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sindy_utils.py
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sindy_utils.py
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import numpy as np
from matplotlib import pyplot as plt
import pandas as pd
from mpl_toolkits.mplot3d import Axes3D
from scipy.interpolate import griddata
from scipy.integrate import simps
import matplotlib.animation as animation
import matplotlib.gridspec as gridspec
from random import randint
def inner_product(Q, R):
"""
Compute the MHD inner product in a uniformly
sampled cylindrical geometry
Parameters
----------
Q: 2D numpy array of floats
(6*n_samples = number of volume-sampled locations for each of the
6 components of the two field vectors, M = number of time samples)
Dimensionalized and normalized matrix of temporal BOD modes
R: numpy array of floats
(6*n_samples = number of volume-sampled locations for each of the
6 components of the two field vectors, M = number of time samples)
Radial coordinates of the volume-sampled locations
Returns
-------
inner_prod: 2D numpy array of floats
(M = number of time samples, M = number of time samples)
The unscaled matrix of inner products X*X
"""
Qr = np.zeros(np.shape(Q))
for i in range(np.shape(Q)[1]):
Qr[:, i] = Q[:, i] * np.sqrt(R)
inner_prod = np.transpose(Qr) @ Qr
return inner_prod
def update_manifold_movie(frame, x_true, x_sim, t_test, i, j, k):
"""
A function for the matplotlib.animation.FuncAnimation object
to update the frame at each timestep. This makes 3D movies
in the BOD state space.
Parameters
----------
frame: int
(1)
A particular frame in the animation
x_true: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The true evolution of the temporal BOD modes
x_sim: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The model evolution of the temporal BOD modes
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
i: int
(1)
Index of one of the POD modes
j: int
(1)
Index of the second of the POD modes
k: int
(1)
Index of the third of the POD modes
"""
print(frame)
r = np.shape(x_sim)[1]
# Erase plot from previous movie frame
plt.clf()
# setup 3D plot, and three 2D projections on the "walls".
fig = plt.figure(101, figsize=(16, 7))
ax1 = fig.add_subplot(121, projection='3d')
ax1.plot(x_true[0:frame, j], x_true[0:frame, k], zs=-0.4, zdir='x',
color='gray', linewidth=3)
ax1.plot(x_true[0:frame, i], x_true[0:frame, k], zs=-0.4, zdir='y',
color='gray', linewidth=3)
ax1.plot(x_true[0:frame, i], x_true[0:frame, j], zs=-0.4, zdir='z',
color='gray', linewidth=3)
ax1.plot(x_true[0:frame, i], x_true[0:frame, j], x_true[0:frame, k],
'k', linewidth=5)
ax1.scatter(x_true[frame - 1, i], x_true[frame - 1, j], x_true[frame - 1, k],
s=80, color='k', marker='o')
ax1.azim = 25 + 0.5 * frame / 9.0
ax1.elev = 5 + 0.5 * frame / 13.0
ax1.set_xticks([-0.3, 0, 0.3])
ax1.set_yticks([-0.3, 0, 0.3])
ax1.set_zticks([-0.3, 0, 0.3])
ax1.set_xticklabels([])
ax1.set_yticklabels([])
ax1.set_zticklabels([])
ax1.set_xlim(-0.4, 0.4)
ax1.set_ylim(-0.4, 0.4)
ax1.set_zlim(-0.4, 0.4)
ax1.grid(True)
ax1.tick_params(axis='both', which='major', labelsize=18)
ax1.tick_params(axis='both', which='minor', labelsize=18)
# First remove fill
ax1.xaxis.pane.fill = False
ax1.yaxis.pane.fill = False
ax1.zaxis.pane.fill = False
# Now set color to light color
ax1.xaxis.pane.set_edgecolor('whitesmoke')
ax1.yaxis.pane.set_edgecolor('whitesmoke')
ax1.zaxis.pane.set_edgecolor('whitesmoke')
