├── .gitattributes ├── .gitignore ├── .travis.yml ├── LICENSE.txt ├── MANIFEST.in ├── README.md ├── README.txt ├── __init__.py ├── fastsst ├── __init__.py ├── sst.py └── util │ ├── __init__.py │ └── linear_algebra.py ├── img ├── example1.png ├── example_freq.png ├── example_step.png └── example_twitter.png ├── notebooks ├── comparison_between_svd_and_lanczos.ipynb ├── data │ ├── TEK16.txt │ ├── ann_gun_CentroidA.txt │ ├── chfdb_chf13_45590.txt │ ├── mitdbx_mitdbx_108.txt │ ├── nprs44.txt │ └── qtdbsel102.txt └── examples.ipynb ├── setup.py └── tests ├── __init__.py ├── test_data ├── __init__.py ├── freq_change.csv └── step_change.csv ├── test_linear_algebra.py └── test_sst.py /.gitattributes: -------------------------------------------------------------------------------- 1 | example/* linguist-documentation 2 | img/* linguist-documentation 3 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | __pycache__ 2 | /fastsst.egg-info/ 3 | /build/ 4 | /dist/ 5 | *.pptx 6 | register.py 7 | .ipynb_checkpoints 8 | .pypirc 9 | /all_data/ 10 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: python 2 | python: 3 | - "3.6" 4 | install: 5 | - python setup.py install 6 | script: 7 | - python setup.py test 8 | -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | Copyright <2018> 2 | 3 | Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: 4 | 5 | The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 6 | 7 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 8 | -------------------------------------------------------------------------------- /MANIFEST.in: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/MANIFEST.in -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![Build Status](https://travis-ci.org/statefb/singular-spectrum-transformation.svg?branch=master)](https://travis-ci.org/statefb/singular-spectrum-transformation) 2 | # SST (Singular Spectrum Transformation) 3 | A fast implementation of Singular Spectrum Transformation for python. 4 | 5 | ## What is SST? 6 | A change point detection algorithm. 7 | ![example](img/example_step.png) 8 | ![example](img/example_freq.png) 9 | see more [examples](./notebooks/examples.ipynb) 10 | 11 | ## Features 12 | #### fast computation 13 | * efficient algorithm using Lanczos method 14 | * [Numba](http://numba.pydata.org/) 15 | 16 | 17 | ## Installation 18 | ``` 19 | $pip install fastsst 20 | ``` 21 | 22 | ## Basic Usage 23 | ```usage.py 24 | from fastsst import SingularSpectrumTransformation 25 | 26 | sst = SingularSpectrumTransformation(win_length=30) 27 | 28 | """ 29 | note: 30 | - data must be 1d np.ndarray 31 | - the first run takes a few seconds for jit compling 32 | """ 33 | score = sst.score_offline(data) 34 | ``` 35 | 36 | ## Others 37 | * [Comparison between conventional method(i.e. SVD) and faster method(i.e. lanczos)](./notebooks/comparison_between_svd_and_lanczos.ipynb) 38 | 39 | ## TODO 40 | * online evaluation 41 | 42 | ## References 43 | 1. Tsuyoshi Ide, Koji Tsuda, Change-Point Detection using Krylov Subspace Learning, SIAM International Conference on Data Mining, pp.515-520, 2007 44 | 2. Tsuyoshi Ide, Speeding up Change-Point Detection using Matrix Compression (Japanse), Workshop on Information-Based Induction Sciences, 2006 45 | 3. Tsuyoshi Ide, Masashi Sugiyama, Anomaly Detection and Change Detection (Japanse), Kodansha, 2015 46 | -------------------------------------------------------------------------------- /README.txt: -------------------------------------------------------------------------------- 1 | A fast implementation of Singular Spectrum Transformation for python. 