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import matplotlib.animation as animation |
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import matplotlib.pyplot as plt |
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import torch |
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from functorch.dim import tree_flatten, tree_map |
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import logging |
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""" |
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Helpers for various PyTests. |
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""" |
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def prune_boundary(array, dim): |
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""" |
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Prune the boundary of an array. |
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""" |
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if dim == 0: |
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return array[1:-2] |
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elif dim == 1: |
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return array[:, 1:-2] |
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elif dim == 2: |
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return array[:, :, 1:-2] |
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elif dim == 3: |
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return array[:, :, :, 1:-2] |
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else: |
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raise ValueError("Invalid dimension.") |
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def array_difference_less_than(a, b, val): |
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""" |
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Check if all elements in A - B are less than val. |
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""" |
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return torch.all((a - b) < val) |
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def generate_synthetic_data_1d(batch_size=4, Nx=100, Nt=1024): |
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""" |
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Generate synthetic data for 1D reaction diffusion. |
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""" |
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x = torch.linspace(0, 1, Nx) |
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t = torch.linspace(0, 1, Nt) |
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tt, xx = torch.meshgrid(t, x) |
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u = torch.sin(xx) * torch.cos(tt) |
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du_dx = torch.cos(tt) * torch.cos(xx) |
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du_dt = -torch.sin(tt) * torch.sin(xx) |
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ddu_dxx = -torch.cos(tt) * torch.sin(xx) |
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du_sqr_dx = 2 * (torch.cos(tt) ** 2) * torch.sin(xx) * torch.cos(xx) |
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u = u.repeat(batch_size, 1, 1) |
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du_dx = du_dx.repeat(batch_size, 1, 1) |
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du_dt = du_dt.repeat(batch_size, 1, 1) |
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ddu_dxx = ddu_dxx.repeat(batch_size, 1, 1) |
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du_sqr_dx = du_sqr_dx.repeat(batch_size, 1, 1) |
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return x, t, u, du_dx, du_dt, ddu_dxx, du_sqr_dx |
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def generate_synthetic_data_2d(batch_size=4, Nx=100, Ny=100, Nt=1024): |
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""" |
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Generate synthetic data to test 2D finite differences. (3D including time). |
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""" |
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x = torch.linspace(0, 1, Nx) |
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y = torch.linspace(0, 1, Ny) |
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t = torch.linspace(0, 1, Nt) |
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tt, xx, yy = torch.meshgrid(t, x, y) |
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u = torch.cos(tt) * torch.sin(xx) * y * y |
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du_dx = y * y * torch.cos(tt) * torch.cos(xx) |
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du_dy = 2 * y * torch.cos(tt) * torch.sin(xx) |
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ddu_dxx = -(y * y) * torch.cos(tt) * torch.sin(xx) |
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ddu_dyy = 2 * torch.cos(tt) * torch.sin(xx) |
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du_dt = -y * y * torch.sin(tt) * torch.sin(xx) |
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u = u.repeat(batch_size, 1, 1, 1) |
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du_dx = du_dx.repeat(batch_size, 1, 1, 1) |
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du_dy = du_dy.repeat(batch_size, 1, 1, 1) |
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ddu_dxx = ddu_dxx.repeat(batch_size, 1, 1, 1) |
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ddu_dyy = ddu_dyy.repeat(batch_size, 1, 1, 1) |
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du_dt = du_dt.repeat(batch_size, 1, 1, 1) |
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return x, y, t, u, du_dx, du_dy, ddu_dxx, ddu_dyy, du_dt |
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def create_gif_and_save(data, filename, title, cmap="magma", interval=50): |
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""" |
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Create a gif from a list of images and save it. |
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:param data: list of frames |
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:param filename: location to save gif |
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:param title: title of the gif |
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:param cmap: colormap |
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:param interval: interval between frames |
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""" |
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vmin = data.min() |
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vmax = data.max() |
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fig, ax = plt.subplots() |
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im = ax.imshow(data[0], animated=True, cmap=cmap, vmin=vmin, vmax=vmax) |
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ax.set_title(title) |
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fig.colorbar(im) |
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def _update(i): |
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im.set_array(data[i]) |
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return (im,) |
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animation_fig = animation.FuncAnimation( |
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fig, |
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_update, |
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frames=len(data), |
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interval=interval, |
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blit=True, |
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repeat_delay=10, |
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) |
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try: |
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animation_fig.save(filename, writer="pillow") |
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except Exception as e: |
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print(f"Pillow writer failed, trying imagemagick: {e}") |
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animation_fig.save(filename, writer="imagemagick") |
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finally: |
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plt.close(fig) |
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