import logging
import matplotlib
import numpy as np
from matplotlib import pyplot as plt
logger = logging.getLogger(__name__)
[docs]def plot_1d_morphing_basis(morpher, xlabel=r"$\theta$", xrange=(-1.0, 1.0), resolution=100):
"""
Visualizes a morphing basis and morphing errors for problems with a two-dimensional parameter space.
Parameters
----------
morpher : PhysicsMorpher
PhysicsMorpher instance with defined basis.
xlabel : str, optional
Label for the x axis. Default value: r'$\theta$'.
xrange : tuple of float, optional
Range `(min, max)` for the x axis. Default value: (-1., 1.).
resolution : int, optional
Number of points per axis for the rendering of the squared morphing weights. Default value: 100.
Returns
-------
figure : Figure
Plot as Matplotlib Figure instance.
"""
basis = morpher.basis
assert basis is not None, "No basis defined"
assert basis.shape[1] == 1, "Only 1d problems can be plotted with this function"
theta_test = np.linspace(xrange[0], xrange[1], resolution).reshape((-1, 1))
squared_weights = []
for theta in theta_test:
wi = morpher.calculate_morphing_weights(theta, None)
squared_weights.append(np.sum(wi * wi) ** 0.5)
fig = plt.figure(figsize=(5, 5))
ax = plt.gca()
ax.plot(theta_test.flatten(), squared_weights)
plt.scatter(basis[:, 0], [0.0 for _ in basis[:, 0]], s=50.0, c="black")
plt.xlabel(xlabel)
plt.ylabel(r"$\sqrt{\sum w_i^2}$")
plt.xlim(xrange[0], xrange[1])
plt.ylim(0.0, None)
plt.tight_layout()
return fig
[docs]def plot_2d_morphing_basis(
morpher,
xlabel=r"$\theta_0$",
ylabel=r"$\theta_1$",
xrange=(-1.0, 1.0),
yrange=(-1.0, 1.0),
crange=(1.0, 100.0),
resolution=100,
):
"""
Visualizes a morphing basis and morphing errors for problems with a two-dimensional parameter space.
Parameters
----------
morpher : PhysicsMorpher
PhysicsMorpher instance with defined basis.
xlabel : str, optional
Label for the x axis. Default value: r'$\theta_0$'.
ylabel : str, optional
Label for the y axis. Default value: r'$\theta_1$'.
xrange : tuple of float, optional
Range `(min, max)` for the x axis. Default value: (-1., 1.).
yrange : tuple of float, optional
Range `(min, max)` for the y axis. Default value: (-1., 1.).
crange : tuple of float, optional
Range `(min, max)` for the color map. Default value: (1., 100.).
resolution : int, optional
Number of points per axis for the rendering of the squared morphing weights. Default value: 100.
Returns
-------
figure : Figure
Plot as Matplotlib Figure instance.
"""
basis = morpher.basis
assert basis is not None, "No basis defined"
assert basis.shape[1] == 2, "Only 2d problems can be plotted with this function"
xi, yi = (np.linspace(xrange[0], xrange[1], resolution), np.linspace(yrange[0], yrange[1], resolution))
xx, yy = np.meshgrid(xi, yi)
xx, yy = xx.reshape((-1, 1)), yy.reshape((-1, 1))
theta_test = np.hstack([xx, yy])
squared_weights = []
for theta in theta_test:
wi = morpher.calculate_morphing_weights(theta, None)
squared_weights.append(np.sum(wi * wi) ** 0.5)
squared_weights = np.array(squared_weights).reshape((resolution, resolution))
fig = plt.figure(figsize=(6.5, 5))
ax = plt.gca()
pcm = ax.pcolormesh(
xi, yi, squared_weights, norm=matplotlib.colors.LogNorm(vmin=crange[0], vmax=crange[1]), cmap="viridis_r"
)
cbar = fig.colorbar(pcm, ax=ax, extend="both")
plt.scatter(basis[:, 0], basis[:, 1], s=50.0, c="black")
plt.xlabel(xlabel)
plt.ylabel(ylabel)
cbar.set_label(r"$\sqrt{\sum w_i^2}$")
plt.xlim(xrange[0], xrange[1])
plt.ylim(yrange[0], yrange[1])
plt.tight_layout()
return fig
[docs]def plot_nd_morphing_basis_scatter(morpher, crange=(1.0, 100.0), n_test_thetas=1000):
"""
Visualizes a morphing basis and morphing errors with scatter plots between each pair of operators.