2 | 3 | Features 4 | -------- 5 | 6 | fast computation 7 | 8 | - efficient algorithm using lanczos method 9 | - [Numba](http://numba.pydata.org/) 10 | 11 | 12 | References 13 | ---------- 14 | 15 | 1. Tsuyoshi Ide, Koji Tsuda, Change-Point Detection using Krylov 16 | Subspace Learning, SIAM International Conference on Data Mining, 17 | pp.515-520, 2007 18 | 2. Tsuyoshi Ide, Speeding up Change-Point Detection using Matrix 19 | Compression (Japanse), Workshop on Information-Based Induction 20 | Sciences, 2006 21 | 3. Tsuyoshi Ide, Masashi Sugiyama, Anomaly Detection and Change 22 | Detection (Japanse), Kodansha, 2015 23 | -------------------------------------------------------------------------------- /__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/__init__.py -------------------------------------------------------------------------------- /fastsst/__init__.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | from .sst import SingularSpectrumTransformation 3 | -------------------------------------------------------------------------------- /fastsst/sst.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """Singluar Spectrum Transformation. 3 | 4 | The MIT License (MIT) 5 | Copyright (c) 2018 statefb. 6 | Permission is hereby granted, free of charge, to any person obtaining a copy 7 | of this software and associated documentation files (the "Software"), to deal 8 | in the Software without restriction, including without limitation the rights 9 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 10 | copies of the Software, and to permit persons to whom the Software is 11 | furnished to do so, subject to the following conditions: 12 | The above copyright notice and this permission notice shall be included in 13 | all copies or substantial portions of the Software. 14 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 20 | THE SOFTWARE. 21 | """ 22 | 23 | import numpy as np 24 | from numba import jit 25 | from sklearn.preprocessing import MinMaxScaler 26 | from .util.linear_algebra import power_method, lanczos, eig_tridiag 27 | 28 | 29 | class SingularSpectrumTransformation(): 30 | """SingularSpectrumTransformation class.""" 31 | 32 | def __init__(self, win_length, n_components=5, order=None, lag=None, 33 | is_scaled=False, use_lanczos=True, rank_lanczos=None, eps=1e-3): 34 | """Change point detection with Singular Spectrum Transformation. 35 | 36 | Parameters 37 | ---------- 38 | win_length : int 39 | window length of Hankel matrix. 40 | n_components : int 41 | specify how many rank of Hankel matrix will be taken. 42 | order : int 43 | number of columns of Hankel matrix. 44 | lag : int 45 | interval between history Hankel matrix and test Hankel matrix. 46 | is_scaled : bool 47 | if false, min-max scaling will be applied(recommended). 48 | use_lanczos : boolean 49 | if true, Lanczos method will be used, which makes faster. 50 | rank_lanczos : int 51 | the rank which will be used for lanczos method. 52 | for the detail of lanczos method, see [1]. 53 | eps : float 54 | specify how much noise will be added to initial vector for 55 | power method. 56 | (FELIX: FEedback impLIcit kernel approXimation method) 57 | for the detail, see [2]. 58 | 59 | References 60 | ---------- 61 | [1]: Tsuyoshi Ide et al., Change-Point Detection using Krylov Subspace Learning 62 | [2]: Tsuyoshi Ide, Speeding up Change-Point Detection using Matrix Compression (Japanse) 63 | 64 | """ 65 | self.win_length = win_length 66 | self.n_components = n_components 67 | self.order = order 68 | self.lag = lag 69 | self.is_scaled = is_scaled 70 | self.use_lanczos = use_lanczos 71 | self.rank_lanczos = rank_lanczos 72 | self.eps = eps 73 | 74 | def score_offline(self, x): 75 | """Calculate anomaly score (offline). 