Note
Go to the end to download the full example code.
Fourier Continuation
An example of usage of our Fourier continuation layer on 1d, 2d, and 3d data.
Import the library
We first import our neuralop library and required dependencies.
import torch
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from mpl_toolkits.mplot3d import Axes3D
from neuralop.layers.fourier_continuation import FCLegendre, FCGram
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
Creating an example of 1D curve
Here we consider sin(16x) - cos(8x), which is not periodic on the interval [0,1]
length_signal = 101 # length of the original 1D signal
add_pts = 50 # number of points to add
batch_size = 3 # the Fourier continuation layer can be applied to batches of signals
x = torch.linspace(0, 1, length_signal).repeat(batch_size,1)
f = torch.sin(16 * x) - torch.cos(8 * x)
Extending the signal
We use the FC-Legendre and FC-Gram Fourier continuation layers to extend the signal. We try both extending the signal on one side (right) and on both sides (left and right)
Extension_Legendre = FCLegendre(d=2, n_additional_pts=add_pts)
f_extend_one_side_Legendre = Extension_Legendre(f, dim=1, one_sided=True)
f_extend_both_sides_Legendre = Extension_Legendre(f, dim=1, one_sided=False)
Extension_Gram = FCGram(d=3, n_additional_pts=add_pts)
f_extend_one_side_Gram = Extension_Gram(f, dim=1, one_sided=True)
f_extend_both_sides_Gram = Extension_Gram(f, dim=1, one_sided=False)
Plot the FC-Legendre results
# Define the extended coordinates
x_extended_one_side = torch.linspace(0, 1.5, 151)
x_extended_both_sides = torch.linspace(-0.25, 1.25, 151)
# Add 0.6 and -0.6 to the extended functions for visualization purposes
f_extend_one_side_Legendre = f_extend_one_side_Legendre + 0.6
f_extend_both_sides_Legendre = f_extend_both_sides_Legendre - 0.6
plt.figure(figsize=(14, 5))
plt.plot(x[0], f[0], 'k', label='Original Function', lw=2.2)
plt.plot(x_extended_one_side, f_extend_one_side_Legendre[0] , 'b',label='One-sided Extension', lw=2.2)
plt.plot(x_extended_both_sides, f_extend_both_sides_Legendre[0] , 'g', label='Two-sided Extension', lw=2.2)
plt.plot([0, 0], [-2.7, 1.8], '-', color='gray', lw=1.5)
plt.plot([1, 1], [-2.7, 1.8], '-', color='gray', lw=1.5)
plt.plot([0, 1.5], [f_extend_one_side_Legendre[0,0],f_extend_one_side_Legendre[0,0]], '--', color='b', lw=1.4)
plt.plot([-0.25, 1.25], [f_extend_both_sides_Legendre[0,0],f_extend_both_sides_Legendre[0,0]], '--', color='g', lw=1.4)
legend_elements = [
Line2D([0], [0], color='none', label='FC-Legendre'),
Line2D([0], [0], color='k', lw=2.2, label='Original Function'),
Line2D([0], [0], color='b', lw=2.2, label='One-sided Extension'),
Line2D([0], [0], color='g', lw=2.2, label='Two-sided Extension')
]
legend = plt.legend(handles=legend_elements, fontsize=19)
plt.xlim([-0.28, 1.56])
plt.ylim([-3.05, 2.7])
legend.get_texts()[0].set_fontweight('bold')
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.tick_params(axis='x', which='major', labelsize=19)
ax.tick_params(axis='y', which='major', labelsize=19)
plt.xticks([-0.25,0,1,1.25, 1.5])
plt.yticks([-2,2])
plt.tight_layout()
plt.show()
Plot the FC-Gram results
# Define the extended coordinates
x_extended_one_side = torch.linspace(0, 1.5, 151)
x_extended_both_sides = torch.linspace(-0.25, 1.25, 151)
# Add 0.6 and -0.6 to the extended functions for visualization purposes
f_extend_one_side_Gram = f_extend_one_side_Gram + 0.6
f_extend_both_sides_Gram = f_extend_both_sides_Gram - 0.6
plt.figure(figsize=(14, 5))
plt.plot(x[0], f[0], 'k', label='Original Function', lw=2.2)
plt.plot(x_extended_one_side, f_extend_one_side_Gram[0] , 'b',label='One-sided Extension', lw=2.2)
plt.plot(x_extended_both_sides, f_extend_both_sides_Gram[0] , 'g', label='Two-sided Extension', lw=2.2)
plt.plot([0, 0], [-2.7, 1.8], '-', color='gray', lw=1.5)
