
tm.assert_index_equal(res, exp)
index = pd.period_range('2001-01-01', periods=2, freq='2D')
exp = pd.PeriodIndex(['2001-01-01', '2001-01-01',
'2001-01-03', '2001-01-03'], freq='2D')
for res in [index.repeat(2), np.repeat(index, 2)]:
tm.assert_index_equal(res, exp)
index = pd.PeriodIndex(['2001-01', 'NaT', '2003-01'], freq='M')
exp = pd.PeriodIndex(['2001-01', '2001-01', '2001-01',
'NaT', 'NaT', 'NaT',
'2003-01', '2003-01', '2003-01'], freq='M')
for res in [index.repeat(3), np.repeat(index, 3)]:
tm.assert_index_equal(res, exp)
def test_nat(self):
self.assertIs(pd.PeriodIndex._na_value, pd.NaT)
self.assertIs(pd.PeriodIndex([], freq='M')._na_value, pd.NaT)
idx = pd.PeriodIndex(['2011-01-01', '2011-01-02'], freq='D')
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, False]))
self.assertFalse(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
np.array([], dtype=np.intp))
idx = pd.PeriodIndex(['2011-01-01', 'NaT'], freq='D')
self.assertTrue(idx._can_hold_na)
tm.assert_numpy_array_equal(idx._isnan, np.array([False, True]))
self.assertTrue(idx.hasnans)
tm.assert_numpy_array_equal(idx._nan_idxs,
| np.array([1], dtype=np.intp) | numpy.array |
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from scipy import optimize
import pint
import math
u = pint.UnitRegistry()
# Constants
n_crew = 4
n_passengers = 50
n_people = n_passengers + n_crew
weight_per_passenger = 100 * u.kg
Swet_Sref = 6
AR = 8
K_ld = 15.5
Rcr = 2000 * u.km
Eltr = 45 * u.minutes
Rdiv = 370 * u.km
# Speed of sound = 589 knots at 35,000 feet
Vcr = 589 * 0.75 * u.knots
# Roskam, page 57 for inefficiencies of c_j
# cj_cr = 0.5 * u.lb / u.lb / u.hr
# cj_ltr = 0.6 * u.lb / u.lb / u.hr
# cj_diversion = 0.9 * u.lb / u.lb / u.hr
g = 9.81 * u.m / (u.s ** 2)
cj_cr = (19.8 * u.milligram / u.newton / u.s) * g
# TODO: Look into better methods for this
cj_ltr = 1.2 * cj_cr
cj_diversion = 1.8 * cj_cr
# Calculate fuel fractions
f_W_to = 0.99 * 0.99 * 0.995
f_W_climb = 0.98
f_W_descent = 0.99
f_W_shutdown = 0.992
# Range equation fractions (x2)
LDmax = 20.67
# Actual calculations now
W_PL = n_people * weight_per_passenger
# Weight fractions...
# Cruise
f_W_cr = 1/math.exp(Rcr / ((Vcr/cj_cr) * (LDmax * 0.867)))
# Loiter
f_W_ltr = 1/math.exp(Eltr / ((1/cj_ltr) * (LDmax)))
# Diversion cruise
f_W_div = 1/math.exp(Rdiv / ((275 * u.knot/cj_diversion) * (LDmax)))
# No penalty for diversion climb/land - only to about 10,000 ft
W = | np.array([1, f_W_to, f_W_climb, f_W_cr, f_W_descent, 1, f_W_div, 1, f_W_ltr, f_W_shutdown]) | numpy.array |
import torch
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
import torch.backends.cudnn as cudnn
import torchvision
import torchvision.transforms as transforms
import os
import argparse
import numpy as np
import itertools
from models import *
from db_quant_utils import rel_index
parser = argparse.ArgumentParser(description='PyTorch CIFAR10 Training')
parser.add_argument('--k', default=64, type=int, help='depth of model')
parser.add_argument('--noise_rate', default=0.2, type=float, help='label noise')
parser.add_argument('--asym', action='store_true')
parser.add_argument('--resolution', default=500, type=float, help='resolution for plot')
parser.add_argument('--range_l', default=0.5, type=float, help='how far `left` to go in the plot')
parser.add_argument('--range_r', default=0.5, type=float, help='how far `right` to go in the plot')
parser.add_argument('--plot_method', default='train', type=str)
parser.add_argument('--mixup', action='store_true')
parser.add_argument('--active_log', action='store_true')
parser.add_argument('--num_samples', default=100 , type=int)
parser.add_argument('--set_seed', default=1 , type=int)
parser.add_argument('--set_data_seed', default=1 , type=int)
args = parser.parse_args()
device = 'cuda' if torch.cuda.is_available() else 'cpu'
print(device)
args.eval = True
if args.mixup:
args.model_path = './checkpoint/mixup'
else:
args.model_path = f'./checkpoint/{args.set_seed}/{args.set_data_seed}'
if args.active_log:
import wandb
if not args.mixup:
wandb.init(project="dd_fragmentation", name = f'frag_{args.noise_rate}noise_{args.k}k_{args.set_seed}')
else:
wandb.init(project="dd_fragmentation", name = f'frag_{args.noise_rate}noise_{args.k}k__{args.set_seed}_wmixup')
wandb.config.update(args)
transform_train = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),
])
transform_test = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),
])
torch.manual_seed(args.set_data_seed)
from data_noisy import cifar10Nosiy
trainset_noisy = cifar10Nosiy(root='./data', train=True,transform=transform_train, download=True,
asym=args.asym,
nosiy_rate=0.2)
if args.noise_rate > 0:
from data_noisy import cifar10Nosiy
trainset = cifar10Nosiy(root='./data', train=True,transform=transform_train, download=True,
asym=args.asym,
nosiy_rate=args.noise_rate)
else:
trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform_train)
trainloader = torch.utils.data.DataLoader(
trainset, batch_size=128, shuffle=True, num_workers=2)
testset = torchvision.datasets.CIFAR10(
root='./data', train=False, download=True, transform=transform_test)
testloader = torch.utils.data.DataLoader(
testset, batch_size=100, shuffle=False, num_workers=2)
l_mis = np.where(np.array(trainset_noisy.targets) != np.array(trainset_noisy.true_targets))[0] #mislabeled images in noisy case
l_corr = np.where(np.array(trainset_noisy.targets) == np.array(trainset_noisy.true_targets))[0] #correctly labeled images in noisy case
l_all = np.arange(len(trainset.targets))
l_test = np.arange(len(testset.targets))
from db.data import make_planeloader
from db.evaluation import decision_boundary
from db.utils import connected_components
def num_connected_components(dlist1,dlist2, loader1,loader2, num_samples,net,device,args):
cc_list = []
for i in range(num_samples):
# import ipdb; ipdb.set_trace()
dirlist = | np.random.choice(dlist1, 2) | numpy.random.choice |
import numpy as np
from astropy.io import fits
import os
import re
import glob
import copy
from vorbin.voronoi_2d_binning import voronoi_2d_binning
import matplotlib.pyplot as plt
from scipy import interpolate, stats, optimize
import gc
from matplotlib import gridspec, animation
try:
import tqdm
except:
tqdm = None
from joblib import Parallel, delayed
plt.style.use('dark_background')
def read_muse_ifu(fits_file,z=0):
"""
Read in a MUSE-formatted IFU cube
:param fits_file: str
File path to the FITS IFU cube
:param z: float, optional
The redshift of the spectrum, since MUSE cubes often do not provide this information
:return nx: int
x-dimension (horizontal axis) of the cube
:return ny: int
y-dimension (vertical axis) of the cube
:return nz: int
z-dimension (wavelength axis) of the cube
:return ra: float
Right ascension
:return dec: float
Declination
:return museid: str
The MUSE ID of the observation
:return wave: array
1-D Wavelength array with dimension (nz,)
:return flux: array
3-D flux array with dimensions (nz, ny, nx)
:return ivar: array
3-D inverse variance array with dimensions (nz, ny, nx)
:return specres: array
1-D spectral resolution ("R") array with dimension (nz,)
:return mask: array
3-D mask array with dimensions (nz, ny, nx)
:return object_name: str
The name of the object, if provided in the FITS header
"""
# Load the file
# https://www.eso.org/rm/api/v1/public/releaseDescriptions/78
with fits.open(fits_file) as hdu:
# First axis is wavelength, then 2nd and 3rd are image x/y
try:
nx, ny, nz = hdu[1].header['NAXIS1'], hdu[1].header['NAXIS2'], hdu[1].header['NAXIS3']
ra = hdu[0].header['RA']
dec = hdu[0].header['DEC']
except:
# ra = hdu[0].header['ESO ADA GUID RA']
# dec = hdu[0].header['ESO ADA GUID DEC']
nx, ny, nz = hdu[0].header['NAXIS1'], hdu[0].header['NAXIS2'], hdu[0].header['NAXIS3']
ra = hdu[0].header['CRVAL1']
dec = hdu[0].header['CRVAL2']
primary = hdu[0].header
try:
object_name = primary['OBJECT']
except:
object_name = None
i = 1
museid = []
while True:
try:
museid.append(primary['OBID'+str(i)])
i += 1
except:
break
# Get unit of flux, assuming 10^-x erg/s/cm2/Angstrom/spaxel
# unit = hdu[0].header['BUNIT']
# power = int(re.search('10\*\*(\(?)(.+?)(\))?\s', unit).group(2))
# scale = 10**(-17) / 10**power
try:
# 3d rectified cube in units of 10(-20) erg/s/cm2/Angstrom/spaxel [NX x NY x NWAVE], convert to 10(-17)
flux = hdu[1].data
# Variance (sigma2) for the above [NX x NY x NWAVE], convert to 10(-17)
var = hdu[2].data
# Wavelength vector must be reconstructed, convert from nm to angstroms
header = hdu[1].header
wave = np.array(header['CRVAL3'] + header['CD3_3']*np.arange(header['NAXIS3']))
# wave = np.linspace(primary['WAVELMIN'], primary['WAVELMAX'], nz) * 10
# Median spectral resolution at (wavelmin + wavelmax)/2
# dlambda = cwave / primary['SPEC_RES']
# specres = wave / dlambda
# Default behavior for MUSE data cubes using https://www.aanda.org/articles/aa/pdf/2017/12/aa30833-17.pdf equation 7
dlambda = 5.835e-8 * wave**2 - 9.080e-4 * wave + 5.983
specres = wave / dlambda
# Scale by the measured spec_res at the central wavelength
spec_cent = primary['SPEC_RES']
cwave = np.nanmedian(wave)
c_dlambda = 5.835e-8 * cwave**2 - 9.080e-4 * cwave + 5.983
scale = 1 + (spec_cent - cwave/c_dlambda) / spec_cent
specres *= scale
except:
flux = hdu[0].data
var = (0.1 * flux)**2
wave = np.arange(primary['CRVAL3'], primary['CRVAL3']+primary['CDELT3']*(nz-1), primary['CDELT3'])
# specres = wave / 2.6
dlambda = 5.835e-8 * wave**2 - 9.080e-4 * wave + 5.983
specres = wave / dlambda
ivar = 1/var
mask = np.zeros_like(flux)
return nx,ny,nz,ra,dec,museid,wave,flux,ivar,specres,mask,object_name
def read_manga_ifu(fits_file,z=0):
"""
Read in a MANGA-formatted IFU cube
:param fits_file: str
File path to the FITS IFU cube
:param z: float, optional
The redshift of the spectrum, this is unused.
:return nx: int
x-dimension (horizontal axis) of the cube
:return ny: int
y-dimension (vertical axis) of the cube
:return nz: int
z-dimension (wavelength axis) of the cube
:return ra: float
Right ascension
:return dec: float
Declination
:return mangaid: str
The MANGA ID of the observation
:return wave: array
1-D Wavelength array with dimension (nz,)
:return flux: array
3-D flux array with dimensions (nz, ny, nx)
:return ivar: array
3-D inverse variance array with dimensions (nz, ny, nx)
:return specres: array
1-D spectral resolution ("R") array with dimension (nz,)
:return mask: array
3-D mask array with dimensions (nz, ny, nx)
:return None:
To mirror the output length of read_muse_ifu
"""
# Load the file
# https://data.sdss.org/datamodel/files/MANGA_SPECTRO_REDUX/DRPVER/PLATE4/stack/manga-CUBE.html#hdu1
with fits.open(fits_file) as hdu:
# First axis is wavelength, then 2nd and 3rd are image x/y
nx, ny, nz = hdu[1].header['NAXIS1'], hdu[1].header['NAXIS2'], hdu[1].header['NAXIS3']
try:
ra = hdu[0].header['OBJRA']
dec = hdu[0].header['OBJDEC']
except:
ra = hdu[1].header['IFURA']
dec = hdu[1].header['IFUDEC']
primary = hdu[0].header
ebv = primary['EBVGAL']
mangaid = primary['MANGAID']
# 3d rectified cube in units of 10(-17) erg/s/cm2/Angstrom/spaxel [NX x NY x NWAVE]
flux = hdu[1].data
# Inverse variance (1/sigma2) for the above [NX x NY x NWAVE]
ivar = hdu[2].data
# Pixel mask [NX x NY x NWAVE]. Defined values are set in sdssMaskbits.par
mask = hdu[3].data
# Wavelength vector [NWAVE]
wave = hdu[6].data
# Median spectral resolution as a function of wavelength for the fibers in this IFU [NWAVE]
specres = hdu[7].data
# ebv = hdu[0].header['EBVGAL']
return nx,ny,nz,ra,dec,mangaid,wave,flux,ivar,specres,mask,None
def prepare_ifu(fits_file,z,format,aperture=None,voronoi_binning=True,fixed_binning=False,targetsn=None,cvt=True,voronoi_plot=True,quiet=True,wvt=False,
maxbins=800,snr_threshold=0.5,fixed_bin_size=10,use_and_mask=True,nx=None,ny=None,nz=None,ra=None,dec=None,dataid=None,wave=None,flux=None,ivar=None,
specres=None,mask=None,objname=None):
"""
Deconstruct an IFU cube into individual spaxel files for fitting with BADASS
:param fits_file: str
The file path to the IFU FITS file; if format == 'user', this field may be left as None, '', or any other filler value
:param z: float
The redshift of the spectrum
:param aperture: array, optional
The lower-left and upper-right corners of a square aperture, formatted as [y0, y1, x0, x1]
:param voronoi_binning: bool
Whether or not to bin spaxels using the voronoi method (grouping to read a certain SNR threshold). Default True.
Mutually exclusive with fixed_binning.
:param fixed_binning: bool
Whether or not to bin spaxels using a fixed size. Default False.
Mutually exclusive with voronoi_binning.
:param targetsn: float, optional
The target SNR to bin by, if using voronoi binning.
:param cvt: bool
Vorbin CVT option (see the vorbin package docs). Default True.
:param voronoi_plot: bool
Whether or not to plot the voronoi bin structure. Default True.
:param quiet: bool
Vorbin quiet option (see the vorbin package docs). Default True.
:param wvt: bool
Vorbin wvt option (see the vorbin package docs). Default False.
:param maxbins: int
If no target SNR is provided for voronoi binning, maxbins may be specified, which will automatically calculate
the target SNR required to reach the number of bins desired. Default 800.
:param snr_threshold: float
Minimum SNR threshold, below which spaxel data will be removed and not fit.
:param fixed_bin_size: int
If using fixed binning, this is the side length of the square bins, in units of spaxels.
:param use_and_mask: bool
Whether or not to save the and_mask data.
:param nx: int, optional
x-dimension of the cube, only required if format == 'user'
:param ny: int, optional
y-dimension of the cube, only required if format == 'user'
:param nz: int, optional
z-dimension of the cube, only required if format == 'user'
:param ra: float, optional
Right ascension of the cube, only required if format == 'user'
:param dec: float, optional
Declination of the cube, only required if format == 'user'
:param dataid: str, optional
ID of the cube, only required if format == 'user'
:param wave: array, optional
1-D wavelength array with shape (nz,), only required if format == 'user'
:param flux: array, optional
3-D flux array with shape (nz, ny, nx), only required if format == 'user'
:param ivar: array, optional
3-D inverse variance array with shape (nz, ny, nx), only required if format == 'user'
:param specres: array, optional
1-D spectral resolution ("R") array with shape (nz,), only required if format == 'user'
:param mask: array, optional
3-D mask array with shape (nz, ny, nx), only required if format == 'user'
:param objname: str, optional
The name of the object, only required if format == 'user'
:return wave: array
1-D wavelength array with shape (nz,)
:return flux: array
3-D masked flux array with shape (nz, ny, nx)
:return ivar: array
3-D masked inverse variance array with shape (nz, ny, nx)
:return mask: array
3-D mask array with shape (nz, ny, nx)
:return fwhm_res: array
1-D FWHM resolution array with shape (nz,)
:return binnum: array
Bin number array that specifies which spaxels are in each bin (see the vorbin docs)
:return npixels: array
Number of spaxels in each bin (see the vorbin docs)
:return xpixbin: array
The x positions of spaxels in each bin
:return ypixbin: array
The y positions of spaxels in each bin
:return z: float
The redshift
:return dataid: str
The data ID
:return objname: str
The object name
"""
assert format in ('manga', 'muse', 'user'), "format must be either 'manga' or 'muse'; no others currently supported!"
# Read the FITS file using the appropriate parsing function
# no more eval 🥲
if format == 'manga':
nx,ny,nz,ra,dec,dataid,wave,flux,ivar,specres,mask,objname = read_manga_ifu(fits_file,z)
elif format == 'muse':
nx,ny,nz,ra,dec,dataid,wave,flux,ivar,specres,mask,objname = read_muse_ifu(fits_file,z)
else:
# wave array shape = (nz,)
# flux, ivar array shape = (nz, ny, nx)
# specres can be a single value or an array of shape (nz,)
# VALIDATE THAT USER INPUTS ARE IN THE CORRECT FORMAT
for value in (nx, ny, nz, ra, dec, wave, flux, specres):
assert value is not None, "For user spec, all of (nx, ny, nz, ra, dec, wave, flux, specres) must be specified!"
if ivar is None:
print("WARNING: No ivar was input. Defaulting to sqrt(flux).")
ivar = np.sqrt(flux)
if mask is None:
mask = np.zeros(flux.shape, dtype=int)
assert wave.shape == (nz,), "Wave array shape should be (nz,)"
assert flux.shape == (nz, ny, nx), "Flux array shape should be (nz, ny, nx)"
assert ivar.shape == (nz, ny, nx), "Ivar array shape should be (nz, ny, nx)"
assert mask.shape == (nz, ny, nx), "Mask array shape should be (nz, ny, nx)"
assert (type(specres) in (int, float, np.int_, np.float_)) or (specres.shape == (nz,)), "Specres should be a float or an array of shape (nz,)"
loglam = np.log10(wave)
# FWHM Resolution in angstroms:
fwhm_res = wave / specres # dlambda = lambda / R; R = lambda / dlambda
if not use_and_mask:
mask = np.zeros(flux.shape, dtype=int)
# Converting to wdisp -- so that 2.355*wdisp*dlam_gal = fwhm_res
# if format == 'manga':
# c = 299792.458 # speed of light in km/s
# frac = wave[1]/wave[0] # Constant lambda fraction per pixel
# dlam_gal = (frac-1)*wave # Size of every pixel in Angstrom
# vdisp = c / (2.355*specres) # delta v = c / R in km/s
# velscale = np.log(frac) * c # Constant velocity scale in km/s per pixel
# wdisp = vdisp / velscale # Intrinsic dispersion of every pixel, in pixels units
minx, maxx = 0, nx
miny, maxy = 0, ny
if aperture:
miny, maxy, minx, maxx = aperture
maxy += 1
maxx += 1
x = np.arange(minx, maxx, 1)
y = np.arange(miny, maxy, 1)
# Create x/y grid for the voronoi binning
X, Y = np.meshgrid(x, y)
_x, _y = X.ravel(), Y.ravel()
if voronoi_binning:
# Average along the wavelength axis so each spaxel has one s/n value
# Note to self: Y AXIS IS ALWAYS FIRST ON NUMPY ARRAYS
signal = np.nanmean(flux[:, miny:maxy, minx:maxx], axis=0)
noise = np.sqrt(1 / np.nanmean(ivar[:, miny:maxy, minx:maxx], axis=0))
sr = signal.ravel()
nr = noise.ravel()
good = np.where(np.isfinite(sr) & np.isfinite(nr) & (sr > 0) & (nr > 0))[0]
# Target S/N ratio to bin for. If none, defaults to value such that the highest pixel isnt binned
# In general this isn't a great choice. Should want to maximize resolution without sacrificing too much
# computation time.
if not targetsn:
# binnum = np.array([maxbins+1])
targetsn0 = np.max([np.sort((sr / nr)[good], kind='quicksort')[-1] / 16, 10])
def objective(targetsn, return_data=False):
vplot = voronoi_plot if return_data else False
qt = quiet if return_data else True
try:
binnum, xbin, ybin, xbar, ybar, sn, npixels, scale = voronoi_2d_binning(_x[good], _y[good], sr[good], nr[good],
targetsn, cvt=cvt, pixelsize=1, plot=vplot,
quiet=qt, wvt=wvt)
except ValueError:
return np.inf
if return_data:
return binnum, xbin, ybin, xbar, ybar, sn, npixels, scale
return (np.max(binnum)+1 - maxbins)**2
print(f'Performing S/N optimization to reach {maxbins} bins. This may take a while...')
soln = optimize.minimize(objective, [targetsn0], method='Nelder-Mead', bounds=[(1, X.size)])
targetsn = soln.x[0]
binnum, xbin, ybin, xbar, ybar, SNR, npixels, scale = objective(targetsn, return_data=True)
else:
binnum, xbin, ybin, xbar, ybar, SNR, npixels, scale = voronoi_2d_binning(_x[good], _y[good], sr[good], nr[good],
targetsn, cvt=cvt, pixelsize=1, plot=voronoi_plot,
quiet=quiet, wvt=wvt)
print(f'Voronoi binning successful with target S/N = {targetsn}! Created {np.max(binnum)+1} bins.')
if voronoi_plot:
# For some reason voronoi makes the plot but doesnt save it or anything
filename = os.path.join(os.path.dirname(fits_file), 'voronoi_binning.pdf')
plt.savefig(filename, bbox_inches='tight', dpi=300)
plt.close()
_x = _x[good]
_y = _y[good]
# Create output arrays for flux, ivar, mask
out_flux = np.zeros((flux.shape[0], np.nanmax(binnum)+1))
out_ivar = np.zeros((ivar.shape[0], np.nanmax(binnum)+1))
out_mask = np.zeros((mask.shape[0], np.nanmax(binnum)+1))
xpixbin = np.full(np.nanmax(binnum)+1, fill_value=np.nan, dtype=object)
ypixbin = np.full(np.nanmax(binnum)+1, fill_value=np.nan, dtype=object)
for j in range(xpixbin.size):
xpixbin[j] = []
ypixbin[j] = []
# Average flux/ivar in each bin
for i, bin in enumerate(binnum):
# there is probably a better way to do this, but I'm lazy
xi, yi = _x[i], _y[i]
out_flux[:, bin] += flux[:, yi, xi]
out_ivar[:, bin] += ivar[:, yi, xi]
out_mask[:, bin] += mask[:, yi, xi]
xpixbin[bin].append(xi)
ypixbin[bin].append(yi)
out_flux /= npixels
out_ivar /= npixels
irange = np.nanmax(binnum)+1
for bin in binnum:
if SNR[bin] < snr_threshold:
flux[:, np.asarray(ypixbin[bin]), np.asarray(xpixbin[bin])] = np.nan
ivar[:, np.asarray(ypixbin[bin]), np.asarray(xpixbin[bin])] = np.nan
mask[:, np.asarray(ypixbin[bin]), np.asarray(xpixbin[bin])] = 1
elif fixed_binning:
print(f'Performing binning with fixed bin size of {fixed_bin_size}')
# Create square bins of a fixed size
binnum = np.zeros((maxy-miny, maxx-minx), dtype=int)
wy = int(np.ceil((maxy-miny)/fixed_bin_size))
wx = int(np.ceil((maxx-minx)/fixed_bin_size))
indx = 0
nbins = wy*wx
out_flux = np.zeros((flux.shape[0], nbins))
out_ivar = np.zeros((ivar.shape[0], nbins))
out_mask = np.zeros((mask.shape[0], nbins))
xpixbin = np.full(nbins, fill_value=np.nan, dtype=object)
ypixbin = np.full(nbins, fill_value=np.nan, dtype=object)
npixels = np.zeros((nbins,), dtype=int)
SNR = np.zeros((nbins,))
for iy in range(wy):
for ix in range(wx):
# Relative axes indices
ylo = iy*fixed_bin_size
yhi = np.min([(iy+1)*fixed_bin_size, binnum.shape[0]])
xlo = ix*fixed_bin_size
xhi = np.min([(ix+1)*fixed_bin_size, binnum.shape[1]])
binnum[ylo:yhi, xlo:xhi] = indx
# Shift axes limits by the aperture
ylo += miny
yhi += miny
xlo += minx
xhi += minx
ybin, xbin = np.meshgrid(np.arange(ylo, yhi, 1), np.arange(xlo, xhi, 1))
ypixbin[indx] = ybin.flatten().tolist()
xpixbin[indx] = xbin.flatten().tolist()
out_flux[:, indx] = np.apply_over_axes(np.nanmean, flux[:, ylo:yhi, xlo:xhi], (1,2)).flatten()
out_ivar[:, indx] = np.apply_over_axes(np.nanmean, ivar[:, ylo:yhi, xlo:xhi], (1,2)).flatten()
out_mask[:, indx] = np.apply_over_axes(np.nansum, mask[:, ylo:yhi, xlo:xhi], (1,2)).flatten()
npixels[indx] = len(ybin)
signal = np.nanmean(flux[:, ylo:yhi, xlo:xhi], axis=0)
noise = np.sqrt(1/np.nanmean(ivar[:, ylo:yhi, xlo:xhi], axis=0))
SNR[indx] = np.nansum(signal) / np.sqrt(np.nansum(noise**2))
if SNR[indx] < snr_threshold:
flux[:, ylo:yhi, xlo:xhi] = np.nan
ivar[:, ylo:yhi, xlo:xhi] = np.nan
mask[:, ylo:yhi, xlo:xhi] = 1
indx += 1
binnum = binnum.flatten()
irange = nbins
print(f'Fixed binning successful, created {nbins} bins')
else:
xpixbin = None
ypixbin = None
out_flux = flux[:, miny:maxy, minx:maxx].reshape(nz, (maxx-minx)*(maxy-miny))
out_ivar = ivar[:, miny:maxy, minx:maxx].reshape(nz, (maxx-minx)*(maxy-miny))
out_mask = mask[:, miny:maxy, minx:maxx].reshape(nz, (maxx-minx)*(maxy-miny))
binnum = np.zeros((maxx-minx)*(maxy-miny))
npixels = np.ones((maxx-minx)*(maxy-miny)) * (maxx-minx)*(maxy-miny)
irange = (maxx-minx)*(maxy-miny)
signal = np.nanmean(flux, axis=0)
noise = np.sqrt(1 / np.nanmean(ivar, axis=0))
SNR = signal / noise
flux[:, SNR < snr_threshold] = np.nan
ivar[:, SNR < snr_threshold] = np.nan
mask[:, SNR < snr_threshold] = 1
for i in range(irange):
# Unpack the spaxel
galaxy_spaxel = out_flux[:,i] # observed flux
ivar_spaxel = out_ivar[:,i] # 1-sigma spectral noise
mask_spaxel = out_mask[:,i] # bad pixels
if voronoi_binning or fixed_binning:
xi = xpixbin[i] # x and y pixel position
yi = ypixbin[i]
snr_thresh = SNR[i] >= snr_threshold # make sure bin has an overall SNR greater than the threshold
else:
xi = [_x[i]]
yi = [_y[i]]
snr_thresh = SNR[_y[i], _x[i]] >= snr_threshold # make sure spaxel has an SNR greater than the threshold
binnum_i = 0 if (not voronoi_binning) and (not fixed_binning) else i # Voronoi bin index that this pixel belongs to
# Package into a FITS file -- but only if the SNR is high enough, otherwise throw out the data
if snr_thresh:
primaryhdu = fits.PrimaryHDU()
primaryhdu.header.append(("FORMAT", format.upper(), "Data format"), end=True)
if type(dataid) is list:
for j, did in enumerate(dataid):
primaryhdu.header.append((f'{format.upper()}ID{j}', did, f'{"MANGA" if format == "manga" else "MUSE"} ID number'), end=True)
else:
primaryhdu.header.append((f'{format.upper()}ID', dataid, f'{"MANGA" if format == "manga" else "MUSE"} ID number'), end=True)
primaryhdu.header.append(('OBJNAME', objname, 'Object Name'), end=True)
primaryhdu.header.append(('RA', ra, 'Right ascension'), end=True)
primaryhdu.header.append(('DEC', dec, 'Declination'), end=True)
primaryhdu.header.append(('BINNUM', binnum_i, 'bin index of the spaxel (Voronoi)'), end=True)
primaryhdu.header.append(('NX', nx, 'x dimension of the full MANGA cube'), end=True)
primaryhdu.header.append(('NY', ny, 'y dimension of the full MANGA cube'), end=True)
coadd = fits.BinTableHDU.from_columns(fits.ColDefs([
fits.Column(name='flux', array=galaxy_spaxel, format='D'),
fits.Column(name='loglam', array=loglam, format='D'),
fits.Column(name='ivar', array=ivar_spaxel, format='D'),
fits.Column(name='and_mask', array=mask_spaxel, format='D'),
fits.Column(name='fwhm_res', array=fwhm_res, format='D')
]))
specobj = fits.BinTableHDU.from_columns(fits.ColDefs([
fits.Column(name='z', array=np.array([z]), format='D'),
# fits.Column(name='ebv', array=np.array([ebv]), format='E')
]))
specobj.header.append(('PLUG_RA', ra, 'Right ascension'), end=True)
specobj.header.append(('PLUG_DEC', dec, 'Declination'), end=True)
binobj = fits.BinTableHDU.from_columns(fits.ColDefs([
fits.Column(name='spaxelx', array=np.array(xi), format='E'),
fits.Column(name='spaxely', array=np.array(yi), format='E')
]))
out_hdu = fits.HDUList([primaryhdu, coadd, specobj, binobj])
# Save output to sub-folder
if voronoi_binning or fixed_binning:
tag = '_'.join(['spaxel', 'bin', str(binnum_i)])
else:
tag = '_'.join(['spaxel', str(xi[0]), str(yi[0])])
outdir = os.path.join(os.path.dirname(fits_file), fits_file.split(os.sep)[-1].replace('.fits',''), tag)
if not os.path.exists(outdir):
os.makedirs(outdir)
outfile = os.path.join(outdir, tag+'.fits')
out_hdu.writeto(outfile, overwrite=True)
# else:
# for xx, yy in zip(xi, yi):
# flux[:, yy, xx] = np.nan
# ivar[:, yy, xx] = np.nan
# mask[:, yy, xx] = 1
return wave,flux,ivar,mask,fwhm_res,binnum,npixels,xpixbin,ypixbin,z,dataid,objname
def plot_ifu(fits_file,wave,flux,ivar,mask,binnum,npixels,xpixbin,ypixbin,z,dataid,aperture=None,object_name=None):
"""
Plot a binned IFU cube and aperture.
:param fits_file: str
The file path to the FITS IFU file.
:param wave: array
1-D wavelength array with shape (nz,)
:param flux: array
3-D masked flux array with shape (nz, ny, nx)
:param ivar: array
3-D masked inverse variance array with shape (nz, ny, nx)
:param mask: array
3-D mask array with shape (nz, ny, nx)
:param binnum: array
Bin number array that specifies which spaxels are in each bin (see the vorbin docs)
:param npixels: array
Number of spaxels in each bin (see the vorbin docs)
:param xpixbin: array
The x positions of spaxels in each bin
:param ypixbin: array
The y positions of spaxels in each bin
:param z: float
The redshift
:param dataid: str
The data ID
:param aperture: array
The lower-left and upper-right corners of a square aperture, formatted as [y0, y1, x0, x1]
:param objname: str
The object name
:return None:
"""
# fig = plt.figure(figsize=(14,4))
fig = plt.figure(figsize=(14, 10))
gs = gridspec.GridSpec(nrows=8, ncols=8)
ax1 = fig.add_subplot(gs[0:5, 0:4])
ax2 = fig.add_subplot(gs[0:5, 4:8])
ax3 = fig.add_subplot(gs[5:8, 0:8])
fig.subplots_adjust(wspace=0.1, hspace=0.5)
ny, nx = flux.shape[1:]
# breakpoint()
center = (nx / 2, ny / 2)
minx, maxx = 0, nx
miny, maxy = 0, ny
if aperture:
miny, maxy, minx, maxx = aperture
maxy += 1
maxx += 1
flux_sum = np.nansum(flux, axis=0)
# flux_sum[flux_sum==0] = np.nan
flux_avg = flux_sum / flux.shape[0]
noise_sum = np.nanmedian(np.sqrt(1/ivar), axis=0)
flux_max_unbinned = np.nanmax(flux, axis=0)
noise_max_unbinned = np.nanmax(np.sqrt(1/ivar), axis=0)
if np.any(binnum):
flux_bin = np.zeros(np.nanmax(binnum)+1)
noise_bin = np.zeros(np.nanmax(binnum)+1)
# flux_max = np.zeros(np.nanmax(binnum)+1)
# noise_max = np.zeros(np.nanmax(binnum)+1)
for bin in range(np.nanmax(binnum)+1):
_x = xpixbin[bin]
_y = ypixbin[bin]
for i in range(len(_x)):
flux_bin[bin] += flux_avg[_y[i], _x[i]]
noise_bin[bin] += noise_sum[_y[i], _x[i]]
# flux_max[bin] = np.nanmax([flux_max[bin], np.nanmax(flux[:, _y[i], _x[i]])])
# noise_max[bin] = np.nanmax([noise_max[bin], np.nanmax(np.sqrt(1/ivar)[:, _y[i], _x[i]])])
flux_bin /= npixels
noise_bin /= npixels
for bin in range(np.nanmax(binnum)+1):
_x = xpixbin[bin]
_y = ypixbin[bin]
for i in range(len(_x)):
flux_avg[_y[i], _x[i]] = flux_bin[bin]
noise_sum[_y[i], _x[i]] = noise_bin[bin]
# flux_max_unbinned[_y[i], _x[i]] = flux_max[bin]
# noise_max_unbinned[_y[i], _x[i]] = noise_max[bin]
# This is rapidly making me lose the will to live
base = 10
cbar_data = ax1.imshow(np.log(flux_avg*base+1)/np.log(base), origin='lower', cmap='cubehelix')
cbar_noise = ax2.imshow(np.log(noise_sum*base+1)/np.log(base), origin='lower', cmap='cubehelix')
cbar = plt.colorbar(cbar_data, ax=ax1, label=r'$\log_{10}{(f_{\lambda,max})}$ ($10^{-17}$ erg s$^{-1}$ cm$^{-2}$ spaxel$^{-1}$)')
cbar2 = plt.colorbar(cbar_noise, ax=ax2, label=r'$\log_{10}{(\Sigma\sigma)}$ ($10^{-17}$ erg s$^{-1}$ cm$^{-2}$ spaxel$^{-1}$)')
if aperture:
aper = plt.Rectangle((aperture[2]-.5, aperture[0]-.5), aperture[3]-aperture[2]+1, aperture[1]-aperture[0]+1, color='red',
fill=False, linewidth=2)
ax1.add_patch(aper)
aper = plt.Rectangle((aperture[2]-.5, aperture[0]-.5), aperture[3]-aperture[2]+1, aperture[1]-aperture[0]+1, color='red',
fill=False, linewidth=2)
ax2.add_patch(aper)
# Oh you're a python coder? Name every numpy function.
coadd = np.nansum(np.nansum(flux, axis=2), axis=1) / (flux.shape[1]*flux.shape[2])
coadd_noise = np.nansum(np.nansum(np.sqrt(1/ivar), axis=2), axis=1) / (ivar.shape[1]*ivar.shape[2])
fontsize = 14
ax3.plot(wave, coadd, linewidth=0.5, color='xkcd:bright aqua', label='Coadded Flux')
ax3.plot(wave, coadd_noise, linewidth=0.5, color='xkcd:bright orange', label='$1\sigma$ uncertainty')
ax3.axhline(0.0, color='white', linewidth=0.5, linestyle='--')
ax3.set_ylabel(r'$f_\lambda$ ($10^{-17}$ erg cm$^{-2}$ s$^{-1}$ $\mathrm{\AA}^{-1}$)', fontsize=fontsize)
# ax4.plot(wave, fwhm)
# ax4.set_ylabel(r'$\Delta\lambda = \lambda/R (\AA)$', fontsize=fontsize)
ax3.set_xlabel(r'$\lambda_{\rm{obs}}$ ($\mathrm{\AA}$)', fontsize=fontsize)
ax3.legend(loc='best')
fig.suptitle(f'OBJECT ID: {dataid}, z={z}' if object_name is None else
f'{object_name}, z={z}', fontsize=fontsize)
plt.tight_layout()
filepath = os.path.join(os.path.dirname(fits_file), 'fitting_aperture.pdf')
plt.savefig(filepath)
ax1.clear()
ax2.clear()
ax3.clear()
fig.clear()
plt.close(fig)
def reconstruct_ifu(fits_file,mcmc_label=None):
"""
Reconstruct an IFU cube using the fit MCMC data from BADASS
:param fits_file: str
The file path to the original IFU FITS file
:param mcmc_label: int, optional
The index of the MCMC_output_* files that should be used in the reconstruction. Defaults to the largest one found.