# Repeat process for the model-predicted temporal POD modes
ax2 = fig.add_subplot(122, projection='3d')
ax2.plot(x_sim[0:frame, j], x_sim[0:frame, k], zs=-0.4, zdir='x',
color='lightsalmon', linewidth=3)
ax2.plot(x_sim[0:frame, i], x_sim[0:frame, k], zs=-0.4, zdir='y',
color='lightsalmon', linewidth=3)
ax2.plot(x_sim[0:frame, i], x_sim[0:frame, j], zs=-0.4, zdir='z',
color='lightsalmon', linewidth=3)
ax2.plot(x_sim[0:frame, i], x_sim[0:frame, j], x_sim[0:frame, k],
color='r', linewidth=5)
ax2.scatter(x_sim[frame - 1, i], x_sim[frame - 1, j], x_sim[frame - 1, k],
s=80, color='r', marker='o')
ax2.azim = 25 + 0.5 * frame / 9.0
ax2.elev = 5 + 0.5 * frame / 13.0
ax2.set_xlim(-0.4, 0.4)
ax2.set_ylim(-0.4, 0.4)
ax2.set_zlim(-0.4, 0.4)
ax2.set_xticks([-0.3, 0, 0.3])
ax2.set_yticks([-0.3, 0, 0.3])
ax2.set_zticks([-0.3, 0, 0.3])
ax2.set_xticklabels([])
ax2.set_yticklabels([])
ax2.set_zticklabels([])
ax2.grid(True)
ax2.tick_params(axis='both', which='major', labelsize=18)
ax2.tick_params(axis='both', which='minor', labelsize=18)
# First remove fill
ax2.xaxis.pane.fill = False
ax2.yaxis.pane.fill = False
ax2.zaxis.pane.fill = False
# Now set color to light color
ax2.xaxis.pane.set_edgecolor('whitesmoke')
ax2.yaxis.pane.set_edgecolor('whitesmoke')
ax2.zaxis.pane.set_edgecolor('whitesmoke')
def update_toroidal_movie(frame, X, Y, Z, B_true,
B_pod, B_sim, t_test, prefix):
"""
A function for the matplotlib.animation.FuncAnimation object
to update the frame at each timestep. This makes a true vs. model
movie at the Z=0 midplane of any of the field components.
Parameters
----------
frame: int
(1)
A particular frame in the animation
X: numpy array of floats
(n_samples = number of volume-sampled locations)
X-coordinate locations of the volume-sampled locations
Y: numpy array of floats
(n_samples = number of volume-sampled locations)
Y-coordinate locations of the volume-sampled locations
Z: numpy array of floats
(n_samples = number of volume-sampled locations)
Z-coordinate locations of the volume-sampled locations
B_true: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The true evolution of a particular field component
at every volume-sampled location
B_pod: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The POD-reconstructed evolution of a particular field component
at every volume-sampled location
B_sim: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The model evolution of a particular field component
at every volume-sampled location
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
prefix: string
(2)
String of the field component being used. For instance,
Bx, By, Bz, Vx, Vy, Vz are all appropriate choices.
"""
print(frame)
R = np.sqrt(X ** 2 + Y ** 2)
# Find location where the probe Z location is approximately at Z=0
Z0 = np.isclose(Z, np.ones(len(Z)) * min(abs(Z)), rtol=1e-3, atol=1e-3)
# Get the indices where Z=0
ind_Z0 = [i for i, p in enumerate(Z0) if p]
# Get the R and phi locations for the Z=0 probes
ri = np.linspace(0, max(R[ind_Z0]), 40)
phii = np.linspace(0, 2 * np.pi, 100)
ri, phii = np.meshgrid(ri, phii)
# Convert to (x,y) coordinates
xi = ri * np.cos(phii)
yi = ri * np.sin(phii)
# Interpolate the true/POD-recon/predicted probe data onto the (xi,yi) mesh
Bi = griddata((X[ind_Z0], Y[ind_Z0]), B_true[ind_Z0, frame],
(xi, yi), method='cubic')
Bi_pod = griddata((X[ind_Z0], Y[ind_Z0]), B_pod[ind_Z0, frame],
(xi, yi), method='cubic')
Bi_sim = griddata((X[ind_Z0], Y[ind_Z0]), B_sim[ind_Z0, frame],
(xi, yi), method='cubic')
# Erase figure from last movie frame
plt.clf()