76 | 77 | Parameters 78 | ---------- 79 | x : 1d numpy array 80 | input time series data. 81 | 82 | Returns 83 | ------- 84 | score : 1d array 85 | change point score. 86 | 87 | """ 88 | if self.order is None: 89 | # rule of thumb 90 | self.order = self.win_length 91 | if self.lag is None: 92 | # rule of thumb 93 | self.lag = self.order // 2 94 | if self.rank_lanczos is None: 95 | # rule of thumb 96 | if self.n_components % 2 == 0: 97 | self.rank_lanczos = 2 * self.n_components 98 | else: 99 | self.rank_lanczos = 2 * self.n_components - 1 100 | 101 | assert isinstance(x, np.ndarray), "input array must be numpy array." 102 | assert x.ndim == 1, "input array dimension must be 1." 103 | assert isinstance(self.win_length, int), "window length must be int." 104 | assert isinstance(self.n_components, int), "number of components must be int." 105 | assert isinstance(self.order, int), "order of partial time series must be int." 106 | assert isinstance(self.lag, int), "lag between test series and history series must be int." 107 | assert isinstance(self.rank_lanczos, int), "rank for lanczos must be int." 108 | assert self.win_length + self.order + self.lag < x.size, "data length is too short." 109 | 110 | # all values should be positive for numerical stabilization 111 | if not self.is_scaled: 112 | x_scaled = MinMaxScaler(feature_range=(1, 2))\ 113 | .fit_transform(x.reshape(-1, 1))[:, 0] 114 | else: 115 | x_scaled = x 116 | 117 | score = _score_offline(x_scaled, self.order, 118 | self.win_length, self.lag, self.n_components, self.rank_lanczos, 119 | self.eps, use_lanczos=self.use_lanczos) 120 | 121 | return score 122 | 123 | 124 | @jit(nopython=True) 125 | def _score_offline(x, order, win_length, lag, n_components, rank, eps, use_lanczos): 126 | """Core implementation of offline score calculation.""" 127 | start_idx = win_length + order + lag + 1 128 | end_idx = x.size + 1 129 | 130 | # initialize vector for power method 131 | x0 = np.empty(order, dtype=np.float64) 132 | x0 = np.random.rand(order) 133 | x0 /= np.linalg.norm(x0) 134 | 135 | score = np.zeros_like(x) 136 | for t in range(start_idx, end_idx): 137 | # compute score at each index 138 | 139 | # get Hankel matrix 140 | X_history = _create_hankel(x, order, 141 | start=t - win_length - lag, 142 | end=t - lag) 143 | X_test = _create_hankel(x, order, 144 | start=t - win_length, 145 | end=t) 146 | 147 | if use_lanczos: 148 | score[t-1], x1 = _sst_lanczos(X_test, X_history, n_components, 149 | rank, x0) 150 | # update initial vector for power method 151 | x0 = x1 + eps * np.random.rand(x0.size) 152 | x0 /= np.linalg.norm(x0) 153 | else: 154 | score[t-1] = _sst_svd(X_test, X_history, n_components) 155 | 156 | return score 157 | 158 | 159 | @jit(nopython=True) 160 | def _create_hankel(x, order, start, end): 161 | """Create Hankel matrix. 162 | 163 | Parameters 164 | ---------- 165 | x : full time series 166 | order : order of Hankel matrix 167 | start : start index 168 | end : end index 169 | 170 | Returns 171 | ------- 172 | 2d array shape (window length, order) 173 | 174 | """ 175 | win_length = end - start 176 | X = np.empty((win_length, order)) 177 | for i in range(order): 178 | X[:, i] = x[(start - i):(end - i)] 179 | return X 180 | 181 | 182 | @jit(nopython=True) 183 | def _sst_lanczos(X_test, X_history, n_components, rank, x0): 184 | """Run sst algorithm with lanczos method (FELIX-SST algorithm).""" 