:return par_out: FITS HDUList
FITS-formatted HDUList mirroring the par_table format from BADASS, but arranged in the cube shape
Each HDU in the list corresponds to one parameter, mapped with a shape (ny, nx)
:return bmc_out: FITS HDUList
FITS-formatted HDUList mirroring the best_model_components format from BADASS, but arranged in the cube shape
Each HDU in the list corresponds to a model component, mapped with a shape (nz, ny, nx)
:return last_mcmc+1: int
The index of the output MCMC_output_* file for the overall cube (independent of the individual MCMC_output_* folders for each spaxel)
"""
# Make sure outputs exist
path = fits_file.replace('.fits', '') + os.sep
if not os.path.exists(path):
raise NotADirectoryError(f"The unpacked folders for {fits_file} do not exist! Fit before calling reconstruct")
subdirs = glob.glob(path + 'spaxel_*_*')
voronoi = subdirs[0].split('_')[1] == 'bin'
subdirs.sort()
if len(subdirs) == 0:
raise NotADirectoryError(f"The unpacked folders for {fits_file} do not exist! Fit before calling reconstruct")
# Get number of bins
if voronoi:
nbins = max([int(subdir.split('_')[-1]) for subdir in subdirs]) + 1
else:
nbins = len(subdirs)
xpixbin = np.full(nbins, fill_value=np.nan, dtype=object)
ypixbin = np.full(nbins, fill_value=np.nan, dtype=object)
i = 0
subdir = subdirs[0]
# Find each MCMC output
if mcmc_label is None:
most_recent_mcmc = glob.glob(subdir + os.sep + 'MCMC_output_*')
if len(most_recent_mcmc) == 0:
raise NotADirectoryError(f"The unpacked folders for {fits_file} do not exist! Fit before calling reconstruct")
most_recent_mcmc = sorted(most_recent_mcmc)[-1]
else:
most_recent_mcmc = glob.glob(subdir + os.sep + f"MCMC_output_{mcmc_label}")
if len(most_recent_mcmc) == 0:
raise NotADirectoryError(f"The unpacked folders for {fits_file}, MCMC_output{mcmc_label} do not exist! Fit before calling reconstruct")
most_recent_mcmc = most_recent_mcmc[0]
par_table = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', '*par_table.fits')))
best_model_components = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', '*best_model_components.fits')))
test_stats = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', 'test_stats.fits')))
if len(par_table) < 1 or len(best_model_components) < 1:
raise FileNotFoundError(
f"The FITS files for {most_recent_mcmc} do not exist! Fit before calling reconstruct")
par_table = par_table[0]
best_model_components = best_model_components[0]
# Load in the FITS files
with fits.open(par_table) as parhdu, fits.open(best_model_components) as bmchdu:
# Get the bin number and x/y coord(s)
hdr = parhdu[0].header
data1 = parhdu[1].data
data2 = parhdu[2].data
bdata = bmchdu[1].data
if len(test_stats) > 0:
test_stats = test_stats[0]
with fits.open(test_stats) as tshdu:
tdata = tshdu[1].data
else:
tdata = None
binnum = copy.deepcopy(hdr['binnum']) if voronoi else i
xpixbin[binnum] = copy.deepcopy(data2['spaxelx'])
ypixbin[binnum] = copy.deepcopy(data2['spaxely'])
# if it's the first iteration, create the arrays based on the proper shape
parameters = data1['parameter']
if tdata is not None:
parameters = np.concatenate((parameters, tdata['parameter']))
parvals = np.full(shape=(nbins,), fill_value=np.nan, dtype=[
(param, float) for param in np.unique(parameters)
])
parvals_low = copy.deepcopy(parvals)
parvals_upp = copy.deepcopy(parvals)
bmcparams = np.array(bdata.columns.names, dtype=str)
bmcvals = np.full(shape=(bdata.size, nbins), fill_value=np.nan, dtype=[
(param, float) for param in np.unique(bmcparams)
])
# Set the par table parameters
mcmc = 'sigma_low' in data1.names and 'sigma_upp' in data1.names
for param in parameters:
w = np.where(data1['parameter'] == param)[0]
if w.size > 0:
w = w[0]
parvals[param][binnum] = copy.deepcopy(data1['best_fit'][w])
if mcmc:
parvals_low[param][binnum] = copy.deepcopy(data1['sigma_low'][w])
parvals_upp[param][binnum] = copy.deepcopy(data1['sigma_upp'][w])
elif tdata is not None:
w2 = np.where(tdata['parameter'] == param)[0]
if w2.size > 0:
parvals[param][binnum] = copy.deepcopy(tdata['best_fit'][w2])
parvals_low[param][binnum] = copy.deepcopy(tdata['sigma_low'][w2])
parvals_upp[param][binnum] = copy.deepcopy(tdata['sigma_upp'][w2])
# Set the best model components
for param in bmcparams:
bmcvals[param][:, binnum] = copy.deepcopy(bdata[param])
parsize = data1.size
if tdata is not None:
parsize += tdata.size
bmcsize = bdata.size
def append_spaxel(i, subdir):
nonlocal parvals, parvals_low, parvals_upp, bmcvals, parameters, xpixbin, ypixbin, voronoi
# Find each MCMC output
if mcmc_label is None:
most_recent_mcmc = glob.glob(subdir + os.sep + 'MCMC_output_*')
if len(most_recent_mcmc) == 0:
# raise NotADirectoryError(
# f"The unpacked folders for {fits_file} do not exist! Fit before calling reconstruct")
print(f"WARNING: MCMC folder for {subdir} not found!")
return
most_recent_mcmc = sorted(most_recent_mcmc)[-1]
else:
most_recent_mcmc = glob.glob(subdir + os.sep + f"MCMC_output_{mcmc_label}")
if len(most_recent_mcmc) == 0:
print(f"WARNING: MCMC folder for {subdir} not found!")
return
most_recent_mcmc = most_recent_mcmc[0]
par_table = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', '*par_table.fits')))
best_model_components = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', '*best_model_components.fits')))
test_stats = sorted(glob.glob(os.path.join(most_recent_mcmc, 'log', 'test_stats.fits')))
if len(par_table) < 1 or len(best_model_components) < 1:
# raise FileNotFoundError(
# f"The FITS files for {most_recent_mcmc} do not exist! Fit before calling reconstruct")
print(f"WARNING: FITS files for {most_recent_mcmc} not found!")
return
par_table = par_table[0]
best_model_components = best_model_components[0]
# Load in the FITS files
with fits.open(par_table) as parhdu, fits.open(best_model_components) as bmchdu:
# Get the bin number and x/y coord(s)
hdr = parhdu[0].header
data1 = parhdu[1].data
data2 = parhdu[2].data
bdata = bmchdu[1].data
if len(test_stats) > 0:
test_stats = test_stats[0]
with fits.open(test_stats) as tshdu:
tdata = tshdu[1].data
else:
tdata = None
binnum = copy.deepcopy(hdr['binnum']) if voronoi else i
xpixbin[binnum] = copy.deepcopy(data2['spaxelx'])
ypixbin[binnum] = copy.deepcopy(data2['spaxely'])
# Set the par table parameters
mcmc = 'sigma_low' in data1.names and 'sigma_upp' in data1.names
for param in parameters:
w = np.where(data1['parameter'] == param)[0]
if w.size > 0:
w = w[0]
parvals[param][binnum] = copy.deepcopy(data1['best_fit'][w])
if mcmc:
parvals_low[param][binnum] = copy.deepcopy(data1['sigma_low'][w])
parvals_upp[param][binnum] = copy.deepcopy(data1['sigma_upp'][w])
elif tdata is not None:
w2 = np.where(tdata['parameter'] == param)[0]
if w2.size > 0:
parvals[param][binnum] = copy.deepcopy(tdata['best_fit'][w2])
parvals_low[param][binnum] = copy.deepcopy(tdata['sigma_low'][w2])
parvals_upp[param][binnum] = copy.deepcopy(tdata['sigma_upp'][w2])
# Set the best model components
for param in bmcparams:
bmcvals[param][:, binnum] = copy.deepcopy(bdata[param])
iterable = enumerate(subdirs) if tqdm is None else tqdm.tqdm(enumerate(subdirs), total=len(subdirs))
Parallel(n_jobs=-1, require='sharedmem')(delayed(append_spaxel)(i, subdir) for i, subdir in iterable)
for i in range(len(xpixbin)):
if type(xpixbin[i]) in (float, np.float_) and np.isnan(xpixbin[i]):
xpixbin[i] = []
if type(ypixbin[i]) in (float, np.float_) and np.isnan(ypixbin[i]):
ypixbin[i] = []
maxx = -np.inf
maxy = -np.inf
minx = np.inf
miny = np.inf
for j in range(nbins):
maxx = np.nanmax([maxx, np.nanmax(xpixbin[j]) if len(xpixbin[j]) > 0 else np.nan])
maxy = np.nanmax([maxy, np.nanmax(ypixbin[j]) if len(ypixbin[j]) > 0 else np.nan])
minx = np.nanmin([minx, np.nanmin(xpixbin[j]) if len(xpixbin[j]) > 0 else np.nan])
miny = np.nanmin([miny, np.nanmin(ypixbin[j]) if len(ypixbin[j]) > 0 else np.nan])
# Reconstruct original shape
nx = int(maxx - minx + 1)
ny = int(maxy - miny + 1)
bmcvals_out = np.full(shape=(bmcparams.size, bmcsize, ny, nx), fill_value=np.nan, dtype=float)
parvals_out = np.full(shape=(parsize, ny, nx), fill_value=np.nan, dtype=float)
parvals_out_low = copy.deepcopy(parvals_out)
parvals_out_upp = copy.deepcopy(parvals_out)
binpix = np.zeros((nx*ny, 3), dtype=int)
ii = 0
for n in range(nbins):
for xi, yi in zip(xpixbin[n], ypixbin[n]):
for j, param in enumerate(parameters):
parvals_out[j, int(yi-miny), int(xi-minx)] = parvals[param][n]
if mcmc:
parvals_out_low[j, int(yi-miny), int(xi-minx)] = parvals_low[param][n]
parvals_out_upp[j, int(yi-miny), int(xi-minx)] = parvals_upp[param][n]
binpix[ii, :] = (int(xi-minx), int(yi-miny), n)
ii += 1
for j, param in enumerate(bmcparams):
for xi, yi in zip(xpixbin[n], ypixbin[n]):
bmcvals_out[j, :, int(yi-miny), int(xi-minx)] = bmcvals[param][:, n]
# Construct FITS outputs
bmc_out = fits.HDUList()
primary = fits.PrimaryHDU()
primary.header.append(('ORIGINX', minx, 'x-coordinate of position (0,0) in full cube'), end=True)
primary.header.append(('ORIGINY', miny, 'y-coordinate of position (0,0) in full cube'), end=True)
primary.header.append(('NBINS', nbins, 'number of Voronoi bins'), end=True)
primary2 = copy.deepcopy(primary)
bininfo = fits.BinTableHDU.from_columns(fits.ColDefs([
fits.Column(name='x', array=binpix[:, 0], format='I'),
fits.Column(name='y', array=binpix[:, 1], format='I'),
fits.Column(name='bin', array=binpix[:, 2], format='I')
]))
bininfo2 = copy.deepcopy(bininfo)
bmc_out.append(primary)
for k, name in enumerate(bmcparams):
if name.upper() == 'WAVE':
# good = np.where(np.isfinite(bmcvals_out[k, ...]))
bmc_out.append(
fits.BinTableHDU.from_columns(fits.ColDefs([
fits.Column(name='wave', array=bmcvals_out[k, :, ny//2, nx//2], format='E'),
]), name=name))
else:
bmc_out.append(
fits.ImageHDU(bmcvals_out[k, ...], name=name)
)
bmc_out.append(bininfo)
par_out = fits.HDUList()
par_out.append(primary2)
for k, name in enumerate(parameters):
par_out.append(
fits.ImageHDU(parvals_out[k, ...], name=name)
)
if mcmc:
par_out.append(
fits.ImageHDU(parvals_out_low[k, ...], name=name + '_SIGMA_LOW')
)
par_out.append(
fits.ImageHDU(parvals_out_upp[k, ...], name=name + '_SIGMA_UPP')
)
par_out.append(bininfo2)
# Write outputs
folders = os.listdir(os.path.dirname(fits_file))
mcmc_outputs = [int(fold.split('_')[-1]) for fold in folders if 'MCMC_output' in fold]
if len(mcmc_outputs) >= 1:
last_mcmc = max(mcmc_outputs)
else:
last_mcmc = 0
logdir = os.path.join(os.path.dirname(fits_file), 'MCMC_output_'+str(last_mcmc+1), 'log')
if not os.path.exists(logdir):
os.makedirs(logdir)
bmc_out.writeto(logdir + os.sep + 'cube_best_model_components.fits', overwrite=True)
par_out.writeto(logdir + os.sep + 'cube_par_table.fits', overwrite=True)
return par_out, bmc_out, last_mcmc+1
def plot_reconstructed_cube(mcmc_output_dir, partable_to_plot=None, bmc_to_plot=None, animated=False):
"""
Make 2D maps and/or videos of the reconstructed par_table and best_model_components parameters
:param mcmc_output_dir: str
The folder to the overall MCMC_output_* folder for the whole cube (not individual spaxels)
:param partable_to_plot: list, optional
List of the par_table parameter names to plot. If None, plots them all.
:param bmc_to_plot: list, optional
List of best_model_components parameter names to plot. If None, plots them all.
:param animated: bool
Whether or not to make the best_model_components plots into videos. Required an installation of FFMpeg.
:return None:
"""
# Get directories
partable = os.path.join(mcmc_output_dir, 'log', 'cube_par_table.fits')
bmc = os.path.join(mcmc_output_dir, 'log', 'cube_best_model_components.fits')
if not os.path.isfile(partable) or not os.path.isfile(bmc):
raise FileNotFoundError(f"Could not find cube_par_table.fits or cube_best_model_components.fits in"
f"{mcmc_output_dir}/log/")
# Load in data
parhdu = fits.open(partable)
bmchdu = fits.open(bmc)
ox, oy = parhdu[0].header['ORIGINX'], parhdu[0].header['ORIGINY']
# First make 2D image maps for each parameter in par table
if not os.path.exists(os.path.join(mcmc_output_dir, 'partable_plots')):
os.mkdir(os.path.join(mcmc_output_dir, 'partable_plots'))
if not os.path.exists(os.path.join(mcmc_output_dir, 'best_model_components_plots')):
os.mkdir(os.path.join(mcmc_output_dir, 'best_model_components_plots'))
if partable_to_plot is None:
partable_to_plot = [p.name for p in parhdu[1:-1]]
if bmc_to_plot is None:
bmc_to_plot = [b.name for b in bmchdu[1:-1]]
for imagehdu in parhdu[1:-1]:
if imagehdu.name not in partable_to_plot:
continue
fig, ax = plt.subplots()
data = imagehdu.data
std = np.nanstd(data)
mad = stats.median_absolute_deviation(data[np.isfinite(data)])
# data[np.abs(data - np.nanmedian(data)) > 10*std] = np.nan
if "FLUX" in imagehdu.name and "SIGMA" not in imagehdu.name:
mask = data >= 0
data[mask] = np.nan
map_ = ax.imshow(data, origin='lower', cmap='cubehelix',
vmin=np.nanpercentile(data, 1),
vmax=np.nanpercentile(data, 99),
extent=[ox-.5, ox+imagehdu.data.shape[0]-.5, oy-.5, oy+imagehdu.data.shape[1]-.5])
plt.colorbar(map_, ax=ax, label=imagehdu.name)
ax.set_title(mcmc_output_dir.split(os.sep)[-1])
plt.savefig(os.path.join(mcmc_output_dir, 'partable_plots', f'{imagehdu.name}.pdf'), bbox_inches='tight', dpi=300)
plt.close()
# Now loop over and plot the model components, averaging/summing over wavelength
if not animated:
for imagehdu in bmchdu[1:-1]:
if imagehdu.name.upper() == 'WAVE' or imagehdu.name not in bmc_to_plot:
continue
# Sum over the 1st axis, aka the wavelength axis
datasum = np.nansum(imagehdu.data, axis=0)
datasum[datasum == 0] = np.nan
# datasum[np.abs(datasum) > 1e5] = np.nan
dataavg = datasum / imagehdu.data.shape[0]
std = np.nanstd(dataavg)
# mad = stats.median_absolute_deviation(dataavg.flatten()[np.isfinite(dataavg.flatten())])
# dataavg[np.abs(dataavg - np.nanmedian(dataavg)) > 10*std] = np.nan
fig, ax = plt.subplots()
map_ = ax.imshow(dataavg, origin='lower', cmap='cubehelix',
vmin= | np.nanpercentile(dataavg, 1) | numpy.nanpercentile |
""" Module containing functions to calculate the 3 most
important wind turbines in a regular wind farm
"""
import numpy as np
def calculate_distance(x, y):
""" calculate the effective distance of a wind turbine
assuming the streamwise direction is 10x more important
than spanwise direction
distance = sqrt(x^2 + 10*y^2)
Parameters
----------
x : float
The spanwise coordinate of the turbine
y: float
The streamwise coordinate of the turbine
Returns
-------
distance : float
The effective distance
"""
distance = np.sqrt(x**2 + 10*y**2)
distance[x < 0] = np.inf
return distance
def make_wind_farm_coords(S_x, S_y, S_off, theta):
""" calculate the x, y coordinates of a wind farm
with regular arrangement
Parameters
----------
S_x: float
The streamwise spacing of the wind farm
S_y: float
The sspanwise spacing of the wind farm
S_off : float
The spanwise offset of rows of turbines
theta: float
The angle of incoming wind above the x axis
Returns
-------
farm_coords: ndarray of shape (49, 3)
(49, :3) The x, y coordinates of the closest 49 wind turbines
(49, 3) The effective distance of the closest 49 wind turbines
"""
farm_coords = np.zeros((49, 3))
for n_y in np.arange(-3, 4):
farm_coords[7*(n_y + 3):7*(n_y + 4), 0:2] = \
[calculate_turbine_coords(S_x, S_y, S_off, theta, n_x, n_y)
for n_x in np.arange(-3, 4)]
farm_coords[:, 2] = calculate_distance(farm_coords[:, 0],
farm_coords[:, 1])
return farm_coords
def calculate_turbine_coords(S_x, S_y, S_off, theta, n_x, n_y):
"""caulcate the x, y coordinates of a single wind
turbine in a regular arrangment
Parameters
----------
S_x: float
The streamwise spacing of the wind farm
S_y: float
The spanwise spacing of the wind farm
S_off : float
The spanwise offset of row of turbines
theta: float
The angle of incoming wind above the x axis
n_x: integer
Turbine number in original streamwise direction
n_y: integer
Turbine number in the original spanwise direction
Returns
-------
turbine coords: tuple of shape (2,)
The x, y coordinates of the wind turbine specified by
the turbine numbers n_x, n_y
"""
x = np.cos(theta)*S_x*n_x + np.sin(theta)*S_off*n_x \
+ np.sin(theta)*S_y*n_y
y = - np.sin(theta)*S_x*n_x + np.cos(theta)*S_off*n_x \
+ | np.cos(theta) | numpy.cos |
import math
import numpy as np
import astropy.units as u
DEG2RAD = math.pi / 180.
class BeamError(Exception):
"""docstring for BeamError"""
pass
class InvalidBeamOperationError(Exception):
pass
class RadioBeamDeprecationWarning(Warning):
pass
def deconvolve_optimized(beamprops1, beamprops2, failure_returns_pointlike=False):
"""
An optimized, non-Quantity version of beam deconvolution.
Because no unit conversions are handled, the inputs MUST be in degrees for the major, minor,
and position angle.
Parameters
----------
beamprops1: dict
Dictionary with keys 'BMAJ', 'BMIN', and 'BPA' for the beam to deconvolve from. Can be
produced with `~radio_beam.Beam.to_fits_keywords`.
beamprops2: dict
Same as `beamprops1` for the second beam.
failure_returns_pointlike : bool, optional
Return a point beam (zero area) when deconvolution fails. If `False`,
this will instead raise a `~radio_beam.utils.BeamError` when deconvolution fails.
Returns
-------
new_major : float
Deconvolved major FWHM.
new_minor : float
Deconvolved minor FWHM.
new_pa : float
Deconvolved position angle.
"""
# blame: https://github.com/pkgw/carma-miriad/blob/CVSHEAD/src/subs/gaupar.for
# (githup checkin of MIRIAD, code by Sault)
maj1 = beamprops1['BMAJ']
min1 = beamprops1['BMIN']
pa1 = beamprops1['BPA'] * DEG2RAD
maj2 = beamprops2['BMAJ']
min2 = beamprops2['BMIN']
pa2 = beamprops2['BPA'] * DEG2RAD
alpha = ((maj1 * math.cos(pa1))**2 +
(min1 * math.sin(pa1))**2 -
(maj2 * math.cos(pa2))**2 -
(min2 * math.sin(pa2))**2)
beta = ((maj1 * math.sin(pa1))**2 +
(min1 * math.cos(pa1))**2 -
(maj2 * math.sin(pa2))**2 -
(min2 * math.cos(pa2))**2)
gamma = 2 * ((min1**2 - maj1**2) * math.sin(pa1) * math.cos(pa1) -
(min2**2 - maj2**2) * math.sin(pa2) * math.cos(pa2))
s = alpha + beta
t = math.sqrt((alpha - beta)**2 + gamma**2)
# Deal with floating point issues
# This matches the arcsec**2 check for deconvolve below
# Difference is we keep things in deg^2 here
atol_t = np.finfo(np.float64).eps / 3600.**2
# To deconvolve, the beam must satisfy:
# alpha < 0
alpha_cond = alpha + np.finfo(np.float64).eps < 0
# beta < 0
beta_cond = beta + np.finfo(np.float64).eps < 0
# s < t
st_cond = s < t + atol_t
if alpha_cond or beta_cond or st_cond:
if failure_returns_pointlike:
return 0., 0., 0.
else:
raise BeamError("Beam could not be deconvolved")
else:
new_major = math.sqrt(0.5 * (s + t))
new_minor = math.sqrt(0.5 * (s - t))
# absolute tolerance needs to be <<1 microarcsec
atol = 1e-7 / 3600.
if (math.sqrt(abs(gamma) + abs(alpha - beta))) < atol:
new_pa = 0.0
else:
new_pa = 0.5 * math.atan2(-1. * gamma, alpha - beta)
# In the limiting case, the axes can be zero to within precision
# Add the precision level onto each axis so a deconvolvable beam
# is always has beam.isfinite == True
new_major += np.finfo(np.float64).eps
new_minor += np.finfo(np.float64).eps
return new_major, new_minor, new_pa
def deconvolve(beam, other, failure_returns_pointlike=False):
"""
Deconvolve a beam from another
Parameters
----------
beam : `Beam`
The defined beam.
other : `Beam`
The beam to deconvolve from this beam
failure_returns_pointlike : bool
Option to return a pointlike beam (i.e., one with major=minor=0) if
the second beam is larger than the first. Otherwise, a ValueError
will be raised
Returns
-------
new_beam : `Beam`
The convolved Beam
Raises
------
failure : ValueError
If the second beam is larger than the first, the default behavior
is to raise an exception. This can be overridden with
failure_returns_pointlike
"""
# The header keywords handle the conversions to degree for BMAJ, BMIN, BPA.
beamprops1 = beam.to_header_keywords()
beamprops2 = other.to_header_keywords()
return deconvolve_optimized(beamprops1, beamprops2,
failure_returns_pointlike=failure_returns_pointlike)
def convolve(beam, other):
"""
Convolve one beam with another.
Parameters
----------
other : `Beam`
The beam to convolve with
Returns
-------
new_beam : `Beam`
The convolved Beam
"""
# blame: https://github.com/pkgw/carma-miriad/blob/CVSHEAD/src/subs/gaupar.for
# (github checkin of MIRIAD, code by Sault)
alpha = ((beam.major * np.cos(beam.pa))**2 +
(beam.minor * np.sin(beam.pa))**2 +
(other.major * np.cos(other.pa))**2 +
(other.minor * np.sin(other.pa))**2)
beta = ((beam.major * np.sin(beam.pa))**2 +
(beam.minor * np.cos(beam.pa))**2 +
(other.major * np.sin(other.pa))**2 +
(other.minor * np.cos(other.pa))**2)
gamma = (2 * ((beam.minor**2 - beam.major**2) *
np.sin(beam.pa) * np.cos(beam.pa) +
(other.minor**2 - other.major**2) *
np.sin(other.pa) * np.cos(other.pa)))
s = alpha + beta
t = np.sqrt((alpha - beta)**2 + gamma**2)
new_major = np.sqrt(0.5 * (s + t))
new_minor = np.sqrt(0.5 * (s - t))
# absolute tolerance needs to be <<1 microarcsec
if np.isclose(((abs(gamma) + abs(alpha - beta))**0.5).to(u.arcsec).value, 1e-7):
new_pa = 0.0 * u.deg
else:
new_pa = 0.5 * np.arctan2(-1. * gamma, alpha - beta)
return new_major, new_minor, new_pa
def transform_ellipse(major, minor, pa, x_scale, y_scale):
'''
Transform an ellipse by scaling in the x and y axes.
Parameters
----------
major : `~astropy.units.Quantity`
Major axis.
minor : `~astropy.units.Quantity`
Minor axis.
pa : `~astropy.units.Quantity`
PA of the major axis.
x_scale : float
x axis scaling factor.
y_scale : float
y axis scaling factor.
Returns
-------
trans_major : `~astropy.units.Quantity`
Major axis in the transformed frame.
trans_minor : `~astropy.units.Quantity`
Minor axis in the transformed frame.
trans_pa : `~astropy.units.Quantity`
PA of the major axis in the transformed frame.
'''
# This code is based on the implementation in CASA:
# https://open-bitbucket.nrao.edu/projects/CASA/repos/casa/browse/code/imageanalysis/ImageAnalysis/CasaImageBeamSet.cc
major = major.to(u.arcsec)
minor = minor.to(u.arcsec)
pa = pa.to(u.rad)
cospa = np.cos(pa)
sinpa = np.sin(pa)
cos2pa = cospa**2
sin2pa = sinpa**2
major2 = major**2
minor2 = minor**2
a = (cos2pa / major2) + (sin2pa / minor2)
b = -2 * cospa * sinpa * (major2**-1 - minor2**-1)
c = (sin2pa / major2) + (cos2pa / minor2)
x2_scale = x_scale**2
y2_scale = y_scale**2
r = a / x2_scale
s = b**2 / (4 * x2_scale * y2_scale)
t = c / y2_scale
udiff = r - t
u2 = udiff**2
f1 = u2 + 4 * s
f2 = np.sqrt(f1) * np.abs(udiff)
j1 = (f2 + f1) / f1 / 2
j2 = (f1 - f2) / f1 / 2
k1 = (j1 * r + j1 * t - t) / (2 * j1 - 1)
k2 = (j2 * r + j2 * t - t) / (2 * j2 - 1)
c1 = | np.sqrt(k1) | numpy.sqrt |
import h5py
from matplotlib import pyplot as plt
import pandas as pd
import numpy as np
from sklearn.manifold import TSNE
h5file = h5py.File("96.jl.h5")
X = h5file["X"].value
# n_samples x n_features
assert X.shape[1] == 300
df = pd.read_csv("./countries.csv")
labels = | np.array(df.iloc[:, 1]) | numpy.array |
# -*- coding: utf-8 -*-
# Copyright 2021 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# wITHOUT wARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""Test operator sparsing."""
import numpy as np
from openfermion import get_sparse_operator
from openfermion.chem import MolecularData
from mindquantum.algorithm.nisq.chem.transform import Transform
from mindquantum.core.operators.utils import get_fermion_operator
from mindquantum.third_party.interaction_operator import InteractionOperator
def test_sparsing_operator():
"""
Description: Test sparsing operator
Expectation: success
"""
molecular = "./tests/st/H4.hdf5"
mol = MolecularData(filename=molecular)
mol.load()
ham_of = mol.get_molecular_hamiltonian()
inter_ops = InteractionOperator(*ham_of.n_body_tensors.values())
ham_hiq = get_fermion_operator(inter_ops)
ham = Transform(ham_hiq).jordan_wigner()
h = ham.to_openfermion()
m1 = get_sparse_operator(h).toarray()
m2 = ham.matrix().toarray()
m3 = ham_hiq.matrix().toarray()
v1 = np.real(np.linalg.eigvals(m1))
v2 = np.real(np.linalg.eigvals(m2))
v3 = np.real( | np.linalg.eigvals(m3) | numpy.linalg.eigvals |
import torch
from torch.autograd import Variable
import torch.nn as nn
import numpy as np
import pdb
from lib.coarsening import lmax_L
from lib.coarsening import rescale_L
from torch.autograd import Variable
import torch.nn.functional as F
from lib.coarsening import perm_data_torch2
if torch.cuda.is_available():
print('cuda available')
dtypeFloat = torch.cuda.FloatTensor
dtypeLong = torch.cuda.LongTensor
torch.cuda.manual_seed(1)
else:
print('cuda not available')
dtypeFloat = torch.FloatTensor
dtypeLong = torch.LongTensor
torch.manual_seed(1)
def isnan(x):
return x != x
class loss_with_consensus(torch.nn.Module):
def __init__(self, loss_fn, config=None):
super().__init__()
self.existing_loss = loss_fn
self.config = config
self.num_c = config['cons']
self.lin = torch.nn.Linear(2*(2 * self.num_c - 1), 2)
def forward(self, pred, labels):
B, cons, plen = pred.shape
pred = pred.view(B, cons * plen)
# pdb.set_trace()
fin_pred = self.lin(pred)
loss = self.existing_loss(fin_pred, labels)
return loss
class loss_with_consensus2(torch.nn.Module):
def __init__(self, loss_fn):
super().__init__()
self.existing_loss = loss_fn
# self.kld = torch.nn.KLDivLoss()
def forward(self, pred, labels):
# Assume pred is of size: B x 5 x 2
# Labels is of size: B x 1
B, cons, plen = pred.shape
pred_curr = pred[:, 0, :]
loss = self.existing_loss(pred_curr, labels)
pred_new = pred.view(B*cons, plen)
pred_new_ls = F.log_softmax(pred_new, dim=1)
pred_new_ls = pred_new_ls.view(B, cons, plen)
pred_curr_ls = pred_new_ls[:, 0, :]
for i in range(1, cons):
pred_tmp = pred_new_ls[:, i, :]
pred_tmp = pred_tmp.detach()
loss += F.kl_div(pred_curr_ls, pred_tmp)
# loss += self.kld(pred_tmp, pred_curr_ls)
return loss
class my_sparse_mm(torch.autograd.Function):
"""
Implementation of a new autograd function for sparse variables,
called "my_sparse_mm", by subclassing torch.autograd.Function
and implementing the forward and backward passes.
"""
def forward(self, W, x): # W is SPARSE
self.save_for_backward(W, x)
# pdb.set_trace()
y = torch.mm(W, x)
return y
def backward(self, grad_output):
W, x = self.saved_tensors
grad_input = grad_output.clone()
grad_input_dL_dW = torch.mm(grad_input, x.t())
grad_input_dL_dx = torch.mm(W.t(), grad_input)
return grad_input_dL_dW, grad_input_dL_dx
class gconv(torch.nn.Module):
def __init__(self, in_c, out_c, kern):
super().__init__()
self.in_c = in_c
self.out_c = out_c
self.kern = kern
self.lin = torch.nn.Linear(in_c * kern, out_c)
return
def forward(self, inp, L):
B, V, Fin = inp.shape
x0 = inp.permute(1, 2, 0).contiguous()
x0 = x0.view([V, Fin*B])
x = x0.unsqueeze(0)
if self.kern > 1:
x1 = my_sparse_mm()(L, x0) # V x Fin*B
x = torch.cat((x, x1.unsqueeze(0)), 0) # 2 x V x Fin*B
for k in range(2, self.kern):
x2 = 2 * my_sparse_mm()(L, x1) - x0
x = torch.cat((x, x2.unsqueeze(0)), 0) # M x Fin*B
x0, x1 = x1, x2
x = x.view([self.kern, V, Fin, B]) # K x V x Fin x B
x = x.permute(3, 1, 2, 0).contiguous() # B x V x Fin x K
x = x.view([B*V, Fin*self.kern]) # B*V x Fin*K
# pdb.set_trace()
x = self.lin(x)
x = x.view([B, V, self.out_c]) # B x V x Fout
return x
class Graph_ConvNet_LeNet5(nn.Module):
def __init__(self, net_parameters):
print('Graph ConvNet: LeNet5')
super(Graph_ConvNet_LeNet5, self).__init__()
# parameters
D, Fin1, CL1_F, CL1_K, CL2_F, CL2_K, FC1_F, FC2_F = net_parameters
p = 2
FC1Fin = CL2_F*(D//(p*p))
# pdb.set_trace()
# graph CL1
self.cl1 = nn.Linear(CL1_K * Fin1, CL1_F)
self.conv1_bn = torch.nn.BatchNorm1d(D, CL1_F)
Fin = CL1_K
Fout = CL1_F
scale = np.sqrt(2.0 / (Fin+Fout))
self.cl1.weight.data.uniform_(-scale, scale)
self.cl1.bias.data.fill_(0.0)
self.CL1_K = CL1_K
self.CL1_F = CL1_F
# graph CL2
self.cl2 = nn.Linear(CL2_K*CL1_F, CL2_F)
self.conv2_bn = torch.nn.BatchNorm1d(D//p, CL2_F)
Fin = CL2_K * CL1_F
Fout = CL2_F
scale = np.sqrt(2.0 / (Fin+Fout))
self.cl2.weight.data.uniform_(-scale, scale)
self.cl2.bias.data.fill_(0.0)
self.CL2_K = CL2_K
self.CL2_F = CL2_F
# FC1
self.fc1 = nn.Linear(FC1Fin, FC1_F)
Fin = FC1Fin
Fout = FC1_F
scale = np.sqrt(2.0 / (Fin+Fout))
self.fc1.weight.data.uniform_(-scale, scale)
self.fc1.bias.data.fill_(0.0)
# pdb.set_trace()
self.FC1Fin = FC1Fin
# FC2
self.fc2 = nn.Linear(FC1_F, FC2_F)
Fin = FC1_F
Fout = FC2_F
scale = np.sqrt(2.0 / (Fin+Fout))
self.fc2.weight.data.uniform_(-scale, scale)
self.fc2.bias.data.fill_(0.0)
# nb of parameters
nb_param = CL1_K * CL1_F + CL1_F # CL1
nb_param += CL2_K * CL1_F * CL2_F + CL2_F # CL2
nb_param += FC1Fin * FC1_F + FC1_F # FC1
nb_param += FC1_F * FC2_F + FC2_F # FC2
print('nb of parameters=', nb_param, '\n')
def init_weights(self, W, Fin, Fout):
scale = np.sqrt(2.0 / (Fin+Fout))
W.uniform_(-scale, scale)
return W
def graph_conv_cheby(self, x, cl, L, lmax, Fout, K):
# parameters
# B = batch size
# V = nb vertices
# Fin = nb input features
# Fout = nb output features
# K = Chebyshev order & support size
# pdb.set_trace()
B, V, Fin = x.size()
B, V, Fin = int(B), int(V), int(Fin)
# rescale Laplacian
lmax = lmax_L(L)
L = rescale_L(L, lmax)
# convert scipy sparse matric L to pytorch
L = L.tocoo()
indices = np.column_stack((L.row, L.col)).T
indices = indices.astype(np.int64)
indices = torch.from_numpy(indices)
indices = indices.type(torch.LongTensor)
L_data = L.data.astype(np.float32)
L_data = torch.from_numpy(L_data)
L_data = L_data.type(torch.FloatTensor)
L = torch.sparse.FloatTensor(indices, L_data, torch.Size(L.shape))
L = Variable(L, requires_grad=False)
if torch.cuda.is_available():
L = L.cuda()
# transform to Chebyshev basis
x0 = x.permute(1, 2, 0).contiguous() # V x Fin x B
# pdb.set_trace()
x0 = x0.view([V, Fin*B]) # V x Fin*B
x = x0.unsqueeze(0) # 1 x V x Fin*B
def concat(x, x_):
x_ = x_.unsqueeze(0) # 1 x V x Fin*B
return torch.cat((x, x_), 0) # K x V x Fin*B
if K > 1:
x1 = my_sparse_mm()(L, x0) # V x Fin*B
x = torch.cat((x, x1.unsqueeze(0)), 0) # 2 x V x Fin*B
# pdb.set_trace()
for k in range(2, K):
x2 = 2 * my_sparse_mm()(L, x1) - x0
x = torch.cat((x, x2.unsqueeze(0)), 0) # M x Fin*B
x0, x1 = x1, x2
x = x.view([K, V, Fin, B]) # K x V x Fin x B
x = x.permute(3, 1, 2, 0).contiguous() # B x V x Fin x K
x = x.view([B*V, Fin*K]) # B*V x Fin*K
# Compose linearly Fin features to get Fout features
# pdb.set_trace()
x = cl(x) # B*V x Fout
# pdb.set_trace()
x = x.view([B, V, Fout]) # B x V x Fout
# pdb.set_trace()
return x
# Max pooling of size p. Must be a power of 2.
def graph_max_pool(self, x, p):
if p > 1:
x = x.permute(0, 2, 1).contiguous() # x = B x F x V
x = nn.MaxPool1d(p)(x) # B x F x V/p
x = x.permute(0, 2, 1).contiguous() # x = B x V/p x F
return x
else:
return x
def forward(self, x, d, L, lmax):
# graph CL1
# pdb.set_trace()
# x = x.squeeze()
# x = x.unsqueeze(2) # B x V x Fin=1
# pdb.set_trace()
# pdb.set_trace()
x = self.graph_conv_cheby(x, self.cl1, L[0], lmax[0], self.CL1_F, self.CL1_K)
# pdb.set_trace()
x = F.relu(x)
x = self.conv1_bn(x)
x = self.graph_max_pool(x, 2)
# graph CL2
x = self.graph_conv_cheby(x, self.cl2, L[1], lmax[1], self.CL2_F, self.CL2_K)
x = F.relu(x)
x = self.conv2_bn(x)
x = self.graph_max_pool(x, 2)
# FC1
x = x.view(-1, self.FC1Fin)
x = self.fc1(x)
x = F.relu(x)
x = nn.Dropout(d)(x)
# FC2
x = self.fc2(x)
# pdb.set_trace()
return x
def loss(self, y, y_target, l2_regularization):
# pdb.set_trace()
loss = nn.CrossEntropyLoss()(y, y_target)
l2_loss = 0.0
for param in self.parameters():
data = param * param
l2_loss += data.sum()
# loss += 0.5 * l2_regularization * l2_loss
return loss
def update(self, lr):
update = torch.optim.SGD(self.parameters(), lr=lr, momentum=0.9)
return update
def update_learning_rate(self, optimizer, lr):
for param_group in optimizer.param_groups:
param_group['lr'] = lr
return optimizer
def evaluation(self, y_predicted, test_l):
_, class_predicted = torch.max(y_predicted.data, 1)
return 100.0 * (class_predicted == test_l).sum() / y_predicted.size(0)
def calc_dim(din, f, s):
return (din - f)//s + 1
class simple_net(torch.nn.Module):
def __init__(self, D_in, inp_channels):
super(simple_net, self).__init__()
# For conv1d the params are N, C, L
# N is the batch size
# C is the number of channels
# L is the len of the signal
# For now keep the number of channels=1
f = 3
s = 1
self.conv1 = torch.nn.Conv1d(inp_channels, 6, f, stride=s)
new_dim = calc_dim(D_in, f, s) // 2
self.conv1_bn = torch.nn.BatchNorm1d(6)
self.conv2 = torch.nn.Conv1d(6, 16, f, stride=s)
new_dim = calc_dim(new_dim, f, s) // 2
self.conv2_bn = torch.nn.BatchNorm1d(16)
# self.conv3 = torch.nn.Conv1d(16, 32, f, stride=s)
# new_dim = calc_dim(new_dim, f, s) // 2
self.lin1 = torch.nn.Linear(16*new_dim, 30)
self.lin2 = torch.nn.Linear(30, 2)
def forward(self, inp):
# out = F.relu(F.max_pool1d(self.conv1_bn(self.conv1(inp)), 2))
layer_outs = dict()
out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1(inp))), 2)
# out = F.dropout(out)
# out = F.relu(F.max_pool1d(self.conv2_bn(self.conv2(out)), 2))
layer_outs['conv1'] = out
out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2(out))), 2)
layer_outs['conv2'] = out
# out = F.relu(self.conv2(out))
# out = F.dropout(out)
# out = F.max_pool1d(out, 2)
# out = F.relu(self.conv3(out))
# out = F.dropout(out)
# out = F.max_pool1d(out, 2)
out = out.view(out.size(0), -1)
layer_outs['fc_inp'] = out
out = F.relu(self.lin1(out))
layer_outs['fc1'] = out
# out = F.dropout(out)
out = self.lin2(out)
layer_outs['fc2'] = out
return out, layer_outs
class complex_net(torch.nn.Module):
def __init__(self, D_in, inp_channels):
super(complex_net, self).__init__()
# For conv1d the params are N, C, L
# N is the batch size
# C is the number of channels
# L is the len of the signal
# For now keep the number of channels=1
self.num_inp_channels = inp_channels
f = 3
s = 1
self.conv1_list = torch.nn.ModuleList()
# for i in range(inp_channels):
# self.conv1_list.append(torch.nn.Conv1d(1, 6, f, stride=s))
new_dim = calc_dim(D_in, f, s) // 2
self.conv1_bn = torch.nn.BatchNorm1d(6)
self.conv2_list = torch.nn.ModuleList()
# for i in range(inp_channels):
# self.conv2_list.append(torch.nn.Conv1d(6, 16, f, stride=s))
new_dim = calc_dim(new_dim, f, s) // 2
self.conv2_bn = torch.nn.BatchNorm1d(16)
# self.conv3 = torch.nn.Conv1d(16, 32, f, stride=s)
# new_dim = calc_dim(new_dim, f, s) // 2
self.lin1_list = torch.nn.ModuleList()
# for i in range(inp_channels):
# self.lin1_list.append(torch.nn.Linear(16*new_dim, 30))
self.lin2_list = torch.nn.ModuleList()
for i in range(inp_channels):
self.conv1_list.append(torch.nn.Conv1d(1, 6, f, stride=s))
self.conv2_list.append(torch.nn.Conv1d(6, 16, f, stride=s))
self.lin1_list.append(torch.nn.Linear(16*new_dim, 30))
self.lin2_list.append(torch.nn.Linear(30, 2))
def forward(self, inp):
# out = F.relu(F.max_pool1d(self.conv1_bn(self.conv1(inp)), 2))
# pdb.set_trace()
num_channels = inp.shape[1]
channel_layer_outs = []
fin_outs = []
for i in range(num_channels):
layer_outs = dict()
# pdb.set_trace()
# inp_chan = inp[:, ]
out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1_list[i](inp[:, [i], :]))), 2)
layer_outs['conv1'] = out
out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2_list[i](out))), 2)
layer_outs['conv2'] = out
out = out.view(out.size(0), -1)
layer_outs['fc_inp'] = out
out = F.relu(self.lin1_list[i](out))
layer_outs['fc1'] = out
out = self.lin2_list[i](out)
layer_outs['fc2'] = out
channel_layer_outs.append(layer_outs)
fin_outs.append(out)
# dict()
# out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1(inp))), 2)
# out = F.dropout(out)
# out = F.relu(F.max_pool1d(self.conv2_bn(self.conv2(out)), 2))
# layer_outs['conv1'] = out
# out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2(out))), 2)
# layer_outs['conv2'] = out
# out = F.relu(self.conv2(out))
# out = F.dropout(out)
# out = F.max_pool1d(out, 2)
# out = F.relu(self.conv3(out))
# out = F.dropout(out)
# out = F.max_pool1d(out, 2)
# out = out.view(out.size(0), -1)
# layer_outs['fc_inp'] = out
# out = F.relu(self.lin1(out))
# layer_outs['fc1'] = out
# out = F.dropout(out)
# out = self.lin2(out)
# layer_outs['fc2'] = out
# pdb.set_trace() #
return out, channel_layer_outs
# def to_cuda(self):
# self.cuda()
# for i in range(self.num_inp_channels):
# self.conv1_list[i].cuda()
# self.conv2_list[i].cuda()
# self.lin1_list[i].cuda()
# self.lin2_list[i].cuda()
# class complex_net2(torch.nn.Module):
# def __init__(self, D_in, inp_channels):
# super(complex_net2, self).__init__()
# # For conv1d the params are N, C, L
# # N is the batch size
# # C is the number of channels
# # L is the len of the signal
# # For now keep the number of channels=1
# self.num_inp_channels = inp_channels
# f = 3
# s = 1
# # for i in range(inp_channels):
# new_dim = calc_dim(D_in, f, s) // 2
# self.conv1_bn = torch.nn.BatchNorm1d(6)
# new_dim = calc_dim(new_dim, f, s) // 2
# self.conv2_bn = torch.nn.BatchNorm1d(16)
# self.basic_block_lenet5 = simple_net(D_in, 1)
# def forward(self, inp):
# # out = F.relu(F.max_pool1d(self.conv1_bn(self.conv1(inp)), 2))
# # pdb.set_trace()
# num_channels = inp.shape[1]
# channel_layer_outs = []
# fin_outs = []
# for i in range(num_channels):
# layer_outs = dict()
# # pdb.set_trace()
# # inp_chan = inp[:, ]
# out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1_list[i](inp[:, [i], :]))), 2)
# layer_outs['conv1'] = out
# out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2_list[i](out))), 2)
# layer_outs['conv2'] = out
# out = out.view(out.size(0), -1)
# layer_outs['fc_inp'] = out
# out = F.relu(self.lin1_list[i](out))
# layer_outs['fc1'] = out
# out = self.lin2_list[i](out)
# layer_outs['fc2'] = out
# channel_layer_outs.append(layer_outs)
# fin_outs.append(out)
# # dict()
# # out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1(inp))), 2)
# # out = F.dropout(out)
# # out = F.relu(F.max_pool1d(self.conv2_bn(self.conv2(out)), 2))
# # layer_outs['conv1'] = out
# # out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2(out))), 2)
# # layer_outs['conv2'] = out
# # out = F.relu(self.conv2(out))
# # out = F.dropout(out)
# # out = F.max_pool1d(out, 2)
# # out = F.relu(self.conv3(out))
# # out = F.dropout(out)
# # out = F.max_pool1d(out, 2)
# # out = out.view(out.size(0), -1)
# # layer_outs['fc_inp'] = out
# # out = F.relu(self.lin1(out))
# # layer_outs['fc1'] = out
# # out = F.dropout(out)
# # out = self.lin2(out)
# # layer_outs['fc2'] = out
# return out, channel_layer_outs
# def to_cuda(self):
# self.cuda()
# for i in range(self.num_inp_channels):
# self.conv1_list[i].cuda()
# self.conv2_list[i].cuda()
# self.lin1_list[i].cuda()
# self.lin2_list[i].cuda()
class small_model(torch.nn.Module):
def __init__(self, cnet_parameters):
super(small_model, self).__init__()
Din, num_inp_channels, f, s, c1o, c2o, fc1o = cnet_parameters
self.conv1 = torch.nn.Conv1d(1, c1o, f, stride=s)
new_dim = calc_dim(Din, f, s) // 2
self.conv2 = torch.nn.Conv1d(c1o, c2o, f, stride=s)
new_dim = calc_dim(new_dim, f, s) // 2
self.lin1 = torch.nn.Linear(c2o*new_dim, fc1o)
self.conv1_bn = torch.nn.BatchNorm1d(c1o)
self.conv2_bn = torch.nn.BatchNorm1d(c2o)
def forward(self, inp):
out = F.max_pool1d(self.conv1_bn(F.relu(self.conv1(inp))), 2)
out = F.max_pool1d(self.conv2_bn(F.relu(self.conv2(out))), 2)
out = out.view(out.size(0), -1)
out = F.relu(self.lin1(out))
return out
class end_to_end_model(torch.nn.Module):
def __init__(self, cnet_parameters, gnet_parameters):
super(end_to_end_model, self).__init__()
Din, num_inp_channels, f, s, c1o, c2o, fc1o = cnet_parameters
self.Din = Din
self.c1o = c1o
self.c2o = c2o
self.fc1o = fc1o
self.f = f
self.s = s
self.num_inp_channels = num_inp_channels
# self.small_model0 = small_model(cnet_parameters)
# self.small_model1 = small_model(cnet_parameters)
# self.small_model2 = small_model(cnet_parameters)
# self.small_model3 = small_model(cnet_parameters)
# self.small_model4 = small_model(cnet_parameters)
# self.small_model5 = small_model(cnet_parameters)
D, CL1_F, CL1_K, CL2_F, CL2_K, FC1_F, FC2_F = gnet_parameters
p = 2
FC1Fin = CL2_F*(D//(p*p))
self.conv1_list = torch.nn.ModuleList()
new_dim = calc_dim(Din, f, s) // 2
self.conv1_bn_list = torch.nn.ModuleList()
# torch.nn.BatchNorm1d(c1o)
self.conv2_list = torch.nn.ModuleList()
new_dim = calc_dim(new_dim, f, s) // 2
self.conv2_bn_list = torch.nn.ModuleList()
# = torch.nn.BatchNorm1d(c2o)
self.lin1_list = torch.nn.ModuleList()
self.lin2_list = torch.nn.ModuleList()
for i in range(self.num_inp_channels):
# Need to change 2->1.
self.conv1_list.append(torch.nn.Conv1d(1, c1o, f, stride=s))
self.conv1_bn_list.append(torch.nn.BatchNorm1d(c1o))
self.conv2_list.append(torch.nn.Conv1d(c1o, c2o, f, stride=s))
self.conv2_bn_list.append(torch.nn.BatchNorm1d(c2o))
self.lin1_list.append(torch.nn.Linear(c2o*new_dim, fc1o))
self.lin2_list.append(torch.nn.Linear(fc1o, 2))
# self.cnet_module_list = torch.nn.ModuleList([self.conv1_list,
# self.conv2_list, self.lin1_list])
self.cnet_module_list = torch.nn.ModuleList()
for i in range(self.num_inp_channels):
tmp_list = torch.nn.ModuleList([self.conv1_list[i], self.conv1_bn_list[i],
self.conv2_list[i], self.conv2_bn_list[i],
self.lin1_list[i], self.lin2_list[i]])
self.cnet_module_list.append(tmp_list)
# FC1Fin = CL2_F*(D//(p*p))
# pdb.set_trace()
# graph CL1
self.cl1 = nn.Linear(CL1_K * fc1o, CL1_F)
self.gconv1_bn = torch.nn.BatchNorm1d(D, CL1_F)
Fin = CL1_K
Fout = CL1_F
scale = | np.sqrt(2.0 / (Fin+Fout)) | numpy.sqrt |
"""Run Demonstration Image Classification Experiments.
