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import numpy as np
from matplotlib.figure import Figure
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.backends.backend_qt5agg import NavigationToolbar2QT as NavigationToolbar
from PyQt5.QtCore import Qt
from PyQt5.QtWidgets import QVBoxLayout, QLabel, QSlider, QSpinBox, QPushButton, QSplitter
from visma.io.checks import getVariables, getTokensType
from visma.io.tokenize import getLHSandRHS
from visma.functions.constant import Constant
from visma.functions.operator import Binary
from visma.functions.structure import FuncOp
from visma.functions.variable import Variable
def graphPlot(workspace, again, tokens):
"""Function for plotting graphs in 2D and 3D space
2D graphs are plotted for expression in one variable and equations in two variables. 3D graphs are plotted for expressions in two variables and equations in three variables.
Arguments:
workspace {QtWidgets.QWidget} -- main layout
Returns:
graphVars {list} -- variables to be plotted on the graph
func {numpy.array(2D)/function(3D)} -- equation converted to compatible data type for plotting
variables {list} -- variables in given equation
again {bool} -- True when an equation can be plotted in 2D and 3D both else False
Note:
The func obtained from graphPlot() function is of different type for 2D and 3D plots. For 2D, func is a numpy array, and for 3D, func is a function.
"""
if tokens is None:
axisRange = workspace.axisRange
tokens = workspace.eqToks[-1]
else:
axisRange = [10, 10, 10, 30]
eqType = getTokensType(tokens)
LHStok, RHStok = getLHSandRHS(tokens)
variables = sorted(getVariables(LHStok, RHStok))
dim = len(variables)
if (dim == 1) or ((dim == 2) and eqType == "equation"):
if again:
variables.append('f(' + variables[0] + ')')
graphVars, func = plotIn3D(LHStok, RHStok, variables, axisRange)
else:
graphVars, func = plotIn2D(LHStok, RHStok, variables, axisRange)
if dim == 1:
variables.append('f(' + variables[0] + ')')
elif (dim == 2 and eqType == "expression") or ((dim == 3) and eqType == "equation"):
graphVars, func = plotIn3D(LHStok, RHStok, variables, axisRange)
if dim == 2:
variables.append('f(' + variables[0] + ',' + variables[1] + ')')
else:
return [], None, None
return graphVars, func, variables
def plotIn2D(LHStok, RHStok, variables, axisRange):
"""Returns function array for 2D plots
Arguments:
LHStok {list} -- expression tokens
RHStok {list} -- expression tokens
variables {list} -- variables in equation
axisRange {list} -- axis limits
Returns:
graphVars {list} -- variables for plotting
func {numpy.array} -- equation to be plotted in 2D
"""
xmin = -axisRange[0]
xmax = axisRange[0]
ymin = -axisRange[1]
ymax = axisRange[1]
xdelta = 0.01 * (xmax - xmin)
ydelta = 0.01 * (ymax - ymin)
xrange = np.arange(xmin, xmax, xdelta)
yrange = np.arange(ymin, ymax, ydelta)
graphVars = np.meshgrid(xrange, yrange)
function = getFunction(LHStok, RHStok, variables, graphVars, 2)
return graphVars, function
def plotIn3D(LHStok, RHStok, variables, axisRange):
"""Returns function for 3D plots
Arguments:
LHStok {list} -- expression tokens
RHStok {list} -- expression tokens
variables {list} -- variables in equation
axisRange {list} -- axis limits
Returns:
graphVars {list} -- variables for plotting
func {function} -- equation to be plotted in 3D
"""
xmin = -axisRange[0]
xmax = axisRange[0]
ymin = -axisRange[1]
ymax = axisRange[1]
zmin = -axisRange[2]
zmax = axisRange[2]
meshLayers = axisRange[3]
xrange = np.linspace(xmin, xmax, meshLayers)
yrange = np.linspace(ymin, ymax, meshLayers)
zrange = np.linspace(zmin, zmax, meshLayers)
graphVars = [xrange, yrange, zrange]
def func(x, y, z):
graphVars = [x, y, z]
return getFunction(LHStok, RHStok, variables, graphVars, 3)
return graphVars, func
def getFunction(LHStok, RHStok, eqnVars, graphVars, dim):
"""Returns function for plotting
Arguments:
LHStok {list} -- expression tokens
RHStok {list} -- expression tokens
eqnVars {list} -- variables in equation
graphVars {list} -- variables for plotting
dim {int} -- dimenion of plot
Returns:
(LHS - RHS) {numpy.array(2D)/function(3D)} -- equation converted to compatible data type for plotting
