Notebook source code: notebooks/08_applications_synthetic_grid_cells.ipynb
Analyze Synthetic Grid Cells: Warping#
Imports & setup#
In [2]:
import setup
setup.main()
import os
os.environ["GEOMSTATS_BACKEND"] = "pytorch"
import geomstats.backend as gs
import matplotlib.pyplot as plt
import numpy as np
from geomstats.geometry.pullback_metric import PullbackMetric
from neurometry.curvature.viz import plot_grid_rate_maps, plot_grids
import neurometry.curvature.datasets.gridcells as gridcells
%load_ext autoreload
%autoreload 2
%matplotlib inline
Working directory: /Users/facosta/Desktop/code/neurometry/neurometry
Directory added to path: /Users/facosta/Desktop/code/neurometry
Directory added to path: /Users/facosta/Desktop/code/neurometry/neurometry
Define diffeomorphism \(\varphi: \mathbb{R}^2 \to \mathbb{R}^2\)#
\((x,y) \mapsto ((1 + \frac{\gamma}{(1 + x^2 + y^2)^{\alpha}})x, (1 + \frac{\gamma}{(1 + x^2 + y^2)^{\beta}})y)\)
\(\gamma \in \mathbb{R}, \alpha, \beta \in \mathbb{R}_{+}\) parameterize the deformation
In [3]:
def get_plane_warp(alpha, beta, gamma):
def plane_warp(point):
x = point[0]
y = point[1]
f_x = (1 + gamma / (1 + x**2 + y**2) ** alpha) * x
f_y = (1 + gamma / (1 + x**2 + y**2) ** beta) * y
return gs.array([f_x, f_y])
return plane_warp
In [ ]:
# TODO: define inverse diffop
Instantiate + plot warp#
In [4]:
warp = get_plane_warp(alpha=2, beta=0.1, gamma=-0.4)
In [5]:
x = gs.linspace(-2, 2, 50)
y = gs.linspace(-2, 2, 50)
x_grid, y_grid = gs.meshgrid(x, y)
x_grid_warp, y_grid_warp = warp((x_grid, y_grid))
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111)
ax.scatter(x_grid, y_grid, s=10, label="Template")
ax.scatter(x_grid_warp, y_grid_warp, s=10, label="Warped", c="red")
ax.legend(fontsize="xx-large");
Compute pull-back metric \((\varphi^*g)_{ij} = \partial_{i}\varphi^{a}\partial_{j}\varphi^{b}g_{ab}\)#
In [9]:
# from geomstats.geometry.euclidean import Euclidean
# from geomstats.geometry.pullback_metric import PullbackDiffeoMetric
# class NeuralPullbackDiffeoMetric(PullbackDiffeoMetric):
# def __init__(self):
# super().__init__(space=Euclidean(dim=2))
# def _define_embedding_space(self):
# return Euclidean(dim=2)
# def diffeormorphism(self, base_point):
# return warp(base_point)
# def inverse_diffeormorphism(self, base_point):
# return warp(base_point)
# pullback_diffeo_metric = NeuralPullbackDiffeoMetric()
Quick distance check#
In [33]:
point_a = gs.array([0.0, 0.0])
point_b = gs.array([1.0, 1.0])
pullback_metric.dist(point_a, point_b)
Out [33]:
tensor(0.5221)
Quick metric matrix check#
In [34]:
pullback_metric.metric_matrix(point_a)
Out [34]:
tensor([[0.2500, 0.0000],
[0.0000, 0.2500]])
Plot volume element \(\sqrt{|\text{det}(g)|}\)#
In [45]:
# Combine and reshape the x and y coordinates into a list of 2D points
points = gs.vstack((x_grid.ravel(), y_grid.ravel())).T
# Define your function
def volume_element(x, y):
point = gs.array([x, y])
g = pullback_metric.metric_matrix(point)
return gs.sqrt(gs.abs(gs.linalg.det(g)))
# Apply the function to each point in the list
values = gs.array([volume_element(x, y) for x, y in points])
# Reshape the values back into a 2D grid
z_values = values.reshape(x_grid.shape)
# Create the heatmap
plt.imshow(
z_values, origin="lower", extent=[x.min(), x.max(), y.min(), y.max()], cmap="RdPu"
)
plt.colorbar(label="Function Value")
plt.xlabel("X")
plt.ylabel("Y")
plt.title("Heatmap of volume element at (x, y)")
plt.show()
Synthetic grid cell deformations#
Grid cell parameters#
In [27]:
warp = get_plane_warp(alpha=2, beta=0.1, gamma=-0.4)
grid_scale = 0.6
arena_dims = np.array([4, 4])
n_cells = 1
grid_orientation_mean = 0
grid_orientation_std = 0
field_width = 0.01
resolution = 50
lx = grid_scale
ly = grid_scale * np.sqrt(3) / 2
Create grid + deformed grid#
In [28]:
grids, grids_warped = gridcells.generate_all_grids(
grid_scale,
arena_dims,
n_cells,
grid_orientation_mean,
grid_orientation_std,
warp=warp,
lattice_type="hexagonal",
)
plot_grids(grids, arena_dims)
plot_grids(grids_warped, arena_dims)
In [29]:
rate_maps = gridcells.create_rate_maps(grids, field_width, arena_dims, resolution)
plot_grid_rate_maps(rate_maps)
In [30]:
rate_maps_warped = gridcells.create_rate_maps(
grids_warped, field_width, arena_dims, resolution