# Plotting, with scaling depending on if this is B or V field.
fig = plt.figure(102, figsize=(7, 20))
plt.subplot(3, 1, 1)
if prefix[0:2] == 'Bv':
plt.pcolor(xi, yi, Bi * 1.0e4, cmap='jet', vmin=-5e1, vmax=5e1)
else:
plt.pcolor(xi, yi, Bi * 1.0e4, cmap='jet', vmin=-5e2, vmax=5e2)
ax = plt.gca()
ax.axis('off')
plt.subplot(3, 1, 2)
if prefix[0:2] == 'Bv':
plt.pcolor(xi, yi, Bi_pod * 1.0e4, cmap='jet', vmin=-5e1, vmax=5e1)
else:
plt.pcolor(xi, yi, Bi_pod * 1.0e4, cmap='jet', vmin=-5e2, vmax=5e2)
ax = plt.gca()
ax.axis('off')
plt.subplot(3, 1, 3)
if prefix[0:2] == 'Bv':
im = plt.pcolor(xi, yi, Bi_sim * 1.0e4, cmap='jet', vmin=-5e1, vmax=5e1)
else:
im = plt.pcolor(xi, yi, Bi_sim * 1.0e4, cmap='jet', vmin=-5e2, vmax=5e2)
ax = plt.gca()
ax.axis('off')
fig.subplots_adjust(right=0.75)
def plot_BOD_Espectrum(S):
"""
This function plots the energy spectrum of the data matrix.
Parameters
----------
S: numpy array of floats
(r = truncation number of the SVD)
Diagonal of the Sigma matrix in the SVD
"""
fig = plt.figure(figsize=(16, 7))
plt.subplot(1, 2, 1)
plt.plot(S[0:30] / S[0], 'ko')
plt.yscale('log')
plt.ylim(1e-4, 2)
plt.box(on=None)
ax = plt.gca()
ax.set_yticks([1e-4, 1e-3, 1e-2, 1e-1, 1e0])
ax.set_yticklabels([r'$10^{-4}$', r'$10^{-3}$',
r'$10^{-2}$', r'$10^{-1}$', r'$10^{0}$'])
ax.tick_params(axis='both', which='major', labelsize=22)
ax.tick_params(axis='both', which='minor', labelsize=22)
plt.savefig('Pictures/BOD_spectrum.pdf')
def make_evo_plots(x_dot, x_dot_train, x_dot_sim,
x_true, x_sim, time, t_train, t_test):
"""
Plots the true evolution of X and Xdot, along with
the model evolution of X and Xdot, for both the
training and test data.
Parameters
----------
x_dot: 2D numpy array of floats
(M = number of time samples, r = truncation number of the SVD)
True Xdot for the entire time range
x_dot_train: 2D numpy array of floats
(M_train = number of time samples in training data region,
r = truncation number of the SVD)
Model Xdot for the training data
x_dot_test: 2D numpy array of floats
(M_test = number of time samples in training data region,
r = truncation number of the SVD)
Model Xdot for the test data
x_true: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The true evolution of the temporal BOD modes
x_sim: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The model evolution of the temporal BOD modes
time: numpy array of floats
(M = number of time samples)
Time in microseconds
t_train: numpy array of floats
(M_train = number of time samples in the test data region)
Time in microseconds in the training data region
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
"""
r = x_true.shape[1]
fig, axs = plt.subplots(r, 1, sharex=True, figsize=(7, 9))
if r == 12 or r == 6:
fig, axs = plt.subplots(3, int(r / 3), figsize=(16, 9))
axs = np.ravel(axs)
# Loop over the r temporal Xdot modes that were fit
for i in range(r):
axs[i].plot(t_test / 1.0e3, x_dot[t_train.shape[0]:, i], color='k',
linewidth=2, label='numerical derivative')
# axs[i].plot(t_train/1.0e3, x_dot_train[:, i], color='red',
# linewidth=2, label='model prediction')
axs[i].plot(t_test / 1.0e3, x_dot_sim[:, i], color='r',
linewidth=2, label='model forecast')
axs[i].set_yticklabels([])
axs[i].set_xticklabels([])
axs[i].tick_params(axis='both', which='major', labelsize=18)
axs[i].tick_params(axis='both', which='minor', labelsize=18)
axs[i].grid(True)
plt.savefig('Pictures/xdot.pdf')
plt.savefig('Pictures/xdot.eps')
# Repeat for X
fig, axs = plt.subplots(r, 1, sharex=True, figsize=(7, 9))
if r == 12 or r == 6:
fig, axs = plt.subplots(3, int(r / 3), figsize=(16, 9))
axs = np.ravel(axs)
for i in range(r):
axs[i].plot(t_test / 1.0e3, x_true[:, i], 'k',
linewidth=2, label='true simulation')
axs[i].plot(t_test / 1.0e3, x_sim[:, i], color='r',
linewidth=2, label='model forecast')
axs[i].set_yticklabels([])
axs[i].set_xticklabels([])
axs[i].tick_params(axis='both', which='major', labelsize=18)
axs[i].tick_params(axis='both', which='minor', labelsize=18)
axs[i].grid(True)
plt.savefig('Pictures/x.pdf')
plt.savefig('Pictures/x.eps')
def make_3d_plots(x_true, x_sim, t_test, prefix, i, j, k):
"""
Plots in 3D the true evolution of X along with
the model evolution of X for the test data.