plt.plot([1, 1], [-2.7, 1.8], '-', color='gray', lw=1.5)
plt.plot([0, 1.5], [f_extend_one_side_Gram[0,0],f_extend_one_side_Gram[0,0]], '--', color='b', lw=1.4)
plt.plot([-0.25, 1.25], [f_extend_both_sides_Gram[0,0],f_extend_both_sides_Gram[0,0]], '--', color='g', lw=1.4)
legend_elements = [
Line2D([0], [0], color='none', label='FC-Gram'),
Line2D([0], [0], color='k', lw=2.2, label='Original Function'),
Line2D([0], [0], color='b', lw=2.2, label='One-sided Extension'),
Line2D([0], [0], color='g', lw=2.2, label='Two-sided Extension')
]
legend = plt.legend(handles=legend_elements, fontsize=19)
plt.xlim([-0.28, 1.56])
plt.ylim([-2.95, 3.1])
legend.get_texts()[0].set_fontweight('bold')
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.tick_params(axis='x', which='major', labelsize=19)
ax.tick_params(axis='y', which='major', labelsize=19)
plt.xticks([-0.25,0,1,1.25,1.5])
plt.yticks([-2,2])
plt.tight_layout()
plt.show()
Creating an example of a 2D function
Here we consider sin(12x) - cos(14y) + 3xy, which is not periodic on [0,1]x[0,1]
length_signal = 101 # length of the signal in each dimension
add_pts = 50 # number of points to add in each dimension
batch_size = 3 # the Fourier continuation layer can be applied to batches of signals
x = torch.linspace(0, 1, length_signal).view(1, length_signal, 1).repeat(batch_size, 1, length_signal)
y = torch.linspace(0, 1, length_signal).view(1, 1, length_signal).repeat(batch_size, length_signal, 1)
f = torch.sin(12 * x) - torch.cos(14 * y) + 3*x*y
Extending the signal
We use the FC-Legendre and FC-Gram Fourier continuation layers to extend the signal. We try both extending the signal on one side (right and bottom) and on both sides (left, right, top, and bottom)
Extension_Legendre = FCLegendre(d=3, n_additional_pts=add_pts)
f_extend_one_side_Legendre = Extension_Legendre(f, dim=2, one_sided=True)
f_extend_both_sides_Legendre = Extension_Legendre(f, dim=2, one_sided=False)
Extension_Gram = FCGram(d=3, n_additional_pts=add_pts)
f_extend_one_side_Gram = Extension_Gram(f, dim=2, one_sided=True)
f_extend_both_sides_Gram = Extension_Gram(f, dim=2, one_sided=False)
Plot the FC-Legendre results
We also add black lines to deliminate the original signal
fig, axs = plt.subplots(figsize=(14,6), nrows=1, ncols=3)
axs[0].imshow(f[0])
axs[0].set_title(r"Original Function", fontsize=15.5)
axs[1].imshow(f_extend_one_side_Legendre[0])
axs[1].plot([length_signal, length_signal], [0, length_signal], '-', color='k', lw=3)
axs[1].plot([0, length_signal], [length_signal, length_signal], '-', color='k', lw=3)
axs[1].set_title(r"FC-Legendre One-sided Extension", fontsize=15.5)
axs[2].set_title(r"FC-Legendre Two-sided Extension", fontsize=15.5)
axs[2].imshow(f_extend_both_sides_Legendre[0])
axs[2].plot([add_pts//2, length_signal + add_pts//2], [add_pts//2, add_pts//2], '-', color='k', lw=3)
axs[2].plot([add_pts//2, add_pts//2], [add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
axs[2].plot([add_pts//2, length_signal + add_pts//2], [length_signal + add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
axs[2].plot([length_signal + add_pts//2, length_signal + add_pts//2], [add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
for ax in axs.flat:
ax.set_xticks([])
ax.set_yticks([])
plt.show()
Plot the FC-Gram results
We also add black lines to deliminate the original signal
fig, axs = plt.subplots(figsize=(14,6), nrows=1, ncols=3)
axs[0].imshow(f[0])
axs[0].set_title(r"Original Function", fontsize=15.5)
axs[1].imshow(f_extend_one_side_Gram[0])
axs[1].plot([length_signal, length_signal], [0, length_signal], '-', color='k', lw=3)
axs[1].plot([0, length_signal], [length_signal, length_signal], '-', color='k', lw=3)
axs[1].set_title(r"FC-Gram One-sided Extension", fontsize=15.5)
axs[2].set_title(r"FC-Gram Two-sided Extension", fontsize=15.5)
axs[2].imshow(f_extend_both_sides_Gram[0])