"""
import sys,os
sys.path.append('..')
import numpy as np
from models.BrokenModel import BrokenModel as BrokenModel
import glob
import tensorflow as tf
import pandas as pd
from timeit import default_timer as timer
from .calloc import loadChannel,quantInit
from .simmods import *
from errConceal.caltec import *
from errConceal.altec import *
from errConceal.tc_algos import *
import cv2 as cv2
from PIL import Image
# ---------------------------------------------------------------------------- #
def fnRunImgClassDemo(modelDict,splitLayerDict,ecDict,batch_size,path_base,transDict,outputDir):
print('TensorFlow version')
print(tf.__version__)
model_path = modelDict['fullModel']
customObjects = modelDict['customObjects']
task = modelDict['task']
normalize = modelDict['normalize']
reshapeDims = modelDict['reshapeDims']
splitLayer = splitLayerDict['split']
mobile_model_path = splitLayerDict['MobileModel']
cloud_model_path = splitLayerDict['CloudModel']
rowsPerPacket = transDict['rowsperpacket']
quantization = transDict['quantization']
numberOfBits_1 = quantization[1]['numberOfBits']
numberOfBits_2 = quantization[2]['numberOfBits']
channel = transDict['channel']
res_data_dir = outputDir['resDataDir'] # directory for loss maps.
sim_data_dir = outputDir['simDataDir'] # directory for simulation results.
# ------------------------------------------------------------------------ #
# tensorflow.keras deep model loading.
loaded_model = tf.keras.models.load_model(os.path.join(model_path))
loaded_model_config = loaded_model.get_config()
loaded_model_name = loaded_model_config['name']
# Check if mobile and cloud sub-models are already available:
if os.path.isfile(mobile_model_path) and os.path.isfile(cloud_model_path):
print(f'Sub-models of {loaded_model_name} split at {splitLayer} are available.')
mobile_model = tf.keras.models.load_model(os.path.join(mobile_model_path))
cloud_model = tf.keras.models.load_model(os.path.join(cloud_model_path))
else:
# if not, split the deep model.
# Object for splitting a tf.keras model into a mobile sub-model and a cloud
# sub-model at the chosen split layer 'splitLayer'.
testModel = BrokenModel(loaded_model, splitLayer, customObjects)
testModel.splitModel()
mobile_model = testModel.deviceModel
cloud_model = testModel.remoteModel
# Save the mobile and cloud sub-model
mobile_model.save(mobile_model_path)
cloud_model.save(cloud_model_path)
# ---------------------------------------------------------------------------- #
# Create results directory
if 'GilbertChannel' in channel:
lossProbability = channel['GilbertChannel']['lossProbability']
burstLength = channel['GilbertChannel']['burstLength']
results_dir = os.path.join(sim_data_dir,path_base,loaded_model_name,'demo',splitLayer+'_lp_'+str(lossProbability)+'_Bl_'+str(burstLength))
channel_flag = 'GC'
elif 'RandomLossChannel' in channel:
lossProbability = channel['RandomLossChannel']['lossProbability']
results_dir = os.path.join(sim_data_dir,path_base,loaded_model_name,'demo',splitLayer+'_lp_'+str(lossProbability))
channel_flag = 'RL'
elif 'ExternalChannel' in channel:
print('External packet traces imported')
results_dir = os.path.join(sim_data_dir,path_base,loaded_model_name,'demo',splitLayer+'_ext_trace')
channel_flag = 'EX'
num_channels = transDict['channel']['ExternalChannel']['num_channels']
ext_dir = os.path.join(res_data_dir,path_base,loaded_model_name,splitLayer)
else:
# No lossy channel. This means we are doing a quantization experiment.
channel_flag = 'NC'
results_dir = os.path.join(sim_data_dir,path_base,loaded_model_name,'demo',splitLayer+'_NoChannel')
MC_runs = [0,1] # with no lossy channel, there's no need to do monte carlo runs because each monte carlo run would give the same results.
if channel_flag in ['GC','RL','EX']:
# Only load altec weights if we will be doing error concealment.
tc_weights_path = ecDict['ALTeC']['weightspath']
altec_w_path = os.path.join(tc_weights_path,loaded_model_name,splitLayer,splitLayer+'_rpp_'+str(rowsPerPacket)+'_'+str(numberOfBits_1)+'Bits_tensor_weights.npy')
altec_pkt_w = np.load(altec_w_path)
print(f'Loaded ALTeC weights for splitLayer {splitLayer} and {rowsPerPacket} rows per packet. Shape {np.shape(altec_pkt_w)}')
halrtc_iters = ecDict['HaLRTC']['numiters']
silrtc_iters = ecDict['SiLRTC']['numiters']
inpaint_radius = ecDict['InpaintNS']['radius']
os.makedirs(results_dir,exist_ok=True)
res_filename = '_'+str(numberOfBits_1)+'Bits_'+str(numberOfBits_2)+'Bits_'
# ------------------------------------------------------------------------ #
# Objects for the channel, quantization.
if channel_flag != 'EX':
channel = loadChannel(channel)
quant_tensor1 = quantInit(quantization,tensor_id = 1)
quant_tensor2 = quantInit(quantization,tensor_id = 2)
# ------------------------------------------------------------------------ #
# Load the dataset
dataset_x_files,dataset_y_labels,file_names = fn_Data_PreProcessing_ImgClass(path_base,reshapeDims,normalize)
# ------------------------------------------------------------------------ #
# Process the dataset.
batched_y_labels = [dataset_y_labels[i:i + batch_size] for i in range(0, len(dataset_y_labels), batch_size)]
batched_x_files = [dataset_x_files[i: i + batch_size] for i in range(0,len(dataset_x_files),batch_size)]
if channel_flag == 'EX':
loss_matrix_mc = []
print('Loading external packet traces')
for i_mc in range(MC_runs[0],MC_runs[1]):
# Load external packet traces as loss matrices.
lossMap_list = []
for i_c in range(num_channels):
df = pd.read_excel(os.path.join(ext_dir,'Rpp_'+str(rowsPerPacket)+'_MC_'+str(i_mc)+'.xlsx'),sheet_name=[str(i_c)],engine='openpyxl')
lossMap_channel = (df[str(i_c)].to_numpy())[:,1:].astype(np.bool)
lossMap_list.append(lossMap_channel)
loss_matrix_all = np.dstack(lossMap_list)
loss_matrix_ex = [loss_matrix_all[k_batch:k_batch+batch_size,:,:] for k_batch in range(0,np.shape(loss_matrix_all)[0],batch_size)]
loss_matrix_mc.append(loss_matrix_ex)
# lists to store results.
true_labels = []
top1_pred_full_model = []
top1_pred_split_model = []
top5_pred_full_model = []
top5_pred_split_model = []
top1_pred_caltec = []
top5_pred_caltec = []
top1_pred_altec = []
top5_pred_altec = []
top1_pred_halrtc = []
top5_pred_halrtc = []
top1_pred_silrtc = []
top5_pred_silrtc = []
top1_pred_inpaint = []
top5_pred_inpaint = []
top1_conf_full = []
top1_conf_split = []
top1_conf_caltec = []
top1_conf_altec = []
top1_conf_halrtc = []
top1_conf_silrtc = []
top1_conf_inpaint = []
for i_b in range(len(batched_y_labels)):
# Run through Monte Carlo experiments through each batch.
print(f"Batch {i_b}")
batch_labels = np.asarray(batched_y_labels[i_b],dtype=np.int64)
true_labels.extend(batch_labels)
batch_imgs = batched_x_files[i_b]
batch_imgs_stacked = np.vstack([i[np.newaxis,...] for i in batch_imgs])
# ---------------------------------------------------------------- #
full_model_out = loaded_model.predict(batch_imgs_stacked)
batch_top1_predictions = np.argmax(full_model_out,axis=1)
batch_confidence = np.max(full_model_out,axis=1)
top1_pred_full_model.extend(batch_top1_predictions)
top1_conf_full.extend(batch_confidence)
for i_item in range(np.shape(full_model_out)[0]):
item_top5_predictions = np.argpartition(-full_model_out[i_item,:],5)[:5]
top5_pred_full_model.append(item_top5_predictions)
# --------------------------------------------------------------- #
deviceOut = mobile_model.predict(batch_imgs_stacked)
print(f'Shape of device out tensor {np.shape(deviceOut)}')
# ---------------------------------------------------------------- #
devOut = []
if not isinstance(deviceOut, list):
devOut.append(deviceOut)
deviceOut = devOut
# deviceOut is the output tensor for a batch of data.
# Quantize the data
quanParams_1 = []
quanParams_2 = []
# If quantization is required:
if len(deviceOut) > 1:
if quant_tensor1!= 'noQuant':
print("Quantizing tensors")
quant_tensor1.bitQuantizer(deviceOut[0])
deviceOut[0] = quant_tensor1.quanData
quanParams_1.append(quant_tensor1.min)
quanParams_1.append(quant_tensor1.max)
quant_tensor2.bitQuantizer(deviceOut[1])
deviceOut[1] = quant_tensor2.quanData
quanParams_2.append(quant_tensor2.min)
quanParams_2.append(quant_tensor2.max)
else:
if quant_tensor1!= 'noQuant':
print("Quantizing tensor.")
quant_tensor1.bitQuantizer(deviceOut[0])
deviceOut[0] = quant_tensor1.quanData
quanParams_1.append(quant_tensor1.min)
quanParams_1.append(quant_tensor1.max)
# Save quantized tensors as image.
for i in range(len(deviceOut)):
quant_tensor = deviceOut[i]
for item_index in range(np.shape(quant_tensor)[0]):
for i_c in range(np.shape(quant_tensor)[-1]):
tensor_channel = Image.fromarray(quant_tensor[item_index,:,:,i_c].astype(np.uint8))
tensor_channel.save(os.path.join(results_dir,'original_batch_'+str(i_b)+'_item_'+str(item_index)+'_tensor_'+str(i)+'_channel_'+str(i_c)+res_filename+'.png'))
# -------------------------------------------------------------------- #
# Transmit the tensor deviceOut through the channel.
if channel_flag in ['GC','RL']:
# if a lossy channel has to be realized.
# if mc_task == 'GenLossPatterns':
# if we want to generate packet loss patterns.
lossMatrix = []
receivedIndices = []
lostIndices = []
dOut = []
for i in range(len(deviceOut)):
dO, lM, rI, lI = transmit(deviceOut[i], channel, rowsPerPacket)
dOut.append(dO)
lossMatrix.append(lM)
receivedIndices.append(rI)
lostIndices.append(lI)
channel.lossMatrix = []
deviceOut = dOut
# ---------------------------------------------------------------- #
# packetize tensor.
pkt_obj_list = []
for i in range(len(deviceOut)):
pkt_obj_list.append(PacketModel(rows_per_packet=rowsPerPacket,data_tensor=np.copy(deviceOut[i].data_tensor)))
# -------------------------------------------------------------------- #
if channel_flag == 'EX':
batch_loss_matrix = loss_matrix_mc[i_mc]
loss_matrix = [batch_loss_matrix[i_b]]
# -------------------------------------------------------------------- #
if channel_flag in ['GC','RL','EX']:
# ---------------------------------------------------------------- #
# apply the loss matrix to the tensor.
for i in range(len(pkt_obj_list)):
loss_map = lossMatrix[i]
#print(np.shape(loss_map))
channel_width = np.shape(pkt_obj_list[i].packet_seq)[3]
# loop through items in batch.
for item_index in range(np.shape(loss_map)[0]):
item_lost_map = loss_map[item_index,:,:]
lost_pkt_indices,lost_channel_indices = np.where(item_lost_map == False)
if len(lost_pkt_indices) != 0:
# drop packet in tensor.
for k in range(len(lost_pkt_indices)):
pkt_obj_list[i].packet_seq[item_index,lost_pkt_indices[k],:,:,lost_channel_indices[k]] = np.zeros([rowsPerPacket,channel_width])
for i in range(len(deviceOut)):
quant_tensor = pkt_obj_list[i].data_tensor
for item_index in range( | np.shape(quant_tensor) | numpy.shape |
# -*- coding: utf-8 -*-
from __future__ import absolute_import, division, unicode_literals
import unittest
import datetime
import warnings
import jsonpickle
from jsonpickle.compat import PY2, PY3, PY_MINOR
from helper import SkippableTest
try:
import numpy as np
import numpy.testing as npt
from numpy.compat import asbytes
from numpy.testing import assert_equal
except ImportError:
np = None
class NumpyTestCase(SkippableTest):
def setUp(self):
if np is None:
self.should_skip = True
return
self.should_skip = False
import jsonpickle.ext.numpy
jsonpickle.ext.numpy.register_handlers()
def tearDown(self):
if self.should_skip:
return
import jsonpickle.ext.numpy
jsonpickle.ext.numpy.unregister_handlers()
def roundtrip(self, obj):
return jsonpickle.decode(jsonpickle.encode(obj))
def test_dtype_roundtrip(self):
if self.should_skip:
return self.skip('numpy is not importable')
dtypes = [
np.int,
np.float,
np.complex,
np.int32,
np.str,
np.object,
np.unicode,
np.dtype('f4,i4,f2,i1'),
np.dtype(('f4', 'i4'), ('f2', 'i1')),
| np.dtype('1i4', align=True) | numpy.dtype |
# Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
import scipy.signal
__all__ = ['calc_discount_sum_rewards', 'calc_gae', 'Scaler']
"""
The following code are copied or modified from:
https://github.com/pat-coady/trpo
Written by <NAME> (pat-coady.github.io)
"""
def calc_discount_sum_rewards(rewards, gamma):
""" Calculate discounted forward sum of a sequence at each point """
return scipy.signal.lfilter([1.0], [1.0, -gamma], rewards[::-1])[::-1]
def calc_gae(rewards, values, gamma, lam):
""" Calculate generalized advantage estimator.
See: https://arxiv.org/pdf/1506.02438.pdf
"""
# temporal differences
tds = rewards - values + np.append(values[1:] * gamma, 0)
advantages = calc_discount_sum_rewards(tds, gamma * lam)
return advantages
class Scaler(object):
""" Generate scale and offset based on running mean and stddev along axis=0
offset = running mean
scale = 1 / (stddev + 0.1) / 3 (i.e. 3x stddev = +/- 1.0)
"""
def __init__(self, obs_dim):
"""
Args:
obs_dim: dimension of axis=1
"""
self.vars = np.zeros(obs_dim)
self.means = np.zeros(obs_dim)
self.cnt = 0
self.first_pass = True
def update(self, x):
""" Update running mean and variance (this is an exact method)
Args:
x: NumPy array, shape = (N, obs_dim)
see: https://stats.stackexchange.com/questions/43159/how-to-calculate-pooled-
variance-of-two-groups-given-known-group-variances-mean
"""
if self.first_pass:
self.means = np.mean(x, axis=0)
self.vars = np.var(x, axis=0)
self.cnt = x.shape[0]
self.first_pass = False
else:
n = x.shape[0]
new_data_var = np.var(x, axis=0)
new_data_mean = np.mean(x, axis=0)
new_data_mean_sq = np.square(new_data_mean)
new_means = (
(self.means * self.cnt) + (new_data_mean * n)) / (self.cnt + n)
self.vars = (((self.cnt * (self.vars + np.square(self.means))) +
(n * (new_data_var + new_data_mean_sq))) /
(self.cnt + n) - | np.square(new_means) | numpy.square |
from __future__ import print_function, division, absolute_import
import time
import matplotlib
matplotlib.use('Agg') # fix execution of tests involving matplotlib on travis
import numpy as np
import six.moves as sm
import cv2
import shapely
import shapely.geometry
import imgaug as ia
from imgaug.testutils import reseed
def main():
time_start = time.time()
test_is_np_array()
test_is_single_integer()
test_is_single_float()
test_is_single_number()
test_is_iterable()
test_is_string()
test_is_single_bool()
test_is_integer_array()
test_is_float_array()
test_is_callable()
test_caller_name()
test_seed()
test_current_random_state()
test_new_random_state()
test_dummy_random_state()
test_copy_random_state()
test_derive_random_state()
test_derive_random_states()
test_forward_random_state()
# test_quokka()
# test_quokka_square()
# test_angle_between_vectors()
# test_draw_text()
test_imresize_many_images()
test_imresize_single_image()
test_pad()
test_compute_paddings_for_aspect_ratio()
test_pad_to_aspect_ratio()
test_pool()
test_avg_pool()
test_max_pool()
test_draw_grid()
# test_show_grid()
# test_do_assert()
# test_HooksImages_is_activated()
# test_HooksImages_is_propagating()
# test_HooksImages_preprocess()
# test_HooksImages_postprocess()
test_Keypoint()
test_KeypointsOnImage()
test_BoundingBox()
test_BoundingBoxesOnImage()
# test_HeatmapsOnImage_get_arr()
# test_HeatmapsOnImage_find_global_maxima()
test_HeatmapsOnImage_draw()
test_HeatmapsOnImage_draw_on_image()
test_HeatmapsOnImage_invert()
test_HeatmapsOnImage_pad()
# test_HeatmapsOnImage_pad_to_aspect_ratio()
test_HeatmapsOnImage_avg_pool()
test_HeatmapsOnImage_max_pool()
test_HeatmapsOnImage_scale()
# test_HeatmapsOnImage_to_uint8()
# test_HeatmapsOnImage_from_uint8()
# test_HeatmapsOnImage_from_0to1()
# test_HeatmapsOnImage_change_normalization()
# test_HeatmapsOnImage_copy()
# test_HeatmapsOnImage_deepcopy()
test_SegmentationMapOnImage_bool()
test_SegmentationMapOnImage_get_arr_int()
# test_SegmentationMapOnImage_get_arr_bool()
test_SegmentationMapOnImage_draw()
test_SegmentationMapOnImage_draw_on_image()
test_SegmentationMapOnImage_pad()
test_SegmentationMapOnImage_pad_to_aspect_ratio()
test_SegmentationMapOnImage_scale()
test_SegmentationMapOnImage_to_heatmaps()
test_SegmentationMapOnImage_from_heatmaps()
test_SegmentationMapOnImage_copy()
test_SegmentationMapOnImage_deepcopy()
test_Polygon___init__()
test_Polygon_xx()
test_Polygon_yy()
test_Polygon_xx_int()
test_Polygon_yy_int()
test_Polygon_is_valid()
test_Polygon_area()
test_Polygon_project()
test_Polygon__compute_inside_image_point_mask()
test_Polygon_is_fully_within_image()
test_Polygon_is_partly_within_image()
test_Polygon_is_out_of_image()
test_Polygon_cut_out_of_image()
test_Polygon_clip_out_of_image()
test_Polygon_shift()
test_Polygon_draw_on_image()
test_Polygon_extract_from_image()
test_Polygon_to_shapely_polygon()
test_Polygon_to_bounding_box()
test_Polygon_from_shapely()
test_Polygon_copy()
test_Polygon_deepcopy()
test_Polygon___repr__()
test_Polygon___str__()
# test_Batch()
test_BatchLoader()
# test_BackgroundAugmenter.get_batch()
# test_BackgroundAugmenter._augment_images_worker()
# test_BackgroundAugmenter.terminate()
time_end = time.time()
print("<%s> Finished without errors in %.4fs." % (__file__, time_end - time_start,))
def test_is_np_array():
class _Dummy(object):
pass
values_true = [
np.zeros((1, 2), dtype=np.uint8),
np.zeros((64, 64, 3), dtype=np.uint8),
np.zeros((1, 2), dtype=np.float32),
np.zeros((100,), dtype=np.float64)
]
values_false = [
"A", "BC", "1", True, False, (1.0, 2.0), [1.0, 2.0], _Dummy(),
-100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4
]
for value in values_true:
assert ia.is_np_array(value) is True
for value in values_false:
assert ia.is_np_array(value) is False
def test_is_single_integer():
assert ia.is_single_integer("A") is False
assert ia.is_single_integer(None) is False
assert ia.is_single_integer(1.2) is False
assert ia.is_single_integer(1.0) is False
assert ia.is_single_integer(np.ones((1,), dtype=np.float32)[0]) is False
assert ia.is_single_integer(1) is True
assert ia.is_single_integer(1234) is True
assert ia.is_single_integer(np.ones((1,), dtype=np.uint8)[0]) is True
assert ia.is_single_integer(np.ones((1,), dtype=np.int32)[0]) is True
def test_is_single_float():
assert ia.is_single_float("A") is False
assert ia.is_single_float(None) is False
assert ia.is_single_float(1.2) is True
assert ia.is_single_float(1.0) is True
assert ia.is_single_float(np.ones((1,), dtype=np.float32)[0]) is True
assert ia.is_single_float(1) is False
assert ia.is_single_float(1234) is False
assert ia.is_single_float(np.ones((1,), dtype=np.uint8)[0]) is False
assert ia.is_single_float(np.ones((1,), dtype=np.int32)[0]) is False
def test_caller_name():
assert ia.caller_name() == 'test_caller_name'
def test_is_single_number():
class _Dummy(object):
pass
values_true = [-100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4]
values_false = ["A", "BC", "1", True, False, (1.0, 2.0), [1.0, 2.0], _Dummy(), np.zeros((1, 2), dtype=np.uint8)]
for value in values_true:
assert ia.is_single_number(value) is True
for value in values_false:
assert ia.is_single_number(value) is False
def test_is_iterable():
class _Dummy(object):
pass
values_true = [
[0, 1, 2],
["A", "X"],
[[123], [456, 789]],
[],
(1, 2, 3),
(1,),
tuple(),
"A",
"ABC",
"",
np.zeros((100,), dtype=np.uint8)
]
values_false = [1, 100, 0, -100, -1, 1.2, -1.2, True, False, _Dummy()]
for value in values_true:
assert ia.is_iterable(value) is True, value
for value in values_false:
assert ia.is_iterable(value) is False
def test_is_string():
class _Dummy(object):
pass
values_true = ["A", "BC", "1", ""]
values_false = [-100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4, True, False, (1.0, 2.0), [1.0, 2.0],
_Dummy(), np.zeros((1, 2), dtype=np.uint8)]
for value in values_true:
assert ia.is_string(value) is True
for value in values_false:
assert ia.is_string(value) is False
def test_is_single_bool():
class _Dummy(object):
pass
values_true = [False, True]
values_false = [-100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4, (1.0, 2.0), [1.0, 2.0], _Dummy(),
np.zeros((1, 2), dtype=np.uint8), np.zeros((1,), dtype=bool)]
for value in values_true:
assert ia.is_single_bool(value) is True
for value in values_false:
assert ia.is_single_bool(value) is False
def test_is_integer_array():
class _Dummy(object):
pass
values_true = [
np.zeros((1, 2), dtype=np.uint8),
np.zeros((100,), dtype=np.uint8),
np.zeros((1, 2), dtype=np.uint16),
np.zeros((1, 2), dtype=np.int32),
np.zeros((1, 2), dtype=np.int64)
]
values_false = [
"A", "BC", "1", "", -100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4, True, False,
(1.0, 2.0), [1.0, 2.0], _Dummy(),
np.zeros((1, 2), dtype=np.float16),
np.zeros((100,), dtype=np.float32),
np.zeros((1, 2), dtype=np.float64),
np.zeros((1, 2), dtype=np.bool)
]
for value in values_true:
assert ia.is_integer_array(value) is True
for value in values_false:
assert ia.is_integer_array(value) is False
def test_is_float_array():
class _Dummy(object):
pass
values_true = [
np.zeros((1, 2), dtype=np.float16),
np.zeros((100,), dtype=np.float32),
np.zeros((1, 2), dtype=np.float64)
]
values_false = [
"A", "BC", "1", "", -100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4, True, False,
(1.0, 2.0), [1.0, 2.0], _Dummy(),
np.zeros((1, 2), dtype=np.uint8),
np.zeros((100,), dtype=np.uint8),
np.zeros((1, 2), dtype=np.uint16),
np.zeros((1, 2), dtype=np.int32),
np.zeros((1, 2), dtype=np.int64),
np.zeros((1, 2), dtype=np.bool)
]
for value in values_true:
assert ia.is_float_array(value) is True
for value in values_false:
assert ia.is_float_array(value) is False
def test_is_callable():
def _dummy_func():
pass
_dummy_func2 = lambda x: x
class _Dummy1(object):
pass
class _Dummy2(object):
def __call__(self):
pass
values_true = [_dummy_func, _dummy_func2, _Dummy2()]
values_false = ["A", "BC", "1", "", -100, 1, 0, 1, 100, -1.2, -0.001, 0.0, 0.001, 1.2, 1e-4, True, False,
(1.0, 2.0), [1.0, 2.0], _Dummy1(), np.zeros((1, 2), dtype=np.uint8)]
for value in values_true:
assert ia.is_callable(value) == True
for value in values_false:
assert ia.is_callable(value) == False
def test_seed():
ia.seed(10017)
rs = np.random.RandomState(10017)
assert ia.CURRENT_RANDOM_STATE.randint(0, 1000*1000) == rs.randint(0, 1000*1000)
reseed()
def test_current_random_state():
assert ia.current_random_state() == ia.CURRENT_RANDOM_STATE
def test_new_random_state():
seed = 1000
ia.seed(seed)
rs_observed = ia.new_random_state(seed=None, fully_random=False)
rs_expected = np.random.RandomState(np.random.RandomState(seed).randint(0, 10**6, 1)[0])
assert rs_observed.randint(0, 10**6) == rs_expected.randint(0, 10**6)
rs_observed1 = ia.new_random_state(seed=None, fully_random=False)
rs_observed2 = ia.new_random_state(seed=None, fully_random=False)
assert rs_observed1.randint(0, 10**6) != rs_observed2.randint(0, 10**6)
ia.seed(seed)
np.random.seed(seed)
rs_observed = ia.new_random_state(seed=None, fully_random=True)
rs_not_expected = np.random.RandomState(np.random.RandomState(seed).randint(0, 10**6, 1)[0])
assert rs_observed.randint(0, 10**6) != rs_not_expected.randint(0, 10**6)
rs_observed1 = ia.new_random_state(seed=None, fully_random=True)
rs_observed2 = ia.new_random_state(seed=None, fully_random=True)
assert rs_observed1.randint(0, 10**6) != rs_observed2.randint(0, 10**6)
rs_observed1 = ia.new_random_state(seed=1234)
rs_observed2 = ia.new_random_state(seed=1234)
rs_expected = np.random.RandomState(1234)
assert rs_observed1.randint(0, 10**6) == rs_observed2.randint(0, 10**6) == rs_expected.randint(0, 10**6)
def test_dummy_random_state():
assert ia.dummy_random_state().randint(0, 10**6) == np.random.RandomState(1).randint(0, 10**6)
def test_copy_random_state():
rs = np.random.RandomState(1017)
rs_copy = ia.copy_random_state(rs)
assert rs != rs_copy
assert rs.randint(0, 10**6) == rs_copy.randint(0, 10**6)
assert ia.copy_random_state(np.random) == np.random
assert ia.copy_random_state(np.random, force_copy=True) != np.random
def test_derive_random_state():
rs = np.random.RandomState(1017)
rs_observed = ia.derive_random_state(np.random.RandomState(1017))
rs_expected = np.random.RandomState(np.random.RandomState(1017).randint(0, 10**6))
assert rs_observed.randint(0, 10**6) == rs_expected.randint(0, 10**6)
def test_derive_random_states():
rs_observed1, rs_observed2 = ia.derive_random_states(np.random.RandomState(1017), n=2)
seed = np.random.RandomState(1017).randint(0, 10**6)
rs_expected1 = np.random.RandomState(seed+0)
rs_expected2 = np.random.RandomState(seed+1)
assert rs_observed1.randint(0, 10**6) == rs_expected1.randint(0, 10**6)
assert rs_observed2.randint(0, 10**6) == rs_expected2.randint(0, 10**6)
def test_forward_random_state():
rs1 = np.random.RandomState(1017)
rs2 = np.random.RandomState(1017)
ia.forward_random_state(rs1)
rs2.uniform()
assert rs1.randint(0, 10**6) == rs2.randint(0, 10**6)
def test_imresize_many_images():
interpolations = [None,
"nearest", "linear", "area", "cubic",
cv2.INTER_NEAREST, cv2.INTER_LINEAR, cv2.INTER_AREA, cv2.INTER_CUBIC]
for c in [1, 3]:
image1 = np.zeros((16, 16, c), dtype=np.uint8) + 255
image2 = np.zeros((16, 16, c), dtype=np.uint8)
image3 = np.pad(
np.zeros((8, 8, c), dtype=np.uint8) + 255,
((4, 4), (4, 4), (0, 0)),
mode="constant",
constant_values=0
)
image1_small = np.zeros((8, 8, c), dtype=np.uint8) + 255
image2_small = np.zeros((8, 8, c), dtype=np.uint8)
image3_small = np.pad(
np.zeros((4, 4, c), dtype=np.uint8) + 255,
((2, 2), (2, 2), (0, 0)),
mode="constant",
constant_values=0
)
image1_large = np.zeros((32, 32, c), dtype=np.uint8) + 255
image2_large = np.zeros((32, 32, c), dtype=np.uint8)
image3_large = np.pad(
np.zeros((16, 16, c), dtype=np.uint8) + 255,
((8, 8), (8, 8), (0, 0)),
mode="constant",
constant_values=0
)
images = np.uint8([image1, image2, image3])
images_small = np.uint8([image1_small, image2_small, image3_small])
images_large = np.uint8([image1_large, image2_large, image3_large])
for images_this_iter in [images, list(images)]: # test for ndarray and list(ndarray) input
for interpolation in interpolations:
images_same_observed = ia.imresize_many_images(images_this_iter, (16, 16), interpolation=interpolation)
for image_expected, image_observed in zip(images_this_iter, images_same_observed):
diff = np.abs(image_expected.astype(np.int32) - image_observed.astype(np.int32))
assert np.sum(diff) == 0
for interpolation in interpolations:
images_small_observed = ia.imresize_many_images(images_this_iter, (8, 8), interpolation=interpolation)
for image_expected, image_observed in zip(images_small, images_small_observed):
diff = np.abs(image_expected.astype(np.int32) - image_observed.astype(np.int32))
diff_fraction = np.sum(diff) / (image_observed.size * 255)
assert diff_fraction < 0.5
for interpolation in interpolations:
images_large_observed = ia.imresize_many_images(images_this_iter, (32, 32), interpolation=interpolation)
for image_expected, image_observed in zip(images_large, images_large_observed):
diff = np.abs(image_expected.astype(np.int32) - image_observed.astype(np.int32))
diff_fraction = np.sum(diff) / (image_observed.size * 255)
assert diff_fraction < 0.5
# test size given as single int
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, 8)
assert observed.shape == (1, 8, 8, 3)
# test size given as single float
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, 2.0)
assert observed.shape == (1, 8, 8, 3)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, 0.5)
assert observed.shape == (1, 2, 2, 3)
# test size given as (float, float)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (2.0, 2.0))
assert observed.shape == (1, 8, 8, 3)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (0.5, 0.5))
assert observed.shape == (1, 2, 2, 3)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (2.0, 0.5))
assert observed.shape == (1, 8, 2, 3)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (0.5, 2.0))
assert observed.shape == (1, 2, 8, 3)
# test size given as int+float or float+int
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (11, 2.0))
assert observed.shape == (1, 11, 8, 3)
images = np.zeros((1, 4, 4, 3), dtype=np.uint8)
observed = ia.imresize_many_images(images, (2.0, 11))
assert observed.shape == (1, 8, 11, 3)
# test no channels
images = np.zeros((1, 4, 4), dtype=np.uint8)
images_rs = ia.imresize_many_images(images, (2, 2))
assert images_rs.shape == (1, 2, 2)
images = [np.zeros((4, 4), dtype=np.uint8)]
images_rs = ia.imresize_many_images(images, (2, 2))
assert isinstance(images_rs, list)
assert images_rs[0].shape == (2, 2)
# test len 0 input
observed = ia.imresize_many_images(np.zeros((0, 8, 8, 3), dtype=np.uint8), (4, 4))
assert ia.is_np_array(observed)
assert observed.dtype.type == np.uint8
assert len(observed) == 0
observed = ia.imresize_many_images([], (4, 4))
assert isinstance(observed, list)
assert len(observed) == 0
# test images with zero height/width
images = [np.zeros((0, 4, 3), dtype=np.uint8)]
got_exception = False
try:
_ = ia.imresize_many_images(images, sizes=(2, 2))
except Exception as exc:
assert "Cannot resize images, because at least one image has a height and/or width of zero." in str(exc)
got_exception = True
assert got_exception
images = [np.zeros((4, 0, 3), dtype=np.uint8)]
got_exception = False
try:
_ = ia.imresize_many_images(images, sizes=(2, 2))
except Exception as exc:
assert "Cannot resize images, because at least one image has a height and/or width of zero." in str(exc)
got_exception = True
assert got_exception
images = [np.zeros((0, 0, 3), dtype=np.uint8)]
got_exception = False
try:
_ = ia.imresize_many_images(images, sizes=(2, 2))
except Exception as exc:
assert "Cannot resize images, because at least one image has a height and/or width of zero." in str(exc)
got_exception = True
assert got_exception
# test invalid sizes
sizes_all = [(-1, 2), (0, 2)]
sizes_all = sizes_all\
+ [(float(a), b) for a, b in sizes_all]\
+ [(a, float(b)) for a, b in sizes_all]\
+ [(float(a), float(b)) for a, b in sizes_all]\
+ [(-a, -b) for a, b in sizes_all]\
+ [(-float(a), -b) for a, b in sizes_all]\
+ [(-a, -float(b)) for a, b in sizes_all]\
+ [(-float(a), -float(b)) for a, b in sizes_all]
sizes_all = sizes_all\
+ [(b, a) for a, b in sizes_all]
sizes_all = sizes_all\
+ [-1.0, 0.0, -1, 0]
for sizes in sizes_all:
images = [np.zeros((4, 4, 3), dtype=np.uint8)]
got_exception = False
try:
_ = ia.imresize_many_images(images, sizes=sizes)
except Exception as exc:
assert "value is zero or lower than zero." in str(exc)
got_exception = True
assert got_exception
# test list input but all with same shape
images = [np.zeros((8, 8, 3), dtype=np.uint8) for _ in range(2)]
observed = ia.imresize_many_images(images, (4, 4))
assert isinstance(observed, list)
assert all([image.shape == (4, 4, 3) for image in observed])
assert all([image.dtype.type == np.uint8 for image in observed])
def test_imresize_single_image():
for c in [-1, 1, 3]:
image1 = np.zeros((16, 16, abs(c)), dtype=np.uint8) + 255
image2 = np.zeros((16, 16, abs(c)), dtype=np.uint8)
image3 = np.pad(
np.zeros((8, 8, abs(c)), dtype=np.uint8) + 255,
((4, 4), (4, 4), (0, 0)),
mode="constant",
constant_values=0
)
image1_small = np.zeros((8, 8, abs(c)), dtype=np.uint8) + 255
image2_small = np.zeros((8, 8, abs(c)), dtype=np.uint8)
image3_small = np.pad(
np.zeros((4, 4, abs(c)), dtype=np.uint8) + 255,
((2, 2), (2, 2), (0, 0)),
mode="constant",
constant_values=0
)
image1_large = np.zeros((32, 32, abs(c)), dtype=np.uint8) + 255
image2_large = np.zeros((32, 32, abs(c)), dtype=np.uint8)
image3_large = np.pad(
np.zeros((16, 16, abs(c)), dtype=np.uint8) + 255,
((8, 8), (8, 8), (0, 0)),
mode="constant",
constant_values=0
)
images = np.uint8([image1, image2, image3])
images_small = np.uint8([image1_small, image2_small, image3_small])
images_large = np.uint8([image1_large, image2_large, image3_large])
if c == -1:
images = images[:, :, 0]
images_small = images_small[:, :, 0]
images_large = images_large[:, :, 0]
interpolations = [None,
"nearest", "linear", "area", "cubic",
cv2.INTER_NEAREST, cv2.INTER_LINEAR, cv2.INTER_AREA, cv2.INTER_CUBIC]
for interpolation in interpolations:
for image in images:
image_observed = ia.imresize_single_image(image, (16, 16), interpolation=interpolation)
diff = np.abs(image.astype(np.int32) - image_observed.astype(np.int32))
assert np.sum(diff) == 0
for interpolation in interpolations:
for image, image_expected in zip(images, images_small):
image_observed = ia.imresize_single_image(image, (8, 8), interpolation=interpolation)
diff = np.abs(image_expected.astype(np.int32) - image_observed.astype(np.int32))
diff_fraction = np.sum(diff) / (image_observed.size * 255)
assert diff_fraction < 0.5
for interpolation in interpolations:
for image, image_expected in zip(images, images_large):
image_observed = ia.imresize_single_image(image, (32, 32), interpolation=interpolation)
diff = np.abs(image_expected.astype(np.int32) - image_observed.astype(np.int32))
diff_fraction = np.sum(diff) / (image_observed.size * 255)
assert diff_fraction < 0.5
def test_pad():
# -------
# uint8, int32
# -------
for dtype in [np.uint8, np.int32]:
arr = np.zeros((3, 3), dtype=dtype) + 255
arr_pad = ia.pad(arr)
assert arr_pad.shape == (3, 3)
assert arr_pad.dtype.type == dtype
assert np.array_equal(arr_pad, arr)
arr_pad = ia.pad(arr, top=1)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[0, :] == 0)
arr_pad = ia.pad(arr, right=1)
assert arr_pad.shape == (3, 4)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[:, -1] == 0)
arr_pad = ia.pad(arr, bottom=1)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[-1, :] == 0)
arr_pad = ia.pad(arr, left=1)
assert arr_pad.shape == (3, 4)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[:, 0] == 0)
arr_pad = ia.pad(arr, top=1, right=2, bottom=3, left=4)
assert arr_pad.shape == (3+(1+3), 3+(2+4))
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[0, :] == 0)
assert np.all(arr_pad[:, -2:] == 0)
assert np.all(arr_pad[-3:, :] == 0)
assert np.all(arr_pad[:, :4] == 0)
arr_pad = ia.pad(arr, top=1, cval=10)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[0, :] == 10)
arr = np.zeros((3, 3, 3), dtype=dtype) + 128
arr_pad = ia.pad(arr, top=1)
assert arr_pad.shape == (4, 3, 3)
assert arr_pad.dtype.type == dtype
assert np.all(arr_pad[0, :, 0] == 0)
assert np.all(arr_pad[0, :, 1] == 0)
assert np.all(arr_pad[0, :, 2] == 0)