)
plot_grid_rate_maps(rate_maps_warped)
Apply LDDMM algorithm to grid cell maps#
In [16]:
import pyLDDMM
from pyLDDMM.utils.visualization import plot_warpgrid
In [17]:
i0 = rate_maps[0]
i1 = rate_maps_warped[0]
In [18]:
lddmm = pyLDDMM.LDDMM2D()
im, v, energies, length, Phi0, Phi1, J0, J1 = lddmm.register(
i0, i1, sigma=0.1, alpha=1, epsilon=0.0001, K=500
)
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iteration 276, energy 347.55, thereof 107.23 regularization and 240.33 intensity difference
iteration 277, energy 347.10, thereof 107.28 regularization and 239.82 intensity difference
iteration 278, energy 346.64, thereof 107.33 regularization and 239.32 intensity difference
iteration 279, energy 346.12, thereof 107.38 regularization and 238.75 intensity difference
iteration 280, energy 345.68, thereof 107.42 regularization and 238.26 intensity difference
iteration 281, energy 345.24, thereof 107.47 regularization and 237.77 intensity difference
iteration 282, energy 344.80, thereof 107.52 regularization and 237.28 intensity difference
iteration 283, energy 344.36, thereof 107.57 regularization and 236.80 intensity difference
iteration 284, energy 343.93, thereof 107.61 regularization and 236.32 intensity difference
iteration 285, energy 343.50, thereof 107.66 regularization and 235.84 intensity difference
iteration 286, energy 343.08, thereof 107.71 regularization and 235.37 intensity difference
iteration 287, energy 342.66, thereof 107.76 regularization and 234.90 intensity difference
iteration 288, energy 342.24, thereof 107.80 regularization and 234.44 intensity difference
iteration 289, energy 341.76, thereof 107.85 regularization and 233.91 intensity difference
iteration 290, energy 341.35, thereof 107.90 regularization and 233.45 intensity difference
iteration 291, energy 340.94, thereof 107.94 regularization and 233.00 intensity difference
iteration 292, energy 340.54, thereof 107.99 regularization and 232.55 intensity difference
iteration 293, energy 340.14, thereof 108.03 regularization and 232.11 intensity difference
iteration 294, energy 339.75, thereof 108.08 regularization and 231.67 intensity difference
iteration 295, energy 339.36, thereof 108.13 regularization and 231.23 intensity difference
iteration 296, energy 338.97, thereof 108.17 regularization and 230.80 intensity difference
iteration 297, energy 338.58, thereof 108.22 regularization and 230.37 intensity difference
iteration 298, energy 338.20, thereof 108.26 regularization and 229.94 intensity difference
iteration 299, energy 337.76, thereof 108.31 regularization and 229.45 intensity difference
iteration 300, energy 337.38, thereof 108.35 regularization and 229.03 intensity difference
iteration 301, energy 337.01, thereof 108.40 regularization and 228.61 intensity difference
iteration 302, energy 336.64, thereof 108.44 regularization and 228.20 intensity difference
iteration 303, energy 336.28, thereof 108.49 regularization and 227.79 intensity difference
iteration 304, energy 335.92, thereof 108.53 regularization and 227.39 intensity difference
iteration 305, energy 335.56, thereof 108.57 regularization and 226.98 intensity difference
iteration 306, energy 335.20, thereof 108.62 regularization and 226.59 intensity difference
iteration 307, energy 334.85, thereof 108.66 regularization and 226.19 intensity difference
iteration 308, energy 334.50, thereof 108.71 regularization and 225.80 intensity difference
iteration 309, energy 334.09, thereof 108.75 regularization and 225.34 intensity difference
iteration 310, energy 333.75, thereof 108.79 regularization and 224.95 intensity difference
iteration 311, energy 333.41, thereof 108.84 regularization and 224.57 intensity difference
iteration 312, energy 333.07, thereof 108.88 regularization and 224.19 intensity difference
iteration 313, energy 332.73, thereof 108.92 regularization and 223.81 intensity difference
iteration 314, energy 332.40, thereof 108.96 regularization and 223.43 intensity difference
iteration 315, energy 332.07, thereof 109.01 regularization and 223.06 intensity difference
iteration 316, energy 331.74, thereof 109.05 regularization and 222.69 intensity difference