axs[2].plot([add_pts//2, length_signal + add_pts//2], [add_pts//2, add_pts//2], '-', color='k', lw=3)
axs[2].plot([add_pts//2, add_pts//2], [add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
axs[2].plot([add_pts//2, length_signal + add_pts//2], [length_signal + add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
axs[2].plot([length_signal + add_pts//2, length_signal + add_pts//2], [add_pts//2, length_signal + add_pts//2], '-', color='k', lw=3)
for ax in axs.flat:
ax.set_xticks([])
ax.set_yticks([])
plt.show()
Creating an example of a 3D function
Here we consider f(x,y,z) = exp(-2z) + 2xz + sin(12xy) + y sin(10yz) which is not periodic on [0,1]x[0,1]x[0,1]
batch_size = 2
length_signal = 101
add_pts = 50
# Create 3D grid
x = torch.linspace(0, 1, length_signal).view(1, length_signal, 1, 1).repeat(batch_size, 1, length_signal, length_signal)
y = torch.linspace(0, 1, length_signal).view(1, 1, length_signal, 1).repeat(batch_size, length_signal, 1, length_signal)
z = torch.linspace(0, 1, length_signal).view(1, 1, 1, length_signal).repeat(batch_size, length_signal, length_signal, 1)
# Create 3D function
f = torch.exp(-2*z) + 2*z*x + torch.sin(12*x*y) + y*torch.sin(10*y*z)
Extending the signal
We use the FC-Legendre and FC-Gram Fourier continuation layers to extend the signal. We try both extending the signal on one side (right, bottom, back) and on both sides (left, right, top, bottom, back, front)
Extension_Legendre = FCLegendre(d=3, n_additional_pts=add_pts)
f_extend_one_side_Legendre = Extension_Legendre(f, dim=3, one_sided=True)
f_extend_both_sides_Legendre = Extension_Legendre(f, dim=3, one_sided=False)
Extension_Gram = FCGram(d=3, n_additional_pts=add_pts)
f_extend_one_side_Gram = Extension_Gram(f, dim=3, one_sided=True)
f_extend_both_sides_Gram = Extension_Gram(f, dim=3, one_sided=False)
Plot the FC-Legendre results
We also add white lines to deliminate the original signal
f_min = f.min().item()
f_max = f.max().item()
f_ext1_min = f_extend_one_side_Legendre.min().item()
f_ext1_max = f_extend_one_side_Legendre.max().item()
f_ext2_min = f_extend_both_sides_Legendre.min().item()
f_ext2_max = f_extend_both_sides_Legendre.max().item()
global_min = min(f_min, f_ext1_min, f_ext2_min)
global_max = max(f_max, f_ext1_max, f_ext2_max)
Figure for X slices
fig = plt.figure(figsize=(20, 15))
fig.suptitle('FC-Legendre 3D Examples: X-Slices', fontsize=24, fontweight='bold', y=0.98)
slice_indices = [length_signal//4, length_signal//2, 3*length_signal//4]
slice_names = ['First Quarter', 'Middle', 'Third Quarter']
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
ax = fig.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# One-sided extension - X-slice
ax = fig.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Legendre[0, idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# Two-sided extension - X-slice
ax = fig.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Legendre[0, ext_idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Figure for Y-slices
fig2 = plt.figure(figsize=(20, 15))
fig2.suptitle('FC-Legendre 3D Examples: Y-Slices', fontsize=24, fontweight='bold', y=0.98)
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
# Original function - Y-slice
ax = fig2.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, :, idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# One-sided extension - Y-slice
ax = fig2.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Legendre[0, :, idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# Two-sided extension - Y-slice
ax = fig2.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Legendre[0, :, ext_idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Figure for Z-slices
fig3 = plt.figure(figsize=(20, 15))
fig3.suptitle('FC-Legendre 3D Examples: Z-Slices', fontsize=24, fontweight='bold', y=0.98)