arr = np.zeros((3, 3), dtype=dtype) + 128
arr[1, 1] = 200
arr_pad = ia.pad(arr, top=1, mode="maximum")
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert arr_pad[0, 0] == 128
assert arr_pad[0, 1] == 200
assert arr_pad[0, 2] == 128
arr = np.zeros((3, 3), dtype=dtype)
arr_pad = ia.pad(arr, top=1, mode="constant", cval=123)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert arr_pad[0, 0] == 123
assert arr_pad[0, 1] == 123
assert arr_pad[0, 2] == 123
assert arr_pad[1, 0] == 0
arr = np.zeros((1, 1), dtype=dtype) + 100
arr_pad = ia.pad(arr, top=4, mode="linear_ramp", cval=200)
assert arr_pad.shape == (5, 1)
assert arr_pad.dtype.type == dtype
assert arr_pad[0, 0] == 200
assert arr_pad[1, 0] == 175
assert arr_pad[2, 0] == 150
assert arr_pad[3, 0] == 125
assert arr_pad[4, 0] == 100
# -------
# float32, float64
# -------
for dtype in [np.float32, np.float64]:
arr = np.zeros((3, 3), dtype=dtype) + 1.0
arr_pad = ia.pad(arr)
assert arr_pad.shape == (3, 3)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad, arr)
arr_pad = ia.pad(arr, top=1)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[0, :], dtype([0, 0, 0]))
arr_pad = ia.pad(arr, right=1)
assert arr_pad.shape == (3, 4)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[:, -1], dtype([0, 0, 0]))
arr_pad = ia.pad(arr, bottom=1)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[-1, :], dtype([0, 0, 0]))
arr_pad = ia.pad(arr, left=1)
assert arr_pad.shape == (3, 4)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[:, 0], dtype([0, 0, 0]))
arr_pad = ia.pad(arr, top=1, right=2, bottom=3, left=4)
assert arr_pad.shape == (3+(1+3), 3+(2+4))
assert arr_pad.dtype.type == dtype
assert 0 - 1e-6 < np.max(arr_pad[0, :]) < 0 + 1e-6
assert 0 - 1e-6 < np.max(arr_pad[:, -2:]) < 0 + 1e-6
assert 0 - 1e-6 < np.max(arr_pad[-3, :]) < 0 + 1e-6
assert 0 - 1e-6 < np.max(arr_pad[:, :4]) < 0 + 1e-6
arr_pad = ia.pad(arr, top=1, cval=0.2)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[0, :], dtype([0.2, 0.2, 0.2]))
arr = np.zeros((3, 3, 3), dtype=dtype) + 0.5
arr_pad = ia.pad(arr, top=1)
assert arr_pad.shape == (4, 3, 3)
assert arr_pad.dtype.type == dtype
assert np.allclose(arr_pad[0, :, 0], dtype([0, 0, 0]))
assert np.allclose(arr_pad[0, :, 1], dtype([0, 0, 0]))
assert np.allclose(arr_pad[0, :, 2], dtype([0, 0, 0]))
arr = np.zeros((3, 3), dtype=dtype) + 0.5
arr[1, 1] = 0.75
arr_pad = ia.pad(arr, top=1, mode="maximum")
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert 0.50 - 1e-6 < arr_pad[0, 0] < 0.50 + 1e-6
assert 0.75 - 1e-6 < arr_pad[0, 1] < 0.75 + 1e-6
assert 0.50 - 1e-6 < arr_pad[0, 2] < 0.50 + 1e-6
arr = np.zeros((3, 3), dtype=dtype)
arr_pad = ia.pad(arr, top=1, mode="constant", cval=0.4)
assert arr_pad.shape == (4, 3)
assert arr_pad.dtype.type == dtype
assert 0.4 - 1e-6 < arr_pad[0, 0] < 0.4 + 1e-6
assert 0.4 - 1e-6 < arr_pad[0, 1] < 0.4 + 1e-6
assert 0.4 - 1e-6 < arr_pad[0, 2] < 0.4 + 1e-6
assert 0.0 - 1e-6 < arr_pad[1, 0] < 0.0 + 1e-6
arr = np.zeros((1, 1), dtype=dtype) + 0.6
arr_pad = ia.pad(arr, top=4, mode="linear_ramp", cval=1.0)
assert arr_pad.shape == (5, 1)
assert arr_pad.dtype.type == dtype
assert 1.0 - 1e-6 < arr_pad[0, 0] < 1.0 + 1e-6
assert 0.9 - 1e-6 < arr_pad[1, 0] < 0.9 + 1e-6
assert 0.8 - 1e-6 < arr_pad[2, 0] < 0.8 + 1e-6
assert 0.7 - 1e-6 < arr_pad[3, 0] < 0.7 + 1e-6
assert 0.6 - 1e-6 < arr_pad[4, 0] < 0.6 + 1e-6
def test_compute_paddings_for_aspect_ratio():
arr = np.zeros((4, 4), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 1.0)
assert top == 0
assert right == 0
assert bottom == 0
assert left == 0
arr = np.zeros((1, 4), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 1.0)
assert top == 2
assert right == 0
assert bottom == 1
assert left == 0
arr = np.zeros((4, 1), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 1.0)
assert top == 0
assert right == 2
assert bottom == 0
assert left == 1
arr = np.zeros((2, 4), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 1.0)
assert top == 1
assert right == 0
assert bottom == 1
assert left == 0
arr = np.zeros((4, 2), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 1.0)
assert top == 0
assert right == 1
assert bottom == 0
assert left == 1
arr = np.zeros((4, 4), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 0.5)
assert top == 2
assert right == 0
assert bottom == 2
assert left == 0
arr = np.zeros((4, 4), dtype=np.uint8)
top, right, bottom, left = ia.compute_paddings_for_aspect_ratio(arr, 2.0)
assert top == 0
assert right == 2
assert bottom == 0
assert left == 2
def test_pad_to_aspect_ratio():
for dtype in [np.uint8, np.int32, np.float32]:
# aspect_ratio = 1.0
arr = np.zeros((4, 4), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
arr = np.zeros((1, 4), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
arr = np.zeros((4, 1), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
arr = np.zeros((2, 4), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
arr = np.zeros((4, 2), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
# aspect_ratio != 1.0
arr = np.zeros((4, 4), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
arr = np.zeros((4, 4), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 0.5)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 8
assert arr_pad.shape[1] == 4
# 3d arr
arr = np.zeros((4, 2, 3), dtype=dtype)
arr_pad = ia.pad_to_aspect_ratio(arr, 1.0)
assert arr_pad.dtype.type == dtype
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 4
assert arr_pad.shape[2] == 3
# cval
arr = np.zeros((4, 4), dtype=np.uint8) + 128
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0)
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
assert np.max(arr_pad[:, 0:2]) == 0
assert np.max(arr_pad[:, -2:]) == 0
assert np.max(arr_pad[:, 2:-2]) == 128
arr = np.zeros((4, 4), dtype=np.uint8) + 128
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0, cval=10)
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
assert np.max(arr_pad[:, 0:2]) == 10
assert np.max(arr_pad[:, -2:]) == 10
assert np.max(arr_pad[:, 2:-2]) == 128
arr = np.zeros((4, 4), dtype=np.float32) + 0.5
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0, cval=0.0)
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
assert 0 - 1e-6 <= np.max(arr_pad[:, 0:2]) <= 0 + 1e-6
assert 0 - 1e-6 <= np.max(arr_pad[:, -2:]) <= 0 + 1e-6
assert 0.5 - 1e-6 <= np.max(arr_pad[:, 2:-2]) <= 0.5 + 1e-6
arr = np.zeros((4, 4), dtype=np.float32) + 0.5
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0, cval=0.1)
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
assert 0.1 - 1e-6 <= np.max(arr_pad[:, 0:2]) <= 0.1 + 1e-6
assert 0.1 - 1e-6 <= np.max(arr_pad[:, -2:]) <= 0.1 + 1e-6
assert 0.5 - 1e-6 <= np.max(arr_pad[:, 2:-2]) <= 0.5 + 1e-6
# mode
arr = np.zeros((4, 4), dtype=np.uint8) + 128
arr[1:3, 1:3] = 200
arr_pad = ia.pad_to_aspect_ratio(arr, 2.0, mode="maximum")
assert arr_pad.shape[0] == 4
assert arr_pad.shape[1] == 8
assert np.max(arr_pad[0:1, 0:2]) == 128
assert np.max(arr_pad[1:3, 0:2]) == 200
assert np.max(arr_pad[3:, 0:2]) == 128
assert np.max(arr_pad[0:1, -2:]) == 128
assert np.max(arr_pad[1:3, -2:]) == 200
assert np.max(arr_pad[3:, -2:]) == 128
# TODO add tests for return_pad_values=True
def test_pool():
# basic functionality with uint8, int32, float32
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, 2, np.average)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.average([10, 11, 14, 15]))
arr = np.int32([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, 2, np.average)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.average([10, 11, 14, 15]))
arr = np.float32([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, 2, np.average)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert np.allclose(arr_pooled[0, 0], np.average([0, 1, 4, 5]))
assert np.allclose(arr_pooled[0, 1], np.average([2, 3, 6, 7]))
assert np.allclose(arr_pooled[1, 0], np.average([8, 9, 12, 13]))
assert np.allclose(arr_pooled[1, 1], np.average([10, 11, 14, 15]))
# preserve_dtype off
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, 2, np.average, preserve_dtype=False)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == np.float64
assert np.allclose(arr_pooled[0, 0], np.average([0, 1, 4, 5]))
assert np.allclose(arr_pooled[0, 1], np.average([2, 3, 6, 7]))
assert np.allclose(arr_pooled[1, 0], np.average([8, 9, 12, 13]))
assert np.allclose(arr_pooled[1, 1], np.average([10, 11, 14, 15]))
# maximum function
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, 2, np.max)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.max([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.max([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.max([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.max([10, 11, 14, 15]))
# 3d array
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr = np.tile(arr[..., np.newaxis], (1, 1, 3))
arr_pooled = ia.pool(arr, 2, np.average)
assert arr_pooled.shape == (2, 2, 3)
assert np.array_equal(arr_pooled[..., 0], arr_pooled[..., 1])
assert np.array_equal(arr_pooled[..., 1], arr_pooled[..., 2])
arr_pooled = arr_pooled[..., 0]
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.average([10, 11, 14, 15]))
# block_size per axis
arr = np.float32([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.pool(arr, (2, 1), np.average)
assert arr_pooled.shape == (2, 4)
assert arr_pooled.dtype == arr.dtype.type
assert np.allclose(arr_pooled[0, 0], np.average([0, 4]))
assert np.allclose(arr_pooled[0, 1], np.average([1, 5]))
assert np.allclose(arr_pooled[0, 2], np.average([2, 6]))
assert np.allclose(arr_pooled[0, 3], np.average([3, 7]))
assert np.allclose(arr_pooled[1, 0], np.average([8, 12]))
assert np.allclose(arr_pooled[1, 1], np.average([9, 13]))
assert np.allclose(arr_pooled[1, 2], np.average([10, 14]))
assert np.allclose(arr_pooled[1, 3], np.average([11, 15]))
# cval
arr = np.uint8([
[0, 1, 2],
[4, 5, 6],
[8, 9, 10]
])
arr_pooled = ia.pool(arr, 2, np.average)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 0, 6, 0]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 0, 0]))
assert arr_pooled[1, 1] == int(np.average([10, 0, 0, 0]))
arr = np.uint8([
[0, 1],
[4, 5]
])
arr_pooled = ia.pool(arr, (4, 1), np.average)
assert arr_pooled.shape == (1, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 4, 0, 0]))
assert arr_pooled[0, 1] == int(np.average([1, 5, 0, 0]))
arr = np.uint8([
[0, 1, 2],
[4, 5, 6],
[8, 9, 10]
])
arr_pooled = ia.pool(arr, 2, np.average, cval=22)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 22, 6, 22]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 22, 22]))
assert arr_pooled[1, 1] == int(np.average([10, 22, 22, 22]))
def test_avg_pool():
# very basic test, as avg_pool() just calls pool(), which is tested in test_pool()
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.avg_pool(arr, 2)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.average([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.average([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.average([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.average([10, 11, 14, 15]))
def test_max_pool():
# very basic test, as avg_pool() just calls pool(), which is tested in test_pool()
arr = np.uint8([
[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]
])
arr_pooled = ia.max_pool(arr, 2)
assert arr_pooled.shape == (2, 2)
assert arr_pooled.dtype == arr.dtype.type
assert arr_pooled[0, 0] == int(np.max([0, 1, 4, 5]))
assert arr_pooled[0, 1] == int(np.max([2, 3, 6, 7]))
assert arr_pooled[1, 0] == int(np.max([8, 9, 12, 13]))
assert arr_pooled[1, 1] == int(np.max([10, 11, 14, 15]))
def test_draw_grid():
image = np.zeros((2, 2, 3), dtype=np.uint8)
image[0, 0] = 64
image[0, 1] = 128
image[1, 0] = 192
image[1, 1] = 256
grid = ia.draw_grid([image], rows=1, cols=1)
assert np.array_equal(grid, image)
grid = ia.draw_grid(np.uint8([image]), rows=1, cols=1)
assert np.array_equal(grid, image)
grid = ia.draw_grid([image, image, image, image], rows=2, cols=2)
expected = np.vstack([
np.hstack([image, image]),
np.hstack([image, image])
])
assert np.array_equal(grid, expected)
grid = ia.draw_grid([image, image], rows=1, cols=2)
expected = np.hstack([image, image])
assert np.array_equal(grid, expected)
grid = ia.draw_grid([image, image, image, image], rows=2, cols=None)
expected = np.vstack([
np.hstack([image, image]),
np.hstack([image, image])
])
assert np.array_equal(grid, expected)
grid = ia.draw_grid([image, image, image, image], rows=None, cols=2)
expected = np.vstack([
np.hstack([image, image]),
np.hstack([image, image])
])
assert np.array_equal(grid, expected)
grid = ia.draw_grid([image, image, image, image], rows=None, cols=None)
expected = np.vstack([
np.hstack([image, image]),
np.hstack([image, image])
])
assert np.array_equal(grid, expected)
def test_Keypoint():
eps = 1e-8
# x/y/x_int/y_int
kp = ia.Keypoint(y=1, x=2)
assert kp.y == 1
assert kp.x == 2
assert kp.y_int == 1
assert kp.x_int == 2
kp = ia.Keypoint(y=1.1, x=2.7)
assert 1.1 - eps < kp.y < 1.1 + eps
assert 2.7 - eps < kp.x < 2.7 + eps
assert kp.y_int == 1
assert kp.x_int == 3
# project
kp = ia.Keypoint(y=1, x=2)
kp2 = kp.project((10, 10), (10, 10))
assert kp2.y == 1
assert kp2.x == 2
kp2 = kp.project((10, 10), (20, 10))
assert kp2.y == 2
assert kp2.x == 2
kp2 = kp.project((10, 10), (10, 20))
assert kp2.y == 1
assert kp2.x == 4
kp2 = kp.project((10, 10), (20, 20))
assert kp2.y == 2
assert kp2.x == 4
# shift
kp = ia.Keypoint(y=1, x=2)
kp2 = kp.shift(y=1)
assert kp2.y == 2
assert kp2.x == 2
kp2 = kp.shift(y=-1)
assert kp2.y == 0
assert kp2.x == 2
kp2 = kp.shift(x=1)
assert kp2.y == 1
assert kp2.x == 3
kp2 = kp.shift(x=-1)
assert kp2.y == 1
assert kp2.x == 1
kp2 = kp.shift(y=1, x=2)
assert kp2.y == 2
assert kp2.x == 4
# __repr__ / __str_
kp = ia.Keypoint(y=1, x=2)
assert kp.__repr__() == kp.__str__() == "Keypoint(x=2.00000000, y=1.00000000)"
kp = ia.Keypoint(y=1.2, x=2.7)
assert kp.__repr__() == kp.__str__() == "Keypoint(x=2.70000000, y=1.20000000)"
def test_KeypointsOnImage():
eps = 1e-8
kps = [ia.Keypoint(x=1, y=2), ia.Keypoint(x=3, y=4)]
# height/width
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(10, 20, 3))
assert kpi.height == 10
assert kpi.width == 20
# image instead of shape
kpi = ia.KeypointsOnImage(keypoints=kps, shape=np.zeros((10, 20, 3), dtype=np.uint8))
assert kpi.shape == (10, 20, 3)
# on()
kpi2 = kpi.on((10, 20, 3))
assert all([kp_i.x == kp_j.x and kp_i.y == kp_j.y for kp_i, kp_j in zip(kpi.keypoints, kpi2.keypoints)])
kpi2 = kpi.on((20, 40, 3))
assert kpi2.keypoints[0].x == 2
assert kpi2.keypoints[0].y == 4
assert kpi2.keypoints[1].x == 6
assert kpi2.keypoints[1].y == 8
kpi2 = kpi.on(np.zeros((20, 40, 3), dtype=np.uint8))
assert kpi2.keypoints[0].x == 2
assert kpi2.keypoints[0].y == 4
assert kpi2.keypoints[1].x == 6
assert kpi2.keypoints[1].y == 8
# draw_on_image
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
image = np.zeros((5, 5, 3), dtype=np.uint8) + 10
kps_mask = np.zeros(image.shape[0:2], dtype=np.bool)
kps_mask[2, 1] = 1
kps_mask[4, 3] = 1
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=3, copy=True, raise_if_out_of_image=False)
kps_mask_size3 = np.copy(kps_mask)
kps_mask_size3[2-1:2+1+1, 1-1:1+1+1] = 1
kps_mask_size3[4-1:4+1+1, 3-1:3+1+1] = 1
assert np.all(image_kps[kps_mask_size3] == [0, 255, 0])
assert np.all(image_kps[~kps_mask_size3] == [10, 10, 10])
image_kps = kpi.draw_on_image(image, color=[0, 0, 255], size=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_kps[kps_mask] == [0, 0, 255])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
image_kps = kpi.draw_on_image(image, color=255, size=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_kps[kps_mask] == [255, 255, 255])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
image2 = np.copy(image)
image_kps = kpi.draw_on_image(image2, color=[0, 255, 0], size=1, copy=False, raise_if_out_of_image=False)
assert np.all(image2 == image_kps)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
assert np.all(image2[kps_mask] == [0, 255, 0])
assert np.all(image2[~kps_mask] == [10, 10, 10])
kpi = ia.KeypointsOnImage(keypoints=kps + [ia.Keypoint(x=100, y=100)], shape=(5, 5, 3))
image = np.zeros((5, 5, 3), dtype=np.uint8) + 10
kps_mask = np.zeros(image.shape[0:2], dtype=np.bool)
kps_mask[2, 1] = 1
kps_mask[4, 3] = 1
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
kpi = ia.KeypointsOnImage(keypoints=kps + [ia.Keypoint(x=100, y=100)], shape=(5, 5, 3))
image = np.zeros((5, 5, 3), dtype=np.uint8) + 10
got_exception = False
try:
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=1, copy=True, raise_if_out_of_image=True)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
except Exception:
got_exception = True
assert got_exception
kpi = ia.KeypointsOnImage(keypoints=kps + [ia.Keypoint(x=5, y=5)], shape=(5, 5, 3))
image = np.zeros((5, 5, 3), dtype=np.uint8) + 10
kps_mask = np.zeros(image.shape[0:2], dtype=np.bool)
kps_mask[2, 1] = 1
kps_mask[4, 3] = 1
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
got_exception = False
try:
image_kps = kpi.draw_on_image(image, color=[0, 255, 0], size=1, copy=True, raise_if_out_of_image=True)
assert np.all(image_kps[kps_mask] == [0, 255, 0])
assert np.all(image_kps[~kps_mask] == [10, 10, 10])
except Exception:
got_exception = True
assert got_exception
# shift
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
kpi2 = kpi.shift(x=0, y=0)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x
assert kpi2.keypoints[0].y == kpi.keypoints[0].y
assert kpi2.keypoints[1].x == kpi.keypoints[1].x
assert kpi2.keypoints[1].y == kpi.keypoints[1].y
kpi2 = kpi.shift(x=1)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x + 1
assert kpi2.keypoints[0].y == kpi.keypoints[0].y
assert kpi2.keypoints[1].x == kpi.keypoints[1].x + 1
assert kpi2.keypoints[1].y == kpi.keypoints[1].y
kpi2 = kpi.shift(x=-1)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x - 1
assert kpi2.keypoints[0].y == kpi.keypoints[0].y
assert kpi2.keypoints[1].x == kpi.keypoints[1].x - 1
assert kpi2.keypoints[1].y == kpi.keypoints[1].y
kpi2 = kpi.shift(y=1)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x
assert kpi2.keypoints[0].y == kpi.keypoints[0].y + 1
assert kpi2.keypoints[1].x == kpi.keypoints[1].x
assert kpi2.keypoints[1].y == kpi.keypoints[1].y + 1
kpi2 = kpi.shift(y=-1)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x
assert kpi2.keypoints[0].y == kpi.keypoints[0].y - 1
assert kpi2.keypoints[1].x == kpi.keypoints[1].x
assert kpi2.keypoints[1].y == kpi.keypoints[1].y - 1
kpi2 = kpi.shift(x=1, y=2)
assert kpi2.keypoints[0].x == kpi.keypoints[0].x + 1
assert kpi2.keypoints[0].y == kpi.keypoints[0].y + 2
assert kpi2.keypoints[1].x == kpi.keypoints[1].x + 1
assert kpi2.keypoints[1].y == kpi.keypoints[1].y + 2
# get_coords_array
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
observed = kpi.get_coords_array()
expected = np.float32([
[1, 2],
[3, 4]
])
assert np.allclose(observed, expected)
# from_coords_array
arr = np.float32([
[1, 2],
[3, 4]
])
kpi = ia.KeypointsOnImage.from_coords_array(arr, shape=(5, 5, 3))
assert 1 - eps < kpi.keypoints[0].x < 1 + eps
assert 2 - eps < kpi.keypoints[0].y < 2 + eps
assert 3 - eps < kpi.keypoints[1].x < 3 + eps
assert 4 - eps < kpi.keypoints[1].y < 4 + eps
# to_keypoint_image
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
image = kpi.to_keypoint_image(size=1)
image_size3 = kpi.to_keypoint_image(size=3)
kps_mask = np.zeros((5, 5, 2), dtype=np.bool)
kps_mask[2, 1, 0] = 1
kps_mask[4, 3, 1] = 1
kps_mask_size3 = np.zeros_like(kps_mask)
kps_mask_size3[2-1:2+1+1, 1-1:1+1+1, 0] = 1
kps_mask_size3[4-1:4+1+1, 3-1:3+1+1, 1] = 1
assert np.all(image[kps_mask] == 255)
assert np.all(image[~kps_mask] == 0)
assert np.all(image_size3[kps_mask] == 255)
assert np.all(image_size3[kps_mask_size3] >= 128)
assert np.all(image_size3[~kps_mask_size3] == 0)
# from_keypoint_image()
kps_image = np.zeros((5, 5, 2), dtype=np.uint8)
kps_image[2, 1, 0] = 255
kps_image[4, 3, 1] = 255
kpi2 = ia.KeypointsOnImage.from_keypoint_image(kps_image, nb_channels=3)
assert kpi2.shape == (5, 5, 3)
assert len(kpi2.keypoints) == 2
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[1].y == 4
assert kpi2.keypoints[1].x == 3
kps_image = np.zeros((5, 5, 2), dtype=np.uint8)
kps_image[2, 1, 0] = 255
kps_image[4, 3, 1] = 10
kpi2 = ia.KeypointsOnImage.from_keypoint_image(kps_image, if_not_found_coords={"x": -1, "y": -2}, threshold=20,
nb_channels=3)
assert kpi2.shape == (5, 5, 3)
assert len(kpi2.keypoints) == 2
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[1].y == -2
assert kpi2.keypoints[1].x == -1
kps_image = np.zeros((5, 5, 2), dtype=np.uint8)
kps_image[2, 1, 0] = 255
kps_image[4, 3, 1] = 10
kpi2 = ia.KeypointsOnImage.from_keypoint_image(kps_image, if_not_found_coords=(-1, -2), threshold=20,
nb_channels=3)
assert kpi2.shape == (5, 5, 3)
assert len(kpi2.keypoints) == 2
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[1].y == -2
assert kpi2.keypoints[1].x == -1
kps_image = np.zeros((5, 5, 2), dtype=np.uint8)
kps_image[2, 1, 0] = 255
kps_image[4, 3, 1] = 10
kpi2 = ia.KeypointsOnImage.from_keypoint_image(kps_image, if_not_found_coords=None, threshold=20, nb_channels=3)
assert kpi2.shape == (5, 5, 3)
assert len(kpi2.keypoints) == 1
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[0].x == 1
got_exception = False
try:
kps_image = np.zeros((5, 5, 2), dtype=np.uint8)
kps_image[2, 1, 0] = 255
kps_image[4, 3, 1] = 10
_ = ia.KeypointsOnImage.from_keypoint_image(kps_image, if_not_found_coords="exception-please", threshold=20,
nb_channels=3)
except Exception as exc:
assert "Expected if_not_found_coords to be" in str(exc)
got_exception = True
assert got_exception
# copy()
kps = [ia.Keypoint(x=1, y=2), ia.Keypoint(x=3, y=4)]
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
kpi2 = kpi.copy()
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[1].x == 3
assert kpi2.keypoints[1].y == 4
kps[0].x = 100
assert kpi2.keypoints[0].x == 100
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[1].x == 3
assert kpi2.keypoints[1].y == 4
# deepcopy()
kps = [ia.Keypoint(x=1, y=2), ia.Keypoint(x=3, y=4)]
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
kpi2 = kpi.deepcopy()
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[1].x == 3
assert kpi2.keypoints[1].y == 4
kps[0].x = 100
assert kpi2.keypoints[0].x == 1
assert kpi2.keypoints[0].y == 2
assert kpi2.keypoints[1].x == 3
assert kpi2.keypoints[1].y == 4
# repr/str
kps = [ia.Keypoint(x=1, y=2), ia.Keypoint(x=3, y=4)]
kpi = ia.KeypointsOnImage(keypoints=kps, shape=(5, 5, 3))
expected = "KeypointsOnImage([Keypoint(x=1.00000000, y=2.00000000), Keypoint(x=3.00000000, y=4.00000000)], " \
+ "shape=(5, 5, 3))"
assert kpi.__repr__() == kpi.__str__() == expected
def test_BoundingBox():
eps = 1e-8
# properties with ints
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
assert bb.y1_int == 10
assert bb.x1_int == 20
assert bb.y2_int == 30
assert bb.x2_int == 40
assert bb.width == 40 - 20
assert bb.height == 30 - 10
center_x = bb.x1 + (bb.x2 - bb.x1)/2
center_y = bb.y1 + (bb.y2 - bb.y1)/2
assert center_x - eps < bb.center_x < center_x + eps
assert center_y - eps < bb.center_y < center_y + eps
# wrong order of y1/y2, x1/x2
bb = ia.BoundingBox(y1=30, x1=40, y2=10, x2=20, label=None)
assert bb.y1_int == 10
assert bb.x1_int == 20
assert bb.y2_int == 30
assert bb.x2_int == 40
# properties with floats
bb = ia.BoundingBox(y1=10.1, x1=20.1, y2=30.9, x2=40.9, label=None)
assert bb.y1_int == 10
assert bb.x1_int == 20
assert bb.y2_int == 31
assert bb.x2_int == 41
assert bb.width == 40.9 - 20.1
assert bb.height == 30.9 - 10.1
center_x = bb.x1 + (bb.x2 - bb.x1)/2
center_y = bb.y1 + (bb.y2 - bb.y1)/2
assert center_x - eps < bb.center_x < center_x + eps
assert center_y - eps < bb.center_y < center_y + eps
# area
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
assert bb.area == (30-10) * (40-20)
# project
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = bb.project((10, 10), (10, 10))
assert 10 - eps < bb2.y1 < 10 + eps
assert 20 - eps < bb2.x1 < 20 + eps
assert 30 - eps < bb2.y2 < 30 + eps
assert 40 - eps < bb2.x2 < 40 + eps
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = bb.project((10, 10), (20, 20))
assert 10*2 - eps < bb2.y1 < 10*2 + eps
assert 20*2 - eps < bb2.x1 < 20*2 + eps
assert 30*2 - eps < bb2.y2 < 30*2 + eps
assert 40*2 - eps < bb2.x2 < 40*2 + eps
bb2 = bb.project((10, 10), (5, 5))
assert 10*0.5 - eps < bb2.y1 < 10*0.5 + eps
assert 20*0.5 - eps < bb2.x1 < 20*0.5 + eps
assert 30*0.5 - eps < bb2.y2 < 30*0.5 + eps
assert 40*0.5 - eps < bb2.x2 < 40*0.5 + eps
bb2 = bb.project((10, 10), (10, 20))
assert 10*1 - eps < bb2.y1 < 10*1 + eps
assert 20*2 - eps < bb2.x1 < 20*2 + eps
assert 30*1 - eps < bb2.y2 < 30*1 + eps
assert 40*2 - eps < bb2.x2 < 40*2 + eps
bb2 = bb.project((10, 10), (20, 10))
assert 10*2 - eps < bb2.y1 < 10*2 + eps
assert 20*1 - eps < bb2.x1 < 20*1 + eps
assert 30*2 - eps < bb2.y2 < 30*2 + eps
assert 40*1 - eps < bb2.x2 < 40*1 + eps
# extend
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = bb.extend(all_sides=1)
assert bb2.y1 == 10-1
assert bb2.y2 == 30+1
assert bb2.x1 == 20-1
assert bb2.x2 == 40+1
bb2 = bb.extend(all_sides=-1)
assert bb2.y1 == 10-(-1)
assert bb2.y2 == 30+(-1)
assert bb2.x1 == 20-(-1)
assert bb2.x2 == 40+(-1)
bb2 = bb.extend(top=1)
assert bb2.y1 == 10-1
assert bb2.y2 == 30+0
assert bb2.x1 == 20-0
assert bb2.x2 == 40+0
bb2 = bb.extend(right=1)
assert bb2.y1 == 10-0
assert bb2.y2 == 30+0
assert bb2.x1 == 20-0
assert bb2.x2 == 40+1
bb2 = bb.extend(bottom=1)
assert bb2.y1 == 10-0
assert bb2.y2 == 30+1
assert bb2.x1 == 20-0
assert bb2.x2 == 40+0
bb2 = bb.extend(left=1)
assert bb2.y1 == 10-0
assert bb2.y2 == 30+0
assert bb2.x1 == 20-1
assert bb2.x2 == 40+0
# intersection
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=10, x1=39, y2=30, x2=59, label=None)
bb_inter = bb1.intersection(bb2)
assert bb_inter.x1 == 39
assert bb_inter.x2 == 40
assert bb_inter.y1 == 10
assert bb_inter.y2 == 30
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=10, x1=41, y2=30, x2=61, label=None)
bb_inter = bb1.intersection(bb2, default=False)
assert bb_inter is False
# union
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=10, x1=39, y2=30, x2=59, label=None)
bb_union = bb1.union(bb2)
assert bb_union.x1 == 20
assert bb_union.x2 == 59
assert bb_union.y1 == 10
assert bb_union.y2 == 30
# iou
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
iou = bb1.iou(bb2)
assert 1.0 - eps < iou < 1.0 + eps
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=10, x1=41, y2=30, x2=61, label=None)
iou = bb1.iou(bb2)
assert 0.0 - eps < iou < 0.0 + eps
bb1 = ia.BoundingBox(y1=10, x1=10, y2=20, x2=20, label=None)
bb2 = ia.BoundingBox(y1=15, x1=15, y2=25, x2=25, label=None)
iou = bb1.iou(bb2)
area_union = 10 * 10 + 10 * 10 - 5 * 5
area_intersection = 5 * 5
iou_expected = area_intersection / area_union
assert iou_expected - eps < iou < iou_expected + eps
# is_fully_within_image
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
assert bb.is_fully_within_image((100, 100, 3)) is True
assert bb.is_fully_within_image((20, 100, 3)) is False
assert bb.is_fully_within_image((100, 30, 3)) is False
assert bb.is_fully_within_image((1, 1, 3)) is False
# is_partly_within_image
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
assert bb.is_partly_within_image((100, 100, 3)) is True
assert bb.is_partly_within_image((20, 100, 3)) is True
assert bb.is_partly_within_image((100, 30, 3)) is True
assert bb.is_partly_within_image((1, 1, 3)) is False
# is_out_of_image()
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
assert bb.is_out_of_image((100, 100, 3), partly=True, fully=True) is False
assert bb.is_out_of_image((100, 100, 3), partly=False, fully=True) is False
assert bb.is_out_of_image((100, 100, 3), partly=True, fully=False) is False
assert bb.is_out_of_image((20, 100, 3), partly=True, fully=True) is True
assert bb.is_out_of_image((20, 100, 3), partly=False, fully=True) is False
assert bb.is_out_of_image((20, 100, 3), partly=True, fully=False) is True
assert bb.is_out_of_image((100, 30, 3), partly=True, fully=True) is True
assert bb.is_out_of_image((100, 30, 3), partly=False, fully=True) is False
assert bb.is_out_of_image((100, 30, 3), partly=True, fully=False) is True
assert bb.is_out_of_image((1, 1, 3), partly=True, fully=True) is True
assert bb.is_out_of_image((1, 1, 3), partly=False, fully=True) is True
assert bb.is_out_of_image((1, 1, 3), partly=True, fully=False) is False
# cut_out_of_image
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb_cut = bb.cut_out_of_image((100, 100, 3))
eps = np.finfo(np.float32).eps
assert bb_cut.y1 == 10
assert bb_cut.x1 == 20
assert bb_cut.y2 == 30
assert bb_cut.x2 == 40
bb_cut = bb.cut_out_of_image(np.zeros((100, 100, 3), dtype=np.uint8))
assert bb_cut.y1 == 10
assert bb_cut.x1 == 20
assert bb_cut.y2 == 30
assert bb_cut.x2 == 40
bb_cut = bb.cut_out_of_image((20, 100, 3))
assert bb_cut.y1 == 10
assert bb_cut.x1 == 20
assert 20 - 2*eps < bb_cut.y2 < 20
assert bb_cut.x2 == 40
bb_cut = bb.cut_out_of_image((100, 30, 3))
assert bb_cut.y1 == 10
assert bb_cut.x1 == 20
assert bb_cut.y2 == 30
assert 30 - 2*eps < bb_cut.x2 < 30
# shift
bb = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb_top = bb.shift(top=0)
bb_right = bb.shift(right=0)
bb_bottom = bb.shift(bottom=0)
bb_left = bb.shift(left=0)
assert bb_top.y1 == 10
assert bb_top.x1 == 20
assert bb_top.y2 == 30
assert bb_top.x2 == 40
assert bb_right.y1 == 10
assert bb_right.x1 == 20
assert bb_right.y2 == 30
assert bb_right.x2 == 40
assert bb_bottom.y1 == 10
assert bb_bottom.x1 == 20
assert bb_bottom.y2 == 30
assert bb_bottom.x2 == 40
assert bb_left.y1 == 10
assert bb_left.x1 == 20
assert bb_left.y2 == 30
assert bb_left.x2 == 40
bb_top = bb.shift(top=1)
bb_right = bb.shift(right=1)
bb_bottom = bb.shift(bottom=1)
bb_left = bb.shift(left=1)
assert bb_top.y1 == 10+1
assert bb_top.x1 == 20
assert bb_top.y2 == 30+1
assert bb_top.x2 == 40
assert bb_right.y1 == 10
assert bb_right.x1 == 20-1
assert bb_right.y2 == 30
assert bb_right.x2 == 40-1
assert bb_bottom.y1 == 10-1
assert bb_bottom.x1 == 20
assert bb_bottom.y2 == 30-1
assert bb_bottom.x2 == 40
assert bb_left.y1 == 10
assert bb_left.x1 == 20+1
assert bb_left.y2 == 30
assert bb_left.x2 == 40+1
bb_top = bb.shift(top=-1)
bb_right = bb.shift(right=-1)
bb_bottom = bb.shift(bottom=-1)
bb_left = bb.shift(left=-1)
assert bb_top.y1 == 10-1
assert bb_top.x1 == 20
assert bb_top.y2 == 30-1
assert bb_top.x2 == 40
assert bb_right.y1 == 10
assert bb_right.x1 == 20+1
assert bb_right.y2 == 30
assert bb_right.x2 == 40+1
assert bb_bottom.y1 == 10+1
assert bb_bottom.x1 == 20
assert bb_bottom.y2 == 30+1
assert bb_bottom.x2 == 40
assert bb_left.y1 == 10
assert bb_left.x1 == 20-1
assert bb_left.y2 == 30
assert bb_left.x2 == 40-1
bb_mix = bb.shift(top=1, bottom=2, left=3, right=4)
assert bb_mix.y1 == 10+1-2
assert bb_mix.x1 == 20+3-4
assert bb_mix.y2 == 30+3-4
assert bb_mix.x2 == 40+1-2
# draw_on_image()
image = np.zeros((10, 10, 3), dtype=np.uint8)
bb = ia.BoundingBox(y1=1, x1=1, y2=3, x2=3, label=None)
bb_mask = np.zeros(image.shape[0:2], dtype=np.bool)
bb_mask[1:3+1, 1] = True
bb_mask[1:3+1, 3] = True
bb_mask[1, 1:3+1] = True
bb_mask[3, 1:3+1] = True
image_bb = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 255, 255])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
assert np.all(image == 0)
image_bb = bb.draw_on_image(image, color=[255, 0, 0], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 0, 0])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
image_bb = bb.draw_on_image(image, color=128, alpha=1.0, thickness=1, copy=True, raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [128, 128, 128])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
image_bb = bb.draw_on_image(image+100, color=[200, 200, 200], alpha=0.5, thickness=1, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [150, 150, 150])
assert np.all(image_bb[~bb_mask] == [100, 100, 100])
image_bb = bb.draw_on_image((image+100).astype(np.float32), color=[200, 200, 200], alpha=0.5, thickness=1,
copy=True, raise_if_out_of_image=False)
assert np.sum(np.abs((image_bb - [150, 150, 150])[bb_mask])) < 0.1
assert np.sum(np.abs((image_bb - [100, 100, 100])[~bb_mask])) < 0.1
image_bb = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=False,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 255, 255])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
assert np.all(image[bb_mask] == [255, 255, 255])
assert np.all(image[~bb_mask] == [0, 0, 0])
image = np.zeros_like(image)
bb = ia.BoundingBox(y1=-1, x1=-1, y2=2, x2=2, label=None)
bb_mask = np.zeros(image.shape[0:2], dtype=np.bool)
bb_mask[2, 0:3] = True
bb_mask[0:3, 2] = True
image_bb = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 255, 255])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
bb = ia.BoundingBox(y1=1, x1=1, y2=3, x2=3, label=None)
bb_mask = np.zeros(image.shape[0:2], dtype=np.bool)
bb_mask[0:5, 0:5] = True
bb_mask[2, 2] = False
image_bb = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=2, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 255, 255])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
bb = ia.BoundingBox(y1=-1, x1=-1, y2=1, x2=1, label=None)
bb_mask = np.zeros(image.shape[0:2], dtype=np.bool)
bb_mask[0:1+1, 1] = True
bb_mask[1, 0:1+1] = True
image_bb = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=False)
assert np.all(image_bb[bb_mask] == [255, 255, 255])
assert np.all(image_bb[~bb_mask] == [0, 0, 0])
bb = ia.BoundingBox(y1=-1, x1=-1, y2=1, x2=1, label=None)
got_exception = False
try:
_ = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=True)
except Exception:
got_exception = True
assert got_exception is False
bb = ia.BoundingBox(y1=-5, x1=-5, y2=-1, x2=-1, label=None)
got_exception = False
try:
_ = bb.draw_on_image(image, color=[255, 255, 255], alpha=1.0, thickness=1, copy=True,
raise_if_out_of_image=True)
except Exception:
got_exception = True
assert got_exception is True
# extract_from_image()
image = np.random.RandomState(1234).randint(0, 255, size=(10, 10, 3))
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