iteration 317, energy 331.42, thereof 109.09 regularization and 222.32 intensity difference
iteration 318, energy 331.10, thereof 109.13 regularization and 221.96 intensity difference
iteration 319, energy 330.71, thereof 109.18 regularization and 221.54 intensity difference
iteration 320, energy 330.40, thereof 109.22 regularization and 221.18 intensity difference
iteration 321, energy 330.08, thereof 109.26 regularization and 220.82 intensity difference
iteration 322, energy 329.77, thereof 109.30 regularization and 220.47 intensity difference
iteration 323, energy 329.47, thereof 109.34 regularization and 220.13 intensity difference
iteration 324, energy 329.18, thereof 109.38 regularization and 219.79 intensity difference
iteration 325, energy 328.88, thereof 109.43 regularization and 219.46 intensity difference
iteration 326, energy 328.59, thereof 109.47 regularization and 219.12 intensity difference
iteration 327, energy 328.30, thereof 109.51 regularization and 218.79 intensity difference
iteration 328, energy 328.02, thereof 109.55 regularization and 218.47 intensity difference
iteration 329, energy 327.67, thereof 109.59 regularization and 218.08 intensity difference
iteration 330, energy 327.39, thereof 109.63 regularization and 217.75 intensity difference
iteration 331, energy 327.11, thereof 109.67 regularization and 217.43 intensity difference
iteration 332, energy 326.83, thereof 109.71 regularization and 217.12 intensity difference
iteration 333, energy 326.55, thereof 109.75 regularization and 216.80 intensity difference
iteration 334, energy 326.29, thereof 109.79 regularization and 216.50 intensity difference
iteration 335, energy 326.03, thereof 109.83 regularization and 216.19 intensity difference
iteration 336, energy 325.76, thereof 109.87 regularization and 215.89 intensity difference
iteration 337, energy 325.51, thereof 109.91 regularization and 215.59 intensity difference
iteration 338, energy 325.25, thereof 109.95 regularization and 215.30 intensity difference
iteration 339, energy 324.93, thereof 109.99 regularization and 214.94 intensity difference
iteration 340, energy 324.68, thereof 110.03 regularization and 214.65 intensity difference
iteration 341, energy 324.44, thereof 110.07 regularization and 214.36 intensity difference
iteration 342, energy 324.19, thereof 110.11 regularization and 214.08 intensity difference
iteration 343, energy 323.95, thereof 110.15 regularization and 213.80 intensity difference
iteration 344, energy 323.70, thereof 110.19 regularization and 213.52 intensity difference
iteration 345, energy 323.47, thereof 110.23 regularization and 213.24 intensity difference
iteration 346, energy 323.23, thereof 110.27 regularization and 212.96 intensity difference
iteration 347, energy 322.99, thereof 110.30 regularization and 212.69 intensity difference
iteration 348, energy 322.76, thereof 110.34 regularization and 212.42 intensity difference
iteration 349, energy 322.47, thereof 110.38 regularization and 212.09 intensity difference
iteration 350, energy 322.24, thereof 110.42 regularization and 211.82 intensity difference
iteration 351, energy 322.01, thereof 110.46 regularization and 211.56 intensity difference
iteration 352, energy 321.79, thereof 110.50 regularization and 211.30 intensity difference
iteration 353, energy 321.57, thereof 110.53 regularization and 211.04 intensity difference
iteration 354, energy 321.35, thereof 110.57 regularization and 210.78 intensity difference
iteration 355, energy 321.13, thereof 110.61 regularization and 210.52 intensity difference
iteration 356, energy 320.92, thereof 110.65 regularization and 210.27 intensity difference
iteration 357, energy 320.70, thereof 110.69 regularization and 210.02 intensity difference
iteration 358, energy 320.49, thereof 110.72 regularization and 209.77 intensity difference
iteration 359, energy 320.22, thereof 110.76 regularization and 209.46 intensity difference
iteration 360, energy 320.01, thereof 110.80 regularization and 209.21 intensity difference
iteration 361, energy 319.80, thereof 110.83 regularization and 208.97 intensity difference
iteration 362, energy 319.60, thereof 110.87 regularization and 208.73 intensity difference
