|
| 1 | +STUFF_cycc = "cycc" |
| 2 | + |
| 3 | +import numpy as np |
| 4 | +from numba import njit, objmode, prange |
| 5 | + |
| 6 | +__author__ = "Romain Tavenard romain.tavenard[at]univ-rennes2.fr" |
| 7 | + |
| 8 | + |
| 9 | +@njit(parallel=True, fastmath=True) |
| 10 | +def normalized_cc(s1, s2, norm1=-1.0, norm2=-1.0): |
| 11 | + """Normalize cc. |
| 12 | +
|
| 13 | + Parameters |
| 14 | + ---------- |
| 15 | + s1 : array-like, shape=[sz, d], dtype=float64 |
| 16 | + s2 : array-like, shape=[sz, d], dtype=float64 |
| 17 | + norm1 : float64, default=-1.0 |
| 18 | + norm2 : float64, default=-1.0 |
| 19 | +
|
| 20 | + Returns |
| 21 | + ------- |
| 22 | + norm_cc : array-like, shape=[2 * sz - 1], dtype=float64 |
| 23 | + """ |
| 24 | + assert s1.shape[1] == s2.shape[1] |
| 25 | + sz = s1.shape[0] |
| 26 | + n_bits = 1 + int(np.log2(2 * sz - 1)) |
| 27 | + fft_sz = 2**n_bits |
| 28 | + |
| 29 | + if norm1 < 0.0: |
| 30 | + norm1 = np.linalg.norm(s1) |
| 31 | + if norm2 < 0.0: |
| 32 | + norm2 = np.linalg.norm(s2) |
| 33 | + |
| 34 | + denom = norm1 * norm2 |
| 35 | + if denom < 1e-9: # To avoid NaNs |
| 36 | + denom = np.inf |
| 37 | + |
| 38 | + with objmode(cc="float64[:, :]"): |
| 39 | + cc = np.real( |
| 40 | + np.fft.ifft( |
| 41 | + np.fft.fft(s1, fft_sz, axis=0) |
| 42 | + * np.conj(np.fft.fft(s2, fft_sz, axis=0)), |
| 43 | + axis=0, |
| 44 | + ) |
| 45 | + ) |
| 46 | + cc = np.vstack((cc[-(sz - 1) :], cc[:sz])) |
| 47 | + norm_cc = np.real(cc).sum(axis=-1) / denom |
| 48 | + return norm_cc |
| 49 | + |
| 50 | + |
| 51 | +@njit(parallel=True, fastmath=True) |
| 52 | +def cdist_normalized_cc(dataset1, dataset2, norms1, norms2, self_similarity): |
| 53 | + """Compute the distance matrix between two time series dataset. |
| 54 | +
|
| 55 | + Parameters |
| 56 | + ---------- |
| 57 | + dataset1 : array-like, shape=[n_ts1, sz, d], dtype=float64 |
| 58 | + dataset2 : array-like, shape=[n_ts2, sz, d], dtype=float64 |
| 59 | + norms1 : array-like, shape=[n_ts1], dtype=float64 |
| 60 | + norms2 : array-like, shape=[n_ts2], dtype=float64 |
| 61 | + self_similarity : bool |
| 62 | +
|
| 63 | + Returns |
| 64 | + ------- |
| 65 | + dists : array-like, shape=[n_ts1, n_ts2], dtype=float64 |
| 66 | + """ |
| 67 | + n_ts1, sz, d = dataset1.shape |
| 68 | + n_ts2 = dataset2.shape[0] |
| 69 | + assert d == dataset2.shape[2] |
| 70 | + dists = np.zeros((n_ts1, n_ts2)) |
| 71 | + |
| 72 | + if (norms1 < 0.0).any(): |
| 73 | + for i_ts1 in prange(n_ts1): |
| 74 | + norms1[i_ts1] = np.linalg.norm(dataset1[i_ts1, ...]) |
| 75 | + if (norms2 < 0.0).any(): |
| 76 | + for i_ts2 in prange(n_ts2): |
| 77 | + norms2[i_ts2] = np.linalg.norm(dataset2[i_ts2, ...]) |
| 78 | + if self_similarity: |
| 79 | + for i in prange(1, n_ts1): |
| 80 | + for j in range(i): |
| 81 | + dists[i, j] = normalized_cc( |
| 82 | + dataset1[i], dataset2[j], norm1=norms1[i], norm2=norms2[j] |
| 83 | + ).max() |
| 84 | + dists += dists.T |
| 85 | + else: |
| 86 | + for i in prange(n_ts1): |
| 87 | + for j in range(n_ts2): |
| 88 | + dists[i, j] = normalized_cc( |
| 89 | + dataset1[i], dataset2[j], norm1=norms1[i], norm2=norms2[j] |
| 90 | + ).max() |
| 91 | + return dists |
| 92 | + |
| 93 | + |
| 94 | +@njit(parallel=True, fastmath=True) |
| 95 | +def y_shifted_sbd_vec(ref_ts, dataset, norm_ref, norms_dataset): |
| 96 | + """Shift a time series dataset w.r.t. a time series of reference. |
| 97 | +
|
| 98 | + Parameters |
| 99 | + ---------- |
| 100 | + ref_ts : array-like, shape=[sz, d], dtype=float64 |
| 101 | + Time series of reference. |
| 102 | + dataset : array-like, shape=[n_ts, sz, d], dtype=float64 |
| 103 | + Time series dataset. |
| 104 | + norm_ref : float64 |
| 105 | + norms_dataset : array-like, shape=[n_ts], dtype=float64 |
| 106 | + Norms of the time series dataset. |
| 107 | +
|
| 108 | + Returns |
| 109 | + ------- |
| 110 | + dataset_shifted : array-like, shape=[n_ts, sz, d], dtype=float64 |
| 111 | + """ |
| 112 | + n_ts = dataset.shape[0] |
| 113 | + sz = dataset.shape[1] |
| 114 | + d = dataset.shape[2] |
| 115 | + assert sz == ref_ts.shape[0] and d == ref_ts.shape[1] |
| 116 | + dataset_shifted = np.zeros((n_ts, sz, d)) |
| 117 | + |
| 118 | + if norm_ref < 0: |
| 119 | + norm_ref = np.linalg.norm(ref_ts) |
| 120 | + if (norms_dataset < 0.0).any(): |
| 121 | + for i_ts in prange(n_ts): |
| 122 | + norms_dataset[i_ts] = np.linalg.norm(dataset[i_ts, ...]) |
| 123 | + |
| 124 | + for i in prange(n_ts): |
| 125 | + cc = normalized_cc(ref_ts, dataset[i], norm1=norm_ref, norm2=norms_dataset[i]) |
| 126 | + idx = np.argmax(cc) |
| 127 | + shift = idx - sz |
| 128 | + if shift > 0: |
| 129 | + dataset_shifted[i, shift:] = dataset[i, :-shift, :] |
| 130 | + elif shift < 0: |
| 131 | + dataset_shifted[i, :shift] = dataset[i, -shift:, :] |
| 132 | + else: |
| 133 | + dataset_shifted[i] = dataset[i] |
| 134 | + |
| 135 | + return dataset_shifted |
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