image_sub = bb.extract_from_image(image)
assert np.array_equal(image_sub, image[1:3, 1:3, :])
image = np.random.RandomState(1234).randint(0, 255, size=(10, 10))
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
image_sub = bb.extract_from_image(image)
assert np.array_equal(image_sub, image[1:3, 1:3])
image = np.random.RandomState(1234).randint(0, 255, size=(10, 10))
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
image_sub = bb.extract_from_image(image)
assert np.array_equal(image_sub, image[1:3, 1:3])
image = np.random.RandomState(1234).randint(0, 255, size=(10, 10, 3))
image_pad = np.pad(image, ((0, 1), (0, 1), (0, 0)), mode="constant", constant_values=0)
bb = ia.BoundingBox(y1=8, y2=11, x1=8, x2=11, label=None)
image_sub = bb.extract_from_image(image)
assert np.array_equal(image_sub, image_pad[8:11, 8:11, :])
image = np.random.RandomState(1234).randint(0, 255, size=(10, 10, 3))
image_pad = np.pad(image, ((1, 0), (1, 0), (0, 0)), mode="constant", constant_values=0)
bb = ia.BoundingBox(y1=-1, y2=3, x1=-1, x2=4, label=None)
image_sub = bb.extract_from_image(image)
assert np.array_equal(image_sub, image_pad[0:4, 0:5, :])
# to_keypoints()
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
kps = bb.to_keypoints()
assert kps[0].y == 1
assert kps[0].x == 1
assert kps[1].y == 1
assert kps[1].x == 3
assert kps[2].y == 3
assert kps[2].x == 3
assert kps[3].y == 3
assert kps[3].x == 1
# copy()
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label="test")
bb2 = bb.copy()
assert bb2.y1 == 1
assert bb2.y2 == 3
assert bb2.x1 == 1
assert bb2.x2 == 3
assert bb2.label == "test"
bb2 = bb.copy(y1=10, x1=20, y2=30, x2=40, label="test2")
assert bb2.y1 == 10
assert bb2.x1 == 20
assert bb2.y2 == 30
assert bb2.x2 == 40
assert bb2.label == "test2"
# deepcopy()
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=["test"])
bb2 = bb.deepcopy()
assert bb2.y1 == 1
assert bb2.y2 == 3
assert bb2.x1 == 1
assert bb2.x2 == 3
assert bb2.label[0] == "test"
# BoundingBox_repr()
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
assert bb.__repr__() == "BoundingBox(x1=1.0000, y1=1.0000, x2=3.0000, y2=3.0000, label=None)"
# test_BoundingBox_str()
bb = ia.BoundingBox(y1=1, y2=3, x1=1, x2=3, label=None)
assert bb.__str__() == "BoundingBox(x1=1.0000, y1=1.0000, x2=3.0000, y2=3.0000, label=None)"
def test_BoundingBoxesOnImage():
reseed()
# test height/width
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=45, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
assert bbsoi.height == 40
assert bbsoi.width == 50
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=45, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=np.zeros((40, 50, 3), dtype=np.uint8))
assert bbsoi.height == 40
assert bbsoi.width == 50
# on()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=45, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=np.zeros((40, 50, 3), dtype=np.uint8))
bbsoi_projected = bbsoi.on((40, 50))
assert bbsoi_projected.bounding_boxes[0].y1 == 10
assert bbsoi_projected.bounding_boxes[0].x1 == 20
assert bbsoi_projected.bounding_boxes[0].y2 == 30
assert bbsoi_projected.bounding_boxes[0].x2 == 40
assert bbsoi_projected.bounding_boxes[1].y1 == 15
assert bbsoi_projected.bounding_boxes[1].x1 == 25
assert bbsoi_projected.bounding_boxes[1].y2 == 35
assert bbsoi_projected.bounding_boxes[1].x2 == 45
bbsoi_projected = bbsoi.on((40*2, 50*2, 3))
assert bbsoi_projected.bounding_boxes[0].y1 == 10*2
assert bbsoi_projected.bounding_boxes[0].x1 == 20*2
assert bbsoi_projected.bounding_boxes[0].y2 == 30*2
assert bbsoi_projected.bounding_boxes[0].x2 == 40*2
assert bbsoi_projected.bounding_boxes[1].y1 == 15*2
assert bbsoi_projected.bounding_boxes[1].x1 == 25*2
assert bbsoi_projected.bounding_boxes[1].y2 == 35*2
assert bbsoi_projected.bounding_boxes[1].x2 == 45*2
bbsoi_projected = bbsoi.on(np.zeros((40*2, 50*2, 3), dtype=np.uint8))
assert bbsoi_projected.bounding_boxes[0].y1 == 10*2
assert bbsoi_projected.bounding_boxes[0].x1 == 20*2
assert bbsoi_projected.bounding_boxes[0].y2 == 30*2
assert bbsoi_projected.bounding_boxes[0].x2 == 40*2
assert bbsoi_projected.bounding_boxes[1].y1 == 15*2
assert bbsoi_projected.bounding_boxes[1].x1 == 25*2
assert bbsoi_projected.bounding_boxes[1].y2 == 35*2
assert bbsoi_projected.bounding_boxes[1].x2 == 45*2
# draw_on_image()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=45, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
image = bbsoi.draw_on_image(np.zeros(bbsoi.shape, dtype=np.uint8), color=[0, 255, 0], alpha=1.0, thickness=1,
copy=True, raise_if_out_of_image=False)
assert np.all(image[10-1, 20-1, :] == [0, 0, 0])
assert np.all(image[10-1, 20-0, :] == [0, 0, 0])
assert np.all(image[10-0, 20-1, :] == [0, 0, 0])
assert np.all(image[10-0, 20-0, :] == [0, 255, 0])
assert np.all(image[10+1, 20+1, :] == [0, 0, 0])
assert np.all(image[30-1, 40-1, :] == [0, 0, 0])
assert np.all(image[30+1, 40-0, :] == [0, 0, 0])
assert np.all(image[30+0, 40+1, :] == [0, 0, 0])
assert np.all(image[30+0, 40+0, :] == [0, 255, 0])
assert np.all(image[30+1, 40+1, :] == [0, 0, 0])
assert np.all(image[15-1, 25-1, :] == [0, 0, 0])
assert np.all(image[15-1, 25-0, :] == [0, 0, 0])
assert np.all(image[15-0, 25-1, :] == [0, 0, 0])
assert np.all(image[15-0, 25-0, :] == [0, 255, 0])
assert np.all(image[15+1, 25+1, :] == [0, 0, 0])
assert np.all(image[35-1, 45-1, :] == [0, 0, 0])
assert np.all(image[35+1, 45+0, :] == [0, 0, 0])
assert np.all(image[35+0, 45+1, :] == [0, 0, 0])
assert np.all(image[35+0, 45+0, :] == [0, 255, 0])
assert np.all(image[35+1, 45+1, :] == [0, 0, 0])
# remove_out_of_image()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
bbsoi_slim = bbsoi.remove_out_of_image(fully=True, partly=True)
assert len(bbsoi_slim.bounding_boxes) == 1
assert bbsoi_slim.bounding_boxes[0] == bb1
# cut_out_of_image()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
eps = np.finfo(np.float32).eps
bbsoi_cut = bbsoi.cut_out_of_image()
assert len(bbsoi_cut.bounding_boxes) == 2
assert bbsoi_cut.bounding_boxes[0].y1 == 10
assert bbsoi_cut.bounding_boxes[0].x1 == 20
assert bbsoi_cut.bounding_boxes[0].y2 == 30
assert bbsoi_cut.bounding_boxes[0].x2 == 40
assert bbsoi_cut.bounding_boxes[1].y1 == 15
assert bbsoi_cut.bounding_boxes[1].x1 == 25
assert bbsoi_cut.bounding_boxes[1].y2 == 35
assert 50 - 2*eps < bbsoi_cut.bounding_boxes[1].x2 < 50
# shift()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
bbsoi_shifted = bbsoi.shift(right=1)
assert len(bbsoi_cut.bounding_boxes) == 2
assert bbsoi_shifted.bounding_boxes[0].y1 == 10
assert bbsoi_shifted.bounding_boxes[0].x1 == 20 - 1
assert bbsoi_shifted.bounding_boxes[0].y2 == 30
assert bbsoi_shifted.bounding_boxes[0].x2 == 40 - 1
assert bbsoi_shifted.bounding_boxes[1].y1 == 15
assert bbsoi_shifted.bounding_boxes[1].x1 == 25 - 1
assert bbsoi_shifted.bounding_boxes[1].y2 == 35
assert bbsoi_shifted.bounding_boxes[1].x2 == 51 - 1
# copy()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
bbsoi_copy = bbsoi.copy()
assert len(bbsoi.bounding_boxes) == 2
assert bbsoi_copy.bounding_boxes[0].y1 == 10
assert bbsoi_copy.bounding_boxes[0].x1 == 20
assert bbsoi_copy.bounding_boxes[0].y2 == 30
assert bbsoi_copy.bounding_boxes[0].x2 == 40
assert bbsoi_copy.bounding_boxes[1].y1 == 15
assert bbsoi_copy.bounding_boxes[1].x1 == 25
assert bbsoi_copy.bounding_boxes[1].y2 == 35
assert bbsoi_copy.bounding_boxes[1].x2 == 51
bbsoi.bounding_boxes[0].y1 = 0
assert bbsoi_copy.bounding_boxes[0].y1 == 0
# deepcopy()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
bbsoi_copy = bbsoi.deepcopy()
assert len(bbsoi.bounding_boxes) == 2
assert bbsoi_copy.bounding_boxes[0].y1 == 10
assert bbsoi_copy.bounding_boxes[0].x1 == 20
assert bbsoi_copy.bounding_boxes[0].y2 == 30
assert bbsoi_copy.bounding_boxes[0].x2 == 40
assert bbsoi_copy.bounding_boxes[1].y1 == 15
assert bbsoi_copy.bounding_boxes[1].x1 == 25
assert bbsoi_copy.bounding_boxes[1].y2 == 35
assert bbsoi_copy.bounding_boxes[1].x2 == 51
bbsoi.bounding_boxes[0].y1 = 0
assert bbsoi_copy.bounding_boxes[0].y1 == 10
# repr() / str()
bb1 = ia.BoundingBox(y1=10, x1=20, y2=30, x2=40, label=None)
bb2 = ia.BoundingBox(y1=15, x1=25, y2=35, x2=51, label=None)
bbsoi = ia.BoundingBoxesOnImage([bb1, bb2], shape=(40, 50, 3))
bb1_expected = "BoundingBox(x1=20.0000, y1=10.0000, x2=40.0000, y2=30.0000, label=None)"
bb2_expected = "BoundingBox(x1=25.0000, y1=15.0000, x2=51.0000, y2=35.0000, label=None)"
expected = "BoundingBoxesOnImage([%s, %s], shape=(40, 50, 3))" % (bb1_expected, bb2_expected)
assert bbsoi.__repr__() == bbsoi.__str__() == expected
def test_HeatmapsOnImage_draw():
heatmaps_arr = np.float32([
[0.5, 0.0, 0.0, 0.5],
[0.0, 1.0, 1.0, 0.0],
[0.0, 1.0, 1.0, 0.0],
[0.5, 0.0, 0.0, 0.5],
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(4, 4, 3))
heatmaps_drawn = heatmaps.draw()[0]
assert heatmaps_drawn.shape == (4, 4, 3)
v1 = heatmaps_drawn[0, 1]
v2 = heatmaps_drawn[0, 0]
v3 = heatmaps_drawn[1, 1]
for y, x in [(0, 1), (0, 2), (1, 0), (1, 3), (2, 0), (2, 3), (3, 1), (3, 2)]:
assert np.allclose(heatmaps_drawn[y, x], v1)
for y, x in [(0, 0), (0, 3), (3, 0), (3, 3)]:
assert np.allclose(heatmaps_drawn[y, x], v2)
for y, x in [(1, 1), (1, 2), (2, 1), (2, 2)]:
assert np.allclose(heatmaps_drawn[y, x], v3)
# size differs from heatmap array size
heatmaps_arr = np.float32([
[0.0, 1.0],
[0.0, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(2, 2, 3))
heatmaps_drawn = heatmaps.draw(size=(4, 4))[0]
assert heatmaps_drawn.shape == (4, 4, 3)
v1 = heatmaps_drawn[0, 0]
v2 = heatmaps_drawn[0, -1]
for y in range(4):
for x in range(2):
assert np.allclose(heatmaps_drawn[y, x], v1)
for y in range(4):
for x in range(2, 4):
assert np.allclose(heatmaps_drawn[y, x], v2)
def test_HeatmapsOnImage_draw_on_image():
heatmaps_arr = np.float32([
[0.0, 1.0],
[0.0, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(2, 2, 3))
image = np.uint8([
[0, 0, 0, 255],
[0, 0, 0, 255],
[0, 0, 0, 255],
[0, 0, 0, 255]
])
image = np.tile(image[..., np.newaxis], (1, 1, 3))
heatmaps_drawn = heatmaps.draw_on_image(image, alpha=0.5, cmap=None)[0]
assert heatmaps_drawn.shape == (4, 4, 3)
assert np.all(heatmaps_drawn[0:4, 0:2, :] == 0)
assert np.all(heatmaps_drawn[0:4, 2:3, :] == 128) or np.all(heatmaps_drawn[0:4, 2:3, :] == 127)
assert np.all(heatmaps_drawn[0:4, 3:4, :] == 255) or np.all(heatmaps_drawn[0:4, 3:4, :] == 254)
image = np.uint8([
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
])
image = np.tile(image[..., np.newaxis], (1, 1, 3))
heatmaps_drawn = heatmaps.draw_on_image(image, alpha=0.5, resize="image", cmap=None)[0]
assert heatmaps_drawn.shape == (2, 2, 3)
assert np.all(heatmaps_drawn[0:2, 0, :] == 0)
assert np.all(heatmaps_drawn[0:2, 1, :] == 128) or np.all(heatmaps_drawn[0:2, 1, :] == 127)
def test_HeatmapsOnImage_invert():
heatmaps_arr = np.float32([
[0.0, 5.0, 10.0],
[-1.0, -2.0, 7.5]
])
expected = np.float32([
[8.0, 3.0, -2.0],
[9.0, 10.0, 0.5]
])
# (H, W)
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(2, 3), min_value=-2.0, max_value=10.0)
assert np.allclose(heatmaps.get_arr(), heatmaps_arr)
assert np.allclose(heatmaps.invert().get_arr(), expected)
# (H, W, 1)
heatmaps = ia.HeatmapsOnImage(heatmaps_arr[..., np.newaxis], shape=(2, 3), min_value=-2.0, max_value=10.0)
assert np.allclose(heatmaps.get_arr(), heatmaps_arr[..., np.newaxis])
assert np.allclose(heatmaps.invert().get_arr(), expected[..., np.newaxis])
def test_HeatmapsOnImage_pad():
heatmaps_arr = np.float32([
[0.0, 1.0],
[0.0, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(2, 2, 3))
heatmaps_padded = heatmaps.pad(top=1, right=2, bottom=3, left=4)
assert heatmaps_padded.arr_0to1.shape == (2+(1+3), 2+(4+2), 1)
assert np.allclose(
heatmaps_padded.arr_0to1[:, :, 0],
np.float32([
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
])
)
heatmaps_padded = heatmaps.pad(top=1, right=2, bottom=3, left=4, cval=0.5)
assert heatmaps_padded.arr_0to1.shape == (2+(1+3), 2+(4+2), 1)
assert np.allclose(
heatmaps_padded.arr_0to1[:, :, 0],
np.float32([
[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5, 0.0, 1.0, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5, 0.0, 1.0, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]
])
)
heatmaps_padded = heatmaps.pad(top=1, right=2, bottom=3, left=4, mode="edge")
assert heatmaps_padded.arr_0to1.shape == (2+(1+3), 2+(4+2), 1)
assert np.allclose(
heatmaps_padded.arr_0to1[:, :, 0],
np.float32([
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0]
])
)
def test_HeatmapsOnImage_avg_pool():
heatmaps_arr = np.float32([
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(4, 4, 3))
heatmaps_pooled = heatmaps.avg_pool(2)
assert heatmaps_pooled.arr_0to1.shape == (2, 2, 1)
assert np.allclose(
heatmaps_pooled.arr_0to1[:, :, 0],
np.float32([[0.0, 0.75],
[0.0, 0.75]])
)
def test_HeatmapsOnImage_max_pool():
heatmaps_arr = np.float32([
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0],
[0.0, 0.0, 0.5, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(4, 4, 3))
heatmaps_pooled = heatmaps.max_pool(2)
assert heatmaps_pooled.arr_0to1.shape == (2, 2, 1)
assert np.allclose(
heatmaps_pooled.arr_0to1[:, :, 0],
np.float32([[0.0, 1.0],
[0.0, 1.0]])
)
def test_HeatmapsOnImage_scale():
heatmaps_arr = np.float32([
[0.0, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(4, 4, 3))
heatmaps_scaled = heatmaps.scale((4, 4), interpolation="nearest")
assert heatmaps_scaled.arr_0to1.shape == (4, 4, 1)
assert heatmaps_scaled.arr_0to1.dtype.type == np.float32
assert np.allclose(
heatmaps_scaled.arr_0to1[:, :, 0],
np.float32([
[0.0, 0.0, 1.0, 1.0],
[0.0, 0.0, 1.0, 1.0],
[0.0, 0.0, 1.0, 1.0],
[0.0, 0.0, 1.0, 1.0]
])
)
heatmaps_arr = np.float32([
[0.0, 1.0]
])
heatmaps = ia.HeatmapsOnImage(heatmaps_arr, shape=(4, 4, 3))
heatmaps_scaled = heatmaps.scale(2.0, interpolation="nearest")
assert heatmaps_scaled.arr_0to1.shape == (2, 4, 1)
assert heatmaps_scaled.arr_0to1.dtype.type == np.float32
assert np.allclose(
heatmaps_scaled.arr_0to1[:, :, 0],
np.float32([
[0.0, 0.0, 1.0, 1.0],
[0.0, 0.0, 1.0, 1.0]
])
)
def test_SegmentationMapOnImage_bool():
# Test for #189 (boolean mask inputs into SegmentationMapOnImage not working)
arr = np.array([
[0, 0, 0],
[0, 1, 0],
[0, 0, 0]
], dtype=bool)
assert arr.dtype.type == np.bool_
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3))
observed = segmap.get_arr_int()
assert observed.dtype.type == np.int32
assert np.array_equal(arr, observed)
arr = np.array([
[0, 0, 0],
[0, 1, 0],
[0, 0, 0]
], dtype=np.bool)
assert arr.dtype.type == np.bool_
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3))
observed = segmap.get_arr_int()
assert observed.dtype.type == np.int32
assert np.array_equal(arr, observed)
def test_SegmentationMapOnImage_get_arr_int():
arr = np.int32([
[0, 0, 1],
[0, 2, 1],
[1, 3, 1]
])
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3), nb_classes=4)
observed = segmap.get_arr_int()
assert observed.dtype.type == np.int32
assert np.array_equal(arr, observed)
arr_c0 = np.float32([
[0.1, 0.1, 0.1],
[0.1, 0.9, 0.1],
[0.0, 0.1, 0.0]
])
arr_c1 = np.float32([
[0.2, 1.0, 0.2],
[0.2, 0.8, 0.2],
[0.0, 0.0, 0.0]
])
arr_c2 = np.float32([
[0.0, 0.0, 0.0],
[0.3, 0.7, 0.3],
[0.1, 0.0, 0.0001]
])
arr = np.concatenate([
arr_c0[..., np.newaxis],
arr_c1[..., np.newaxis],
arr_c2[..., np.newaxis]
], axis=2)
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3))
observed = segmap.get_arr_int()
expected = np.int32([
[2, 2, 2],
[3, 1, 3],
[3, 1, 0]
])
assert observed.dtype.type == np.int32
assert np.array_equal(observed, expected)
got_exception = False
try:
_ = segmap.get_arr_int(background_class_id=2)
except Exception as exc:
assert "The background class id may only be changed if " in str(exc)
got_exception = True
assert got_exception
observed = segmap.get_arr_int(background_threshold=0.21)
expected = np.int32([
[0, 2, 0],
[3, 1, 3],
[0, 0, 0]
])
assert observed.dtype.type == np.int32
assert np.array_equal(observed, expected)
def test_SegmentationMapOnImage_draw():
arr = np.int32([
[0, 1, 1],
[0, 1, 1],
[0, 1, 1]
])
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3), nb_classes=2)
# simple example with 2 classes
observed = segmap.draw()
col0 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[0]
col1 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[1]
expected = np.uint8([
[col0, col1, col1],
[col0, col1, col1],
[col0, col1, col1]
])
assert np.array_equal(observed, expected)
# same example, with resizing to 2x the size
observed = segmap.draw(size=(6, 6))
expected = ia.imresize_single_image(expected, (6, 6), interpolation="nearest")
assert np.array_equal(observed, expected)
# custom choice of colors
col0 = (10, 10, 10)
col1 = (50, 51, 52)
observed = segmap.draw(colors=[col0, col1])
expected = np.uint8([
[col0, col1, col1],
[col0, col1, col1],
[col0, col1, col1]
])
assert np.array_equal(observed, expected)
# background_threshold, background_class and foreground mask
arr_c0 = np.float32([
[0, 0, 0],
[1.0, 0, 0],
[0, 0, 0]
])
arr_c1 = np.float32([
[0, 1, 1],
[0, 1, 1],
[0.1, 1, 1]
])
arr = np.concatenate([
arr_c0[..., np.newaxis],
arr_c1[..., np.newaxis]
], axis=2)
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3))
observed, observed_fg = segmap.draw(background_threshold=0.01, return_foreground_mask=True)
col0 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[0]
col1 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[1]
col2 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[2]
expected = np.uint8([
[col0, col2, col2],
[col1, col2, col2],
[col2, col2, col2]
])
expected_fg = np.array([
[False, True, True],
[True, True, True],
[True, True, True]
], dtype=np.bool)
assert np.array_equal(observed, expected)
assert np.array_equal(observed_fg, expected_fg)
# background_threshold, background_class and foreground mask
# here with higher threshold so that bottom left pixel switches to background
observed, observed_fg = segmap.draw(background_threshold=0.11, return_foreground_mask=True)
col0 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[0]
col1 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[1]
col2 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[2]
expected = np.uint8([
[col0, col2, col2],
[col1, col2, col2],
[col0, col2, col2]
])
expected_fg = np.array([
[False, True, True],
[True, True, True],
[False, True, True]
], dtype=np.bool)
assert np.array_equal(observed, expected)
assert np.array_equal(observed_fg, expected_fg)
def test_SegmentationMapOnImage_draw_on_image():
arr = np.int32([
[0, 1, 1],
[0, 1, 1],
[0, 1, 1]
])
segmap = ia.SegmentationMapOnImage(arr, shape=(3, 3), nb_classes=2)
image = np.uint8([
[0, 10, 20],
[30, 40, 50],
[60, 70, 80]
])
image = np.tile(image[:, :, np.newaxis], (1, 1, 3))
# only image visible
observed = segmap.draw_on_image(image, alpha=0)
assert np.array_equal(observed, image)
# only segmap visible
observed = segmap.draw_on_image(image, alpha=1.0, draw_background=True)
col0 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[0]
col1 = ia.SegmentationMapOnImage.DEFAULT_SEGMENT_COLORS[1]
expected = np.uint8([
[col0, col1, col1],
[col0, col1, col1],
[col0, col1, col1]
])
assert | np.array_equal(observed, expected) | numpy.array_equal |
from __future__ import print_function
import string
import sys
import os
from collections import deque
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
plt.switch_backend('Agg')
import tensorflow as tf
import keras
keras.backend.image_data_format()
from keras import backend as K
from keras import regularizers
from keras.layers import Input, Dense, Reshape, Lambda, Conv1D, Flatten, MaxPooling1D, UpSampling1D, GlobalMaxPooling1D
from keras.layers import LSTM, Bidirectional, BatchNormalization, Dropout, Concatenate, Embedding, Activation, Dot, dot
from keras.models import Model, clone_model, Sequential
from keras.optimizers import Adam
from keras.callbacks import EarlyStopping,ModelCheckpoint
from keras.constraints import unitnorm
from keras_layer_normalization import LayerNormalization
tf.keras.backend.set_floatx('float32')
import sklearn as sk
from sklearn.base import BaseEstimator, _pprint
from sklearn.utils import check_array, check_random_state
from sklearn.utils.validation import check_is_fitted
from sklearn.preprocessing import StandardScaler
from sklearn.manifold import LocallyLinearEmbedding, MDS, Isomap, TSNE
from sklearn.decomposition import PCA, IncrementalPCA, KernelPCA, SparsePCA, TruncatedSVD, FastICA, NMF, MiniBatchDictionaryLearning
from sklearn.random_projection import GaussianRandomProjection, SparseRandomProjection
from sklearn.linear_model import LinearRegression, LogisticRegression
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import KFold, GroupKFold, train_test_split
from sklearn.metrics import mean_squared_error, explained_variance_score, mean_absolute_error, median_absolute_error, r2_score
from sklearn.metrics import average_precision_score, precision_score, recall_score, f1_score, roc_auc_score, matthews_corrcoef
from sklearn.metrics import roc_curve, precision_recall_curve, RocCurveDisplay, PrecisionRecallDisplay
from sklearn.metrics import roc_auc_score,accuracy_score,matthews_corrcoef
from scipy import stats
from scipy.stats import multivariate_normal, kurtosis, skew, pearsonr, spearmanr
import processSeq
from processSeq import load_seq_1, kmer_dict, load_signal_1, load_seq_2, load_seq_2_kmer, load_seq_altfeature
import xgboost
import pickle
import os.path
from optparse import OptionParser
import time
from timeit import default_timer as timer
import utility_1
from utility_1 import mapping_Idx
import h5py
import json
# generate sequences
# idx_sel_list: chrom, serial
# seq_list: relative positions
def generate_sequences(idx_sel_list, gap_tol=5, region_list=[]):
chrom = idx_sel_list[:,0]
chrom_vec = np.unique(chrom)
chrom_vec = np.sort(chrom_vec)
seq_list = []
print(len(chrom),chrom_vec)
for chrom_id in chrom_vec:
b1 = np.where(chrom==chrom_id)[0]
t_serial = idx_sel_list[b1,1]
prev_serial = t_serial[0:-1]
next_serial = t_serial[1:]
distance = next_serial-prev_serial
b2 = np.where(distance>gap_tol)[0]
if len(b2)>0:
if len(region_list)>0:
# print('region_list',region_list,len(b2))
b_1 = np.where(region_list[:,0]==chrom_id)[0]
# print(b2)
t_serial = idx_sel_list[b2,1]
if len(b_1)>0:
# b2 = np.setdiff1d(b2,region_list[b_1,1])
# print(region_list,region_list[b_1,1],len(b2))
t_id1 = utility_1.mapping_Idx(t_serial,region_list[b_1,1])
t_id1 = t_id1[t_id1>=0]
t_id2 = b2[t_id1]
b2 = np.setdiff1d(b2,t_id2)
# print(len(b2))
# print(idx_sel_list[b2])
# return
# print('gap',len(b2))
if len(b2)>0:
t_seq = list(np.vstack((b2[0:-1]+1,b2[1:])).T)
t_seq.insert(0,np.asarray([0,b2[0]]))
t_seq.append(np.asarray([b2[-1]+1,len(b1)-1]))
else:
t_seq = [np.asarray([0,len(b1)-1])]
# print(t_seq)
# print(chrom_id,len(t_seq),max(distance))
seq_list.extend(b1[np.asarray(t_seq)])
return np.asarray(seq_list)
# select sample
def sample_select2a1(x_mtx, y, idx_sel_list, seq_list, tol=5, L=5):
num_sample = len(idx_sel_list)
num1 = len(seq_list)
size1 = 2*L+1
print(num_sample,num1,size1)
feature_dim = x_mtx.shape[1]
vec1_local = np.zeros((num_sample,size1),dtype=int)
vec1_serial = np.zeros((num_sample,size1),dtype=int)
feature_mtx = np.zeros((num_sample,size1,feature_dim),dtype=np.float32)
signal_mtx = np.zeros((num_sample,size1))
ref_serial = idx_sel_list[:,1]
id_vec = np.zeros(num_sample,dtype=np.int8)
for i in range(0,num1):
s1, s2 = seq_list[i][0], seq_list[i][1]+1
serial = ref_serial[s1:s2]
id_vec[s1:s2] = 1
# print('start stop',s1,s2,serial)
num2 = len(serial)
t1 = np.outer(list(range(s1,s2)),np.ones(size1))
t2 = t1 + np.outer(np.ones(num2),list(range(-L,L+1)))
t2[t2<s1] = s1
t2[t2>=s2] = s2-1
idx = np.int64(t2)
# print(idx)
vec1_local[s1:s2] = idx
vec1_serial[s1:s2] = ref_serial[idx]
feature_mtx[s1:s2] = x_mtx[idx]
signal_mtx[s1:s2] = y[idx]
# if i%10000==0:
# print(i,num2,vec1_local[s1],vec1_serial[s1])
id1 = np.where(id_vec>0)[0]
num2 = len(id1)
if num2<num_sample:
feature_mtx, signal_mtx = feature_mtx[id1], signal_mtx[id1]
# vec1_serial, vec1_local = vec1_serial[id1], vec1_local[id1]
vec1_serial = vec1_serial[id1]
id_1 = -np.ones(sample_num,dtype=np.int64)
id_1[id1] = np.arange(num2)
vec1_local = id_1[vec1_local]
b1 = np.where(vec1_local<0)[0]
if len(b1)>0:
print('error!',b1)
return -1
# signal_mtx = signal_mtx[:,np.newaxis]
signal_mtx = np.expand_dims(signal_mtx, axis=-1)
# signal_mtx = np.expand_dims(signal_ntx, axis=-1)
return feature_mtx, signal_mtx, vec1_serial, vec1_local
def score_2a(y, y_predicted):
score1 = mean_squared_error(y, y_predicted)
score2 = pearsonr(y, y_predicted)
score3 = explained_variance_score(y, y_predicted)
score4 = mean_absolute_error(y, y_predicted)
score5 = median_absolute_error(y, y_predicted)
score6 = r2_score(y, y_predicted)
score7, pvalue = spearmanr(y,y_predicted)
# vec1 = [score1, score2[0], score2[1], score3, score4, score5, score6]
vec1 = [score1, score2[0], score2[1], score3, score4, score5, score6, score7, pvalue]
return vec1
def read_phyloP(species_name):
path1 = './'
filename1 = '%s/estimate_rt/estimate_rt_%s.txt'%(path1,species_name)
# filename2a = 'test_seq_%s.1.txt'%(species_name)
file1 = pd.read_csv(filename1,sep='\t')
col1, col2, col3 = '%s.chrom'%(species_name), '%s.start'%(species_name), '%s.stop'%(species_name)
chrom_ori, start_ori, stop_ori, serial_ori = np.asarray(file1[col1]), np.asarray(file1[col2]), np.asarray(file1[col3]), np.asarray(file1['serial'])
num_sample = len(chrom_ori)
chrom_vec = np.unique(chrom_ori)
chrom_vec = ['chr22']
for chrom_id in chrom_vec:
filename1 = '%s/phyloP/hg19.phyloP100way.%s.bedGraph'%(path1,chrom_id)
data1 = pd.read_csv(filename1,header=None,sep='\t')
chrom, start, stop, score = data1[0], data1[1], data1[2], data1[3]
len1 = stop-start
b = np.where(chrom_ori==chrom_id)[0]
num_sample1 = len(b)
vec1 = np.zeros((num_sample1,16))
print(chrom_id,len(chrom),len(b))
cnt = 0
b1 = [-1]
for i in b:
t1 = b1[-1]+1
b1 = np.where((start[t1:]>=start_ori[i])&(stop[t1:]<stop_ori[i]))[0]+t1
if len(b1)==0:
b1 = [-1]
continue
t_len1, t_score = np.asarray(len1[b1]), np.asarray(score[b1])
s1 = 0
s2 = np.sum(t_len1)
i1 = cnt
for j in range(0,12):
temp1 = (j-8)*2.5
b2 = np.where((t_score<temp1+2.5)&(t_score>=temp1))[0]
print(b2)
vec1[i1,j] = np.sum(t_len1[b2])*1.0/s2
s1 = s1+temp1*vec1[i1,j]
vec1[i1,12] = s1 # average
vec1[i1,13] = np.median(t_score)
vec1[i1,14] = np.max(t_score)
vec1[i1,15] = np.min(t_score)
cnt += 1
if cnt%1000==0:
print(cnt,len(b1),s2,vec1[i1,12:16])
break
# dict1 = dict()
# dict1['vec'], dict1['index'] = vec1,b
# np.save('phyloP_%s'%(chrom_id),dict1,allow_pickle=True)
fields = ['index']
for j in range(0,12):
temp1 = (j-8)*2.5
fields.append('%s-%s'%(temp1,temp1+2.5))
fields.extend(range(0,4))
data1 = pd.DataFrame(data = np.hstack((b[:,np.newaxis],vec1)),columns=fields)
data1.to_csv('phyloP_%s.txt'%(chrom_id),sep='\t',index=False)
return vec1
def read_phyloP_1(ref_filename,header,file_path,chrom_vec,n_level=15,offset=10,magnitude=2):
file1 = pd.read_csv(ref_filename,header=header,sep='\t')
# col1, col2, col3 = '%s.chrom'%(species_name), '%s.start'%(species_name), '%s.stop'%(species_name)
colnames = list(file1)
col1, col2, col3, col4 = colnames[0], colnames[1], colnames[2], colnames[3]
chrom_ori, start_ori, stop_ori, serial_ori = np.asarray(file1[col1]), np.asarray(file1[col2]), np.asarray(file1[col3]), np.asarray(file1[col4])
num_sample = len(chrom_ori)
# chrom_vec = np.unique(chrom_ori)
# chrom_vec = [chrom_id]
# n_level, offset, magnitude = 15, 10, 2
score_max = (n_level-offset)*magnitude
for chrom_id in chrom_vec:
# filename1 = '%s/hg19.phyloP100way.%s.bedGraph'%(file_path,chrom_id)
filename1 = '%s/chr%s.phyloP100way.bedGraph'%(file_path,chrom_id)
data1 = pd.read_csv(filename1,header=None,sep='\t')
chrom, start, stop, score = data1[0], data1[1], data1[2], data1[3]
len1 = stop-start
chrom_id1 = 'chr%s'%(chrom_id)
b = np.where(chrom_ori==chrom_id1)[0]
num_sample1 = len(b)
vec1 = np.zeros((num_sample1,n_level+4))
print(chrom_id,len(chrom),len(b))
cnt = 0
m_idx = len(start)-1
start_idx = 0
print("number of regions", len(b))
for i in b:
t_start, t_stop = start_ori[i], stop_ori[i] # position of zero region
position = [t_start,t_stop]
if start_idx<=m_idx:
b1, start_idx = utility_1.search_region_include(position, start, stop, m_idx, start_idx)
# print(count,t_start,t_stop,t_stop-t_start,start_idx,len(id3))
if len(b1)==0:
continue
t_len1, t_score = np.asarray(len1[b1]), np.asarray(score[b1])
t_score[t_score>score_max] = score_max-1e-04
s1 = 0
s2 = np.sum(t_len1)
for j in range(0,n_level):
temp1 = (j-offset)*magnitude
b2 = np.where((t_score<temp1+magnitude)&(t_score>=temp1))[0]
# print(b2)
vec1[cnt,j] = np.sum(t_len1[b2])*1.0/s2
s1 = s1+temp1*vec1[cnt,j]
vec1[cnt,n_level:n_level+4] = [s1,np.median(t_score),np.max(t_score),np.min(t_score)]
cnt += 1
pre_b1 = b1
if cnt%1000==0:
print(chrom_id,cnt,len(b1),s2,vec1[cnt,-4:])
# break
# dict1 = dict()
# dict1['vec'], dict1['index'] = vec1,b
# np.save('phyloP_%s'%(chrom_id),dict1,allow_pickle=True)
fields = ['index']
for j in range(0,n_level):
temp1 = (j-offset)*magnitude
fields.append('%s-%s'%(temp1,temp1+magnitude))
fields.extend(range(0,4))
idx = serial_ori[b]
data1 = pd.DataFrame(data = np.hstack((idx[:,np.newaxis],vec1)),columns=fields)
data1.to_csv('phyloP_%s.txt'%(chrom_id),sep='\t',index=False)
return vec1
def read_motif_1(filename,output_filename=-1):
data1 = pd.read_csv(filename,sep='\t')
colnames = list(data1)
col1, col2, col3 = colnames[0], colnames[1], colnames[2]
chrom, start, stop = np.asarray(data1[col1]), np.asarray(data1[col2]), np.asarray(data1[col3])
region_len = stop-start
m1, m2, median_len = np.max(region_len), np.min(region_len), np.median(region_len)
b1 = np.where(region_len!=median_len)[0]
print(m1,m2,median_len,len(b1))
bin_size = median_len
motif_name = colnames[3:]
mtx1 = np.asarray(data1.loc[:,motif_name])
mtx1 = mtx1*1000.0/np.outer(region_len,np.ones(mtx1.shape[1]))
print('motif',len(motif_name))
print(mtx1.shape)
print(np.max(mtx1),np.min(mtx1),np.median(mtx1))
if output_filename!=-1:
fields = colnames
data1 = pd.DataFrame(columns=fields)
data1[colnames[0]], data1[colnames[1]], data1[colnames[2]] = chrom, start, stop
num1 = len(fields)-3
for i in range(0,num1):
data1[colnames[i+3]] = mtx1[:,i]
data1.to_csv(output_filename,header=True,index=False,sep='\t')
print(output_filename, data1.shape)
return mtx1, chrom, start, stop, colnames
def read_gc_1(ref_filename,header,filename,output_filename):
sel_idx = []
file1 = pd.read_csv(ref_filename,header=header,sep='\t')
f_list = load_seq_altfeature(filename,sel_idx)
# col1, col2, col3 = '%s.chrom'%(species_name), '%s.start'%(species_name), '%s.stop'%(species_name)
colnames = list(file1)
col1, col2, col3, col4 = colnames[0], colnames[1], colnames[2], colnames[3]
chrom_ori, start_ori, stop_ori, serial_ori = np.asarray(file1[col1]), np.asarray(file1[col2]), np.asarray(file1[col3]), np.asarray(file1[col4])
num_sample = len(chrom_ori)
if num_sample!=f_list.shape[0]:
print('error!',num_sample,f_list.shape[0])
fields = ['chrom','start','stop','serial','GC','GC_N','GC_skew']
file2 = pd.DataFrame(columns=fields)
file2['chrom'], file2['start'], file2['stop'], file2['serial'] = chrom_ori, start_ori, stop_ori, serial_ori
for i in range(0,3):
file2[fields[i+4]] = f_list[:,i]
file2.to_csv(output_filename,index=False,sep='\t')
return f_list
def generate_serial(filename1,chrom,start,stop):
# chrom_vec = np.sort(np.unique(chrom))
# print(chrom_vec)
chrom_vec = []
for i in range(1,23):
chrom_vec.append('chr%d'%(i))
chrom_vec += ['chrX']
chrom_vec += ['chrY']
print(chrom_vec)
# print(chrom)
print(len(chrom))
data1 = pd.read_csv(filename1,header=None,sep='\t')
ref_chrom, chrom_size = np.asarray(data1[0]), np.asarray(data1[1])
serial_start = 0
serial_vec = np.zeros(len(chrom))
bin_size = stop[1]-start[1]
print(bin_size)
for chrom_id in chrom_vec:
b1 = np.where(ref_chrom==chrom_id)[0]
t_size = chrom_size[b1[0]]
b2 = np.where(chrom==chrom_id)[0]
if len(b1)>0:
size1 = int(np.ceil(t_size*1.0/bin_size))
serial = np.int64(start[b2]/bin_size)+serial_start
serial_vec[b2] = serial
print(chrom_id,b2,len(serial),serial_start,size1)
serial_start = serial_start+size1
else:
print("error!")
return
return np.int64(serial_vec)
def generate_serial_local(filename1,chrom,start,stop,chrom_num):
# chrom_vec = np.sort(np.unique(chrom))
# print(chrom_vec)
chrom_vec = []
for i in range(1,chrom_num+1):
chrom_vec.append('chr%d'%(i))
chrom_vec += ['chrX']
chrom_vec += ['chrY']
chrom_vec += ['chrM']
print(chrom_vec)
print(chrom)
print(len(chrom))
t_chrom = np.unique(chrom)
data1 = pd.read_csv(filename1,header=None,sep='\t')
ref_chrom, chrom_size = np.asarray(data1[0]), np.asarray(data1[1])
# serial_start = np.zeros(len(chrom))
serial_start = 0
serial_start_1 = dict()
serial_vec = np.zeros(len(chrom))
bin_size = stop[1]-start[1]
print(bin_size)
for chrom_id in chrom_vec:
b1 = np.where(ref_chrom==chrom_id)[0]
t_size = chrom_size[b1[0]]
serial_start_1[chrom_id] = serial_start
size1 = int(np.ceil(t_size*1.0/bin_size))
serial_start = serial_start+size1
for chrom_id in t_chrom:
b2 = np.where(chrom==chrom_id)
serial = np.int64(start[b2]/bin_size)+serial_start_1[chrom_id]
serial_vec[b2] = serial
return np.int64(serial_vec)
def generate_serial_start(filename1,chrom,start,stop,chrom_num=19):
# chrom_vec = np.sort(np.unique(chrom))
# print(chrom_vec)
chrom_vec = []
for i in range(1,chrom_num+1):
chrom_vec.append('chr%d'%(i))
chrom_vec += ['chrX']
chrom_vec += ['chrY']
print(chrom_vec)
print(chrom)
print(len(chrom))
data1 = pd.read_csv(filename1,header=None,sep='\t')
ref_chrom, chrom_size = np.asarray(data1[0]), np.asarray(data1[1])
serial_start = 0
serial_vec = -np.ones(len(chrom))
bin_size = stop[1]-start[1]
print(bin_size)
start_vec = dict()
for chrom_id in chrom_vec:
start_vec[chrom_id] = serial_start
b1 = np.where(ref_chrom==chrom_id)[0]
t_size = chrom_size[b1[0]]
b2 = np.where(chrom==chrom_id)[0]
if len(b1)>0:
size1 = int(np.ceil(t_size*1.0/bin_size))
serial = np.int64(start[b2]/bin_size)+serial_start
serial_vec[b2] = serial
print(chrom_id,b2,len(serial),serial_start,size1)
serial_start = serial_start+size1
else:
print("error!")