iteration 363, energy 319.40, thereof 110.91 regularization and 208.49 intensity difference
iteration 364, energy 319.20, thereof 110.95 regularization and 208.25 intensity difference
iteration 365, energy 319.00, thereof 110.98 regularization and 208.02 intensity difference
iteration 366, energy 318.81, thereof 111.02 regularization and 207.79 intensity difference
iteration 367, energy 318.61, thereof 111.06 regularization and 207.56 intensity difference
iteration 368, energy 318.42, thereof 111.09 regularization and 207.33 intensity difference
iteration 369, energy 318.17, thereof 111.13 regularization and 207.04 intensity difference
iteration 370, energy 317.98, thereof 111.17 regularization and 206.81 intensity difference
iteration 371, energy 317.79, thereof 111.20 regularization and 206.59 intensity difference
iteration 372, energy 317.61, thereof 111.24 regularization and 206.37 intensity difference
iteration 373, energy 317.42, thereof 111.27 regularization and 206.15 intensity difference
iteration 374, energy 317.24, thereof 111.31 regularization and 205.93 intensity difference
iteration 375, energy 317.08, thereof 111.35 regularization and 205.73 intensity difference
iteration 376, energy 316.91, thereof 111.38 regularization and 205.53 intensity difference
iteration 377, energy 316.75, thereof 111.42 regularization and 205.33 intensity difference
iteration 378, energy 316.58, thereof 111.45 regularization and 205.13 intensity difference
iteration 379, energy 316.36, thereof 111.49 regularization and 204.87 intensity difference
iteration 380, energy 316.20, thereof 111.52 regularization and 204.68 intensity difference
iteration 381, energy 316.04, thereof 111.56 regularization and 204.48 intensity difference
iteration 382, energy 315.89, thereof 111.59 regularization and 204.29 intensity difference
iteration 383, energy 315.74, thereof 111.63 regularization and 204.11 intensity difference
iteration 384, energy 315.58, thereof 111.66 regularization and 203.92 intensity difference
iteration 385, energy 315.43, thereof 111.70 regularization and 203.74 intensity difference
iteration 386, energy 315.29, thereof 111.73 regularization and 203.55 intensity difference
iteration 387, energy 315.14, thereof 111.77 regularization and 203.37 intensity difference
iteration 388, energy 315.00, thereof 111.80 regularization and 203.19 intensity difference
iteration 389, energy 314.79, thereof 111.84 regularization and 202.95 intensity difference
iteration 390, energy 314.65, thereof 111.87 regularization and 202.77 intensity difference
iteration 391, energy 314.51, thereof 111.91 regularization and 202.60 intensity difference
iteration 392, energy 314.37, thereof 111.94 regularization and 202.43 intensity difference
iteration 393, energy 314.24, thereof 111.98 regularization and 202.26 intensity difference
iteration 394, energy 314.11, thereof 112.01 regularization and 202.10 intensity difference
iteration 395, energy 313.98, thereof 112.04 regularization and 201.94 intensity difference
iteration 396, energy 313.85, thereof 112.08 regularization and 201.78 intensity difference
iteration 397, energy 313.73, thereof 112.11 regularization and 201.62 intensity difference
iteration 398, energy 313.61, thereof 112.15 regularization and 201.46 intensity difference
iteration 399, energy 313.43, thereof 112.18 regularization and 201.25 intensity difference
iteration 400, energy 313.32, thereof 112.21 regularization and 201.10 intensity difference
iteration 401, energy 313.21, thereof 112.25 regularization and 200.96 intensity difference
iteration 402, energy 313.10, thereof 112.28 regularization and 200.82 intensity difference
iteration 403, energy 312.99, thereof 112.31 regularization and 200.67 intensity difference
iteration 404, energy 312.88, thereof 112.35 regularization and 200.53 intensity difference
iteration 405, energy 312.78, thereof 112.38 regularization and 200.39 intensity difference
iteration 406, energy 312.67, thereof 112.41 regularization and 200.26 intensity difference
iteration 407, energy 312.57, thereof 112.45 regularization and 200.12 intensity difference
iteration 408, energy 312.47, thereof 112.48 regularization and 199.99 intensity difference