185 | P_history = X_history.T @ X_history 186 | P_test = X_test.T @ X_test 187 | # calculate the first singular vec of test matrix 188 | u, _, _ = power_method(P_test, x0, n_iter=1) 189 | T = lanczos(P_history, u, rank) 190 | vec, val = eig_tridiag(T) 191 | return 1 - (vec[0, :n_components] ** 2).sum(), u 192 | 193 | 194 | @jit("f8(f8[:,:],f8[:,:],u1)", nopython=True) 195 | def _sst_svd(X_test, X_history, n_components): 196 | """Run sst algorithm with svd.""" 197 | U_test, _, _ = np.linalg.svd(X_test, full_matrices=False) 198 | U_history, _, _ = np.linalg.svd(X_history, full_matrices=False) 199 | _, s, _ = np.linalg.svd(U_test[:, :n_components].T @ 200 | U_history[:, :n_components], full_matrices=False) 201 | return 1 - s[0] 202 | -------------------------------------------------------------------------------- /fastsst/util/__init__.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | -------------------------------------------------------------------------------- /fastsst/util/linear_algebra.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """Utility funcs for linear algebra.""" 3 | 4 | from numba import jit 5 | import numpy as np 6 | from numpy.linalg import norm 7 | 8 | 9 | @jit(nopython=True) 10 | def power_method(A, x0, n_iter=1): 11 | """Compute the first singular components by power method.""" 12 | for i in range(n_iter): 13 | x0 = A.T @ A @ x0 14 | 15 | v = x0 / norm(x0) 16 | s = norm(A @ v) 17 | u = A @ v / s 18 | 19 | return u, s, v 20 | 21 | 22 | @jit(nopython=True) 23 | def lanczos(C, a, s): 24 | """Perform lanczos algorithm.""" 25 | # initialization 26 | r = np.copy(a) 27 | a_pre = np.zeros_like(a, dtype=np.float64) 28 | beta_pre = 1 29 | T = np.zeros((s, s)) 30 | 31 | for j in range(s): 32 | a_post = r / beta_pre 33 | alpha = a_post.T @ C @ a_post 34 | r = C @ a_post - alpha*a_post - beta_pre*a_pre 35 | beta_post = norm(r) 36 | 37 | T[j, j] = alpha 38 | if j - 1 >= 0: 39 | T[j, j-1] = beta_pre 40 | T[j-1, j] = beta_pre 41 | 42 | # update 43 | a_pre = a_post 44 | beta_pre = beta_post 45 | 46 | return T 47 | 48 | 49 | @jit(nopython=True) 50 | def eig_tridiag(T): 51 | """Compute eigen value decomposition for tridiag matrix.""" 52 | # TODO: efficient implementation 53 | # ------------------------------------------------------ 54 | # Is it really necessary to implement fast eig computation ? 55 | # The size of matrix T is practically at most 20 since almost 2 times 56 | # larger than n_components. Therefore fast implementation such as 57 | # QL algorithm may not provide computational cost benefit in total. 58 | # ------------------------------------------------------ 59 | u, s, _ = np.linalg.svd(T) 60 | # NOTE: return value must be ordered 61 | return u, s 62 | -------------------------------------------------------------------------------- /img/example1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/img/example1.png -------------------------------------------------------------------------------- /img/example_freq.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/img/example_freq.png -------------------------------------------------------------------------------- /img/example_step.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/img/example_step.png -------------------------------------------------------------------------------- /img/example_twitter.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/img/example_twitter.png -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """setup.py 3 | """ 4 | import os 5 | from setuptools import setup 6 | from setuptools import find_packages 7 | 8 | # meta info 9 | NAME = "fastsst" 10 | VERSION = "0.0.4" 11 | AUTHOR = "Takehiro Suzuki" 12 | AUTHOR_EMAIL = "" 13 | URL = "https://github.com/statefb/singular-spectrum-transformation" 14 | DESCRIPTION = 'A fast implementation of change point detection algorithm(SST).' 