return
return np.int64(serial_vec), start_vec
def shuffle_array(vec):
num1 = len(vec)
idx = np.random.permutation(num1)
vec = vec[idx]
return vec, idx
# input: estimated attention, type_id: training, validation, or test data
# output: ranking of attention
def select_region1_sub(filename,type_id):
data1 = pd.read_csv(filename,sep='\t')
colnames = list(data1)
# chrom start stop serial signal predicted_signal predicted_attention
chrom, start, serial = data1['chrom'], data1['start'], data1['serial']
chrom, start, serial = np.asarray(chrom), np.asarray(start), np.asarray(serial)
predicted_attention = data1['predicted_attention']
predicted_attention = np.asarray(predicted_attention)
ranking = stats.rankdata(predicted_attention,'average')/len(predicted_attention)
rank1 = np.zeros((len(predicted_attention),2))
rank1[:,0] = ranking
chrom_vec = np.unique(chrom)
for t_chrom in chrom_vec:
b1 = np.where(chrom==t_chrom)[0]
t_attention = predicted_attention[b1]
t_ranking = stats.rankdata(t_attention,'average')/len(t_attention)
rank1[b1,1] = t_ranking
data1['Q1'] = rank1[:,0] # rank across all the included chromosomes
data1['Q2'] = rank1[:,1] # rank by each chromosome
data1['typeId'] = np.int8(type_id*np.ones(len(rank1)))
return data1,chrom_vec
# merge estimated attention from different training/test splits
# type_id1: chromosome order; type_id2: training: 0, test: 1, valid: 2
def select_region1_merge(filename_list,output_filename,type_id1=0,type_id2=1):
list1 = []
chrom_numList = []
# b1 = np.where((self.chrom!='chrX')&(self.chrom!='chrY'))[0]
# ref_chrom, ref_start, ref_serial = self.chrom[b1], self.start[b1], self.serial[b1]
# num_sameple = len(ref_chrom)
i = 0
serial1 = []
num1 = len(filename_list)
vec1 = list(range(num1))
if type_id1==1:
vec1 = list(range(num1-1,-1,-1))
for i in vec1:
filename1 = filename_list[i]
# data1: chrom, start, stop, serial, signal, predicted_signal, predicted_attention, Q1, Q2, typeId
# typeId: training: 0, test: 1, valid: 2
data1, chrom_vec = select_region1_sub(filename1,type_id2)
print(filename1,len(data1))
# list1.append(data1)
# if i==0:
# serial1 = np.asarray(data1['serial'])
t_serial = np.asarray(data1['serial'],dtype=np.int64)
t_serial2 = np.setdiff1d(t_serial,serial1)
serial1 = np.union1d(serial1,t_serial)
id1 = mapping_Idx(t_serial,t_serial2)
colnames = list(data1)
data1 = data1.loc[id1,colnames]
list1.append(data1)
chrom_numList.append(chrom_vec)
data2 = pd.concat(list1, axis=0, join='outer', ignore_index=True,
keys=None, levels=None, names=None, verify_integrity=False, copy=True)
print('sort')
data2 = data2.sort_values(by=['serial'])
data2.to_csv(output_filename,index=False,sep='\t')
return data2, chrom_numList
class Reader(object):
def __init__(self, ref_filename, feature_idvec = [1,1,1,1]):
# Initializes RepliSeq
self.ref_filename = ref_filename
self.feature_idvec = feature_idvec
def generate_serial(self,filename1,filename2,output_filename,header=None):
data1 = pd.read_csv(filename2, header=header, sep='\t')
colnames = list(data1)
chrom, start, stop = np.asarray(data1[colnames[0]]), np.asarray(data1[colnames[1]]), np.asarray(data1[colnames[2]])
serial_vec, start_vec = generate_serial_start(filename1,chrom,start,stop)
if output_filename!=None:
colnames2 = colnames[0:3]+['serial']+colnames[3:]
data2 = pd.DataFrame(columns=colnames2)
data2['serial'] = serial_vec
for colname1 in colnames:
data2[colname1] = data1[colname1]
flag = False
if header!=None:
flag = True
data2.to_csv(output_filename,header=flag,index=False,sep='\t')
return serial_vec, start_vec
def load_motif(self,filename1,motif_filename,output_filename):
# output_filename = None
# ref_filename = 'hg38.5k.serial.bed'
# motif_filename = 'hg38.motif.count.txt'
# output_filename1 = None
mtx1, chrom, start, stop, colnames = read_motif_1(motif_filename)
serial_vec, start_vec = generate_serial_start(filename1,chrom,start,stop)
if output_filename!=None:
colnames2 = ['chrom','start','stop','serial']
data2 = pd.DataFrame(columns=colnames2)
data2['chrom'], data2['start'], data2['stop'], data2['serial'] = chrom, start, stop, serial_vec
data3 = pd.DataFrame(columns=colnames[3:],data=mtx1)
data1 = pd.concat([data2,data3], axis=1, join='outer', ignore_index=True,
keys=None, levels=None, names=None, verify_integrity=False, copy=True)
data1.to_csv(output_filename,header=True,index=False,sep='\t')
print('data1',data1.shape)
return True
class ConvergenceMonitor(object):
_template = "{iter:>10d} {logprob:>16.4f} {delta:>+16.4f}"
def __init__(self, tol, n_iter, verbose):
self.tol = tol
self.n_iter = n_iter
self.verbose = verbose
self.history = deque(maxlen=2)
self.iter = 0
def __repr__(self):
class_name = self.__class__.__name__
params = dict(vars(self), history=list(self.history))
return "{0}({1})".format(
class_name, _pprint(params, offset=len(class_name)))
def report(self, logprob):
if self.verbose:
delta = logprob - self.history[-1] if self.history else np.nan
message = self._template.format(
iter=self.iter + 1, logprob=logprob, delta=delta)
print(message, file=sys.stderr)
self.history.append(logprob)
self.iter += 1
@property
def converged(self):
return (self.iter == self.n_iter or
(len(self.history) == 2 and
self.history[1] - self.history[0] < self.tol))
class _Base1(BaseEstimator):
def __init__(self, file_path, species_id, resolution, run_id, generate,
chromvec,test_chromvec,
featureid,type_id,cell,method,ftype,ftrans,tlist,
flanking,normalize,
config,
attention=1,feature_dim_motif=1,
kmer_size=[6,5]):
# Initializes RepliSeq
self.run_id = run_id
self.cell = cell
self.generate = generate
self.train_chromvec = chromvec
self.chromosome = chromvec[0]
print('train_chromvec',train_chromvec)
print('test_chromvec',test_chromvec)
self.test_chromvec = test_chromvec
self.config = config
self.n_epochs = config['n_epochs']
self.species_id = species_id
self.type_id = type_id
self.cell_type = cell
self.cell_type1 = config['celltype_id']
self.method = method
self.ftype = ftype
self.ftrans = ftrans[0]
self.ftrans1 = ftrans[1]
self.t_list = tlist
self.flanking = flanking
self.flanking1 = 3
self.normalize = normalize
self.batch_size = config['batch_size']
# config = dict(output_dim=hidden_unit,fc1_output_dim=fc1,fc2_output_dim=fc2,units1=units1[0],
# units2=units1[1],n_epochs=n_epochs,batch_size=batch_size)
# config['feature_dim_vec'] = units1[2:]
self.tol = config['tol']
self.attention = attention
self.attention_vec = [12,17,22,32,51,52,58,60]
self.attention_vec1 = [1]
self.lr = config['lr']
self.step = config['step']
self.feature_type = -1
self.kmer_size = kmer_size
self.activation = config['activation']
self.min_delta = config['min_delta']
self.chromvec_sel = chromvec
self.feature_dim_transform = config['feature_dim_transform']
feature_idvec = [1,1,1,1]
# ref_filename = 'hg38_5k_serial.bed'
if 'ref_filename' in config:
ref_filename = config['ref_filename']
else:
ref_filename = 'hg38_5k_serial.bed'
self.reader = Reader(ref_filename, feature_idvec)
self.predict_type_id = 0
self.method = method
self.train = self.config['train_mode']
self.path = file_path
self.model_path = '%s/test_%d.h5'%(self.path,run_id)
self.pos_code = config['pos_code']
self.feature_dim_select1 = config['feature_dim_select']
self.method_vec = [[11,31],[22,32,52,17,51,58,60],[56,62]]
self.resolution = resolution
# if self.species_id=='mm10':
# self.cell_type1 = config['cell_type1']
if 'cell_type1' in self.config:
self.cell_type1 = config['cell_type1']
if ('load_type' in self.config) and (self.config['load_type']==1):
self.load_type = 1
else:
self.load_type = 0
if (method>10) and not(method in [56]) :
self.predict_context = 1
else:
self.predict_context = 0
if ftype[0]==-5:
self.feature_idx1= -5 # full dimensions
elif ftype[0]==-6:
self.feature_idx1 = -6 # frequency dimensions
else:
self.feature_idx1 = ftype
if 'est_attention_type1' in self.config:
self.est_attention_type1 = self.config['est_attention_type1']
else:
self.est_attention_type1 = 1
if 'est_attention_sel1' in self.config:
self.est_attention_sel1 = self.config['est_attention_sel1']
else:
self.est_attention_sel1 = 0
# self.feature_idx = [0,2]
self.feature_idx = featureid
self.x, self.y = dict(), dict() # feature matrix and signals
self.vec = dict() # serial
self.vec_local = dict()
if self.species_id.find('hg')>=0:
self.chrom_num = 22
elif self.species_id.find('mm')>=0:
self.chrom_num = 19
else:
self.chrom_num = -1
self.region_list_test, self.region_list_train, self.region_list_valid = [],[],[]
if 'region_list_test' in config:
self.region_list_test = config['region_list_test']
if 'region_list_train' in config:
self.region_list_train = config['region_list_train']
if 'region_list_valid' in config:
self.region_list_valid = config['region_list_valid']
flag = False
if 'scale' in config:
flag = True
self.scale = config['scale']
else:
self.scale = [0,1]
if ('activation_basic' in config) and (config['activation_basic']=='tanh'):
if (flag==True) and (self.scale[0]>=0):
flag = False
if flag==False:
self.scale = [-1,1]
self.region_boundary = []
self.serial_vec = []
self.f_mtx = []
print('scale',self.scale)
print(self.test_chromvec)
filename1 = '%s_chr%s-chr%s_chr%s-chr%s'%(self.cell_type, self.train_chromvec[0], self.train_chromvec[-1], self.test_chromvec[0], self.test_chromvec[-1])
self.filename_load = filename1
print(self.filename_load,self.method,self.predict_context,self.attention)
self.set_generate(generate,filename1)
def load_ref_serial(self, ref_filename, header=None):
if header==None:
file1 = pd.read_csv(ref_filename,header=header,sep='\t')
else:
file1 = pd.read_csv(ref_filename,sep='\t')
colnames = list(file1)
# col1, col2, col3 = '%s.chrom'%(species_name), '%s.start'%(species_name), '%s.stop'%(species_name)
col1, col2, col3, col_serial = colnames[0], colnames[1], colnames[2], colnames[3]
self.chrom_ori, self.start_ori, self.stop_ori, self.serial_ori = np.asarray(file1[col1]), np.asarray(file1[col2]), np.asarray(file1[col3]), np.asarray(file1[col_serial])
print('load ref serial', self.serial_ori.shape)
return self.serial_ori
# load local serial and signal
def load_local_serial(self, filename1, header=None, region_list=[], type_id2=1, signal_normalize=1,region_list_1=[]):
if header==None:
file2 = pd.read_csv(filename1,header=header,sep='\t')
else:
file2 = pd.read_csv(filename1,sep='\t')
colnames = list(file2)
col1, col2, col3, col_serial = colnames[0], colnames[1], colnames[2], colnames[3]
# sort the table by serial
file2 = file2.sort_values(by=[col_serial])
self.chrom, self.start, self.stop, self.serial = np.asarray(file2[col1]), np.asarray(file2[col2]), np.asarray(file2[col3]), np.asarray(file2[col_serial])
b = np.where((self.chrom!='chrX')&(self.chrom!='chrY')&(self.chrom!='chrM'))[0]
self.chrom, self.start, self.stop, self.serial = self.chrom[b], self.start[b], self.stop[b], self.serial[b]
if self.chrom_num>0:
chrom_num = self.chrom_num
else:
chrom_num = len(np.unique(self.chrom))
chrom_vec = [str(i) for i in range(1,chrom_num+1)]
print('chrom_vec', chrom_vec)
self.bin_size = self.stop[1]-self.start[1]
scale = self.scale
if len(colnames)>=5:
col_signal = colnames[4]
self.signal = np.asarray(file2[col_signal])
self.signal = self.signal[b]
self.signal_pre = self.signal.copy()
if signal_normalize==1:
if self.run_id>10:
# self.signal = signal_normalize(self.signal,[0,1]) # normalize signals
self.signal_pre1, id1, signal_vec1 = self.signal_normalize_chrom(self.chrom,self.signal,chrom_vec,scale)
if not('train_signal_update' in self.config) or (self.config['train_signal_update']==1):
train_signal, id2, signal_vec2 = self.signal_normalize_chrom(self.chrom,self.signal,self.train_chromvec,scale)
id_1 = mapping_Idx(id1,id2)
self.signal = self.signal_pre1.copy()
self.signal[id_1] = train_signal
else:
self.signal = self.signal_pre1.copy()
else:
print('signal_normalize_bychrom')
self.signal, id1, signal_vec = self.signal_normalize_bychrom(self.chrom,self.signal,chrom_vec,scale)
else:
self.signal = np.ones(len(b))
# print(self.signal.shape)
print('load local serial', self.serial.shape, self.signal.shape, np.max(self.signal), np.min(self.signal))
if 'tol_region_search' in self.config:
tol = self.config['tol_region_search']
else:
tol = 2
# only train or predict on some regions
print('load_local_serial',len(self.chrom))
if len(region_list_1)>0:
num1 = len(region_list_1)
list1 = []
for i in range(num1):
t_region = region_list_1[i]
t_chrom, t_start, t_stop = 'chr%d'%(t_region[0]), t_region[1], t_region[2]
t_id1 = np.where((self.chrom==t_chrom)&(self.start<t_stop)&(self.stop>t_start))[0]
list1.extend(t_id1)
b1 = np.asarray(list1)
self.chrom, self.start, self.stop, self.serial = self.chrom[b1], self.start[b1], self.stop[b1], self.serial[b1]
print('load_local_serial',num1,len(self.chrom))
print(region_list_1)
if len(region_list)>0:
# print('load_local_serial',region_list)
# id1, region_list = self.region_search_1(chrom,start,stop,serial,region_list)
id1, region_list = self.region_search_1(self.chrom,self.start,self.stop,self.serial,region_list,type_id2,tol)
self.chrom, self.start, self.stop, self.serial, self.signal = self.chrom[id1], self.start[id1], self.stop[id1], self.serial[id1], self.signal[id1]
id2 = self.region_search_boundary(self.chrom,self.start,self.stop,self.serial,region_list)
# print('region_search_boundary', id2[:,0], self.start[id2[:,1:3]],self.stop[id2[:,1:3]])
self.region_boundary = id2
# print(self.serial[id2[:,1:3]])
print('region_boundary',id2)
# return
else:
print('load_local_serial',region_list)
# assert len(region_list)>0
# return
return self.serial, self.signal
# training, validation and test data index
def prep_training_test(self,train_sel_list_ori):
train_id1, test_id1, y_signal_train1, y_signal_test, train1_sel_list, test_sel_list = self.generate_train_test_1(train_sel_list_ori)
self.idx_list = {'test':test_id1}
self.y_signal = {'test':y_signal_test}
if len(y_signal_test)>0:
print('y_signal_test',np.max(y_signal_test),np.min(y_signal_test))
if len(y_signal_train1)>0:
print('y_signal_train',np.max(y_signal_train1),np.min(y_signal_train1))
self.idx_list.update({'train':[],'valid':[]})
else:
return
# y_signal_test_ori = signal_normalize(y_signal_test,[0,1])
# shuffle array
# x_test_trans, shuffle_id2 = shuffle_array(x_test_trans)
# test_sel_list = test_sel_list[shuffle_id2]
# x_train1_trans, shuffle_id1 = shuffle_array(x_train1_trans)
# train_sel_list = train_sel_list[shuffle_id1]
print(train1_sel_list[0:5])
# split training and validation data
if 'ratio1' in self.config:
ratio = self.config['ratio1']
else:
ratio = 0.95
if 'type_id1' in self.config:
type_id_1 = self.config['type_id1']
else:
type_id_1 = 0
idx_train, idx_valid, idx_test = self.generate_index_1(train1_sel_list, test_sel_list, ratio, type_id_1)
print('idx_train,idx_valid,idx_test', len(idx_train), len(idx_valid), len(idx_test))
if (len(self.region_list_train)>0) or (len(self.region_list_valid)>0):
idx_train, idx_valid = self.generate_train_test_2(train1_sel_list,idx_train,idx_valid)
print('idx_train,idx_valid', len(idx_train), len(idx_valid))
train_sel_list, val_sel_list = train1_sel_list[idx_train], train1_sel_list[idx_valid]
self.idx_list.update({'train':train_id1[idx_train],'valid':train_id1[idx_valid]})
self.idx_train_val = {'train':idx_train,'valid':idx_valid}
self.y_signal.update({'train':y_signal_train1[idx_train],'valid':y_signal_train1[idx_valid]})
return train_sel_list, val_sel_list, test_sel_list
# prepare data from predefined features: kmer frequency feature and motif feature
def prep_data_sub2(self,path1,file_prefix,type_id2,feature_dim1,feature_dim2,flag_1):
species_id = self.species_id
celltype_id = self.cell_type1
if species_id=='mm10':
kmer_dim_ori, motif_dim_ori = 100, 50
filename1 = '%s/%s_%d_%d_%d.npy'%(path1,file_prefix,type_id2,kmer_dim_ori,motif_dim_ori)
# filename2 = 'test_%s_genome%d_kmer7.h5'%(species_id,celltype_id)
filename2 = '%s_%d_kmer7_0_200_trans.h5'%(species_id,celltype_id)
else:
kmer_dim_ori, motif_dim_ori = 50, 50
filename1 = '%s/%s_%d_%d_%d.npy'%(path1,file_prefix,type_id2,kmer_dim_ori,motif_dim_ori)
# filename2 = 'test_%s_kmer7.h5'%(species_id)
filename2 = '%s_kmer7_0_200_trans.h5'%(species_id)
kmer_size1, kmer_size2, kmer_size3 = 5,6,7
x_train1_trans, train_sel_list_ori = [], []
flag1, flag2 = 0, 0
flag3 = True
# if kmer_size2 in self.kmer_size:
if flag3==True:
if os.path.exists(filename1)==True:
print("loading data...")
data1 = np.load(filename1,allow_pickle=True)
data_1 = data1[()]
x_train1_trans_ori, train_sel_list_ori = np.asarray(data_1['x1']), np.asarray(data_1['idx'])
print('train_sel_list',train_sel_list_ori.shape)
print('x_train1_trans',x_train1_trans_ori.shape)
if kmer_size2 in self.kmer_size:
flag1 = 1
serial1 = train_sel_list_ori[:,1]
dim1 = x_train1_trans_ori.shape[1]
if (self.feature_dim_motif==0) or (flag_1==True):
x_train1_trans = x_train1_trans_ori[:,0:-motif_dim_ori]
else:
# d1 = np.min((dim1-motif_dim_ori+feature_dim2,d1))
# d2 = dim1-motif_dim_ori
# sel_id1 = list(range(21))+list(range(21,21+feature_dim1))
# x_train1_trans_1 = x_train1_trans[:,sel_id1]
# x_train1_trans_2 = x_train1_trans[:,d2:d1]
x_train1_trans_1 = x_train1_trans_ori[:,0:dim1-motif_dim_ori]
x_train1_trans_2 = x_train1_trans_ori[:,dim1-motif_dim_ori:]
else:
print('data not found!')
print(filename1)
return x_train1_trans, trans_sel_list_ori
if kmer_size3 in self.kmer_size:
with h5py.File(filename2,'r') as fid:
serial2 = fid["serial"][:]
feature_mtx = fid["vec"][:]
# feature_mtx = feature_mtx[:,0:kmer_dim_ori]
print(serial2)
print(len(serial2),feature_mtx.shape)
flag2 = 1
if flag1==1:
if flag2==1:
t_serial = np.intersect1d(serial1,serial2)
id1 = mapping_Idx(serial1,t_serial)
id2 = mapping_Idx(serial2,t_serial)
if 'feature_dim_transform_1' in self.config:
sel_idx = self.config['feature_dim_transform_1']
sel_id1, sel_id2 = list(0,21)+list(range(sel_idx[0])), range(sel_idx[1])
else:
sel_id1 = list(0,21)+list(range(10))
sel_id2 = range(feature_dim1-sel_idx1)
if (self.feature_dim_motif==0) or (flag_1==True):
x_train1_trans = np.hstack((x_train1_trans[id1,sel_id1],feature_mtx[id2,sel_id2]))
else:
x_train1_trans = np.hstack((x_train1_trans_1[id1,sel_id1],feature_mtx[id2,sel_id2],x_train1_trans_2[id1,0:feature_dim2]))
train_sel_list_ori = train_sel_list_ori[id1]
else:
pass
elif flag2==1:
t_serial = np.intersect1d(serial1,serial2)
id1 = mapping_Idx(serial1,t_serial)
id2 = mapping_Idx(serial2,t_serial)
x_train1_trans = np.hstack((x_train1_trans_ori[id1,0:2],feature_mtx[id2,0:feature_dim1]))
train_sel_list_ori = train_sel_list_ori[id1]
self.feature_dim_select1 = -1
if (self.feature_dim_motif==1) and (flag_1==False):
x_train1_trans = np.hstack((x_train1_trans,x_train1_trans_2[id1,0:feature_dim2]))
# id1 = mapping_Idx(self.serial_ori,serial2)
# b1 = (id1>=0)
# id1 = id1[b1]
# serial2, feature_mtx = serial2[b1], feature_mtx[b1]
# chrom1 = self.chrom_ori[id1]
# chrom2 = np.zeros(len(serial2),dtype=np.int32)
# chrom_vec = np.unique(chrom1)
# for chrom_id in chrom_vec:
# b2 = np.where(chrom1==chrom_id)[0]
# chrom_id1 = int(chrom_id[3:])
# chrom2[b2] = chrom_id1
# x_train1_trans = feature_mtx[:,0:feature_dim1]
# trans_sel_list_ori = np.vstack((chrom2,serial2)).T
else:
print('data not found!')
return x_train1_trans, train_sel_list_ori
# prepare data from predefined features
def prep_data_sub1(self,path1,file_prefix,type_id2,feature_dim_transform,load_type=0):
self.feature_dim_transform = feature_dim_transform
# map_idx = mapping_Idx(serial_ori,serial)
sub_sample_ratio = 1
shuffle = 0
normalize, flanking, attention, run_id = self.normalize, self.flanking, self.attention, self.run_id
config = self.config
vec2 = dict()
tol = self.tol
L = flanking
# np.save(filename1)
print("feature transform")
# filename1 = '%s/%s_%d_%d_%d.npy'%(path1,file_prefix,type_id2,feature_dim_transform[0],feature_dim_transform[1])
print(self.species_id)
t_featuredim1, t_featuredim2 = feature_dim_transform[0], feature_dim_transform[1]
flag1 = False
if self.species_id=='hg38':
if 'motif_trans_typeid' in self.config:
flag1 = True
if (self.species_id=='mm10'):
flag1 = True
if (t_featuredim1>0) or (flag1==False):
x_train1_trans, train_sel_list_ori = self.prep_data_sub2(path1,file_prefix,type_id2,t_featuredim1,t_featuredim2,flag1)
if len(x_train1_trans)==0:
print('data not found!')
return -1
if t_featuredim2>0:
print('train_sel_list',train_sel_list_ori.shape)
print('x_train1_trans',x_train1_trans.shape)
if (self.feature_dim_motif>=1) and (flag1==True):
if self.species_id=='mm10':
annot1 = '%s_%d_motif'%(self.species_id,self.cell_type1)
else:
annot1 = '%s_motif'%(self.species_id)
motif_trans_typeid = self.config['motif_trans_typeid']
motif_featuredim = self.config['motif_featuredim']
motif_filename = '%s_%d_%d_trans.h5'%(annot1,motif_trans_typeid,motif_featuredim)
if motif_featuredim<t_featuredim2:
print('error! %d %d',motif_featuredim,t_featuredim2)
t_featuredim2 = motif_featuredim
with h5py.File(motif_filename,'r') as fid:
serial_1 = fid["serial"][:]
motif_data = fid["vec"][:]
print(len(serial_1),motif_data.shape)
serial1 = train_sel_list_ori[:,1]
serial2 = serial_1
t_serial = np.intersect1d(serial1,serial2)
id1 = mapping_Idx(serial1,t_serial)
id2 = mapping_Idx(serial2,t_serial)
x_train1_trans = np.hstack((x_train1_trans[id1],motif_data[id2,0:t_featuredim2]))
train_sel_list_ori = train_sel_list_ori[id1]
# train_sel_list_ori2 = serial_1[id2]
else:
print("data not found!")
return
x_train1_trans = self.feature_dim_select(x_train1_trans,feature_dim_transform)
# feature loaded not specific to cell type
if load_type==1:
return x_train1_trans, train_sel_list_ori
list1 = ['motif_feature','feature2']
for t_feature in list1:
if (t_feature in self.config) and (self.config[t_feature]==1):
if t_feature=='feature2':
pre_config = self.config['pre_config']
if self.chrom_num>0:
chrom_num = self.chrom_num
else:
chrom_num = len(np.unique(self.chrom))
chrom_vec = list(range(1,chrom_num+1))
feature_mtx2, serial_2 = self.prep_data_sequence_3(pre_config,chrom_vec)
else:
x = 1
x_train1_trans_ori1 = x_train1_trans.copy()
train_sel_list_ori1 = train_sel_list_ori.copy()
serial1 = train_sel_list_ori[:,1]
serial2 = serial_2[:,1]
t_serial = np.intersect1d(serial1,serial2)
id1 = mapping_Idx(serial1,t_serial)[0]
id2 = mapping_Idx(serial2,t_serial)[0]
x_train1_trans = np.hstack((x_train1_trans[id1],feature_mtx2[id2]))
train_sel_list_ori = train_sel_list_ori[id1]
train_sel_list_ori2 = serial_2[id2]
b1 = np.where(train_sel_list_ori[:,0]!=train_sel_list_ori2[:,0])[0]
if len(b1)>0:
print('error! train_sel_list_ori',len(b1))
if ('centromere' in self.config) and (self.config['centromere']==1):
regionlist_filename = 'hg38.centromere.bed'
serial1 = train_sel_list_ori[:,1]
serial_list1, centromere_serial = self.select_region(serial1, regionlist_filename)
id1 = mapping_Idx(serial1,serial_list1)
id1 = id1[id1>=0]
x_train1_trans = x_train1_trans[id1]
train_sel_list_ori = train_sel_list_ori[id1]
print(x_train1_trans.shape,train_sel_list_ori.shape)
print('positional encoding', self.pos_code)
print('feature dim',x_train1_trans.shape)
self.feature_dim = x_train1_trans.shape[1]
start = time.time()
if self.pos_code ==1:
x_train1_trans = self.positional_encoding1(x_train1_trans,train_sel_list_ori,self.feature_dim)
print(x_train1_trans.shape)
stop = time.time()
print('positional encoding', stop-start)
## shuffle array
if ('shuffle' in self.config) and (self.config['shuffle']==1):
x_train1_trans, shuffle_id1 = shuffle_array(x_train1_trans)
print('array shuffled')
# np.random.shuffle(x_tran1_trans)
# train_sel_list = train_sel_list[shuffle_id1]
elif ('noise' in self.config) and (self.config['noise']>0):
if self.config['noise']==1:
x_train1_trans = np.zeros_like(x_train1_trans)
print('x_train1_trans, noise 1', x_train1_trans[0:5])
elif self.config['noise']==2:
x_train1_trans = np.random.uniform(0,1,x_train1_trans.shape)
else:
x_train1_trans = np.random.normal(0,1,x_train1_trans.shape)
else:
pass
if 'sub_sample_ratio' in self.config:
sub_sample_ratio = self.config['sub_sample_ratio']
num_sample = len(train_sel_list_ori)
sub_sample = int(num_sample*sub_sample_ratio)
train_sel_list_ori = train_sel_list_ori[0:sub_sample]
x_train1_trans = x_train1_trans[0:sub_sample]
# align train_sel_list_ori and serial
print(train_sel_list_ori.shape,len(self.serial))
id1 = mapping_Idx(train_sel_list_ori[:,1],self.serial)
id2 = (id1>=0)
print('mapping',len(self.serial),np.sum(id2),len(self.serial),len(id2))
# self.chrom, self.start, self.stop, self.serial, self.signal = self.chrom[id2], self.start[id2], self.stop[id2], self.serial[id2], self.signal[id2]
self.local_serial_1(id2)
id1 = id1[id2]
train_sel_list_ori = train_sel_list_ori[id1]
x_train1_trans = x_train1_trans[id1]
self.x_train1_trans = x_train1_trans
self.train_sel_list = train_sel_list_ori
return x_train1_trans, train_sel_list_ori
def output_generate_sequences(self,idx_sel_list,seq_list):
num1 = len(seq_list)
t_serial1 = idx_sel_list[:,1]
seq_list = np.asarray(seq_list)
t_serial = t_serial1[seq_list]
id1 = mapping_Idx(self.serial,t_serial[:,0])
chrom1, start1, stop1 = self.chrom[id1], self.start[id1], self.stop[id1]
id2 = mapping_Idx(self.serial,t_serial[:,1])
chrom2, start2, stop2 = self.chrom[id2], self.start[id2], self.stop[id2]
fields = ['chrom','start','stop','serial1','serial2']
data1 = pd.DataFrame(columns=fields)
data1['chrom'], data1['start'], data1['stop'] = chrom1, start1, stop2
data1['serial1'], data1['serial2'] = t_serial[:,0], t_serial[:,1]
data1['region_len'] = t_serial[:,1]-t_serial[:,0]+1
output_filename = 'test_seqList_%d_%d.txt'%(idx_sel_list[0][0],idx_sel_list[0][1])
data1.to_csv(output_filename,index=False,sep='\t')
return True
# prepare data from predefined features
def prep_data(self,path1,file_prefix,type_id2,feature_dim_transform):
x_train1_trans, train_sel_list_ori = self.prep_data_sub1(path1,file_prefix,type_id2,feature_dim_transform)
train_sel_list, val_sel_list, test_sel_list = self.prep_training_test(train_sel_list_ori)
# keys = ['train','valid','test']
keys = ['train','valid']
# self.idx_sel_list = {'train':train1_sel_list,'valid':val_sel_list,'test':test_sel_list}
idx_sel_list = {'train':train_sel_list,'valid':val_sel_list,'test':test_sel_list}
# self.idx_sel_list = idx_sel_list
# seq_list_train, seq_list_valid: both locally calculated
self.seq_list = dict()
start = time.time()
for i in keys:
self.seq_list[i] = generate_sequences(idx_sel_list[i],region_list=self.region_boundary)
print(len(self.seq_list[i]))
self.output_generate_sequences(idx_sel_list[i],self.seq_list[i])
stop = time.time()
print('generate_sequences', stop-start)
# generate initial state index
self.init_id = dict()
self.init_index(keys)
# training and validation data
# x_train1_trans = self.x_train1_trans
for i in keys:
idx = self.idx_list[i]
if self.method<5 or self.method in [56]:
self.x[i] = x_train1_trans[idx]
self.y[i] = self.y_signal[i]
print(self.x[i].shape, self.y[i].shape)
else:
idx_sel_list = self.train_sel_list[idx]
start = time.time()
x, y, self.vec[i], self.vec_local[i] = sample_select2a1(x_train1_trans[idx],self.y_signal[i],
idx_sel_list, self.seq_list[i], self.tol, self.flanking)
stop = time.time()
print('sample_select2a1',stop-start)
# concate context for baseline methods
if self.method<=10:
# x_train, x_valid, y_train, y_valid = train_test_split(x_train1, y_train1, test_size=0.2, random_state=42)
x = x.reshape(x.shape[0],x.shape[1]*x.shape[-1])
y = y[:,self.flanking]
self.x[i], self.y[i] = x, y
print(self.x[i].shape, self.y[i].shape)
return True
# prepare data from predefined features
def prep_data_1(self,path1,file_prefix,type_id2,feature_dim_transform,
n_fold=5, ratio=0.9, type_id=1):
x_train1_trans, train_sel_list_ori = self.prep_data_sub1(path1,file_prefix,type_id2,feature_dim_transform)
print(train_sel_list_ori)
id1 = mapping_Idx(train_sel_list_ori[:,1],self.serial)
id2 = (id1>=0)
print('mapping',len(self.serial),np.sum(id2))
self.chrom, self.start, self.stop, self.serial, self.signal = self.chrom[id2], self.start[id2], self.stop[id2], self.serial[id2], self.signal[id2]
id1 = id1[id2]
train_sel_list_ori = train_sel_list_ori[id1]
self.x_train1_trans = self.x_train1_trans[id1]
print(train_sel_list_ori.shape,self.x_train1_trans.shape)
id_vec = self.generate_index_2(train_sel_list_ori, n_fold=n_fold, ratio=ratio, type_id=type_id)
return id_vec
def find_serial_ori_1_local(self,chrom_vec,type_id2=1):
# filename1 = 'mm10_%d_%s_encoded1.h5'%(self.config['cell_type1'],chrom_id1)
self.species_id = 'mm10'
self.cell_type1 = self.config['cell_type1']
file_path1 = '/work/magroup/yy3/data1/replication_timing3/mouse'
# filename1 = '%s/mm10_5k_seq_genome%d_1.txt'%(file_path1,self.config['cell_type1'])
chrom_id1 = 'chr1'
filename1 = '%s_%d_%s_encoded1.h5'%(self.species_id,self.cell_type1,chrom_id1)
list1, list2 = [], []
serial_vec = []
print(filename1)
if os.path.exists(filename1)==False:
# prepare data from predefined features
# one hot encoded feature vectors for each chromosome
self.prep_data_sequence_ori()
print('prep_data_sequence_ori',filename1)
for chrom_id in chrom_vec:
# if chrom_id<22:
# continue
chrom_id1 = 'chr%s'%(chrom_id)
# if self.config['species_id']==0:
# filename2 = 'mm10_%d_%s_encoded1.h5'%(self.config['cell_type1'],chrom_id1)
# else:
# filename2 = '%s_%s_encoded1.h5'%(self.species_id,chrom_id1)
filename2 = '%s_%d_%s_encoded1.h5'%(self.species_id,self.cell_type1,chrom_id1)
with h5py.File(filename2,'r') as fid:
serial1 = fid["serial"][:]
if type_id2==1:
seq1 = fid["vec"][:]
list2.extend(seq1)
list1.extend([chrom_id]*len(serial1))
serial_vec.extend(serial1)
print(chrom_id,len(serial1))
list1, serial_vec = np.asarray(list1), np.asarray(serial_vec)
serial_vec = np.hstack((list1[:,np.newaxis],serial_vec))
f_mtx = np.asarray(list2)
# data_1 = pd.read_csv(filename1,sep='\t')
# colnames = list(data_1)
# local_serial = np.asarray(data_1['serial'])
# local_seq = np.asarray(data_1['seq'])
# print('local_seq', local_seq.shape)
# serial_vec = local_serial
# f_mtx = local_seq
# filename2 = '%s/mm10_5k_serial.bed'%(file_path1)
# file2 = pd.read_csv(filename2,header=None,sep='\t')
# ref_chrom, ref_start, ref_stop, ref_serial = np.asarray(file2[0]), np.asarray(file2[1]), np.asarray(file2[2]), np.asarray(file2[3])
# # assert list(local_serial==list(ref_serial))
# id_vec1 = []
# for chrom_id in chrom_vec:
# # if chrom_id<22:
# # continue
# # chrom_id1 = 'chr%s'%(chrom_id)
# id1 = np.where(ref_chrom=='chr%d'%(chrom_id))[0]
# id_vec1.extend(id1)
# print(chrom_id,len(id1))
# id_vec1 = np.asarray(id_vec1)
# ref_chrom_1, ref_serial_1 = ref_chrom[id_vec1], ref_serial[id_vec1]
# print('ref chrom local', len(ref_chrom_1), len(ref_serial_1))
# id1 = utility_1.mapping_Idx(ref_serial_1,local_serial)
# id2 = np.where(id1>=0)[0]
# id1 = id1[id2]
# # assert len(id2)==len(id1)
# chrom1 = ref_chrom_1[id1]
# local_chrom = [int(chrom1[3:]) for chrom1 in ref_chrom_1]
# local_chrom = np.asarray(local_chrom)
# local_serial, local_seq = local_serial[id2], local_seq[id2]
# serial_vec = np.column_stack((local_chrom,local_serial))
# f_mtx = np.asarray(local_seq)
return serial_vec, f_mtx
# find serial and feature vectors
# input: type_id1: load sequence feature or kmer frequency feature, motif feature
# type_id2: load serial or feature vectors
def find_serial_ori_1(self,file_path,file_prefix,chrom_vec,type_id1=0,type_id2=0,select_config={}):
# load the sequences
if type_id1==0:
# list2 = np.zeros((interval,region_unit_size,4),dtype=np.int8)
filename1 = '%s_serial_2.txt'%(self.species_id)
list1, list2 = [], []
serial_vec = []
if (os.path.exists(filename1)==False) or (type_id2==1):
if self.config['species_id']==0:
serial_vec, list2 = self.find_serial_ori_1_local(chrom_vec)
else:
for chrom_id in chrom_vec:
# if chrom_id<22:
# continue
chrom_id1 = 'chr%s'%(chrom_id)
filename2 = '%s_%s_encoded1.h5'%(self.species_id,chrom_id1)
with h5py.File(filename2,'r') as fid:
serial1 = fid["serial"][:]
if type_id2==1:
seq1 = fid["vec"][:]
list2.extend(seq1)
list1.extend([chrom_id]*len(serial1))
serial_vec.extend(serial1)
print(chrom_id,len(serial1))
list1, serial_vec = np.asarray(list1), np.asarray(serial_vec)
serial_vec = np.hstack((list1[:,np.newaxis],serial_vec))
np.savetxt(filename1,serial_vec,fmt='%d',delimiter='\t')
else:
serial_vec = np.loadtxt(filename1,dtype=np.int64)
if serial_vec.shape[-1]>2:
cnt1 = serial_vec[:,-1]
b1 = np.where(cnt1>0)[0]
ratio1 = len(b1)/len(serial_vec)
print('sequence with N', len(b1),len(serial_vec),ratio1)
# serial_vec = serial_vec[:,0]
f_mtx = np.asarray(list2)
elif type_id1==2:
filename1 = select_config['input_filename1']
layer_name = select_config['layer_name']
with h5py.File(filename1,'r') as fid:
f_mtx = np.asarray(fid[layer_name][:],dtype=np.float32)
print(f_mtx.shape)
serial_vec = fid["serial"][:]
assert len(serial_vec )==f_mtx.shape[0]
print(serial_vec[0:5])
else:
# load kmer frequency features and motif features
load_type_id2 = 0
x_train1_trans, train_sel_list_ori = self.prep_data_sub1(file_path,file_prefix,load_type_id2,self.feature_dim_transform,load_type=1)
# serial_vec = train_sel_list_ori[:,1]
serial_vec = np.asarray(train_sel_list_ori)
f_mtx = np.asarray(x_train1_trans)
return serial_vec, f_mtx
def find_serial_ori(self,file_path,file_prefix,type_id1=0,type_id2=0,select_config={}):
chrom_vec = np.unique(self.chrom)
chrom_vec1 = []
for chrom_id in chrom_vec:
try:
id1 = chrom_id.find('chr')
if id1>=0:
chrom_id1 = int(chrom_id[3:])
chrom_vec1.append(chrom_id1)
except:
continue
chrom_vec1 = np.sort(chrom_vec1)
serial_vec, f_mtx = self.find_serial_ori_1(file_path,file_prefix,chrom_vec1,
type_id1=type_id1,type_id2=type_id2,
select_config=select_config)
self.serial_vec = serial_vec
self.f_mtx = f_mtx
# list2 = np.zeros((interval,region_unit_size,4),dtype=np.int8)
print(len(self.chrom),len(self.serial))
# cnt1 = serial_vec[:,1]
# b1 = np.where(cnt1>0)[0]
# ratio1 = len(b1)/len(serial_vec)
# print(len(b1),len(serial_vec),ratio1)
id1 = mapping_Idx(serial_vec[:,1],self.serial)
b1 = np.where(id1>=0)[0]
self.local_serial_1(b1,type_id=0)
print(len(self.chrom),len(self.serial))
return True
def prep_data_2(self,file_path,file_prefix,seq_len_thresh=50):
self.find_serial_ori(file_path,file_prefix)
chrom_vec = np.unique(self.chrom)
chrom_vec1 = []
for chrom_id in chrom_vec:
try:
id1 = chrom_id.find('chr')
if id1>=0:
chrom_id1 = int(chrom_id[3:])
chrom_vec1.append(chrom_id1)
except:
continue
chrom_vec1 = np.sort(chrom_vec1)
sample_num = len(self.chrom)
idx_sel_list = -np.ones((sample_num,2),dtype=np.int64)
for chrom_id in chrom_vec1:
chrom_id1 = 'chr%d'%(chrom_id)
b1 = np.where(self.chrom==chrom_id1)[0]
idx_sel_list[b1,0] = [chrom_id]*len(b1)
idx_sel_list[b1,1] = self.serial[b1]
id1 = idx_sel_list[:,0]>=0
idx_sel_list = idx_sel_list[id1]
sample_num = len(id1)
y = self.signal[id1]
x_mtx = idx_sel_list[id1]
seq_list = generate_sequences(idx_sel_list, gap_tol=5, region_list=[])
seq_len = seq_list[:,1]-seq_list[:,0]+1
thresh1 = seq_len_thresh
b1 = np.where(seq_len>thresh1)[0]
print(len(seq_list),len(b1))
seq_list = seq_list[b1]
seq_len1 = seq_list[:,1]-seq_list[:,0]+1
print(sample_num,np.sum(seq_len1),seq_list.shape,np.max(seq_len),np.min(seq_len),np.median(seq_len), | np.max(seq_len1) | numpy.max |
# -*- coding: utf-8 -*-
"""
Created on Tue May 5 17:11:19 2020
@author: TOMAS (UDEA-FAU)
"""
import numpy as np
from scipy.fftpack import dct
from scipy.signal import lfilter
### UTILITY FUNCTIONS ###
def erb_space(low_freq=50, high_freq=8000, n=64):
ear_q = 9.26449
min_bw = 24.7
cf_array = -(ear_q * min_bw) + np.exp(np.linspace(1,n,n) * (-np.log(high_freq + ear_q * min_bw) + np.log(low_freq + ear_q * min_bw)) / n) \
* (high_freq + ear_q * min_bw)
return cf_array
def powerspec(X,n_padded):
# Fourier transform
# Y = np.fft.rfft(X, n=n_padded)
Y = np.fft.fft(X, n=n_padded)
Y = np.absolute(Y)
# non-redundant part
m = int(n_padded / 2) + 1
Y = Y[:, :m]
return np.abs(Y) ** 2, n_padded
### GAMMATONE IMPULSE RESPONSE ###
def gammatone_impulse_response(samplerate_hz, length_in_samples, center_freq_hz,p):
# Generate a Glasberg&Moore parametrized gammatone filter
erb = 24.7 + (center_freq_hz/9.26449) # equivalent rectangular bandwidth.
#Center frequencies
an = (np.pi * np.math.factorial(2*p-2) * np.power(2, float(-(2*p-2))) )/ np.square(np.math.factorial(p-1))
b = erb/an # bandwidth parameter
a = 1 # amplitude. This is varied later by the normalization process.
t = np.linspace(1./samplerate_hz, length_in_samples/samplerate_hz, length_in_samples)
gammatone_ir = a * np.power(t, p-1)*np.exp(-2*np.pi*b*t) * np.cos(2*np.pi*center_freq_hz*t)
return gammatone_ir
### MP-GTF CONSTRUCTION ###
def generate_filterbank(fs,fmax, L, N,p=4):
"""
L: Size of the signal measured in samples
N: Number of filters
p: Order of the Gammatone impulse response
"""
#Center frequencies
if fs==8000:
fmax = 4000
center_freqs = erb_space(50,fmax, N)
center_freqs = np.flip(center_freqs)
n_center_freqs = len(center_freqs)
# Initialize variables
filterbank = | np.zeros((N, L)) | numpy.zeros |
import numpy as np
from multiagent.core import World, Agent, Landmark
from multiagent.scenario import BaseScenario
import cmath, math, os, time
from UTILS.tensor_ops import np_normalize_last_dim, dir3d_rad
def Norm(x): # 求长度
return np.linalg.norm(x)
def Unit(m):
return m * 0.05
def ToMeter(x):
return x / 0.05
def assert_and_break(cond):
if cond:
return
else:
print("fail!")
class ScenarioConfig(object):
hunter_num = 15
invader_num = 5
num_landmarks = 6
num_dummy_coordinate = 4
num_entity = invader_num + num_landmarks + num_dummy_coordinate
num_subject_in_obs = (hunter_num + invader_num) + num_landmarks + num_dummy_coordinate # 观测向量长度
uid_dictionary = { # need to contain at least 'agent_uid' and 'entity_uid'
'invader_uid' : range(0, invader_num),
'agent_uid' : range(invader_num, invader_num+hunter_num),
'landmark_uid': range(invader_num+hunter_num, invader_num+hunter_num+num_landmarks),
'dummy_uid': range(invader_num+hunter_num+num_landmarks, invader_num+hunter_num+num_landmarks+num_dummy_coordinate),
}
uid_dictionary['entity_uid'] = list(uid_dictionary['invader_uid']) + list(uid_dictionary['landmark_uid']) + list(uid_dictionary['dummy_uid'])
N_TEAM = 2
N_AGENT_EACH_TEAM = [invader_num, hunter_num]
AGENT_ID_EACH_TEAM = [list(range(0,invader_num)), list(range(invader_num, invader_num+hunter_num))]
TEAM_NAMES = ['script-team', 'rl-team']
obs_vec_length = 8
obs_vec_dictionary = {
'pos' : (0,1,2),
'vel' : (3,4,5),
'alive': (6),
'other': (7),
}
discrete_action = True
MaxEpisodeStep = 140
arena_size = Unit(m=140)
num_MPE_agent = hunter_num + invader_num
nest_center_pos = np.array([Unit(m=0), Unit(m=0), Unit(m=0)])
hunter_spawn_pos_lim = Unit(m=25)
landmark_spawn_limit = Unit(m=20)
invader_spawn_limit = Unit(m=80)
distance_dectection = Unit(m=25)
intercept_hunter_needed = 3
hunter_affect_range = Unit(m=5.999)
hunter_speed_pressure = Unit(m=5.999)
Invader_Size = Unit(m=2)
Invader_Accel = Unit(m=400)
Invader_MaxSpeed = Unit(m=12) # 12 * 0.05=0.6
Hunter_Size = Unit(m=1.5)
Hunter_Accel = Unit(m=400)
Hunter_MaxSpeed = Unit(m=12) # 12
Landmark_Size = Unit(m=6)
Invader_Kill_Range = Unit(m=5.999) #
Invader_Spawn_Times = invader_num*2-invader_num
invader_spawn_cd = 20
RewardAsUnity = True
render = False
extreme_sparse = True
class Scenario(BaseScenario):
def __init__(self, process_id=-1):
self.invader_spawn_cd = ScenarioConfig.invader_spawn_cd
self.num_agents = ScenarioConfig.num_MPE_agent
self.arena_size = ScenarioConfig.arena_size
self.discrete_action = ScenarioConfig.discrete_action
self.cam_range = ScenarioConfig.arena_size * 1.2
self.hunter_spawn_pos_lim = ScenarioConfig.hunter_spawn_pos_lim
self.nest_center_pos = ScenarioConfig.nest_center_pos
self.invader_spawn_limit = ScenarioConfig.invader_spawn_limit
self.distance_dectection = ScenarioConfig.distance_dectection
self.Invader_MaxSpeed = ScenarioConfig.Invader_MaxSpeed
self.hunter_affect_range = ScenarioConfig.hunter_affect_range
self.hunter_speed_pressure = ScenarioConfig.hunter_speed_pressure
self.intercept_hunter_needed = ScenarioConfig.intercept_hunter_needed
self.num_subject_in_obs = ScenarioConfig.num_subject_in_obs
self.Invader_Kill_Range = ScenarioConfig.Invader_Kill_Range
self.Invader_Spawn_Times = ScenarioConfig.Invader_Spawn_Times
self.obs_vec_length = ScenarioConfig.obs_vec_length
self.invader_num = ScenarioConfig.invader_num
self.Invader_To_Intercept = self.invader_num + self.Invader_Spawn_Times
# self.thread_index = thread_index # thread_index = 0 是主进程
self.caught = 0
self.rew_other = 0
self.manual_render = None
self.eval_mode = False
self.show_off = False if process_id != 0 else ScenarioConfig.render
def render(self):
if not hasattr(self, 'threejs_bridge'):
from VISUALIZE.mcom import mcom
self.threejs_bridge = mcom(path='RECYCLE/v2d_logger/', digit=8, rapid_flush=False, draw_mode='Threejs')
self.threejs_bridge.v2d_init()
# self.threejs_bridge.set_style('star')
# self.threejs_bridge.set_style('grid')
self.threejs_bridge.set_style('background', color='Lavender')
# self.threejs_bridge.geometry_rotate_scale_translate('monkey',0, 0, np.pi/2, 1, 1, 1, 0,0,0)
self.threejs_bridge.geometry_rotate_scale_translate('box', 0, 0, 0, 0.5, 0.5, 1.5, 0,0,0)
self.threejs_bridge.geometry_rotate_scale_translate('ball', 0, 0, 0, 1, 1, 1, 0,0,0)
self.threejs_bridge.geometry_rotate_scale_translate('cone', 0, np.pi/2, 0, 1.2, 0.9, 0.9, -0.5,0,0) # x -> y -> z
self.threejs_bridge.其他几何体之旋转缩放和平移('oct', 'OctahedronGeometry(1,0)', 0,0,0, 1,1,1, 0,0,0) # 八面体
self.threejs_bridge.advanced_geometry_material('oct', map='/wget/hex_texture.jpg')
self.threejs_bridge.agent_alive_pos = {}
self.threejs_bridge.agent_alive_time = {}
for index, agent in enumerate(self.invaders + self.hunters):
dir_1, dir_2 = dir3d_rad(agent.state.p_vel) # # Euler Angle y-x-z
x = agent.state.p_pos[0]; y=agent.state.p_pos[1]; z=agent.state.p_pos[2]
if agent.live:
self.threejs_bridge.agent_alive_pos[index] = (x,y,z)
if agent.IsInvader:
color = 'Red'
size = 0.04
if not agent.IsInvader:
color = 'Blue'
size = 0.01
opacity = 0.99
if index not in self.threejs_bridge.agent_alive_time: self.threejs_bridge.agent_alive_time[index] = 0
self.threejs_bridge.agent_alive_time[index] += 1
else:
color = 'black'
opacity = 0
self.threejs_bridge.agent_alive_time[index] = 0
self.threejs_bridge.v2dx(
'cone|%d|%s|%.2f'%(index, color, size),
self.threejs_bridge.agent_alive_pos[index][0],
self.threejs_bridge.agent_alive_pos[index][1],
self.threejs_bridge.agent_alive_pos[index][2],
ro_x=0, ro_y=-dir_2, ro_z=dir_1, # rotation
label='', label_color='white',
opacity=opacity if agent.live else 0,
track_n_frame = max(min(self.threejs_bridge.agent_alive_time[index]-1, 10),0)
)
x_ = self.threejs_bridge.agent_alive_pos[index][0]
y_ = self.threejs_bridge.agent_alive_pos[index][1]
z_ = self.threejs_bridge.agent_alive_pos[index][2]
self.threejs_bridge.line3d(
'fat|%d|%s|%.3f'%(index+3999, color, 0.004),
x_arr=np.array([x_, x_]),
y_arr=np.array([y_, y_]),
z_arr=np.array([0, z_]),
dashScale=20, # to make dash denser, Increase this instead of decrease !!
dashSize=1,
gapSize=1,
tension=0,
opacity=1,
)
for index, agent in enumerate(self.hunters):
dir_1, dir_2 = dir3d_rad(agent.state.p_vel) # Euler Angle y-x-z
dis2invader = self.distance[index, :]
mindis2invader_id = np.argmin(dis2invader)
if dis2invader[mindis2invader_id]<self.hunter_affect_range:
self.threejs_bridge.flash('beam', src=index+len(self.invaders), dst=mindis2invader_id, dur=0.5, size=0.03, color='DeepSkyBlue')
for index, agent in enumerate(self.landmarks):
nearest_invader_dis = min(self.distance_landmark[:, index])
self.threejs_bridge.v2dx(
'oct|%d|LawnGreen|0.2'%(index+999),
agent.state.p_pos[0],
agent.state.p_pos[1],
agent.state.p_pos[2],
ro_x=0, ro_y=0, ro_z=0, # Euler Angle y-x-z
label='Danger@ %.1f'%nearest_invader_dis,
label_color='Black' if nearest_invader_dis>1 else 'red',
opacity=1
)
self.threejs_bridge.v2dx(
'oct|%d|green|0.3'%(1999),
0,
2.5,
-1.6,
ro_x=0, ro_y=0, ro_z=0, # Euler Angle y-x-z
label='Time %d/%d'%(self.step, ScenarioConfig.MaxEpisodeStep),
label_color='BlueViolet',
opacity=0
)
self.threejs_bridge.v2d_show()
if (self.step)==0:
self.threejs_bridge.set_env('clear_track')
self.threejs_bridge.set_env('clear_flash')
def scenario_step(self, agent, world):
invaders = self.invaders
hunters = self.hunters
# 计算距离矩阵（invader2landmark）
self.distance, self.distance_landmark = self.get_distance_landmark()
# 二重循环，对出现在周围的invader造成减速
self.threat_clear = True # 检查invader是否被驱除出
for invader in invaders:
invader.tracked_by = []
if np.linalg.norm(invader.state.p_pos) < ScenarioConfig.invader_spawn_limit*1.11:
self.threat_clear = False
for i, hunter in enumerate(hunters):
hunter_index = i
assert hunter.live
for j, invader in enumerate(invaders):
distance_i_j = self.distance[i, j]
if distance_i_j > self.hunter_affect_range: continue
invader.tracked_by.append(hunter_index)
# push invaders to opposite direction
for invader_index, invader in enumerate(invaders):
if invader.state.previous_pos is None: continue # special situations
if not hasattr(invader, 'force'): continue # special situations
invader.state.p_vel = invader.state.previous_vel * (1 - world.damping) # read vel
if (invader.force is not None): # use force to update vel
invader.force_real = invader.force + (-invader.force) * len(invader.tracked_by) * 0.55
invader.state.p_vel += (invader.force_real / invader.mass) * world.dt
# limit max speed
if (invader.max_speed is not None):
speed = np.linalg.norm(invader.state.p_vel)
if speed > invader.max_speed:
invader.state.p_vel = invader.state.p_vel / speed * invader.max_speed
# update position
invader.state.p_pos = invader.state.previous_pos + invader.state.p_vel * world.dt
# 检查landmark是否被摧毁 self.distance_landmark [self.num_invaders, self.num_landmarks]
if np.min(self.distance_landmark) <= self.Invader_Kill_Range:
self.hunter_failed = True
def observation(self, agent, world):
if agent.iden == 0:
# by now the agents has already moved according to action
self.scenario_step(agent, world) # 第一步更新距离矩阵，更新智能体live的状态
self.joint_rewards = self.reward_forall(world) #第二步更新奖励
if self.show_off: self.render() # 第三步更新UI
self.step += 1
self.obs_dimension = self.obs_vec_length*self.num_subject_in_obs
self.obs_pointer = 0
self.obs = np.zeros(shape=(self.obs_dimension,))
self.load_obs(
np.concatenate(
[
np.concatenate(
(entity.state.p_pos, entity.state.p_vel, [entity.live, agent.iden])
)
for entity in world.agents]
)
)
self.load_obs(
np.concatenate(
[
np.concatenate(
(entity.state.p_pos, entity.state.p_vel, [1, agent.iden])
)
for entity in world.landmarks]
)
)
# dummy coordinate
self.load_obs(
np.concatenate(
[
np.concatenate( ([0, 0, 0], [0,0,0], [world.steps, agent.iden]) ),
np.concatenate( ([1, 0, 0], [0,0,0], [world.steps, agent.iden]) ),
np.concatenate( ([0, 1, 0], [0,0,0], [world.steps, agent.iden]) ),
np.concatenate( ([0, 0, 1], [0,0,0], [world.steps, agent.iden]) ),
]
)
)
return self.obs.copy()
def reward_forall(self, world):
# 初始化奖励列表
hunter_reward = np.array([0.] * self.num_hunters)
invader_reward = np.array([0.] * self.num_invaders)
win_cond1 = world.steps >= world.MaxEpisodeStep
win_cond2 = self.threat_clear
win_cond = win_cond1 or win_cond2
loss_cond = self.hunter_failed
if loss_cond: win_cond = False # lose condition has higher priority
if ScenarioConfig.extreme_sparse:
# 极度稀疏奖励
if win_cond:
hunter_reward += 1
invader_reward -= 1
if loss_cond:
hunter_reward -= 1
invader_reward += 1
else:
# 一般型稀疏奖励
HUNT_INVDR_SUCCESSFUL_REWARD = 0.05
REWARD_WHEN_TRACKED_BY_N = 3
WIN_REWARD = 1
for invader_index, invader in enumerate(self.invaders):
if len(invader.tracked_by) >= REWARD_WHEN_TRACKED_BY_N and (not invader.intercepted):
invader.intercepted = True
hunter_reward += HUNT_INVDR_SUCCESSFUL_REWARD
invader_reward -= HUNT_INVDR_SUCCESSFUL_REWARD
if win_cond:
hunter_reward += WIN_REWARD
invader_reward -= WIN_REWARD
if loss_cond:
hunter_reward -= WIN_REWARD
invader_reward += WIN_REWARD
self.reward_sample += hunter_reward[0]
return invader_reward.tolist() + hunter_reward.tolist()
def spawn_position(self, agent, world):
if not agent.IsInvader:
# 处理hunter
# 初始化，随机地分布在一个正方形内
agent.state.p_pos = np.random.uniform(-self.hunter_spawn_pos_lim, self.hunter_spawn_pos_lim,
world.dim_p) + self.nest_center_pos
agent.state.previous_pos = agent.state.p_pos.copy()
# 速度，初始化为0
agent.state.p_vel = np.zeros(world.dim_p)
agent.state.previous_vel = agent.state.p_vel.copy()
agent.state.c = np.zeros(world.dim_c)
agent.live = True
agent.movable = True
agent.intercepted = False
else:
# 处理invader
# spawn direction relative to nest
self.process_invader_pos(agent)
# 速度，初始化为0
agent.state.p_vel = np.zeros(world.dim_p)
agent.state.previous_vel = agent.state.p_vel.copy()
agent.state.c = np.zeros(world.dim_c)
agent.live = True
agent.movable = True
agent.intercepted = False
def process_invader_pos(self, agent):
while True:
theta = (np.random.rand() * 2 * np.pi - np.pi)*0.35
phi = (np.random.rand() * 2 * np.pi - np.pi)
d = self.rand(low=1.0 * self.invader_spawn_limit, high=1.1 * self.invader_spawn_limit)
agent.state.p_pos = d * np.array([ np.cos(theta)*np.cos(phi), np.cos(theta)*np.sin(phi), np.sin(theta) ]) + self.nest_center_pos
agent.state.previous_pos = agent.state.p_pos.copy()
x = agent.state.p_pos[0]
y = agent.state.p_pos[1]
z = agent.state.p_pos[2]
if x < self.arena_size and x > -self.arena_size \
and y < self.arena_size and y > -self.arena_size \
and z < self.arena_size and z > -self.arena_size:
break
else:
assert False
def invader_revise(self, agent, world):
self.spawn_position(agent, world)
agent.live = True
agent.movable = True
agent.spawn_cd = -1
def reset_world(self, world):
self.step = 0
for agent in world.agents:
self.spawn_position(agent, world)
self.spawn_vip_landmark(world)
world.steps = 0
self.rew_other = 0
self.hunter_failed = False
self.threat_clear = False
self.reward_sample = 0
# self.invader_spawn_time_left = self.Invader_Spawn_Times
# self.indader_left_to_hunt = self.Invader_To_Intercept
if self.show_off:
print('reset world')
def spawn_vip_landmark(self, world):
theta = np.pi/2
phi = np.random.rand() * 2 * np.pi - np.pi
phi_dis = np.pi * 2 / self.num_landmarks
for i, landmark in enumerate(world.landmarks):
self.landmark_spawn_position(landmark, world, theta, phi + phi_dis * i)
# 按顺序 return all agents that are not invaders
def hunters(self, world):
return [agent for agent in world.agents if not agent.IsInvader]
# 按顺序 return all adversarial agents
def invaders(self, world):
return [agent for agent in world.agents if agent.IsInvader]
def reward(self, agent, world):
assert self.joint_rewards is not None
reward = self.joint_rewards[agent.iden]
if agent.iden == self.num_agents:
self.joint_rewards = None
return reward
def get_distance_landmark(self):
hunters = self.hunters
invaders = self.invaders
landmarks = self.landmarks
distance = np.zeros(shape=(self.num_hunters, self.num_invaders), dtype=np.float32)
distance_landmark = np.zeros(shape=(self.num_invaders, self.num_landmarks), dtype=np.float32)
for b, B in enumerate(invaders):
for a, A in enumerate(hunters):
distance[a, b] = Norm(A.state.p_pos - B.state.p_pos) if B.live else np.inf
for c, C in enumerate(landmarks):
distance_landmark[b, c] = Norm(B.state.p_pos - C.state.p_pos) if B.live else np.inf
return distance, distance_landmark
def done(self, agent, world):
win_cond1 = world.steps >= world.MaxEpisodeStep
win_cond2 = self.threat_clear
win_cond = win_cond1 or win_cond2
self.is_success = win_cond
loss_cond = self.hunter_failed
if loss_cond: win_cond = False # lose condition has higher priority
done = win_cond or loss_cond
if done: assert loss_cond != win_cond
if agent.iden==0 and self.show_off and win_cond:
print('hunt success')
return done
def load_obs(self, fragment):
L = len(fragment) if isinstance(fragment, np.ndarray) else 1
# assert self.obs_pointer + L <= self.obs_dimension
self.obs[self.obs_pointer:self.obs_pointer + L] = fragment
# print('[%d ~ %d] filled / Total Length %d / total [0 ~ %d]'%(self.obs_pointer, self.obs_pointer + L -1, self.obs_pointer + L, self.obs_dimension-1))
self.obs_pointer = self.obs_pointer + L
def check_obs(self):
assert self.obs_pointer == self.obs_dimension
def info(self, agent, world):
return {'hunter_failed': self.hunter_failed, 'world_steps': world.steps, 'is_success': self.is_success}
def make_world(self):
self.num_good_agents = ScenarioConfig.hunter_num
self.num_hunters = ScenarioConfig.hunter_num
self.num_adversaries = ScenarioConfig.invader_num
self.num_invaders = ScenarioConfig.invader_num
self.num_landmarks = ScenarioConfig.num_landmarks
world = World() # set any world properties first
world.dim_c = 3
world.dim_p = 3
num_agents = self.num_agents
# add agents, 包括 hunter 和 invader
world.agents = [Agent(iden=i) for i in range(num_agents)]
for i, agent in enumerate(world.agents):
agent.name = 'agent %d' % i
agent.collide = False # no collide any more
agent.silent = True
# 前面的 num_adversaries 是 Invader，剩下的是 Hunter， Invader is adversary
if i < self.num_adversaries:
agent.IsInvader = True
agent.adversary = True
agent.id_in_team = i
agent.require_mannual_control = True
else:
agent.IsInvader = False
agent.adversary = False
agent.id_in_team = i - self.num_invaders
agent.size = ScenarioConfig.Invader_Size if agent.IsInvader else ScenarioConfig.Hunter_Size # size 中的数值是半径
agent.accel = ScenarioConfig.Invader_Accel if agent.IsInvader else ScenarioConfig.Hunter_Accel
agent.max_speed = self.Invader_MaxSpeed if agent.IsInvader else ScenarioConfig.Hunter_MaxSpeed
agent.caught = False
# agent.life = 1
agent.live = True
agent.movable = True
agent.live_adv = 1
agent.initial_mass = 14
# add landmarks
world.landmarks = [Landmark() for i in range(self.num_landmarks)]
for i, landmark in enumerate(world.landmarks):
landmark.name = 'landmark %d' % i
landmark.collide = False
landmark.movable = False
landmark.size = ScenarioConfig.Landmark_Size
landmark.boundary = False
# make initial conditions
# self.reset_world(world)
world.MaxEpisodeStep = ScenarioConfig.MaxEpisodeStep
self.hunters = [agent for agent in world.agents if not agent.IsInvader]
self.invaders = [agent for agent in world.agents if agent.IsInvader]
self.landmarks = world.landmarks
return world
@staticmethod
def rand(low, high):
return np.random.rand() * (high - low) + low
def landmark_spawn_position(self, landmark, world, theta=45 * np.pi / 180, phi = 45 * np.pi / 180):
d = ScenarioConfig.landmark_spawn_limit
offset = d * np.array([ np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), | np.cos(theta) | numpy.cos |
# coding: utf-8
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
""" Dataset for 3D object detection on SUN RGB-D (with support of vote supervision).
A sunrgbd oriented bounding box is parameterized by (cx,cy,cz), (l,w,h) -- (dx,dy,dz) in upright depth coord
(Z is up, Y is forward, X is right ward), heading angle (from +X rotating to -Y) and semantic class
Point clouds are in **upright_depth coordinate (X right, Y forward, Z upward)**
Return heading class, heading residual, size class and size residual for 3D bounding boxes.
Oriented bounding box is parameterized by (cx,cy,cz), (l,w,h), heading_angle and semantic class label.
(cx,cy,cz) is in upright depth coordinate
(l,h,w) are length of the object sizes
The heading angle is a rotation rad from +X rotating towards -Y. (+X is 0, -Y is pi/2)
Author: <NAME>
Date: 2019
"""
import os
import sys
import numpy as np
from torch.utils.data import Dataset
BASE_DIR = os.path.dirname(os.path.abspath(__file__))
ROOT_DIR = os.path.dirname(BASE_DIR)
sys.path.append(BASE_DIR)
sys.path.append(os.path.join(ROOT_DIR, 'utils'))
import pc_util
import sunrgbd_utils
from sunrgbd_utils import extract_pc_in_box3d
from model_util_sunrgbd import SunrgbdDatasetConfig
DC = SunrgbdDatasetConfig() # dataset specific config
MAX_NUM_OBJ = 64 # maximum number of objects allowed per scene
MEAN_COLOR_RGB = np.array([0.5,0.5,0.5]) # sunrgbd color is in 0~1
DIST_THRESH = 0.1#0.2
VAR_THRESH = 5e-3
CENTER_THRESH = 0.1
LOWER_THRESH = 1e-6
NUM_POINT = 50
NUM_POINT_LINE = 10
LINE_THRESH = 0.1#0.2
MIND_THRESH = 0.1
NUM_POINT_SEM_THRESHOLD = 1
def check_upright(para_points):
return (para_points[0][-1] == para_points[1][-1]) and (para_points[1][-1] == para_points[2][-1]) and (para_points[2][-1] == para_points[3][-1])
def check_z(plane_equ, para_points):
return np.sum(para_points[:,2] + plane_equ[-1]) / 4.0 < LOWER_THRESH
def clockwise2counter(angle):
'''
@Args:
angle: clockwise from x axis, from 0 to 2*pi,
@Returns:
theta: counter clockwise, -pi / 2 ~ pi / 2, +x~+y: (0, pi/2), +x~-y: (0, -pi/2)
'''
return -((angle + np.pi / 2) % np.pi) + np.pi / 2;
def point2line_dist(points, a, b):
'''
@Args:
points: (N, 3)
a / b: (3,)
@Returns:
distance: (N,)
'''
x = b - a
t = np.dot(points - a, x) / np.dot(x, x)
c = a + t[:, None] * np.tile(x, (t.shape[0], 1))
return np.linalg.norm(points - c, axis=1)
def get_linesel(points, corners, direction):
''' corners:
[[xmin, ymin, zmin], [xmin, ymin, zmax], [xmin, ymax, zmin], [xmin, ymax, zmax],
[xmax, ymin, zmin], [xmax, ymin, zmax], [xmax, ymax, zmin], [xmax, ymax, zmax]]
'''
if direction == 'lower':
sel1 = point2line_dist(points, corners[0], corners[2]) < LINE_THRESH
sel2 = point2line_dist(points, corners[4], corners[6]) < LINE_THRESH
sel3 = point2line_dist(points, corners[0], corners[4]) < LINE_THRESH
sel4 = point2line_dist(points, corners[2], corners[6]) < LINE_THRESH
return sel1, sel2, sel3, sel4
elif direction == 'upper':
sel1 = point2line_dist(points, corners[1], corners[3]) < LINE_THRESH
sel2 = point2line_dist(points, corners[5], corners[7]) < LINE_THRESH
sel3 = point2line_dist(points, corners[1], corners[5]) < LINE_THRESH
sel4 = point2line_dist(points, corners[3], corners[7]) < LINE_THRESH
return sel1, sel2, sel3, sel4
elif direction == 'left':
sel1 = point2line_dist(points, corners[0], corners[1]) < LINE_THRESH
sel2 = point2line_dist(points, corners[2], corners[3]) < LINE_THRESH
return sel1, sel2
elif direction == 'right':
sel1 = point2line_dist(points, corners[4], corners[5]) < LINE_THRESH
sel2 = point2line_dist(points, corners[6], corners[7]) < LINE_THRESH
return sel1, sel2
else:
AssertionError('direction = lower / upper / left')
def get_linesel2(points, ymin, ymax, zmin, zmax, axis=0):
#sel3 = sweep(points, axis, ymax, 2, zmin, zmax)
#sel4 = sweep(points, axis, ymax, 2, zmin, zmax)
sel3 = np.abs(points[:,axis] - ymin) < LINE_THRESH
sel4 = np.abs(points[:,axis] - ymax) < LINE_THRESH
return sel3, sel4
''' ATTENTION: SUNRGBD, size_label is only half the actual size
'''
def params2bbox(center, size, angle):
''' from bbox_center, angle and size to bbox
@Args:
center: (3,)
size: (3,)
angle: -pi ~ pi, +x~+y: (0, pi/2), +x~-y: (0, -pi/2)
@Returns:
bbox: 8 x 3, order:
[[xmin, ymin, zmin], [xmin, ymin, zmax], [xmin, ymax, zmin], [xmin, ymax, zmax],
[xmax, ymin, zmin], [xmax, ymin, zmax], [xmax, ymax, zmin], [xmax, ymax, zmax]]
'''
xsize = size[0]
ysize = size[1]
zsize = size[2]
vx = np.array([np.cos(angle), np.sin(angle), 0])
vy = np.array([-np.sin(angle), np.cos(angle), 0])
vx = vx * np.abs(xsize) / 2
vy = vy * np.abs(ysize) / 2
vz = np.array([0, 0, np.abs(zsize) / 2])
bbox = np.array([\
center - vx - vy - vz, center - vx - vy + vz,
center - vx + vy - vz, center - vx + vy + vz,
center + vx - vy - vz, center + vx - vy + vz,
center + vx + vy - vz, center + vx + vy + vz])
return bbox
class SunrgbdDetectionVotesDataset(Dataset):
def __init__(self, data_path=None, split_set='train', num_points=20000,
use_color=False, use_height=False, use_v1=False,
augment=False, scan_idx_list=None):
assert(num_points<=50000)
self.use_v1 = use_v1
if use_v1:
self.data_path = os.path.join(data_path, 'sunrgbd_pc_bbox_votes_50k_v1_' + split_set)
# self.data_path = os.path.join('/scratch/cluster/yanght/Dataset/sunrgbd/sunrgbd_pc_bbox_votes_50k_v1_' + split_set)
else:
AssertionError("v2 data is not prepared")
self.raw_data_path = os.path.join(ROOT_DIR, 'sunrgbd/sunrgbd_trainval')
self.scan_names = sorted(list(set([os.path.basename(x)[0:6] \
for x in os.listdir(self.data_path)])))
if scan_idx_list is not None:
self.scan_names = [self.scan_names[i] for i in scan_idx_list]
self.num_points = num_points
self.augment = augment
self.use_color = use_color
self.use_height = use_height
def __len__(self):
return len(self.scan_names)
def __getitem__(self, idx):
"""
Returns a dict with following keys:
point_clouds: (N,3+C)
center_label: (MAX_NUM_OBJ,3) for GT box center XYZ
heading_class_label: (MAX_NUM_OBJ,) with int values in 0,...,NUM_HEADING_BIN-1
heading_residual_label: (MAX_NUM_OBJ,)
size_classe_label: (MAX_NUM_OBJ,) with int values in 0,...,NUM_SIZE_CLUSTER
size_residual_label: (MAX_NUM_OBJ,3)
sem_cls_label: (MAX_NUM_OBJ,) semantic class index
box_label_mask: (MAX_NUM_OBJ) as 0/1 with 1 indicating a unique box
vote_label: (N,9) with votes XYZ (3 votes: X1Y1Z1, X2Y2Z2, X3Y3Z3)
if there is only one vote than X1==X2==X3 etc.
vote_label_mask: (N,) with 0/1 with 1 indicating the point
is in one of the object's OBB.
scan_idx: int scan index in scan_names list
max_gt_bboxes: unused
"""
scan_name = self.scan_names[idx]
point_color_sem = np.load(os.path.join(self.data_path, scan_name)+'_pc.npz')['pc'] # Nx6
bboxes = np.load(os.path.join(self.data_path, scan_name)+'_bbox.npy') # K,8
point_votes = np.load(os.path.join(self.data_path, scan_name)+'_votes.npz')['point_votes'] # Nx10
semantics37 = point_color_sem[:, 6]
semantics10 = np.array([DC.class37_2_class10[k] for k in semantics37])
semantics10_multi = [DC.class37_2_class10_multi[k] for k in semantics37]
if not self.use_color:
point_cloud = point_color_sem[:, 0:3]
else:
point_cloud = point_color_sem[:,0:6]
point_cloud[:,3:6] = (point_color_sem[:,3:6]-MEAN_COLOR_RGB)
if self.use_height:
floor_height = np.percentile(point_cloud[:,2],0.99)
height = point_cloud[:,2] - floor_height
point_cloud = np.concatenate([point_cloud, np.expand_dims(height, 1)],1) # (N,4) or (N,7)
# ------------------------------- DATA AUGMENTATION ------------------------------
if self.augment:
if np.random.random() > 0.5:
# Flipping along the YZ plane
point_cloud[:,0] = -1 * point_cloud[:,0]
bboxes[:,0] = -1 * bboxes[:,0]
bboxes[:,6] = np.pi - bboxes[:,6]
point_votes[:,[1,4,7]] = -1 * point_votes[:,[1,4,7]]
# Rotation along up-axis/Z-axis
rot_angle = (np.random.random()*np.pi/3) - np.pi/6 # -30 ~ +30 degree
rot_mat = sunrgbd_utils.rotz(rot_angle)
point_votes_end = np.zeros_like(point_votes)
point_votes_end[:,1:4] = np.dot(point_cloud[:,0:3] + point_votes[:,1:4], np.transpose(rot_mat))
point_votes_end[:,4:7] = np.dot(point_cloud[:,0:3] + point_votes[:,4:7], np.transpose(rot_mat))
point_votes_end[:,7:10] = np.dot(point_cloud[:,0:3] + point_votes[:,7:10], np.transpose(rot_mat))
point_cloud[:,0:3] = np.dot(point_cloud[:,0:3], np.transpose(rot_mat))
bboxes[:,0:3] = np.dot(bboxes[:,0:3], np.transpose(rot_mat))
bboxes[:,6] -= rot_angle
point_votes[:,1:4] = point_votes_end[:,1:4] - point_cloud[:,0:3]
point_votes[:,4:7] = point_votes_end[:,4:7] - point_cloud[:,0:3]
point_votes[:,7:10] = point_votes_end[:,7:10] - point_cloud[:,0:3]
# Augment RGB color
if self.use_color:
rgb_color = point_cloud[:,3:6] + MEAN_COLOR_RGB
rgb_color *= (1+0.4*np.random.random(3)-0.2) # brightness change for each channel
rgb_color += (0.1*np.random.random(3)-0.05) # color shift for each channel
rgb_color += np.expand_dims((0.05*np.random.random(point_cloud.shape[0])-0.025), -1) # jittering on each pixel
rgb_color = np.clip(rgb_color, 0, 1)
# randomly drop out 30% of the points' colors
rgb_color *= np.expand_dims(np.random.random(point_cloud.shape[0])>0.3,-1)
point_cloud[:,3:6] = rgb_color - MEAN_COLOR_RGB
# Augment point cloud scale: 0.85x-1.15x
scale_ratio = np.random.random()*0.3+0.85
scale_ratio = np.expand_dims(np.tile(scale_ratio,3),0)
point_cloud[:,0:3] *= scale_ratio
bboxes[:,0:3] *= scale_ratio
bboxes[:,3:6] *= scale_ratio
point_votes[:,1:4] *= scale_ratio
point_votes[:,4:7] *= scale_ratio
point_votes[:,7:10] *= scale_ratio
if self.use_height:
point_cloud[:,-1] *= scale_ratio[0,0]
# ------------------------------- LABELS ------------------------------
box3d_centers = np.zeros((MAX_NUM_OBJ, 3))
box3d_sizes = np.zeros((MAX_NUM_OBJ, 3))
angle_classes = np.zeros((MAX_NUM_OBJ,))
angle_residuals = np.zeros((MAX_NUM_OBJ,))
size_classes = np.zeros((MAX_NUM_OBJ,))
size_residuals = np.zeros((MAX_NUM_OBJ, 3))
label_mask = np.zeros((MAX_NUM_OBJ))
label_mask[0:bboxes.shape[0]] = 1
max_bboxes = np.zeros((MAX_NUM_OBJ, 8))
max_bboxes[0:bboxes.shape[0],:] = bboxes
# new items
box3d_angles = np.zeros((MAX_NUM_OBJ,))
point_boundary_mask_z = np.zeros(self.num_points)
point_boundary_mask_xy = np.zeros(self.num_points)
point_boundary_offset_z = np.zeros([self.num_points, 3])
point_boundary_offset_xy = np.zeros([self.num_points, 3])
point_boundary_sem_z = np.zeros([self.num_points, 3+2+1])
point_boundary_sem_xy = np.zeros([self.num_points, 3+1+1])
point_line_mask = np.zeros(self.num_points)
point_line_offset = np.zeros([self.num_points, 3])
point_line_sem = np.zeros([self.num_points, 3+1])
for i in range(bboxes.shape[0]):
bbox = bboxes[i]
semantic_class = bbox[7]
box3d_center = bbox[0:3]
angle_class, angle_residual = DC.angle2class(bbox[6])
# NOTE: The mean size stored in size2class is of full length of box edges,
# while in sunrgbd_data.py data dumping we dumped *half* length l,w,h.. so have to time it by 2 here
box3d_size = bbox[3:6]*2
size_class, size_residual = DC.size2class(box3d_size, DC.class2type[semantic_class])
box3d_centers[i,:] = box3d_center
angle_classes[i] = angle_class
angle_residuals[i] = angle_residual
size_classes[i] = size_class
size_residuals[i] = size_residual
box3d_sizes[i,:] = box3d_size
box3d_angles[i] = bbox[6]
target_bboxes_mask = label_mask
target_bboxes = np.zeros((MAX_NUM_OBJ, 6))
for i in range(bboxes.shape[0]):
bbox = bboxes[i]
corners_3d = sunrgbd_utils.my_compute_box_3d(bbox[0:3], bbox[3:6], bbox[6])
# compute axis aligned box
xmin = np.min(corners_3d[:,0])
ymin = np.min(corners_3d[:,1])
zmin = np.min(corners_3d[:,2])
xmax = np.max(corners_3d[:,0])
ymax = np.max(corners_3d[:,1])
zmax = np.max(corners_3d[:,2])
target_bbox = np.array([(xmin+xmax)/2, (ymin+ymax)/2, (zmin+zmax)/2, xmax-xmin, ymax-ymin, zmax-zmin])
target_bboxes[i,:] = target_bbox
point_cloud, choices = pc_util.random_sampling(point_cloud, self.num_points, return_choices=True)
semantics37 = semantics37[choices]
semantics10 = semantics10[choices]
semantics10_multi = [semantics10_multi[i] for i in choices]
point_votes_mask = point_votes[choices,0]
point_votes = point_votes[choices,1:]
# box angle is -pi to pi
for i in range(bboxes.shape[0]):
bbox = bboxes[i]
corners = params2bbox(bbox[:3], 2 * bbox[3:6], clockwise2counter(bbox[6]))
# corners_votenet = sunrgbd_utils.my_compute_box_3d(bbox[:3], bbox[3:6], bbox[6])
try:
x_all_cls, ind_all_cls = extract_pc_in_box3d(point_cloud, corners)
except:
continue
ind_all_cls = np.where(ind_all_cls)[0] # T/F to index
# find point with same semantic as bbox, note semantics is 37 cls in sunrgbd
# ind = ind_all_cls[np.where(semantics10[ind_all_cls] == bbox[7])[0]]
ind = []
for j in ind_all_cls:
if bbox[7] in semantics10_multi[j]:
ind.append(j)
ind = np.array(ind)
if ind.shape[0] < NUM_POINT_SEM_THRESHOLD:
pass
else:
x = point_cloud[ind, :3]
###Get bb planes and boundary points
plane_lower_temp = np.array([0,0,1,-corners[6,-1]])
para_points = np.array([corners[1], corners[3], corners[5], corners[7]])
newd = np.sum(para_points * plane_lower_temp[:3], 1)
if check_upright(para_points) and plane_lower_temp[0]+plane_lower_temp[1] < LOWER_THRESH:
plane_lower = np.array([0,0,1,plane_lower_temp[-1]])
plane_upper = np.array([0,0,1,-np.mean(newd)])
else:
import pdb;pdb.set_trace()
print ("error with upright")
if check_z(plane_upper, para_points) == False:
import pdb;pdb.set_trace()
### Get the boundary points here
#alldist = np.abs(np.sum(point_cloud[:,:3]*plane_lower[:3], 1) + plane_lower[-1])
alldist = np.abs(np.sum(x*plane_lower[:3], 1) + plane_lower[-1])
mind = np.min(alldist)
#[count, val] = np.histogram(alldist, bins=20)
#mind = val[np.argmax(count)]
sel = np.abs(alldist - mind) < DIST_THRESH
#sel = (np.abs(alldist - mind) < DIST_THRESH) & (point_cloud[:,0] >= xmin) & (point_cloud[:,0] <= xmax) & (point_cloud[:,1] >= ymin) & (point_cloud[:,1] <= ymax)
## Get lower four lines
line_sel1, line_sel2, line_sel3, line_sel4 = get_linesel(x[sel], corners, 'lower')
if np.sum(line_sel1) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel1]] = 1.0
linecenter = (corners[0] + corners[2]) / 2.0
point_line_offset[ind[sel][line_sel1]] = linecenter - x[sel][line_sel1]
point_line_sem[ind[sel][line_sel1]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel2) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel2]] = 1.0
linecenter = (corners[4] + corners[6]) / 2.0
point_line_offset[ind[sel][line_sel2]] = linecenter - x[sel][line_sel2]
point_line_sem[ind[sel][line_sel2]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel3) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel3]] = 1.0
linecenter = (corners[0] + corners[4]) / 2.0
point_line_offset[ind[sel][line_sel3]] = linecenter - x[sel][line_sel3]
point_line_sem[ind[sel][line_sel3]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel4) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel4]] = 1.0
linecenter = (corners[2] + corners[6]) / 2.0
point_line_offset[ind[sel][line_sel4]] = linecenter - x[sel][line_sel4]
point_line_sem[ind[sel][line_sel4]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(sel) > NUM_POINT and np.var(alldist[sel]) < VAR_THRESH:
# center = np.array([(xmin+xmax)/2.0, (ymin+ymax)/2.0, np.mean(x[sel][:,2])])
center = (corners[0] + corners[6]) / 2.0
center[2] = np.mean(x[sel][:,2])
sel_global = ind[sel]
point_boundary_mask_z[sel_global] = 1.0
point_boundary_sem_z[sel_global] = np.array([center[0], center[1], center[2], np.linalg.norm(corners[4] - corners[0]), np.linalg.norm(corners[2] - corners[0]), bbox[7]])
point_boundary_offset_z[sel_global] = center - x[sel]
'''
### Check for middle z surfaces
[count, val] = np.histogram(alldist, bins=20)
mind_middle = val[np.argmax(count)]
sel_pre = np.copy(sel)
sel = np.abs(alldist - mind_middle) < DIST_THRESH
if np.abs(np.mean(x[sel_pre][:,2]) - np.mean(x[sel][:,2])) > MIND_THRESH:
### Do not use line for middle surfaces
if np.sum(sel) > NUM_POINT and np.var(alldist[sel]) < VAR_THRESH:
center = (corners[0] + corners[6]) / 2.0
center[2] = np.mean(x[sel][:,2])
# center = np.array([(xmin+xmax)/2.0, (ymin+ymax)/2.0, np.mean(x[sel][:,2])])
sel_global = ind[sel]
point_boundary_mask_z[sel_global] = 1.0
point_boundary_sem_z[sel_global] = np.array([center[0], center[1], center[2], np.linalg.norm(corners[4] - corners[0]), np.linalg.norm(corners[2] - corners[0]), bbox[7]])
point_boundary_offset_z[sel_global] = center - x[sel]
'''
### Get the boundary points here
alldist = np.abs(np.sum(x*plane_upper[:3], 1) + plane_upper[-1])
mind = np.min(alldist)
#[count, val] = np.histogram(alldist, bins=20)
#mind = val[np.argmax(count)]
sel = np.abs(alldist - mind) < DIST_THRESH
#sel = (np.abs(alldist - mind) < DIST_THRESH) & (point_cloud[:,0] >= xmin) & (point_cloud[:,0] <= xmax) & (point_cloud[:,1] >= ymin) & (point_cloud[:,1] <= ymax)
## Get upper four lines
line_sel1, line_sel2, line_sel3, line_sel4 = get_linesel(x[sel], corners, 'upper')
if np.sum(line_sel1) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel1]] = 1.0
linecenter = (corners[1] + corners[3]) / 2.0
point_line_offset[ind[sel][line_sel1]] = linecenter - x[sel][line_sel1]
point_line_sem[ind[sel][line_sel1]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel2) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel2]] = 1.0
linecenter = (corners[5] + corners[7]) / 2.0
point_line_offset[ind[sel][line_sel2]] = linecenter - x[sel][line_sel2]
point_line_sem[ind[sel][line_sel2]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel3) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel3]] = 1.0
linecenter = (corners[1] + corners[5]) / 2.0
point_line_offset[ind[sel][line_sel3]] = linecenter - x[sel][line_sel3]
point_line_sem[ind[sel][line_sel3]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel4) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel4]] = 1.0
linecenter = (corners[3] + corners[7]) / 2.0
point_line_offset[ind[sel][line_sel4]] = linecenter - x[sel][line_sel4]
point_line_sem[ind[sel][line_sel4]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(sel) > NUM_POINT and np.var(alldist[sel]) < VAR_THRESH:
# center = np.array([(xmin+xmax)/2.0, (ymin+ymax)/2.0, np.mean(x[sel][:,2])])
center = (corners[1] + corners[7]) / 2.0
center[2] = np.mean(x[sel][:,2])
sel_global = ind[sel]
point_boundary_mask_z[sel_global] = 1.0
point_boundary_sem_z[sel_global] = np.array([center[0], center[1], center[2], np.linalg.norm(corners[5] - corners[1]), np.linalg.norm(corners[3] - corners[1]), bbox[7]])
point_boundary_offset_z[sel_global] = center - x[sel]
v1 = corners[3] - corners[2]
v2 = corners[2] - corners[0]
cp = np.cross(v1, v2)
d = -np.dot(cp,corners[0])
a,b,c = cp
plane_left_temp = np.array([a, b, c, d])
para_points = np.array([corners[4], corners[5], corners[6], corners[7]])
### Normalize xy here
plane_left_temp /= np.linalg.norm(plane_left_temp[:3])
newd = np.sum(para_points * plane_left_temp[:3], 1)
if plane_left_temp[2] < LOWER_THRESH:
plane_left = plane_left_temp#np.array([cls,res,tempsign,plane_left_temp[-1]])
plane_right = np.array([plane_left_temp[0], plane_left_temp[1], plane_left_temp[2], -np.mean(newd)])
else:
import pdb;pdb.set_trace()
print ("error with upright")
### Get the boundary points here
alldist = np.abs(np.sum(x*plane_left[:3], 1) + plane_left[-1])
mind = np.min(alldist)
#[count, val] = np.histogram(alldist, bins=20)
#mind = val[np.argmax(count)]
sel = np.abs(alldist - mind) < DIST_THRESH
#sel = (np.abs(alldist - mind) < DIST_THRESH) & (point_cloud[:,2] >= zmin) & (point_cloud[:,2] <= zmax) & (point_cloud[:,1] >= ymin) & (point_cloud[:,1] <= ymax)
## Get upper four lines
line_sel1, line_sel2 = get_linesel(x[sel], corners, 'left')
if np.sum(line_sel1) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel1]] = 1.0
linecenter = (corners[0] + corners[1]) / 2.0
point_line_offset[ind[sel][line_sel1]] = linecenter - x[sel][line_sel1]
point_line_sem[ind[sel][line_sel1]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(line_sel2) > NUM_POINT_LINE:
point_line_mask[ind[sel][line_sel2]] = 1.0
linecenter = (corners[2] + corners[3]) / 2.0
point_line_offset[ind[sel][line_sel2]] = linecenter - x[sel][line_sel2]
point_line_sem[ind[sel][line_sel2]] = np.array([linecenter[0], linecenter[1], linecenter[2], bbox[7]])
if np.sum(sel) > NUM_POINT and np.var(alldist[sel]) < VAR_THRESH:
# center = np.array([np.mean(x[sel][:,0]), np.mean(x[sel][:,1]), (zmin+zmax)/2.0])
center = np.array([np.mean(x[sel][:,0]), np.mean(x[sel][:,1]), (corners[0, 2] + corners[1, 2])/2.0])
sel_global = ind[sel]
point_boundary_mask_xy[sel_global] = 1.0
# point_boundary_sem_xy[sel_global] = np.array([center[0], center[1], center[2], zmax - zmin, np.where(DC.nyu40ids == meta_vertices[ind[0],-1])[0][0]])
point_boundary_sem_xy[sel_global] = np.array([center[0], center[1], center[2], corners[1, 2] - corners[0, 2], bbox[7]])
point_boundary_offset_xy[sel_global] = center - x[sel]
'''
[count, val] = np.histogram(alldist, bins=20)
mind_middle = val[np.argmax(count)]
#sel = (np.abs(alldist - mind) < DIST_THRESH) & (point_cloud[:,2] >= zmin) & (point_cloud[:,2] <= zmax) & (point_cloud[:,1] >= ymin) & (point_cloud[:,1] <= ymax)
## Get upper four lines
sel_pre = np.copy(sel)
sel = np.abs(alldist - mind_middle) < DIST_THRESH
if np.abs(np.mean(x[sel_pre][:,0]) - np.mean(x[sel][:,0])) > MIND_THRESH:
### Do not use line for middle surfaces
if np.sum(sel) > NUM_POINT and np.var(alldist[sel]) < VAR_THRESH:
# center = np.array([np.mean(x[sel][:,0]), np.mean(x[sel][:,1]), (zmin+zmax)/2.0])
center = np.array([np.mean(x[sel][:,0]), np.mean(x[sel][:,1]), (corners[0, 2] + corners[1, 2])/2.0])
sel_global = ind[sel]
point_boundary_mask_xy[sel_global] = 1.0
point_boundary_sem_xy[sel_global] = np.array([center[0], center[1], center[2], corners[1, 2] - corners[0, 2], bbox[7]])
point_boundary_offset_xy[sel_global] = center - x[sel]
'''
### Get the boundary points here
alldist = np.abs(np.sum(x*plane_right[:3], 1) + plane_right[-1])
mind = | np.min(alldist) | numpy.min |
import cv2
import numpy as np
import configparser
from configparser import SafeConfigParser
def frame_change(pos):
global posicao, new
posicao = pos
new = True
def sliders_update(val):
global new
new = True
def main():
config = configparser.ConfigParser()
config.read('config.ini')
arquivo = config['default']['video']
font = cv2.FONT_HERSHEY_SIMPLEX
posicao = 1
new = False
capture = cv2.VideoCapture(arquivo)
_, image = capture.read()
image_line1 = np.hstack((image, image))
image_line2 = np.hstack((image, image))
image = np.vstack((image_line1, image_line2))
blur = int(config['default']['blur'])
Bsize = int(config['default']['Bsize'])
Hmin = int(config['default']['Hmin'])
Hmax = int(config['default']['Hmax'])
Smin = int(config['default']['Smin'])
Smax = int(config['default']['Smax'])
Vmin = int(config['default']['Vmin'])
Vmax = int(config['default']['Vmax'])
cv2.namedWindow("image")
cv2.createTrackbar('Frame','image',0,int(capture.get(cv2.CAP_PROP_FRAME_COUNT)),frame_change)
cv2.createTrackbar('Blur','image',blur,30,sliders_update)
cv2.createTrackbar('Hmin','image',Hmin,100,sliders_update)
cv2.createTrackbar('Hmax','image',Hmax,179,sliders_update)
cv2.createTrackbar('Smin','image',Smin,255,sliders_update)
cv2.createTrackbar('Smax','image',Smax,255,sliders_update)
cv2.createTrackbar('Vmin','image',Vmin,255,sliders_update)
cv2.createTrackbar('Vmax','image',Vmax,255,sliders_update)
cv2.createTrackbar('Bsize','image',Bsize,50,sliders_update)
rmin = Bsize - int(Bsize/3) # Raio minimo para ser considerado um objeto circular (em pixels)
rmax = Bsize + int(Bsize/3)
while True:
if new:
new = False
capture.set(cv2.CAP_PROP_POS_FRAMES, posicao)
_, image_raw = capture.read()
blur = int(cv2.getTrackbarPos('Blur', 'image'))
if blur%2 == 0:
blur += 1
Hmin = int(cv2.getTrackbarPos('Hmin', 'image'))
Hmax = int(cv2.getTrackbarPos('Hmax', 'image'))
Smin = int(cv2.getTrackbarPos('Smin', 'image'))
Smax = int(cv2.getTrackbarPos('Smax', 'image'))
Vmin = int(cv2.getTrackbarPos('Vmin', 'image'))
Vmax = int(cv2.getTrackbarPos('Vmax', 'image'))
Bsize = int(cv2.getTrackbarPos('Bsize', 'image'))
Hmax = int(cv2.getTrackbarPos('Hmax', 'image'))
# TODO: max nao pode ser menor que min para H, S e V
image_blur = cv2.blur(image_raw, (blur, blur))
image_hsv = cv2.cvtColor(image_blur, cv2.COLOR_BGR2HSV)
image_thresh = cv2.inRange(image_hsv,np.array((Hmin, Smin, Vmin)), | np.array((Hmax, Smax, Vmax)) | numpy.array |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(223, 'P m -3 n', transformations)
space_groups[223] = sg
space_groups['P m -3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(224, 'P n -3 m :2', transformations)
space_groups[224] = sg
space_groups['P n -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = | N.array([1,0,1]) | numpy.array |
# -*- coding: utf-8 -*-
"""Copyright 2015 <NAME>.