iteration 409, energy 312.30, thereof 112.51 regularization and 199.79 intensity difference
iteration 410, energy 312.20, thereof 112.55 regularization and 199.66 intensity difference
iteration 411, energy 312.11, thereof 112.58 regularization and 199.53 intensity difference
iteration 412, energy 312.01, thereof 112.61 regularization and 199.40 intensity difference
iteration 413, energy 311.92, thereof 112.65 regularization and 199.27 intensity difference
iteration 414, energy 311.83, thereof 112.68 regularization and 199.15 intensity difference
iteration 415, energy 311.74, thereof 112.71 regularization and 199.02 intensity difference
iteration 416, energy 311.65, thereof 112.74 regularization and 198.90 intensity difference
iteration 417, energy 311.56, thereof 112.78 regularization and 198.78 intensity difference
iteration 418, energy 311.47, thereof 112.81 regularization and 198.66 intensity difference
iteration 419, energy 311.32, thereof 112.84 regularization and 198.48 intensity difference
iteration 420, energy 311.24, thereof 112.87 regularization and 198.36 intensity difference
iteration 421, energy 311.15, thereof 112.91 regularization and 198.25 intensity difference
iteration 422, energy 311.07, thereof 112.94 regularization and 198.13 intensity difference
iteration 423, energy 310.99, thereof 112.97 regularization and 198.02 intensity difference
iteration 424, energy 310.92, thereof 113.00 regularization and 197.92 intensity difference
iteration 425, energy 310.85, thereof 113.03 regularization and 197.81 intensity difference
iteration 426, energy 310.77, thereof 113.07 regularization and 197.71 intensity difference
iteration 427, energy 310.70, thereof 113.10 regularization and 197.61 intensity difference
iteration 428, energy 310.64, thereof 113.13 regularization and 197.51 intensity difference
iteration 429, energy 310.50, thereof 113.16 regularization and 197.34 intensity difference
iteration 430, energy 310.43, thereof 113.19 regularization and 197.24 intensity difference
iteration 431, energy 310.37, thereof 113.22 regularization and 197.15 intensity difference
iteration 432, energy 310.31, thereof 113.26 regularization and 197.05 intensity difference
iteration 433, energy 310.25, thereof 113.29 regularization and 196.96 intensity difference
iteration 434, energy 310.18, thereof 113.32 regularization and 196.87 intensity difference
iteration 435, energy 310.11, thereof 113.35 regularization and 196.76 intensity difference
iteration 436, energy 310.04, thereof 113.38 regularization and 196.66 intensity difference
iteration 437, energy 309.98, thereof 113.41 regularization and 196.56 intensity difference
iteration 438, energy 309.91, thereof 113.44 regularization and 196.47 intensity difference
iteration 439, energy 309.79, thereof 113.47 regularization and 196.32 intensity difference
iteration 440, energy 309.73, thereof 113.51 regularization and 196.23 intensity difference
iteration 441, energy 309.68, thereof 113.54 regularization and 196.14 intensity difference
iteration 442, energy 309.62, thereof 113.57 regularization and 196.06 intensity difference
iteration 443, energy 309.57, thereof 113.60 regularization and 195.97 intensity difference
iteration 444, energy 309.52, thereof 113.63 regularization and 195.89 intensity difference
iteration 445, energy 309.47, thereof 113.66 regularization and 195.81 intensity difference
iteration 446, energy 309.42, thereof 113.69 regularization and 195.73 intensity difference
iteration 447, energy 309.37, thereof 113.72 regularization and 195.65 intensity difference
iteration 448, energy 309.32, thereof 113.75 regularization and 195.57 intensity difference
iteration 449, energy 309.21, thereof 113.78 regularization and 195.43 intensity difference
iteration 450, energy 309.17, thereof 113.81 regularization and 195.36 intensity difference
iteration 451, energy 309.12, thereof 113.84 regularization and 195.28 intensity difference
iteration 452, energy 309.08, thereof 113.87 regularization and 195.21 intensity difference
iteration 453, energy 309.04, thereof 113.90 regularization and 195.14 intensity difference
iteration 454, energy 309.00, thereof 113.93 regularization and 195.07 intensity difference