Parameters
----------
x_true: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The true evolution of the temporal BOD modes
x_sim: 2D numpy array of floats
(M_test = number of time samples in the test data region,
r = truncation number of the SVD)
The model evolution of the temporal BOD modes
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
i: int
(1)
Index of one of the POD modes
j: int
(1)
Index of the second of the POD modes
k: int
(1)
Index of the third of the POD modes
"""
# Setup plots in anticipation for animation-making
r = np.shape(x_true)[1]
fig = plt.figure(101, figsize=(18, 10))
ax1 = fig.add_subplot(121, projection='3d')
ax1.plot(x_true[0:2, i], x_true[0:2, j], x_true[0:2, k], 'k', linewidth=3)
ax1.set_xlabel(r'$a_1$', fontsize=22)
ax1.set_ylabel(r'$a_2$', fontsize=22)
ax1.set_xticklabels([])
ax1.set_yticklabels([])
ax1.set_zticklabels([])
ax1.zaxis.set_rotate_label(False)
ax1.set_zlabel(r'$a_3$', fontsize=22)
ax1.xaxis.labelpad = 10
ax1.yaxis.labelpad = 12
ax1.zaxis.labelpad = 22
ax1.grid(True)
ax1.axis('off')
ax2 = fig.add_subplot(122, projection='3d')
ax2.plot(x_sim[0:2, i], x_sim[0:2, j], x_sim[0:2, k], 'r', linewidth=3)
ax2.set_xlabel(r'$a_1$', fontsize=22)
ax2.set_ylabel(r'$a_2$', fontsize=22)
ax2.set_xticklabels([])
ax2.set_yticklabels([])
ax2.set_zticklabels([])
ax2.zaxis.set_rotate_label(False)
ax2.set_zlabel(r'$a_3$', fontsize=22)
ax2.xaxis.labelpad = 10
ax2.yaxis.labelpad = 12
ax2.zaxis.labelpad = 22
ax2.grid(True)
ax2.axis('off')
# Make animation object and loop over the time corresponding to test data
ani = animation.FuncAnimation(fig, update_manifold_movie,
range(2, len(t_test)),
fargs=(x_true, x_sim,
t_test, i, j, k),
repeat=False,
interval=100,
blit=False)
# Set the frames-per-second and save the animation
FPS = 25
ani.save('Pictures/' + prefix + 'manifold' + str(i) + str(j) + str(k) + '.mp4',
fps=FPS, dpi=100)
def plot_pod_temporal_modes(x, time):
"""
Illustrate the temporal POD modes
Parameters
----------
x: 2D numpy array of floats
(M = number of time samples, r = POD truncation number)
The temporal POD modes
time: numpy array of floats
(M = number of time samples)
Time range of interest
"""
r = np.shape(x)[1]
time = time / 1.0e3
plt.figure(figsize=(8, 5))
# Use gridspec to make a nice gridded plot with no internal spacings
gs1 = gridspec.GridSpec(2, 12)
gs1.update(wspace=0.0, hspace=0.0)
# Loop over the first 12 normalized temporal modes
for i in range(12):
plt.subplot(gs1[i])
plt.plot(time, x[:, i] / np.max(abs(x[:, i])), 'k')
ax = plt.gca()
# ax.set_xticks([1.5, 2.75, 4.0])
ax.set_xticks([1.0, 1.5, 2.0, 2.5, 3.0])
ax.set_yticks([-1, 0, 1])
plt.ylim(-1.1, 1.1)
ax.set_xticklabels([])
ax.set_yticklabels([])
plt.grid(True)
# Save the figure
plt.savefig('Pictures/temporal_modes.pdf')
plt.savefig('Pictures/temporal_modes.eps')
# Checking that the temporal POD modes approximately integrate to zero
print('Simpson results: ')
print(simps(x[:, 0], time)/(time[-1] - time[0]))
print(simps(x[:, 1], time)/(time[-1] - time[0]))
print(simps(x[:, 2], time)/(time[-1] - time[0]))
print(simps(x[:, 3], time)/(time[-1] - time[0]))
print(simps(x[:, 4], time)/(time[-1] - time[0]))
print(simps(x[:, 5], time)/(time[-1] - time[0]))
print(simps(x[:, 6], time)/(time[-1] - time[0]))
# Now plot the fourier transforms OF THE MODES
time_uniform = np.linspace(time[0], time[-1], len(time) * 2)
x_uniform = np.zeros((len(time) * 2, x.shape[1]))
# Interpolate onto a uniform time base for the DFT
for i in range(x.shape[1]):
x_uniform[:, i] = np.interp(time_uniform, time, x[:, i])
fftx = np.fft.fft(x_uniform, axis=0) / len(time)
freq = np.fft.fftfreq(len(time_uniform), time_uniform[1] - time_uniform[0])
fftx = fftx[:len(time) - 1, :]
freq = freq[:len(time) - 1]
# Loop over the first 12 temporal mode FFTs
for i in range(12):
plt.subplot(gs1[12 + i])
plt.plot(freq, abs(fftx[:, i]), 'k', linewidth=3)
ax = plt.gca()
ax.set_xticks([0, 14.5, 14.5 * 2, 14.5 * 3, 14.5 * 4, 14.5 * 5])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_yticklabels([])
plt.xlim(0, 80)
plt.grid(True)
# Save the finished figure
plt.savefig('Pictures/frequency_modes.pdf')
plt.savefig('Pictures/frequency_modes.eps')
# Plot the modes in each of their 2D state spaces
plot_pairwise(x)
# now save trajectories to a file
np.savetxt('Pictures/trajectories_modes.txt', x)
np.savetxt('Pictures/trajectories_time.txt', time)
def plot_pod_spatial_modes(X, Y, Z, U):
"""
Makes midplane (Z=0) 2D contours of the spatial POD modes
Parameters
----------
X: numpy array of floats
(n_samples = number of volume-sampled locations)
X-coordinate locations of the volume-sampled locations
Y: numpy array of floats
(n_samples = number of volume-sampled locations)
Y-coordinate locations of the volume-sampled locations
Z: numpy array of floats
(n_samples = number of volume-sampled locations)
Z-coordinate locations of the volume-sampled locations
U: 2D numpy array of floats
(D = number of probe locations x 6, 12)
The first 12 spatial modes from the SVD of the data matrix
"""
R = np.sqrt(X ** 2 + Y ** 2)
# Find location where the probe Z location is approximately at Z=0
Z0 = np.isclose(Z, np.ones(len(Z)) * min(abs(Z)), rtol=1e-3, atol=1e-3)
# Get the indices where Z=0
ind_Z0 = [i for i, p in enumerate(Z0) if p]
# Get the R and phi locations for the Z=0 probes
ri = np.linspace(0, max(R[ind_Z0]), 40)
phii = np.linspace(0, 2 * np.pi, 100)
ri, phii = np.meshgrid(ri, phii)
# Convert to (x,y) coordinates
xi = ri * np.cos(phii)
yi = ri * np.sin(phii)
n_sample = len(R)
U = U.real
fig = plt.figure(figsize=(12, 12))
# prepare Gridspec object with no internal spacings
gs1 = gridspec.GridSpec(12, 12)
gs1.update(wspace=0.0, hspace=0.0)
# Loop over Bx, By, Bz, Bvx, Bvy, Bvz
for i in range(6):
# Loop over the first 12 POD modes
for j in range(12):
U_sub = U[i * n_sample:(i + 1) * n_sample, :]
# Interpolate spatial data onto the (xi, yi) grid
U_grid = griddata((X[ind_Z0], Y[ind_Z0]), U_sub[ind_Z0, j],
(xi, yi), method='cubic')
plt.subplot(gs1[i + j * 12])