15 | LICENSE = "MIT" 16 | 17 | if not os.path.exists('README.txt'): 18 | os.system("pandoc -o README.txt README.md") 19 | LONG_DESCRIPTION = open('README.txt').read() 20 | 21 | def main(): 22 | 23 | setup( 24 | name=NAME, 25 | version=VERSION, 26 | author=AUTHOR, 27 | author_email=AUTHOR_EMAIL, 28 | url=URL, 29 | description=DESCRIPTION, 30 | long_description=LONG_DESCRIPTION, 31 | zip_safe=False, 32 | include_package_data=True, 33 | packages=find_packages(), 34 | install_requires=[ 35 | "numpy", 36 | "pandas", 37 | "scipy", 38 | "sklearn", 39 | "numba", 40 | ], 41 | dependency_links=[ 42 | 43 | ], 44 | tests_require=[], 45 | setup_requires=[], 46 | license=LICENSE, 47 | test_suite="tests", 48 | classifiers=[ 49 | "Programming Language :: Python :: 3.5", 50 | "Programming Language :: Python :: 3.6", 51 | "License :: OSI Approved :: GNU General Public License v2 (GPLv2)", 52 | "Topic :: Scientific/Engineering", 53 | ] 54 | ) 55 | 56 | 57 | if __name__ == '__main__': 58 | main() 59 | -------------------------------------------------------------------------------- /tests/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/tests/__init__.py -------------------------------------------------------------------------------- /tests/test_data/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/statefb/singular-spectrum-transformation/9ef208b9e2566865e10f1e9ed7090240965234ce/tests/test_data/__init__.py -------------------------------------------------------------------------------- /tests/test_data/freq_change.csv: 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4.119764660837914 1437 | 4.843979248587849 1438 | 4.928782383560243 1439 | 3.6784844284711378 1440 | 3.201039718242973 1441 | 4.97724985251266 1442 | 5.068764154005622 1443 | 3.967269858600165 1444 | 3.385517060162325 1445 | 4.227522315578463 1446 | 4.87704568231212 1447 | 4.726321209798555 1448 | 5.029787367680426 1449 | 5.211154364986572 1450 | 3.7061474826384915 1451 | 3.88448630607485 1452 | 3.896555035736242 1453 | 4.706732252324918 1454 | 4.641152796110028 1455 | 3.8372469443953627 1456 | 4.849816613308553 1457 | 5.058828804316718 1458 | 5.754630433358662 1459 | 3.8093896764867865 1460 | 5.194057518897269 1461 | 3.793743266591504 1462 | 4.79321502927806 1463 | 5.418905022443667 1464 | 5.646735799633657 1465 | 4.381003155909181 1466 | 4.7425439677893 1467 | 4.276486086543228 1468 | 4.700246593784404 1469 | 5.151437852458371 1470 | 3.953220682997868 1471 | 5.5233213716455465 1472 | 4.361541509608241 1473 | 4.816116705369969 1474 | 5.263383869080142 1475 | 4.155076840947885 1476 | 5.137528545469515 1477 | 4.8459254451277385 1478 | 4.193033167244714 1479 | 5.638272897408651 1480 | 3.9901420781187604 1481 | 5.098953661849504 1482 | 4.9660771589685 1483 | 5.52109936277086 1484 | 4.414801121022877 1485 | 3.26708114521835 1486 | 3.7463781200614648 1487 | 5.749651315593335 1488 | 5.196573925901678 1489 | 4.512444172105401 1490 | 4.140888059006972 1491 | 3.59861690495603 1492 | 4.785637210645273 1493 | 4.121895169081029 1494 | 5.087269890599368 1495 | 3.800199608206634 1496 | 4.302246676455773 1497 | 4.0792121380254995 1498 | 3.5425333864292434 1499 | 4.629880573378968 1500 | 4.960834493215876 1501 | 5.492584860107906 1502 | 4.017498183682329 1503 | 3.6888899620699416 1504 | 4.453138368430331 1505 | 4.6151912197371505 1506 | 4.210701725076787 1507 | 3.6196376983879563 1508 | 4.007906483706737 1509 | 4.698758949546164 1510 | 3.9466545533727095 1511 | 5.290323613623279 1512 | 4.508572992799321 1513 | 4.729778874929934 1514 | 3.70007537648503 1515 | 3.8343223897758265 1516 | 4.752838122232358 1517 | 3.6922422265266124 1518 | 4.065992738120821 1519 | 3.650763654767168 1520 | 4.844018737434207 1521 | 4.486372810763981 1522 | 4.168784990995169 1523 | 4.211795262321922 1524 | 4.237915886290969 1525 | 4.491227236000711 1526 | 4.412843940039369 1527 | 4.089985011227346 1528 | 5.091312200798637 1529 | 5.549503962404625 1530 | 4.81221397787878 1531 | 4.488406533868089 1532 | 5.084630554962517 1533 | 4.905978537499334 1534 | 5.461911991126507 1535 | 4.615074216614833 1536 | 4.219271524974833 1537 | 4.328139117696913 1538 | 3.4915754516458226 1539 | 5.058273376577406 1540 | 5.737229345765546 1541 | 3.8324000739850486 1542 | 5.22954716253277 1543 | 5.261079135292578 1544 | 3.7066576825252 1545 | 4.250876404707677 1546 | 5.320619741860298 1547 | 3.3507934411319855 1548 | 4.004961885549041 1549 | 4.1194059346393646 1550 | 5.256602762829598 1551 | 5.488455406120054 1552 | 3.347270072278925 1553 | 3.923349839689169 1554 | 5.282799346314367 1555 | 5.0251368936323235 1556 | 5.622419870851882 1557 | 5.388675506825444 1558 | 3.864651716630566 1559 | 4.289134137019248 1560 | 4.02489639824078 1561 | 5.490592800844308 1562 | 4.819413535361735 1563 | 4.101122017382782 1564 | 4.30512414909949 1565 | 4.333424396354945 1566 | 4.683684073881735 1567 | 4.7638872865626025 1568 | 4.388439156594792 1569 | 5.28169379472325 1570 | 3.7434367488789206 1571 | 5.340327051663927 1572 | 5.625071221560226 1573 | 4.108080854939471 1574 | 5.264712063647586 1575 | 4.536845802717936 1576 | 4.20090270344741 1577 | 3.21921351101098 1578 | 4.049869019821378 1579 | 5.104661191445268 1580 | 5.4307169120957735 1581 | 5.574132815782984 1582 | 5.4373167856932945 1583 | 4.020849874011541 1584 | 4.739057492646723 1585 | 4.5922070561727795 1586 | 5.425556972261607 1587 | 5.0595461860670135 1588 | 4.054173999445441 1589 | 4.517844695676038 1590 | 5.232454344640875 1591 | 4.237331243215476 1592 | 5.2956466466691205 1593 | 5.671316546837851 1594 | 5.695898397370498 1595 | 4.07950095791889 1596 | 3.7087344564470603 1597 | 5.494233437146258 1598 | 3.9972683426897415 1599 | 3.991546187930018 1600 | 3.3548583982503075 1601 | 4.508630001435027 1602 | 4.9100848910877914 1603 | 5.675025040989769 1604 | 3.8375361837309736 1605 | 5.187923097911856 1606 | 3.6623032689493273 1607 | 4.328850207491714 1608 | 4.3233393798514745 1609 | 4.468248031032912 1610 | 3.441347091483035 1611 | 4.200458244986158 1612 | 4.097320517886857 1613 | 4.795705533238957 1614 | 4.380820629423428 1615 | 4.687114765477041 1616 | 3.6107302974705684 1617 | 3.8449688227271555 1618 | 3.8428182575661705 1619 | 5.47742346703545 1620 | 4.112104863199358 1621 | 3.7258463401056643 1622 | 3.860307572069819 1623 | 4.363898920498776 1624 | 4.962585094926212 1625 | 5.083568120198662 1626 | 5.073333454259203 1627 | 4.342730122700707 1628 | 4.859452411368534 1629 | 5.823936738239207 1630 | 3.5403398673006263 1631 | 4.9659219476954535 1632 | 3.4015192768515132 1633 | 4.558531135429204 1634 | 3.818467050045853 1635 | 3.7462256640476514 1636 | 4.17759868558385 1637 | 5.732692497667884 1638 | 3.8267818841924477 1639 | 4.657827421443983 1640 | 4.573151901125402 1641 | 4.012149507699054 1642 | 4.968156573771079 1643 | 5.200006193399429 1644 | 4.853061294442465 1645 | 5.175392791820735 1646 | 4.8358600115890535 1647 | 4.002267259500042 1648 | 3.6507501662374775 1649 | 3.9376623170166405 1650 | 4.227917387659452 1651 | 4.5482225971909305 1652 | 4.211534044611286 1653 | 3.4198849554365007 1654 | 5.308028250265714 1655 | 5.210703117411315 1656 | 4.384500219811914 1657 | 4.584368043813901 1658 | 4.9417545174548145 1659 | 4.61335949190498 1660 | 4.1628442817825935 1661 | 3.9788394141410492 1662 | 3.1632670027471046 1663 | 