FilterPy library.
http://github.com/rlabbe/filterpy
Documentation at:
https://filterpy.readthedocs.org
Supporting book at:
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
This is licensed under an MIT license. See the readme.MD file
for more information.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numpy.random as random
import numpy as np
import matplotlib.pyplot as plt
from filterpy.common import Saver
from filterpy.kalman import KalmanFilter, InformationFilter
DO_PLOT = False
def test_1d_0P():
global inf
f = KalmanFilter (dim_x=2, dim_z=1)
inf = InformationFilter (dim_x=2, dim_z=1)
f.x = np.array([[2.],
[0.]]) # initial state (location and velocity)
f.F = (np.array([[1., 1.],
[0., 1.]])) # state transition matrix
f.H = np.array([[1., 0.]]) # Measurement function
f.R = | np.array([[5.]]) | numpy.array |
# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for optimizers with weight decay."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.contrib.opt.python.training import weight_decay_optimizers
from tensorflow.python.eager import context
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import test_util
from tensorflow.python.ops import resource_variable_ops
from tensorflow.python.ops import variables
from tensorflow.python.platform import test
from tensorflow.python.training import adam
WEIGHT_DECAY = 0.01
def adamw_update_numpy(param, g_t, t, m, v, lr=0.001, beta1=0.9,
beta2=0.999, epsilon=1e-8):
lr_t = lr * np.sqrt(1 - beta2**t) / (1 - beta1**t)
m_t = beta1 * m + (1 - beta1) * g_t
v_t = beta2 * v + (1 - beta2) * g_t * g_t
param_t = (param - lr_t * m_t / (np.sqrt(v_t) + epsilon) -
(param * WEIGHT_DECAY))
return param_t, m_t, v_t
def momentumw_update_numpy(param, g_t, m, lr=0.001, momentum=0.9, **_):
# v, t are not needed for momentum optimizer
m = momentum * m + g_t
param_t = param - lr * m - param * WEIGHT_DECAY
return param_t, m, None
class WeightDecayOptimizerTest(test.TestCase):
def doTest(self, optimizer, update_fn, optimizer_name, slot_name,
use_resource=False, do_sparse=False):
for i, dtype in enumerate([dtypes.half, dtypes.float32, dtypes.float64]):
with self.test_session(graph=ops.Graph()):
# Initialize variables for numpy implementation.
m0, v0, m1, v1 = 0.0, 0.0, 0.0, 0.0
var0_np = | np.array([1.0, 2.0], dtype=dtype.as_numpy_dtype) | numpy.array |
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from sympy.solvers import solve
from sympy import Symbol
from matplotlib import patches
import matplotlib.patches as mpatches
import scipy.io as sio
from matplotlib.colors import LogNorm
from matplotlib.colors import LinearSegmentedColormap
from sympy.solvers import solve
from sympy import Symbol
from wolframclient.evaluation import WolframLanguageSession
from wolframclient.language import wl, wlexpr
session = WolframLanguageSession()
ratio = 1.25
# plotting configuration
figure_len, figure_width = 15*1.5, 12*1.5
font_size_1, font_size_2 = 36*ratio, 36*ratio
legend_size = 18*ratio
line_width, tick_len = 3*ratio, 10*ratio
marker_size = 15*ratio
plot_line_width = 5*ratio
hfont = {'fontname': 'Arial'}
sns.set(style='ticks')
tau_e = 0.02
tau_i = 0.01
k = 0.1
l = 0.5
beta = 0.9
N = 2
e = 1/tau_e
f = 1/tau_i
l_a = np.arange(0, 201, 1)
l_d = np.arange(0, 201, 1)
uni_3D_mat = np.zeros((len(l_d), len(l_a))) * np.nan
uni_4D_mat = np.zeros((len(l_d), len(l_a))) * np.nan
example_global_unistable_x = (1.3*2*np.power(0.1619020544546218, 1/2))/tau_e
example_global_unistable_y = (0.6*2*np.power(1.0145746970782272, 1/2))/tau_i
example_global_multistable_x = (1.4*2*np.power(0.29638770180500046, 1/2))/tau_e
example_global_multistable_y = (0.6*2*np.power(1.0396121792300297, 1/2))/tau_i
for a_idx in np.arange(len(l_a)):
a = l_a[a_idx]
for d_idx in np.arange(len(l_d)):
d = l_d[d_idx]
bc = beta * a * d
uni_3D_mat[d_idx, a_idx] = a - e - k * a
if | np.power(a - e - k * a + N * d - N * l * d + f, 2) | numpy.power |
from pyscf.gto import eval_gto
from pyscf import gto
import numpy as np
import pyqmc
class J3:
def __init__(self, mol):
self.mol = mol
randpos = | np.random.random((1,3)) | numpy.random.random |
#v2.3
import numpy as np
from util import *
L_SOFTPLUS = 0
L_RELU = 1
L_LINEAR = 2
L_SIGMOID = 3
L_DISCRETE = 4
L_BINARY_Z = 5
L_BINARY_N = 6
LS_REAL = [L_SOFTPLUS, L_RELU, L_LINEAR, L_SIGMOID]
LS_DISCRETE = [L_DISCRETE, L_BINARY_Z, L_BINARY_N, ]
ACT_F = {L_SOFTPLUS: softplus,
L_RELU: relu,
L_SIGMOID: sigmoid,
L_LINEAR: lambda x: x,
L_BINARY_Z: sigmoid,
L_BINARY_N: lambda x: 2*sigmoid(x)-1,
}
ACT_D_F = {L_SOFTPLUS: sigmoid,
L_RELU: relu_d,
L_SIGMOID: sigmoid_d,
L_LINEAR: lambda x: 1,
L_BINARY_Z: sigmoid_d,
L_BINARY_N: lambda x: 2*sigmoid_d(x),
}
class eq_prop_layer():
def __init__(self, name, input_size, output_size, optimizer, var, temp, l_type, unbiased=False):
if l_type not in [L_SOFTPLUS, L_RELU, L_LINEAR, L_SIGMOID, L_DISCRETE, L_BINARY_Z, L_BINARY_N, ]:
raise Exception('l_type (%d) not implemented' % l_type)
self.name = name
self.input_size = input_size
self.output_size = output_size
self.optimizer = optimizer
self.l_type = l_type
self.temp = temp if l_type in LS_DISCRETE else 1
self.unbiased = unbiased
lim = np.sqrt(6 / (input_size + output_size))
if l_type == L_DISCRETE: output_size -= 1
self._w = np.random.uniform(-lim, lim, size=(input_size, output_size))
self._b = np.random.uniform(-1e-3, 1e-3, size=(output_size))
self._inv_var = np.full(output_size, 1/var) if var > 0 else None
self.prev_layer = None # Set manually
self.next_layer = None # Set manually
self.values = np.zeros((1, output_size))
self.w_trace = np.zeros((1, input_size, output_size,))
self.b_trace = np.zeros((1, output_size,))
if self.unbiased:
self.p_w_trace = np.zeros((1, input_size, output_size,))
self.p_b_trace = np.zeros((1, output_size,))
def sample(self, inputs, det=False):
self.compute_pot_mean(inputs)
if self.l_type in LS_REAL:
if self._inv_var is None or det:
self.values = self.mean
else:
sigma = | np.sqrt(1/self._inv_var) | numpy.sqrt |
import os
import numpy as np
# Tiles are 10x10 squares
TILE_LENGTH = 10
# 2d array representing the seamonster
SEA_MONSTER = np.array([
[" ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", "#", " "],
["#", " ", " ", " ", " ", "#", "#", " ", " ", " ", " ", "#", "#", " ", " ", " ", " ", "#", "#", "#"],
[" ", "#", " ", " ", "#", " ", " ", "#", " ", " ", "#", " ", " ", "#", " ", " ", "#", " ", " ", " "],
])
# Possible values for flipX and flipY
FLIP_VALUES = [False, True]
class Tile:
def __init__(self, number):
self.number = number
self.top = set()
self.right = set()
self.bottom = set()
self.left = set()
class Transformation:
def __init__(self, flipX, flipY, numRot):
self.flipX = flipX
self.flipY = flipY
self.numRot = numRot
def areTilesAdjacent(tilePixels, otherTilePixels, getTargetArray, getComparisonArray):
targetArray = getTargetArray(tilePixels)
for flipX in FLIP_VALUES:
for flipY in FLIP_VALUES:
comparisonTile = np.copy(otherTilePixels)
if flipX:
comparisonTile = np.fliplr(comparisonTile)
if flipY:
comparisonTile = np.flipud(comparisonTile)
# Rotate the tile 0, 90, 180, and 270 degrees
numRot = 0
while numRot < 4:
rotatedTile = np.rot90(comparisonTile, numRot)
# Check other tile to see if it fits...
if (targetArray == getComparisonArray(rotatedTile)).all():
return True, Transformation(flipX, flipY, numRot)
numRot += 1
return False, Transformation(False, False, 0)
def tileMatchesTop(tilePixels, otherTilePixels):
return areTilesAdjacent(tilePixels, otherTilePixels, lambda tile: tile[0], lambda tile: tile[-1])
def tileMatchesRight(tilePixels, otherTilePixels):
return areTilesAdjacent(tilePixels, otherTilePixels, lambda tile: tile[:, -1], lambda tile: tile[:, 0])
def tileMatchesBottom(tilePixels, otherTilePixels):
return areTilesAdjacent(tilePixels, otherTilePixels, lambda tile: tile[-1], lambda tile: tile[0])
def tileMatchesLeft(tilePixels, otherTilePixels):
return areTilesAdjacent(tilePixels, otherTilePixels, lambda tile: tile[:, 0], lambda tile: tile[:, -1])
def populateTileMatches(tileObjs):
# Find the matching top, right, bottom, left tiles for each individual tile...
tileIdx = 0
while tileIdx < len(tileObjs):
tileObj = tileObjs[tileIdx]
otherTileIdx = 0
while otherTileIdx < len(tileObjs):
if tileIdx == otherTileIdx:
otherTileIdx += 1
continue
otherTileObj = tileObjs[otherTileIdx]
# check if other tile matches top
(tileMatches, _) = tileMatchesTop(tiles[tileObj.number], tiles[otherTileObj.number])
if tileMatches:
tileObj.top.add(otherTileObj.number)
# check if other tile matches right
(tileMatches, _) = tileMatchesRight(tiles[tileObj.number], tiles[otherTileObj.number])
if tileMatches:
tileObj.right.add(otherTileObj.number)
# check if other tile matches bottom
(tileMatches, _) = tileMatchesBottom(tiles[tileObj.number], tiles[otherTileObj.number])
if tileMatches:
tileObj.bottom.add(otherTileObj.number)
# check if other tile matches left
(tileMatches, _) = tileMatchesLeft(tiles[tileObj.number], tiles[otherTileObj.number])
if tileMatches:
tileObj.left.add(otherTileObj.number)
otherTileIdx += 1
tileIdx += 1
def getCornerTiles(tileObjs):
cornerTiles = []
for tileObj in tileObjs:
# Determine if this is a corner tile
hasAdjacentTopRight = (len(tileObj.top) == 0 and len(tileObj.right) == 0)
hasAdjacentBottomRight = (len(tileObj.right) == 0 and len(tileObj.bottom) == 0)
hasAdjacentBottomLeft = (len(tileObj.bottom) == 0 and len(tileObj.left) == 0)
hasAdjacentTopLeft = (len(tileObj.left) == 0 and len(tileObj.top) == 0)
if hasAdjacentTopRight or hasAdjacentBottomRight or hasAdjacentBottomLeft or hasAdjacentTopLeft:
cornerTiles.append(tileObj)
return cornerTiles
def setPixelsOnImage(image, rowOffset, colOffset, tilePixels):
for rowIdx, row in enumerate(tilePixels):
for colIdx, pixel in enumerate(row):
image[rowOffset + rowIdx, colOffset + colIdx] = pixel
def getMatchingTile(matchFunction, currentTilePixels, tiles, usedTilesNumbers):
matches = []
for candidateTileNumber in tiles:
if candidateTileNumber in usedTilesNumbers:
continue
candidateTilePixels = tiles[candidateTileNumber]
# Check if candidate tile can be placed as determined by the matchFunction (one of the tileMatches* functions defined above)
isMatch, transformations = matchFunction(currentTilePixels, candidateTilePixels)
if isMatch:
if transformations.flipX:
candidateTilePixels = np.fliplr(candidateTilePixels)
if transformations.flipY:
candidateTilePixels = np.flipud(candidateTilePixels)
candidateTilePixels = np.rot90(candidateTilePixels, transformations.numRot)
matches.append((candidateTileNumber, candidateTilePixels))
if len(matches) == 0:
raise Exception("No matching tiles found.")
return matches[0]
def generateImageFromTopLeft(tiles, currentTileNumber, currentTilePixels):
# Determine size of final image
imageLength = int(np.ceil(np.sqrt(len(tiles))))
imagePixelLength = imageLength * TILE_LENGTH
image = np.empty((imagePixelLength, imagePixelLength), str)
imageNoBordersPixelLength = imageLength * (TILE_LENGTH - 2)
imageNoBorders = np.empty((imageNoBordersPixelLength, imageNoBordersPixelLength), str)
# Track used tiles
usedTilesNumbers = []
rowOffset = 0
rowOffsetNoBorders = 0
while rowOffset < imagePixelLength:
rowTilePixels = currentTilePixels
colOffset = 0
colOffsetNoBorders = 0
while colOffset < imagePixelLength:
setPixelsOnImage(image, rowOffset, colOffset, currentTilePixels)
setPixelsOnImage(imageNoBorders, rowOffsetNoBorders, colOffsetNoBorders, currentTilePixels[1:-1, 1:-1])
usedTilesNumbers.append(currentTileNumber)
colOffset += TILE_LENGTH
colOffsetNoBorders += (TILE_LENGTH - 2)
if colOffset < imagePixelLength:
currentTileNumber, currentTilePixels = getMatchingTile(tileMatchesRight, currentTilePixels, tiles, usedTilesNumbers)
rowOffset += TILE_LENGTH
rowOffsetNoBorders += (TILE_LENGTH - 2)
if rowOffset < imagePixelLength:
currentTileNumber, currentTilePixels = getMatchingTile(tileMatchesBottom, rowTilePixels, tiles, usedTilesNumbers)
return image, imageNoBorders
def hasSeaMonster(imageSegment):
for rowIdx, imageRow in enumerate(imageSegment):
for colIdx, imagePixel in enumerate(imageRow):
seaMonsterPixel = SEA_MONSTER[rowIdx, colIdx]
if seaMonsterPixel == "#" and imagePixel != seaMonsterPixel:
return False
return True
def countSeaMonsters(image):
count = 0
imageRowIdx = 0
while imageRowIdx <= image.shape[0] - SEA_MONSTER.shape[0]:
imageColIdx = 0
while imageColIdx <= image.shape[1] - SEA_MONSTER.shape[1]:
if hasSeaMonster(image[imageRowIdx:imageRowIdx + SEA_MONSTER.shape[0], imageColIdx:imageColIdx + SEA_MONSTER.shape[1]]):
count += 1
imageColIdx += 1
imageRowIdx += 1
return count
def printImage(image, tileInterval):
for rowIdx, row in enumerate(image):
if rowIdx % tileInterval == 0:
print("")
outputLine = ""
for colIdx, pixel in enumerate(row):
if colIdx % tileInterval == 0:
outputLine += " "
if pixel == "":
outputLine += " "
else:
outputLine += pixel
print(outputLine)
def part1(tiles):
tileObjs = [Tile(tileNumber) for tileNumber in tiles]
populateTileMatches(tileObjs)
cornerTiles = getCornerTiles(tileObjs)
productOfCornerTiles = np.prod([cornerTile.number for cornerTile in cornerTiles])
print(f"Part 1 - Solution: {productOfCornerTiles}")
def part2(tiles):
tileNumberToObjs = {}
for tileNumber in tiles:
tileObj = Tile(tileNumber)
tileNumberToObjs[tileNumber] = tileObj
populateTileMatches(list(tileNumberToObjs.values()))
cornerTiles = getCornerTiles(list(tileNumberToObjs.values()))
# Get corner tiles
topRightTiles = [cornerTile for cornerTile in cornerTiles if (len(cornerTile.top) == 0 and len(cornerTile.right) == 0)]
bottomRightTiles = [cornerTile for cornerTile in cornerTiles if (len(cornerTile.bottom) == 0 and len(cornerTile.right) == 0)]
bottomLeftTiles = [cornerTile for cornerTile in cornerTiles if (len(cornerTile.bottom) == 0 and len(cornerTile.left) == 0)]
topLeftTiles = [cornerTile for cornerTile in cornerTiles if (len(cornerTile.top) == 0 and len(cornerTile.left) == 0)]
currentTileNumber = None
currentTilePixels = None
if len(topLeftTiles) == 1:
currentTileNumber = topLeftTiles[0].number
currentTilePixels = tiles[currentTileNumber]
elif len(topRightTiles) == 1:
currentTileNumber = topRightTiles[0].number
currentTilePixels = tiles[currentTileNumber]
# Make top right into top left... (flip X)
currentTilePixels = np.fliplr(currentTilePixels)
elif len(bottomRightTiles) == 1:
currentTileNumber = bottomRightTiles[0].number
currentTilePixels = tiles[currentTileNumber]
# Make bottom right into top left... (flip X and flip Y)
currentTilePixels = | np.fliplr(currentTilePixels) | numpy.fliplr |
from cgitb import grey
from matplotlib.pyplot import axis, close, hot
import numpy as np
from numpy.random import default_rng
import random
import copy
import math
class ImageManipulator:
def __init__(self):
self._rng = default_rng(seed=42)
def salt_pepper_noise(self, gray_img, ratio):
noise = self._rng.choice(
[-1, 0, 255], size=gray_img.shape, p=[1 - ratio, ratio / 2, ratio / 2]
)
np.copyto(noise, gray_img, where=noise == -1)
gray_img = noise.astype(np.uint8)
return gray_img
def gaussian_noise(self, gray_img, mean, std):
noise = self._rng.normal(loc=mean, scale=std, size=gray_img.shape)
gray_img = gray_img + noise
gray_img = np.clip(gray_img, 0, 255)
gray_img = np.rint(gray_img)
gray_img = gray_img.astype(np.uint8)
return gray_img
def calc_histogram(self, gray_img):
hist = np.zeros(256)
for i in range(len(hist)):
hist[i] = np.sum(gray_img == i)
hist = hist.astype(np.uint)
return hist
def avg_histograms(self, hist_list):
hist_arr = np.array(hist_list)
hist = np.mean(hist_arr, axis=0)
hist = | np.rint(hist) | numpy.rint |
import numpy as np
import scipy as scipy
from numpy.random import uniform
import scipy.stats
import cv2
np.set_printoptions(threshold=3)
np.set_printoptions(suppress=True)
# The code is copied from http://ros-developer.com/2019/04/10/parcticle-filter-explained-with-python-code-from-scratch/.
def drawLines(img, points, b, g, r):
cv2.polylines(img, [np.int32(points)], isClosed=False, color=(b, g, r))
def drawCross(img, center, b, g, r):
d = 5
t = 2
LINE_AA = cv2.LINE_AA
# LINE_AA = cv2.LINE_AA if cv2.__version__[0] == '3' else cv2.CV_AA
color = (b, g, r)
ctrx = center[0, 0]
ctry = center[0, 1]
cv2.line(img, (ctrx - d, ctry - d), (ctrx + d, ctry + d), color, t, LINE_AA)
cv2.line(img, (ctrx + d, ctry - d), (ctrx - d, ctry + d), color, t, LINE_AA)
def mouseCallback(event, x, y, flags, null):
global center
global trajectory
global previous_x
global previous_y
global zs
center = np.array([[x, y]])
trajectory = np.vstack((trajectory, np.array([x, y])))
# noise=sensorSigma * np.random.randn(1,2) + sensorMu
if previous_x > 0:
heading = np.arctan2(np.array([y - previous_y]), np.array([previous_x - x]))
if heading > 0:
heading = -(heading - np.pi)
else:
heading = -(np.pi + heading)
distance = np.linalg.norm(np.array([[previous_x, previous_y]]) - np.array([[x, y]]), axis=1)
std = np.array([2, 4])
u = np.array([heading, distance])
predict(particles, u, std, dt=1.)
zs = (np.linalg.norm(landmarks - center, axis=1) + (np.random.randn(NL) * sensor_std_err))
# weights = np.ones(len(particles))/len(particles)
update(particles, weights, z=zs, R=50, landmarks=landmarks)
indexes = systematic_resample(weights)
resample_from_index(particles, weights, indexes)
previous_x = x
previous_y = y
WIDTH = 800
HEIGHT = 600
WINDOW_NAME = "Particle Filter"
# sensorMu=0
# sensorSigma=3
sensor_std_err = 5
def create_uniform_particles(x_range, y_range, N):
particles = np.empty((N, 2))
particles[:, 0] = uniform(x_range[0], x_range[1], size=N)
particles[:, 1] = uniform(y_range[0], y_range[1], size=N)
return particles
def predict(particles, u, std, dt=1.):
N = len(particles)
dist = (u[1] * dt) + (np.random.randn(N) * std[1])
particles[:, 0] += np.cos(u[0]) * dist
particles[:, 1] += np.sin(u[0]) * dist
def update(particles, weights, z, R, landmarks):
weights.fill(1.)
for i, landmark in enumerate(landmarks):
distance = | np.power((particles[:, 0] - landmark[0]) ** 2 + (particles[:, 1] - landmark[1]) ** 2, 0.5) | numpy.power |
# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Tests for lift metrics."""
from absl.testing import parameterized
import apache_beam as beam
from apache_beam.testing import util
import numpy as np
import tensorflow as tf
from tensorflow_model_analysis.addons.fairness.metrics import lift
from tensorflow_model_analysis.eval_saved_model import testutil
from tensorflow_model_analysis.metrics import metric_types
from tensorflow_model_analysis.metrics import metric_util
from tensorflow_model_analysis.proto import config_pb2
class LiftTest(testutil.TensorflowModelAnalysisTest, parameterized.TestCase):
def _assert_test(self,
num_buckets,
baseline_examples,
comparison_examples,
lift_metric_value,
ignore_out_of_bound_examples=False):
eval_config = config_pb2.EvalConfig(
cross_slicing_specs=[config_pb2.CrossSlicingSpec()])
computations = lift.Lift(
num_buckets=num_buckets,
ignore_out_of_bound_examples=ignore_out_of_bound_examples).computations(
eval_config=eval_config)
histogram = computations[0]
lift_metrics = computations[1]
with beam.Pipeline() as pipeline:
# pylint: disable=no-value-for-parameter
baseline_result = (
pipeline
| 'CreateB' >> beam.Create(baseline_examples)
| 'ProcessB' >> beam.Map(metric_util.to_standard_metric_inputs)
| 'AddSliceB' >> beam.Map(lambda x: ((), x))
| 'ComputeHistogramB' >> beam.CombinePerKey(histogram.combiner)
) # pyformat: ignore
comparison_result = (
pipeline
| 'CreateC' >> beam.Create(comparison_examples)
| 'ProcessC' >> beam.Map(metric_util.to_standard_metric_inputs)
| 'AddSliceC' >> beam.Map(lambda x: (('slice'), x))
| 'ComputeHistogramC' >> beam.CombinePerKey(histogram.combiner)
) # pyformat: ignore
# pylint: enable=no-value-for-parameter
merged_result = ((baseline_result, comparison_result)
| 'MergePCollections' >> beam.Flatten())
def check_result(got):
try:
self.assertLen(got, 2)
slice_1, metric_1 = got[0]
slice_2, metric_2 = got[1]
lift_value = None
if not slice_1:
lift_value = lift_metrics.cross_slice_comparison(metric_1, metric_2)
else:
lift_value = lift_metrics.cross_slice_comparison(metric_2, metric_1)
self.assertDictElementsAlmostEqual(
lift_value, {
metric_types.MetricKey(name=f'lift@{num_buckets}'):
lift_metric_value,
})
except AssertionError as err:
raise util.BeamAssertException(err)
util.assert_that(merged_result, check_result, label='result')
def testLift_continuousLabelsAndPredictions(self):
baseline_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([0.1]),
'example_weights': np.array([3.0]),
}, {
'labels': np.array([0.3]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
}, {
'labels': np.array([0.6]),
'predictions': np.array([0.8]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([0.9]),
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
}, {
'labels': np.array([0.9]),
'predictions': np.array([0.9]),
'example_weights': np.array([3.0]),
}]
comparison_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([0.8]),
'example_weights': np.array([1.0]),
}, {
'labels': np.array([0.2]),
'predictions': np.array([0.3]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([0.5]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
}, {
'labels': np.array([0.7]),
'predictions': np.array([0.4]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([0.9]),
'predictions': np.array([0.3]),
'example_weights': np.array([3.0]),
}]
self._assert_test(3, baseline_examples, comparison_examples, -0.136013986)
def testLift_baselineAndComparisonAreSame(self):
baseline_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([0.1]),
'example_weights': np.array([3.0]),
}, {
'labels': np.array([0.3]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
}, {
'labels': np.array([0.6]),
'predictions': np.array([0.8]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([0.9]),
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.9]),
'example_weights': np.array([3.0]),
}]
self._assert_test(3, baseline_examples, baseline_examples, 0.0)
def testLift_ignoringOutOfBoundExamples(self):
baseline_examples = [
{
'labels': np.array([0.0]),
'predictions': np.array([0.1]),
'example_weights': np.array([3.0]),
},
{
'labels': np.array([0.3]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
},
{
'labels': np.array([0.6]),
'predictions': np.array([0.8]),
'example_weights': np.array([2.0]),
},
{
'labels': np.array([0.9]),
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
},
{
'labels': np.array([-0.9]), # Ignore this example
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
},
{
'labels': np.array([0.9]),
'predictions': np.array([0.9]),
'example_weights': np.array([3.0]),
}
]
comparison_examples = [
{
'labels': np.array([0.0]),
'predictions': np.array([0.8]),
'example_weights': np.array([1.0]),
},
{
'labels': np.array([0.2]),
'predictions': np.array([0.3]),
'example_weights': np.array([2.0]),
},
{
'labels': np.array([0.5]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
},
{
'labels': np.array([0.7]),
'predictions': np.array([0.4]),
'example_weights': np.array([2.0]),
},
{
'labels': np.array([1.9]), # Ignore this example
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
},
{
'labels': np.array([0.9]),
'predictions': np.array([0.3]),
'example_weights': np.array([3.0]),
}
]
self._assert_test(
3,
baseline_examples,
comparison_examples,
-0.136013986,
ignore_out_of_bound_examples=True)
def testLift_binaryLabelsAndContinuousPredictions(self):
baseline_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([0.1]),
'example_weights': np.array([3.0]),
}, {
'labels': np.array([0.0]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.8]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.3]),
'example_weights': np.array([8.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.9]),
'example_weights': np.array([3.0]),
}]
comparison_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([0.8]),
'example_weights': np.array([1.0]),
}, {
'labels': np.array([0.0]),
'predictions': np.array([0.3]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([0.0]),
'predictions': np.array([0.5]),
'example_weights': np.array([5.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.4]),
'example_weights': np.array([2.0]),
}, {
'labels': np.array([1.0]),
'predictions': np.array([0.3]),
'example_weights': np.array([3.0]),
}]
self._assert_test(2, baseline_examples, comparison_examples, 0.01715976331)
def testLift_binaryLabelsAndPredictions(self):
baseline_examples = [{
'labels': np.array([0.0]),
'predictions': np.array([1.0]),
'example_weights': np.array([3.0]),
}, {
'labels': | np.array([0.0]) | numpy.array |
# -*- coding: utf-8 -*-
"""
Spyder Editor
This is a temporary script file.
"""
import numpy as np
def subarray_multislice(array_ndim, fixed_axes, indices):
'''
Return tuple of slices that if indexed into an array with given dimensions
will return subarray with the axes in axes fixed at given indices
'''
indices = np.array(indices)
colon = slice(None, None, None)
multislice = ()
for i in range(array_ndim):
if i in fixed_axes:
multislice = multislice + \
(indices[ | np.where(fixed_axes == i) | numpy.where |
# this script assumes Python 3.5 is in use
# imports
import numpy as np
from scipy import ndimage
from astropy.io import fits
#..........................................................................main
def main(file, scale) :
science = fits.open(file) # open the background-subtracted science image
image = science[0].data # get the science data that will be used
science.close()
smooth_image = ndimage.gaussian_filter(image, scale) # smooth the original
# image by the Gaussian kernel
return clumpiness(image, smooth_image)
#....................................................................clumpiness
def clumpiness(image, smoothed) :
numer = image - smoothed
numer = np.ma.masked_where(numer < 0, numer)
np.ma.set_fill_value(numer, 0)
numer = numer.filled()
denom = image
clumpy = | np.sum(numer) | numpy.sum |
# Copyright 2018 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Defines the various functions for training the pre-defined MentorNet."""
import numpy as np
import scipy.stats as st
import tensorflow as tf
def logistic(inputs):
"""A baseline logistic model."""
feat_dim = int(inputs.get_shape()[1])
with tf.variable_scope('logistic'):
layer_1 = tf.add(
tf.matmul(inputs, tf.get_variable('W1', [feat_dim, 1])),
tf.get_variable('b1', [1]))
return layer_1
def mlp(inputs, num_hidden_nodes=10):
"""A baseline MLP model."""
feat_dim = int(inputs.get_shape()[1])
with tf.variable_scope('mlp'):
layer_1 = tf.add(
tf.matmul(inputs,
tf.Variable(tf.random_normal([feat_dim, num_hidden_nodes]))),
tf.Variable(tf.random_normal([num_hidden_nodes])))
layer_1 = tf.nn.tanh(layer_1)
# output layer has the linear activation
out_layer = tf.matmul(
layer_1,
tf.Variable(tf.random_normal([num_hidden_nodes, 1])) + tf.Variable(
tf.random_normal([1])))
return out_layer
def vstar_baseline(inbatch, **kwargs):
"""Variable star function for equally weighting every sample.
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
del kwargs # Unused.
v = np.ones(inbatch.shape[0])
return v
def vstar_self_paced(inbatch, **kwargs):
"""Variable star function for self-paced learning.
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
del kwargs # Unused.
loss_diff = inbatch[:, 1]
v = np.copy(loss_diff)
v[np.where(loss_diff <= 0)] = 1
v[np.where(loss_diff > 0)] = 0
return v
def vstar_hard_example_mining(inbatch, **kwargs):
"""Variable v_star function for self-paced learning.
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
del kwargs # Unused.
loss_diff = inbatch[:, 1]
y = inbatch[:, 2]
v = np.copy(loss_diff)
v[np.where(loss_diff >= 0)] = 1
v[np.where(loss_diff < 0)] = 0
v[np.where(y > 0)] = 1 # Select all positive
return v
def vstar_focal_loss(inbatch, **kwargs):
"""Variable v_star function for focal loss.
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
if 'vstar_gamma' in kwargs:
gamma = kwargs['vstar_gamma']
else:
gamma = 2
assert gamma > 0
loss = inbatch[:, 0]
v = np.power((1 - np.exp(-1 * loss)), gamma)
return v
def vstar_spcl_linear(inbatch, **kwargs):
"""Variable v_star function for self-paced curriculum learning (linear).
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
if 'vstar_gamma' in kwargs:
gamma = kwargs['vstar_gamma']
else: gamma = 1
assert gamma != 0
loss_diff = inbatch[:, 1]
v = -1.0 / gamma * loss_diff + 1
v = np.maximum(np.minimum(v, 1), 0)
return v
def vstar_mentornet_pd(inbatch, **kwargs):
"""Variable v_star function for the pre-defined mentornet: MentorNet PD.
Args:
inbatch: a numpy array with the following
Index 0: Loss
Index 1: Loss difference from moving average
Index 3: Label
Index 4: Epoch
**kwargs: hyper-parameter specified in vtsar_gamma
Returns:
v: [batch_size, 1] weight vector.
"""
epoch = inbatch[:, 3]
v1 = vstar_self_paced(inbatch, **kwargs)
v2 = vstar_spcl_linear(inbatch, **kwargs)
v = np.zeros(len(epoch))
ids = np.where(epoch >= 90)
v[ids] = v2[ids]
ids = | np.where(epoch < 90) | numpy.where |
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