plt.pcolor(xi, yi, U_grid / np.nanmax(np.nanmax(U_grid)),
cmap='jet', vmin=-1e0, vmax=1e0)
ax = plt.gca()
ax.set_xticks([])
ax.set_yticks([])
# Save figure
plt.savefig('Pictures/spatial_modes.pdf', dpi=50)
np.savetxt("Pictures/compressible1_spatialmodes.csv", U, delimiter=",")
def plot_pairwise(x):
"""
Makes pairwise feature space plots with the temporal
POD modes
Parameters
----------
x: 2D numpy array of floats
(M = number of time samples, r = POD truncation number)
The temporal POD modes
"""
r = np.shape(x)[1]
plt.figure(figsize=(r, r))
# Create GridSpec object with no internal spacings
gs1 = gridspec.GridSpec(r, r)
gs1.update(wspace=0.0, hspace=0.0)
# Loop over all r temporal POD modes being modeled
for i in range(r):
# Loop over remaining POD modes
for j in range(r - i):
plt.subplot(gs1[i, j])
ax = plt.gca()
plt.plot(x[:, i], x[:, r - j - 1], 'k')
ax.set_xticks([])
ax.set_yticks([])
ax.set_xticklabels([])
ax.set_yticklabels([])
# Save figure
plt.savefig('Pictures/pairwise_plots.pdf', dpi=100)
def plot_density(time, dens):
"""
Makes density plots at a number of random
locations to see how large the fluctuations are.
Parameters
----------
time: 1D numpy array of floats
(M = number of time samples)
Time samples
dens: 2D numpy array of floats
(n_samples = number of probe locations, M = number of time samples)
Simulation density at every spatio-temporal location
"""
# Rescale to ms and m^-3
time = time / 1.0e3
dens = dens / 1.0e19
# Pick some random locations to see density fluctuation sizes
plt.figure(figsize=(10, 14))
for i in range(12):
plt.subplot(6, 2, i + 1)
plt.plot(time, dens[randint(0, dens.shape[0] - 1), :], 'k')
plt.ylim(0.5, 3.5)
ax = plt.gca()
if i != 0 and i != 5:
ax.set_yticklabels([])
if i <= 9:
ax.set_xticklabels([])
# Save figure
plt.savefig('Pictures/density_samples.pdf')
def make_toroidal_movie(X, Y, Z, B_true, B_pod,
B_sim, t_test, prefix):
"""
Function to make a true vs. model movie at the Z=0 midplane of any
of the field components.
Parameters
----------
X: numpy array of floats
(n_samples = number of volume-sampled locations)
X-coordinate locations of the volume-sampled locations
Y: numpy array of floats
(n_samples = number of volume-sampled locations)
Y-coordinate locations of the volume-sampled locations
Z: numpy array of floats
(n_samples = number of volume-sampled locations)
Z-coordinate locations of the volume-sampled locations
B_true: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The true evolution of a particular field component
at every volume-sampled location
B_pod: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The POD-reconstructed evolution of a particular field component
at every volume-sampled location
B_sim: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The model evolution of a particular field component
at every volume-sampled location
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
prefix: string
(2)
String of the field component being used. For instance,
Bx, By, Bz, Vx, Vy, Vz are all appropriate choices.
