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import torch |
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import numpy as np |
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import matplotlib.pyplot as plt |
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from gmm import GaussianMixtureModel |
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def initialize_gmm(mu_list, Sigma_list, pi_list): |
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mu = torch.tensor(mu_list, dtype=torch.float32) |
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Sigma = torch.tensor(Sigma_list, dtype=torch.float32) |
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pi = torch.tensor(pi_list, dtype=torch.float32) |
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return GaussianMixtureModel(mu, Sigma, pi) |
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def generate_grid(dx): |
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x_positions = np.arange(-10, 10.5, 0.5) |
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y_positions = np.arange(-10, 10.5, 0.5) |
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fine_points = np.arange(-10, 10 + dx, dx) |
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ones_same_size = np.ones_like(fine_points) |
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vertical_lines = [np.stack([x*ones_same_size, fine_points], axis=1) for x in x_positions] |
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horizontal_lines = [np.stack([fine_points, y*ones_same_size], axis=1) for y in y_positions] |
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grid_points = np.concatenate(vertical_lines + horizontal_lines, axis=0) |
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return torch.tensor(grid_points, dtype=torch.float32) |
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def generate_contours(dtheta): |
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angles = np.linspace(0, 2 * np.pi, int(2 * np.pi / dtheta)) |
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std_normal_contours = np.concatenate([np.stack([r * np.cos(angles), r * np.sin(angles)], axis=1) for r in range(1, 4)], axis=0) |
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return torch.tensor(std_normal_contours, dtype=torch.float32) |
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def transform_std_to_gmm_contours(std_contours, mu, Sigma): |
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gmm_contours = [] |
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for k in range(mu.shape[0]): |
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L = torch.linalg.cholesky(Sigma[k]) |
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gmm_contours.append(mu[k] + torch.matmul(std_contours, L.T)) |
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return torch.cat(gmm_contours, dim=0) |
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def generate_intermediate_points(gmm, grid_points, std_normal_contours, gmm_samples, normal_samples, T, N): |
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gmm_contours = transform_std_to_gmm_contours(std_normal_contours, gmm.mu.squeeze(), gmm.Sigma) |
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intermediate_points_gmm_to_normal = gmm.flow_gmm_to_normal(gmm_samples.clone(), T, N) |
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contour_intermediate_points_gmm_to_normal = gmm.flow_gmm_to_normal(gmm_contours.clone(), T, N) |
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grid_intermediate_points_gmm_to_normal = gmm.flow_gmm_to_normal(grid_points.clone(), T, N) |
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intermediate_points_normal_to_gmm = gmm.flow_normal_to_gmm(normal_samples.clone(), T, N) |
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contour_intermediate_points_normal_to_gmm = gmm.flow_normal_to_gmm(std_normal_contours.clone(), T, N) |
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grid_intermediate_points_normal_to_gmm = gmm.flow_normal_to_gmm(grid_points.clone(), T, N) |
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return (intermediate_points_gmm_to_normal, contour_intermediate_points_gmm_to_normal, grid_intermediate_points_gmm_to_normal, |
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intermediate_points_normal_to_gmm, contour_intermediate_points_normal_to_gmm, grid_intermediate_points_normal_to_gmm) |
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def plot_samples_and_contours(samples, contours, grid_points, title): |
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fig, ax = plt.subplots(figsize=(8, 6)) |
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ax.scatter(grid_points[:, 0], grid_points[:, 1], alpha=0.5, c='black', s=1, label='Grid Points') |
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ax.scatter(contours[:, 0], contours[:, 1], alpha=0.5, s=3, c='blue', label='Contours') |
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ax.scatter(samples[:, 0], samples[:, 1], alpha=0.5, c='red', label='Samples') |
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ax.set_title(title) |
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ax.set_xlabel("x1") |
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ax.set_ylabel("x2") |
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ax.grid(True) |
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ax.legend(loc='upper right') |
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ax.set_xlim(-5, 5) |
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ax.set_ylim(-5, 5) |
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ax.set_aspect('equal', adjustable='box') |
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plt.close(fig) |
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return fig, ax |
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