"""
LHS = getFuncExpr(LHStok, eqnVars, graphVars)
if len(eqnVars) == dim:
RHS = getFuncExpr(RHStok, eqnVars, graphVars)
elif len(eqnVars) == dim - 1:
RHS = graphVars[-1]
return LHS - RHS
def getFuncExpr(exprTok, eqnVars, graphVars):
"""Allocates variables in equation to graph variables to give final function compatible for plotting
Arguments:
exprTok {list} -- expression tokens
eqnVars {list} -- variables in equation
graphVars {list} -- variables for plotting
Returns:
expr {numpy.array(2D)/function(3D)} -- expression converted to compatible data type for plotting
"""
expr = 0
coeff = 1
for token in exprTok:
if isinstance(token, Variable):
varProduct = 1
for value, power in zip(token.value, token.power):
varProduct *= graphVars[eqnVars.index(value)]**power
expr += coeff * token.coefficient * varProduct
elif isinstance(token, Constant):
expr += coeff * token.value
elif isinstance(token, FuncOp):
pass
elif isinstance(token, Binary) and token.value == '-':
coeff = -1
elif isinstance(token, Binary) and token.value == '+':
coeff = 1
return expr
#######
# GUI #
#######
def plotFigure2D(workspace):
"""GUI layout for plot figure
Arguments:
workspace {QtWidgets.QWidget} -- main layout
Returns:
layout {QtWidgets.QVBoxLayout} -- contains matplot figure
"""
workspace.figure2D = Figure()
workspace.canvas2D = FigureCanvas(workspace.figure2D)
# workspace.figure2D.patch.set_facecolor('white')
class NavigationCustomToolbar(NavigationToolbar):
toolitems = [t for t in NavigationToolbar.toolitems if t[0] in ()]
workspace.toolbar2D = NavigationCustomToolbar(workspace.canvas2D, workspace)
layout = QVBoxLayout()
layout.addWidget(workspace.canvas2D)
layout.addWidget(workspace.toolbar2D)
return layout
def plotFigure3D(workspace):
"""GUI layout for plot figure
Arguments:
workspace {QtWidgets.QWidget} -- main layout
Returns:
layout {QtWidgets.QVBoxLayout} -- contains matplot figure
"""
workspace.figure3D = Figure()
workspace.canvas3D = FigureCanvas(workspace.figure3D)
# workspace.figure3D.patch.set_facecolor('white')
class NavigationCustomToolbar(NavigationToolbar):
toolitems = [t for t in NavigationToolbar.toolitems if t[0] in ()]
workspace.toolbar3D = NavigationCustomToolbar(workspace.canvas3D, workspace)
layout = QVBoxLayout()
layout.addWidget(workspace.canvas3D)
layout.addWidget(workspace.toolbar3D)
return layout
def renderPlot(workspace, graphVars, func, variables, tokens=None):
"""Renders plot for functions in 2D and 3D
Maps points from the numpy arrays for variables in given equation on the 2D/3D plot figure
Arguments:
workspace {QtWidgets.QWidget} -- main layout
graphVars {list} -- variables for plotting
dim {int} -- dimenion of plot
variables {list} -- variables in equation
"""
if len(graphVars) == 2:
X, Y = graphVars[0], graphVars[1]
ax = workspace.figure2D.add_subplot(111)
ax.clear()
ax.contour(X, Y, func, [0])
ax.grid()
ax.set_xlabel(r'$' + variables[0] + '$')
ax.set_ylabel(r'$' + variables[1] + '$')
workspace.figure2D.set_tight_layout({"pad": 1}) # removes extra padding
workspace.canvas2D.draw()
workspace.tabPlot.setCurrentIndex(0)
elif len(graphVars) == 3:
xrange = graphVars[0]
yrange = graphVars[1]
zrange = graphVars[2]
ax = Axes3D(workspace.figure3D)
for z in zrange:
X, Y = np.meshgrid(xrange, yrange)
Z = func(X, Y, z)
ax.contour(X, Y, Z + z, [z], zdir='z')
for y in yrange:
X, Z = np.meshgrid(xrange, zrange)
Y = func(X, y, Z)
ax.contour(X, Y + y, Z, [y], zdir='y')
for x in xrange:
Y, Z = np.meshgrid(yrange, zrange)
X = func(x, Y, Z)
ax.contour(X + x, Y, Z, [x], zdir='x')
if tokens is None:
axisRange = workspace.axisRange
else:
axisRange = [10, 10, 10, 30]
xmin = -axisRange[0]
xmax = axisRange[0]
ymin = -axisRange[1]
ymax = axisRange[1]
zmin = -axisRange[2]
zmax = axisRange[2]
ax.set_xlim3d(xmin, xmax)
ax.set_ylim3d(ymin, ymax)
ax.set_zlim3d(zmin, zmax)
ax.set_xlabel(r'$' + variables[0] + '$')
ax.set_ylabel(r'$' + variables[1] + '$')
ax.set_zlabel(r'$' + variables[2] + '$')
workspace.canvas3D.draw()
workspace.tabPlot.setCurrentIndex(1)
def plot(workspace, tokens=None):
"""When called from window.py it initiates rendering of equations.