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
# Original function - Z-slice
ax = fig3.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, :, :, idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# One-sided extension - Z-slice
ax = fig3.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Legendre[0, :, :, idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
# Two-sided extension - Z-slice
ax = fig3.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Legendre[0, :, :, ext_idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Plot the FC-Gram results
We also add white lines to deliminate the original signal
f_min = f.min().item()
f_max = f.max().item()
f_ext1_min = f_extend_one_side_Gram.min().item()
f_ext1_max = f_extend_one_side_Gram.max().item()
f_ext2_min = f_extend_both_sides_Gram.min().item()
f_ext2_max = f_extend_both_sides_Gram.max().item()
global_min = min(f_min, f_ext1_min, f_ext2_min)
global_max = max(f_max, f_ext1_max, f_ext2_max)
Figure for X slices
fig = plt.figure(figsize=(20, 15))
fig.suptitle('FC-Gram 3D Examples: X-Slices', fontsize=24, fontweight='bold', y=0.98)
slice_indices = [length_signal//4, length_signal//2, 3*length_signal//4]
slice_names = ['First Quarter', 'Middle', 'Third Quarter']
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
ax = fig.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Gram[0, idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Gram[0, ext_idx, :, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: X-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('Y', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Figure for Y-slices
fig2 = plt.figure(figsize=(20, 15))
fig2.suptitle('FC-Gram 3D Examples: Y-Slices', fontsize=24, fontweight='bold', y=0.98)
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
ax = fig2.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, :, idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig2.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Gram[0, :, idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig2.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Gram[0, :, ext_idx, :].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: Y-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Z', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Figure for Z-slices
fig3 = plt.figure(figsize=(20, 15))
fig3.suptitle('FC-Gram 3D Examples: Z-Slices', fontsize=24, fontweight='bold', y=0.98)
for i, (idx, name) in enumerate(zip(slice_indices, slice_names)):
ax = fig3.add_subplot(3, 3, i+1)
im = ax.imshow(f[0, :, :, idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Original: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig3.add_subplot(3, 3, i+4)
im = ax.imshow(f_extend_one_side_Gram[0, :, :, idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'One-sided: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
# Draw boundary lines
ax.axhline(y=length_signal, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
ax = fig3.add_subplot(3, 3, i+7)
ext_idx = idx + add_pts//2
im = ax.imshow(f_extend_both_sides_Gram[0, :, :, ext_idx].numpy(), cmap='viridis', aspect='auto', vmin=global_min, vmax=global_max)
ax.set_title(f'Two-sided: Z-slice {name}', fontsize=22, fontweight='bold')
ax.set_xlabel('X', fontsize=20)
ax.set_ylabel('Y', fontsize=20)
# Draw boundary lines
ax.axhline(y=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axhline(y=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=add_pts//2, color='white', linewidth=2, linestyle='-')
ax.axvline(x=length_signal + add_pts//2, color='white', linewidth=2, linestyle='-')
ax.set_xticks([])
ax.set_yticks([])
cbar = plt.colorbar(im, ax=ax)
cbar.ax.tick_params(labelsize=18)
plt.subplots_adjust(hspace=0.3, wspace=0.2, top=0.92)
plt.show()
Total running time of the script: (0 minutes 3.951 seconds)