iteration 455, energy 308.96, thereof 113.96 regularization and 195.00 intensity difference
iteration 456, energy 308.92, thereof 113.99 regularization and 194.93 intensity difference
iteration 457, energy 308.89, thereof 114.02 regularization and 194.86 intensity difference
iteration 458, energy 308.85, thereof 114.05 regularization and 194.80 intensity difference
iteration 459, energy 308.75, thereof 114.08 regularization and 194.67 intensity difference
iteration 460, energy 308.71, thereof 114.11 regularization and 194.60 intensity difference
iteration 461, energy 308.68, thereof 114.14 regularization and 194.54 intensity difference
iteration 462, energy 308.65, thereof 114.17 regularization and 194.48 intensity difference
iteration 463, energy 308.62, thereof 114.20 regularization and 194.42 intensity difference
iteration 464, energy 308.59, thereof 114.23 regularization and 194.36 intensity difference
iteration 465, energy 308.56, thereof 114.26 regularization and 194.30 intensity difference
iteration 466, energy 308.54, thereof 114.29 regularization and 194.25 intensity difference
iteration 467, energy 308.52, thereof 114.32 regularization and 194.20 intensity difference
iteration 468, energy 308.50, thereof 114.35 regularization and 194.15 intensity difference
iteration 469, energy 308.40, thereof 114.38 regularization and 194.03 intensity difference
iteration 470, energy 308.38, thereof 114.41 regularization and 193.98 intensity difference
iteration 471, energy 308.36, thereof 114.44 regularization and 193.93 intensity difference
iteration 472, energy 308.35, thereof 114.46 regularization and 193.88 intensity difference
iteration 473, energy 308.33, thereof 114.49 regularization and 193.84 intensity difference
iteration 474, energy 308.32, thereof 114.52 regularization and 193.79 intensity difference
iteration 475, energy 308.30, thereof 114.55 regularization and 193.75 intensity difference
iteration 476, energy 308.29, thereof 114.58 regularization and 193.71 intensity difference
iteration 477, energy 308.28, thereof 114.61 regularization and 193.67 intensity difference
iteration 478, energy 308.26, thereof 114.64 regularization and 193.63 intensity difference
iteration 479, energy 308.19, thereof 114.67 regularization and 193.52 intensity difference
iteration 480, energy 308.18, thereof 114.70 regularization and 193.48 intensity difference
iteration 481, energy 308.17, thereof 114.72 regularization and 193.44 intensity difference
iteration 482, energy 308.16, thereof 114.75 regularization and 193.41 intensity difference
iteration 483, energy 308.15, thereof 114.78 regularization and 193.37 intensity difference
iteration 484, energy 308.15, thereof 114.81 regularization and 193.34 intensity difference
iteration 485, energy 308.14, thereof 114.84 regularization and 193.30 intensity difference
iteration 486, energy 308.14, thereof 114.87 regularization and 193.27 intensity difference
iteration 487, energy 308.14, thereof 114.90 regularization and 193.24 intensity difference
iteration 488, energy 308.13, thereof 114.92 regularization and 193.21 intensity difference
iteration 489, energy 308.06, thereof 114.95 regularization and 193.11 intensity difference
iteration 490, energy 308.06, thereof 114.98 regularization and 193.08 intensity difference
iteration 491, energy 308.06, thereof 115.01 regularization and 193.05 intensity difference
iteration 492, energy 308.06, thereof 115.04 regularization and 193.03 intensity difference
iteration 493, energy 308.07, thereof 115.06 regularization and 193.00 intensity difference
iteration 494, energy 308.07, thereof 115.09 regularization and 192.98 intensity difference
iteration 495, energy 308.07, thereof 115.12 regularization and 192.95 intensity difference
iteration 496, energy 308.08, thereof 115.15 regularization and 192.93 intensity difference
iteration 497, energy 308.08, thereof 115.18 regularization and 192.91 intensity difference
iteration 498, energy 308.09, thereof 115.20 regularization and 192.88 intensity difference
iteration 499, energy 308.02, thereof 115.23 regularization and 192.79 intensity difference
In [25]:
plot = plot_warpgrid(Phi0[-1], interval=1)
In [ ]: