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# Created by John Travers, Robert Hetland, 2007
""" Test functions for rbf module """
import numpy as np
from scipy._lib._array_api import assert_array_almost_equal, assert_almost_equal
from numpy import linspace, sin, cos, exp, allclose
from scipy.interpolate._rbf import Rbf
from scipy._lib._testutils import _run_concurrent_barrier
import pytest
FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian',
'cubic', 'quintic', 'thin-plate', 'linear')
def check_rbf1d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (1D)
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y, function=function)
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0], check_0d=False)
def check_rbf2d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (2D).
rng = np.random.RandomState(1234)
x = rng.rand(50,1)*4-2
y = rng.rand(50,1)*4-2
z = x*exp(-x**2-1j*y**2)
rbf = Rbf(x, y, z, epsilon=2, function=function)
zi = rbf(x, y)
zi.shape = x.shape
assert_array_almost_equal(z, zi)
def check_rbf3d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (3D).
rng = np.random.RandomState(1234)
x = rng.rand(50, 1)*4 - 2
y = rng.rand(50, 1)*4 - 2
z = rng.rand(50, 1)*4 - 2
d = x*exp(-x**2 - y**2)
rbf = Rbf(x, y, z, d, epsilon=2, function=function)
di = rbf(x, y, z)
di.shape = x.shape
assert_array_almost_equal(di, d)
def test_rbf_interpolation():
for function in FUNCTIONS:
check_rbf1d_interpolation(function)
check_rbf2d_interpolation(function)
check_rbf3d_interpolation(function)
def check_2drbf1d_interpolation(function):
# Check that the 2-D Rbf function interpolates through the nodes (1D)
x = linspace(0, 10, 9)
y0 = sin(x)
y1 = cos(x)
y = np.vstack([y0, y1]).T
rbf = Rbf(x, y, function=function, mode='N-D')
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0])
def check_2drbf2d_interpolation(function):
# Check that the 2-D Rbf function interpolates through the nodes (2D).
rng = np.random.RandomState(1234)
x = rng.rand(50, ) * 4 - 2
y = rng.rand(50, ) * 4 - 2
z0 = x * exp(-x ** 2 - 1j * y ** 2)
z1 = y * exp(-y ** 2 - 1j * x ** 2)
z = np.vstack([z0, z1]).T
rbf = Rbf(x, y, z, epsilon=2, function=function, mode='N-D')
zi = rbf(x, y)
zi.shape = z.shape
assert_array_almost_equal(z, zi)
def check_2drbf3d_interpolation(function):
# Check that the 2-D Rbf function interpolates through the nodes (3D).
rng = np.random.RandomState(1234)
x = rng.rand(50, ) * 4 - 2
y = rng.rand(50, ) * 4 - 2
z = rng.rand(50, ) * 4 - 2
d0 = x * exp(-x ** 2 - y ** 2)
d1 = y * exp(-y ** 2 - x ** 2)
d = np.vstack([d0, d1]).T
rbf = Rbf(x, y, z, d, epsilon=2, function=function, mode='N-D')
di = rbf(x, y, z)
di.shape = d.shape
assert_array_almost_equal(di, d)
def test_2drbf_interpolation():
for function in FUNCTIONS:
check_2drbf1d_interpolation(function)
check_2drbf2d_interpolation(function)
check_2drbf3d_interpolation(function)
def check_rbf1d_regularity(function, atol):
# Check that the Rbf function approximates a smooth function well away
# from the nodes.
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
xi = linspace(0, 10, 100)
yi = rbf(xi)
msg = f"abs-diff: {abs(yi - sin(xi)).max():f}"
assert allclose(yi, sin(xi), atol=atol), msg
def test_rbf_regularity():
tolerances = {
'multiquadric': 0.1,
'inverse multiquadric': 0.15,
'gaussian': 0.15,
'cubic': 0.15,
'quintic': 0.1,
'thin-plate': 0.1,
'linear': 0.2
}
for function in FUNCTIONS:
check_rbf1d_regularity(function, tolerances.get(function, 1e-2))
def check_2drbf1d_regularity(function, atol):
# Check that the 2-D Rbf function approximates a smooth function well away
# from the nodes.
x = linspace(0, 10, 9)
y0 = sin(x)
y1 = cos(x)
y = np.vstack([y0, y1]).T
rbf = Rbf(x, y, function=function, mode='N-D')
xi = linspace(0, 10, 100)
yi = rbf(xi)
msg = f"abs-diff: {abs(yi - np.vstack([sin(xi), cos(xi)]).T).max():f}"
assert allclose(yi, np.vstack([sin(xi), cos(xi)]).T, atol=atol), msg
def test_2drbf_regularity():
tolerances = {
'multiquadric': 0.1,
'inverse multiquadric': 0.15,
'gaussian': 0.15,
'cubic': 0.15,
'quintic': 0.1,
'thin-plate': 0.15,
'linear': 0.2
}
for function in FUNCTIONS:
check_2drbf1d_regularity(function, tolerances.get(function, 1e-2))
def check_rbf1d_stability(function):
# Check that the Rbf function with default epsilon is not subject
# to overshoot. Regression for issue #4523.
#
# Generate some data (fixed random seed hence deterministic)
rng = np.random.RandomState(1234)
x = np.linspace(0, 10, 50)
z = x + 4.0 * rng.randn(len(x))
rbf = Rbf(x, z, function=function)
xi = np.linspace(0, 10, 1000)
yi = rbf(xi)
# subtract the linear trend and make sure there no spikes
assert np.abs(yi-xi).max() / np.abs(z-x).max() < 1.1
def test_rbf_stability():
for function in FUNCTIONS:
check_rbf1d_stability(function)
def test_default_construction():
# Check that the Rbf class can be constructed with the default
# multiquadric basis function. Regression test for ticket #1228.
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_function_is_callable():
# Check that the Rbf class can be constructed with function=callable.
x = linspace(0,10,9)
y = sin(x)
def linfunc(x):
return x
rbf = Rbf(x, y, function=linfunc)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_two_arg_function_is_callable():
# Check that the Rbf class can be constructed with a two argument
# function=callable.
def _func(self, r):
return self.epsilon + r
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y, function=_func)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_rbf_epsilon_none():
x = linspace(0, 10, 9)
y = sin(x)
Rbf(x, y, epsilon=None)
def test_rbf_epsilon_none_collinear():
# Check that collinear points in one dimension doesn't cause an error
# due to epsilon = 0
x = [1, 2, 3]
y = [4, 4, 4]
z = [5, 6, 7]
rbf = Rbf(x, y, z, epsilon=None)
assert rbf.epsilon > 0
@pytest.mark.thread_unsafe
def test_rbf_concurrency():
x = linspace(0, 10, 100)
y0 = sin(x)
y1 = cos(x)
y = np.vstack([y0, y1]).T
rbf = Rbf(x, y, mode='N-D')
def worker_fn(_, interp, xp):
interp(xp)
_run_concurrent_barrier(10, worker_fn, rbf, x)
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