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| import numpy as np | |
| import tqdm | |
| import os | |
| """ | |
| Preprocessing for the SO(2)/torus sampling and score computations, truncated infinite series are computed and then | |
| cached to memory, therefore the precomputation is only run the first time the repository is run on a machine | |
| """ | |
| def p(x, sigma, N=10): | |
| p_ = 0 | |
| for i in tqdm.trange(-N, N + 1): | |
| p_ += np.exp(-(x + 2 * np.pi * i) ** 2 / 2 / sigma ** 2) | |
| return p_ | |
| def grad(x, sigma, N=10): | |
| p_ = 0 | |
| for i in tqdm.trange(-N, N + 1): | |
| p_ += (x + 2 * np.pi * i) / sigma ** 2 * np.exp(-(x + 2 * np.pi * i) ** 2 / 2 / sigma ** 2) | |
| return p_ | |
| X_MIN, X_N = 1e-5, 5000 # relative to pi | |
| SIGMA_MIN, SIGMA_MAX, SIGMA_N = 3e-3, 2, 5000 # relative to pi | |
| x = 10 ** np.linspace(np.log10(X_MIN), 0, X_N + 1) * np.pi | |
| sigma = 10 ** np.linspace(np.log10(SIGMA_MIN), np.log10(SIGMA_MAX), SIGMA_N + 1) * np.pi | |
| if os.path.exists('.p.npy'): | |
| p_ = np.load('.p.npy') | |
| score_ = np.load('.score.npy') | |
| else: | |
| p_ = p(x, sigma[:, None], N=100) | |
| np.save('.p.npy', p_) | |
| score_ = grad(x, sigma[:, None], N=100) / p_ | |
| np.save('.score.npy', score_) | |
| def score(x, sigma): | |
| x = (x + np.pi) % (2 * np.pi) - np.pi | |
| sign = np.sign(x) | |
| x = np.log(np.abs(x) / np.pi) | |
| x = (x - np.log(X_MIN)) / (0 - np.log(X_MIN)) * X_N | |
| x = np.round(np.clip(x, 0, X_N)).astype(int) | |
| sigma = np.log(sigma / np.pi) | |
| sigma = (sigma - np.log(SIGMA_MIN)) / (np.log(SIGMA_MAX) - np.log(SIGMA_MIN)) * SIGMA_N | |
| sigma = np.round(np.clip(sigma, 0, SIGMA_N)).astype(int) | |
| return -sign * score_[sigma, x] | |
| def p(x, sigma): | |
| x = (x + np.pi) % (2 * np.pi) - np.pi | |
| x = np.log(np.abs(x) / np.pi) | |
| x = (x - np.log(X_MIN)) / (0 - np.log(X_MIN)) * X_N | |
| x = np.round(np.clip(x, 0, X_N)).astype(int) | |
| sigma = np.log(sigma / np.pi) | |
| sigma = (sigma - np.log(SIGMA_MIN)) / (np.log(SIGMA_MAX) - np.log(SIGMA_MIN)) * SIGMA_N | |
| sigma = np.round(np.clip(sigma, 0, SIGMA_N)).astype(int) | |
| return p_[sigma, x] | |
| def sample(sigma): | |
| out = sigma * np.random.randn(*sigma.shape) | |
| out = (out + np.pi) % (2 * np.pi) - np.pi | |
| return out | |
| score_norm_ = score( | |
| sample(sigma[None].repeat(10000, 0).flatten()), | |
| sigma[None].repeat(10000, 0).flatten() | |
| ).reshape(10000, -1) | |
| score_norm_ = (score_norm_ ** 2).mean(0) | |
| def score_norm(sigma): | |
| sigma = np.log(sigma / np.pi) | |
| sigma = (sigma - np.log(SIGMA_MIN)) / (np.log(SIGMA_MAX) - np.log(SIGMA_MIN)) * SIGMA_N | |
| sigma = np.round(np.clip(sigma, 0, SIGMA_N)).astype(int) | |
| return score_norm_[sigma] | |