"""
R = np.sqrt(X ** 2 + Y ** 2)
# Find location where the probe Z location is approximately at Z=0
Z0 = np.isclose(Z, np.ones(len(Z)) * min(abs(Z)), rtol=1e-3, atol=1e-3)
# Get the indices where Z=0
ind_Z0 = [i for i, p in enumerate(Z0) if p]
# Get the R and phi locations for the Z=0 probes
ri = np.linspace(0, max(R[ind_Z0]), 40)
phii = np.linspace(0, 2 * np.pi, 100)
ri, phii = np.meshgrid(ri, phii)
# Convert to (x,y) coordinates
xi = ri * np.cos(phii)
yi = ri * np.sin(phii)
# Interpolate measurements to the (xi,yi) mesh
Bi = griddata((X[ind_Z0], Y[ind_Z0]), B_true[ind_Z0, 0],
(xi, yi), method='cubic')
Bi_pod = griddata((X[ind_Z0], Y[ind_Z0]), B_pod[ind_Z0, 0],
(xi, yi), method='cubic')
Bi_sim = griddata((X[ind_Z0], Y[ind_Z0]), B_sim[ind_Z0, 0],
(xi, yi), method='cubic')
# Setup figure for animation
fig = plt.figure(102, figsize=(7, 20))
plt.subplot(3, 1, 1)
plt.contourf(xi, yi, Bi * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
plt.colorbar()
plt.subplot(3, 1, 2)
plt.contourf(xi, yi, Bi_pod * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
plt.subplot(3, 1, 3)
plt.contourf(xi, yi, Bi_sim * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
# Setup animation object, looping over times corresponding to test data
ani = animation.FuncAnimation(fig, update_toroidal_movie,
range(0, len(t_test)),
fargs=(X, Y, Z, B_true,
B_pod, B_sim, t_test, prefix),
repeat=False,
interval=100,
blit=False)
# Set frames-per-second and save the animation
FPS = 30
ani.save('Pictures/' + prefix + '_toroidal_contour.mp4', fps=FPS, dpi=200)
def make_poloidal_movie(X, Y, Z, B_true, B_pod, B_sim, t_test, prefix):
"""
Function to make a true vs. model movie at the Y=0 cross-section
of any of the field components.
Parameters
----------
X: numpy array of floats
(n_samples = number of volume-sampled locations)
X-coordinate locations of the volume-sampled locations
Y: numpy array of floats
(n_samples = number of volume-sampled locations)
Y-coordinate locations of the volume-sampled locations
Z: numpy array of floats
(n_samples = number of volume-sampled locations)
Z-coordinate locations of the volume-sampled locations
B_true: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The true evolution of a particular field component
at every volume-sampled location
B_pod: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The POD-reconstructed evolution of a particular field component
at every volume-sampled location
B_sim: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The model evolution of a particular field component
at every volume-sampled location
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
prefix: string
(2)
String of the field component being used. For instance,
Bx, By, Bz, Vx, Vy, Vz are all appropriate choices.
"""
R = np.sqrt(X ** 2 + Y ** 2)
# Find where X > 0 and Y = 0 (so a poloidal cross-section)
X0 = np.ravel(np.where(np.array(X) > 0.0))
Y0 = np.isclose(Y, np.ones(len(Y)) * min(abs(Y)), rtol=1e-3, atol=1e-3)
# Get indices with both X > 0 and Y = 0
ind_Y0 = [i for i, p in enumerate(Y0) if p]
ind_Y0 = np.intersect1d(X0, ind_Y0)
# Make (X,Z) mesh
xi = np.linspace(min(X[ind_Y0]), max(X[ind_Y0]))
zi = np.linspace(min(Z[ind_Y0]), max(Z[ind_Y0]))
xi, zi = np.meshgrid(xi, zi)
# Interpolate measurements onto the (xi,zi) mesh
Bi = griddata((X[ind_Y0], Z[ind_Y0]), B_true[ind_Y0, 0],
(xi, zi), method='cubic')
Bi_pod = griddata((X[ind_Y0], Z[ind_Y0]), B_pod[ind_Y0, 0],
(xi, zi), method='cubic')
Bi_sim = griddata((X[ind_Y0], Z[ind_Y0]), B_sim[ind_Y0, 0],
(xi, zi), method='cubic')
# Setup figure for animation
fig = plt.figure(103, figsize=(5, 20))
plt.subplot(3, 1, 1)
plt.contourf(xi, zi, Bi * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
plt.colorbar()
plt.subplot(3, 1, 2)
plt.contourf(xi, zi, Bi_pod * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
plt.subplot(3, 1, 3)
plt.contourf(xi, zi, Bi_sim * 1.0e4, cmap='jet')
ax = plt.gca()
ax.axis('off')
# Setup animation object, looping over times corresponding to testing data
ani = animation.FuncAnimation(fig, update_poloidal_movie,
range(0, len(t_test)),
fargs=(X, Y, Z, B_true, B_pod,
B_sim, t_test, prefix),
repeat=False,
interval=100,
blit=False)
# Set frames-per-second and save animation
FPS = 30
ani.save('Pictures/' + prefix + '_poloidal_contour.mp4', fps=FPS, dpi=200)
def update_poloidal_movie(frame, X, Y, Z, B_true,
B_pod, B_sim, t_test, prefix):
"""
A function for the matplotlib.animation.FuncAnimation object
to update the frame at each timestep. This makes a true vs. model
movie at the Z=0 midplane of any of the field components.
Parameters
----------
frame: int
(1)
A particular frame in the animation
X: numpy array of floats
(n_samples = number of volume-sampled locations)
X-coordinate locations of the volume-sampled locations
Y: numpy array of floats
(n_samples = number of volume-sampled locations)
Y-coordinate locations of the volume-sampled locations
Z: numpy array of floats
(n_samples = number of volume-sampled locations)
Z-coordinate locations of the volume-sampled locations
B_true: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The true evolution of a particular field component
at every volume-sampled location
B_pod: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The POD-reconstructed evolution of a particular field component
at every volume-sampled location
B_sim: 2D numpy array of floats
(n_samples = number of volume-sampled locations,
M_test = number of time samples in the test data region)
The model evolution of a particular field component
at every volume-sampled location
t_test: numpy array of floats
(M_test = number of time samples in the test data region)
Time in microseconds in the test data region
prefix: string
(2)
String of the field component being used. For instance,
Bx, By, Bz, Vx, Vy, Vz are all appropriate choices.
"""
print(frame)
R = np.sqrt(X ** 2 + Y ** 2)
# Find where X > 0 and Y = 0 (so a poloidal cross-section)
X0 = np.ravel(np.where(np.array(X) > 0.0))
Y0 = np.isclose(Y, np.ones(len(Y)) * min(abs(Y)), rtol=1e-3, atol=1e-3)
# Get indices with both X > 0 and Y = 0
ind_Y0 = [i for i, p in enumerate(Y0) if p]
ind_Y0 = np.intersect1d(X0, ind_Y0)
# Make (X,Z) mesh
xi = np.linspace(min(X[ind_Y0]), max(X[ind_Y0]))
zi = np.linspace(min(Z[ind_Y0]), max(Z[ind_Y0]))
xi, zi = np.meshgrid(xi, zi)
# Interpolate measurements onto the (xi,zi) mesh
Bi = griddata((X[ind_Y0], Z[ind_Y0]), B_true[ind_Y0, frame],
(xi, zi), method='cubic')
Bi_pod = griddata((X[ind_Y0], Z[ind_Y0]), B_pod[ind_Y0, frame],
(xi, zi), method='cubic')
Bi_sim = griddata((X[ind_Y0], Z[ind_Y0]), B_sim[ind_Y0, frame],
(xi, zi), method='cubic')
# Clear figure from previous frame
plt.clf()
# Plot data, scaling depending on whether B or V is plotted
fig = plt.figure(103, figsize=(5, 20))
plt.subplot(3, 1, 1)
if prefix[0:2] == 'Bv':
plt.pcolor(xi, zi, Bi * 1.0e4, cmap='jet', vmin=-5e1, vmax=5e1)
else:
plt.pcolor(xi, zi, Bi * 1.0e4, cmap='jet', vmin=-5e2, vmax=5e2)
ax = plt.gca()
ax.axis('off')
plt.subplot(3, 1, 2)
if prefix[0:2] == 'Bv':
plt.pcolor(xi, zi, Bi_pod * 1.0e4, cmap='jet', vmin=-5e1, vmax=5e1)
else:
plt.pcolor(xi, zi, Bi_pod * 1.0e4, cmap='jet', vmin=-5e2, vmax=5e2)
ax = plt.gca()