Parameters
----------
morpher : PhysicsMorpher
PhysicsMorpher instance with defined basis.
crange : tuple of float, optional
Range `(min, max)` for the color map. Default value: (1. 100.).
n_test_thetas : int, optional
Number of random points evaluated. Default value: 1000.
Returns
-------
figure : Figure
Plot as Matplotlib Figure instance.
"""
basis = morpher.basis
assert basis is not None, "No basis defined"
n_parameters = basis.shape[1]
# Get squared weights
thetas, squared_weights = morpher.evaluate_morphing(n_test_thetas=n_test_thetas, return_weights_and_thetas=True)
# Plot
fig = plt.figure(figsize=((n_parameters - 1) * 5.0, (n_parameters - 1) * 4.0))
for iy in range(1, n_parameters):
for ix in range(0, iy):
i_panel = 1 + (iy - 1) * (n_parameters - 1) + ix
ax = plt.subplot(n_parameters - 1, n_parameters - 1, i_panel)
sc = plt.scatter(
thetas[:, ix],
thetas[:, iy],
c=squared_weights,
s=20.0,
norm=matplotlib.colors.LogNorm(vmin=crange[0], vmax=crange[1]),
cmap="viridis_r",
)
cbar = fig.colorbar(sc, ax=ax, extend="both")
plt.scatter(basis[:, ix], basis[:, iy], s=100.0, lw=1.0, edgecolor="black", c="white")
plt.xlabel(r"$\theta_" + str(ix) + "$")
plt.ylabel(r"$\theta_" + str(iy) + "$")
cbar.set_label(r"$\sqrt{\sum w_i^2}$")
plt.tight_layout()
return fig
[docs]def plot_nd_morphing_basis_slices(morpher, crange=(1.0, 100.0), resolution=50):
"""
Visualizes a morphing basis and morphing errors with two-dimensional slices through parameter space.
Parameters
----------
morpher : PhysicsMorpher
PhysicsMorpher instance with defined basis.
crange : tuple of float, optional
Range `(min, max)` for the color map.
resolution : int, optional
Number of points per panel and axis for the rendering of the squared morphing weights. Default value: 50.
Returns
-------
figure : Figure
Plot as Matplotlib Figure instance.
"""
basis = morpher.basis
assert basis is not None, "No basis defined"
n_parameters = basis.shape[1]
# Plot
fig = plt.figure(figsize=((n_parameters - 1) * 5.0, (n_parameters - 1) * 4.0))
for iy in range(1, n_parameters):
for ix in range(0, iy):
i_panel = 1 + (iy - 1) * (n_parameters - 1) + ix
ax = plt.subplot(n_parameters - 1, n_parameters - 1, i_panel)
# Grid
xrange = morpher.parameter_range[ix]
yrange = morpher.parameter_range[iy]
xi = np.linspace(xrange[0], xrange[1], resolution)
yi = np.linspace(yrange[0], yrange[1], resolution)
xx, yy = np.meshgrid(xi, yi)
xx, yy = xx.flatten(), yy.flatten()
theta_test = np.zeros((resolution**2, n_parameters))
theta_test[:, ix] = xx
theta_test[:, iy] = yy
# Get squared weights
squared_weights = []
for theta in theta_test:
wi = morpher.calculate_morphing_weights(theta, None)
squared_weights.append(np.sum(wi * wi) ** 0.5)
squared_weights = np.array(squared_weights).reshape((resolution, resolution))
pcm = ax.pcolormesh(
xi,
yi,
squared_weights,
norm=matplotlib.colors.LogNorm(vmin=crange[0], vmax=crange[1]),
cmap="viridis_r",
)
cbar = fig.colorbar(pcm, ax=ax, extend="both")
plt.scatter(basis[:, ix], basis[:, iy], s=100.0, lw=1.0, edgecolor="black", c="white")
plt.xlabel(r"$\theta_" + str(ix) + "$")
plt.ylabel(r"$\theta_" + str(iy) + "$")
cbar.set_label(r"$\sqrt{\sum w_i^2}$")
plt.tight_layout()
return fig