Arguments:
workspace {QtWidgets.QWidget} -- main layout
"""
from visma.io.tokenize import tokenizer
workspace.figure2D.clear()
workspace.figure3D.clear()
if tokens is None:
tokens = workspace.eqToks[-1]
eqType = getTokensType(tokens)
LHStok, RHStok = getLHSandRHS(tokens)
variables = sorted(getVariables(LHStok, RHStok))
dim = len(variables)
graphVars, func, variables = graphPlot(workspace, False, tokens)
renderPlot(workspace, graphVars, func, variables, tokens)
if (dim == 1):
var2, var3 = selectAdditionalVariable(variables[0])
if tokens is None:
workspace.eqToks[-1] += tokenizer("0" + var2 + "+" + "0" + var3)
else:
tokens += tokenizer("0" + var2 + "+" + "0" + var3)
if (((dim == 2) or (dim == 1)) & (eqType == 'equation')):
graphVars, func, variables = graphPlot(workspace, True, tokens)
renderPlot(workspace, graphVars, func, variables, tokens)
def selectAdditionalVariable(var1):
if var1 == 'z':
var2 = 'a'
var3 = 'b'
return var2, var3
if var1 == 'Z':
var2 = 'A'
var3 = 'B'
return var2, var3
var2 = chr(ord(var1) + 1)
var3 = chr(ord(var1) + 2)
return var2, var3
def refreshPlot(workspace):
if workspace.resultOut is True and workspace.showPlotter is True:
plot(workspace)
###############
# preferences #
###############
# TODO: Add status tips, Fix docstrings
def plotPref(workspace):
prefLayout = QSplitter(Qt.Horizontal)
workspace.xLimitValue = QLabel(
"X-axis range: (-" + str(workspace.axisRange[0]) + ", " + str(workspace.axisRange[0]) + ")")
workspace.yLimitValue = QLabel(
"Y-axis range: (-" + str(workspace.axisRange[1]) + ", " + str(workspace.axisRange[1]) + ")")
workspace.zLimitValue = QLabel(
"Z-axis range: (-" + str(workspace.axisRange[2]) + ", " + str(workspace.axisRange[2]) + ")")
def customSlider():
limitSlider = QSlider(Qt.Horizontal)
limitSlider.setMinimum(-3)
limitSlider.setMaximum(3)
limitSlider.setValue(1)
limitSlider.setTickPosition(QSlider.TicksBothSides)
limitSlider.setTickInterval(1)
limitSlider.valueChanged.connect(lambda: valueChange(workspace))
limitSlider.setStatusTip("Change axes limit")
return limitSlider
workspace.xLimitSlider = customSlider()
workspace.yLimitSlider = customSlider()
workspace.zLimitSlider = customSlider()
workspace.meshDensityValue = QLabel(
"Mesh Layers: " + str(workspace.axisRange[3]))
workspace.meshDensityValue.setStatusTip("Increment for a denser mesh in 3D plot")
workspace.meshDensity = QSpinBox()
workspace.meshDensity.setFixedSize(200, 30)
workspace.meshDensity.setRange(10, 75)
workspace.meshDensity.setValue(30)
workspace.meshDensity.valueChanged.connect(lambda: valueChange(workspace))
workspace.meshDensity.setStatusTip("Incrementing mesh density may affect performance")
refreshPlotterText = QLabel("Apply plotter settings")
refreshPlotter = QPushButton('Apply')
refreshPlotter.setFixedSize(200, 30)
refreshPlotter.clicked.connect(lambda: refreshPlot(workspace))
refreshPlotter.setStatusTip("Apply modified settings to plotter.")
axisPref = QSplitter(Qt.Vertical)
axisPref.addWidget(workspace.xLimitValue)
axisPref.addWidget(workspace.xLimitSlider)
axisPref.addWidget(workspace.yLimitValue)
axisPref.addWidget(workspace.yLimitSlider)
axisPref.addWidget(workspace.zLimitValue)
axisPref.addWidget(workspace.zLimitSlider)
plotSetPref = QSplitter(Qt.Vertical)
plotSetPref.addWidget(workspace.meshDensityValue)
plotSetPref.addWidget(workspace.meshDensity)
plotSetPref.addWidget(refreshPlotterText)
plotSetPref.addWidget(refreshPlotter)
prefLayout.addWidget(plotSetPref)
prefLayout.addWidget(axisPref)
prefLayout.setFixedWidth(400)
return prefLayout
def valueChange(workspace):
xlimit = 10**workspace.xLimitSlider.value()
ylimit = 10**workspace.yLimitSlider.value()
zlimit = 10**workspace.zLimitSlider.value()
meshLayers = workspace.meshDensity.value()
workspace.axisRange = [xlimit, ylimit, zlimit, meshLayers]
workspace.xLimitValue.setText(
"X-axis range: (-" + str(workspace.axisRange[0]) + ", " + str(workspace.axisRange[0]) + ")")
workspace.yLimitValue.setText(
"Y-axis range: (-" + str(workspace.axisRange[1]) + ", " + str(workspace.axisRange[1]) + ")")
workspace.zLimitValue.setText(
"Z-axis range: (-" + str(workspace.axisRange[2]) + ", " + str(workspace.axisRange[2]) + ")")
workspace.meshDensityValue.setText(
"Mesh Layers: " + str(workspace.axisRange[3]))
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