4.843666871189957 1664 | 4.882365174493021 1665 | 5.046214166241001 1666 | 3.4428411858739683 1667 | 4.157485054291739 1668 | 4.980409597109189 1669 | 5.7227440442454665 1670 | 4.790934139904323 1671 | 4.342970911711832 1672 | 4.272778343347493 1673 | 4.2906759511321635 1674 | 4.823715332626009 1675 | 3.632576260821704 1676 | 4.150319629071945 1677 | 3.74626587556277 1678 | 3.750170069319775 1679 | 4.44176886256421 1680 | 3.700941397182677 1681 | 4.32108148292063 1682 | 4.1716641528821174 1683 | 5.1945985789983204 1684 | 4.3352855950761775 1685 | 4.685439309153692 1686 | 3.863832994994592 1687 | 5.550615787619472 1688 | 5.4064650266361856 1689 | 4.299269078796394 1690 | 4.95803985557032 1691 | 4.787679995266236 1692 | 4.322236738300509 1693 | 3.478127094881815 1694 | 5.483281620154453 1695 | 3.7576347926179046 1696 | 4.765741832918232 1697 | 4.475959709002025 1698 | 3.7285558780076977 1699 | 3.705035696972713 1700 | 3.6369352665811148 1701 | 3.812392816255644 1702 | 4.928572401212015 1703 | 3.816400269927303 1704 | 5.348510181168436 1705 | 4.498402131038118 1706 | 4.848487736268069 1707 | 4.193301421796983 1708 | 4.535625182938636 1709 | 5.273472022642891 1710 | 3.9040620043932797 1711 | 4.374774486146334 1712 | 4.358477326394544 1713 | 4.721803943871513 1714 | 3.8954124244665 1715 | 4.059946664000737 1716 | 3.9440234458958505 1717 | 4.0958381461360585 1718 | 4.806621206344216 1719 | 4.580668044803306 1720 | 4.406090994987819 1721 | 5.430745927964245 1722 | 4.0369926208036 1723 | 3.571495260901034 1724 | 5.045467420996456 1725 | 4.982750601742872 1726 | 5.066348463680628 1727 | 4.204636854226368 1728 | 3.905350730962822 1729 | 5.069165350814445 1730 | 4.032258661690621 1731 | 4.5496308703116926 1732 | 4.561921289267081 1733 | 5.203331510645705 1734 | 4.751886556371331 1735 | 4.302521586031802 1736 | 3.207124029768943 1737 | 4.497674162226902 1738 | 4.67952261416442 1739 | 5.321085111142921 1740 | 4.119923502082335 1741 | 3.625739987781455 1742 | 5.259518067406401 1743 | 4.319198654683015 1744 | 4.1093554777095775 1745 | 4.207563827606372 1746 | 4.328873589687053 1747 | 4.149996534065859 1748 | 5.070320060995752 1749 | 5.263449822588404 1750 | 3.8713656098939477 1751 | 3.82490831046586 1752 | 5.339671553968302 1753 | 4.643728403696671 1754 | 5.2873551428369145 1755 | 3.9842833155663104 1756 | 4.943962446693376 1757 | 4.594645015679806 1758 | 5.394656342157341 1759 | 3.5961945847898793 1760 | 3.8070381663994506 1761 | 5.440415606645196 1762 | 4.723737236311421 1763 | 4.400586313838574 1764 | 5.232867322631194 1765 | 3.908551890532153 1766 | 4.749416009182795 1767 | 4.146500947635231 1768 | 4.671491177287225 1769 | 4.435011379157211 1770 | 3.977182525730458 1771 | 4.5039232536401705 1772 | 5.113813197148694 1773 | 3.8710687330524873 1774 | 5.524210335414132 1775 | 4.0561684321004 1776 | 5.353432548271006 1777 | 3.6670263345660525 1778 | 4.027853526301052 1779 | 3.796184570413332 1780 | 4.937082420263065 1781 | 4.7149664838880305 1782 | 5.558361463627662 1783 | 4.847525833007066 1784 | 4.162178664078681 1785 | 5.004480141823704 1786 | 4.376049554686325 1787 | 4.5581056255618275 1788 | 4.440270455628536 1789 | 4.718002337156295 1790 | 3.9291070153404566 1791 | 5.318558468012174 1792 | 3.6430044875753316 1793 | 3.635492268668723 1794 | 4.956416419288159 1795 | 4.303097904401453 1796 | 3.8520020542779405 1797 | 4.966012609084583 1798 | 4.5684432488403495 1799 | 5.122796524558451 1800 | 4.851081845512879 1801 | 3.4165981540425197 1802 | 3.382426209325993 1803 | 5.6860422365060845 1804 | 3.845516107925657 1805 | 5.162345495034875 1806 | 4.359319780013605 1807 | 4.906645084295729 1808 | 4.26759176202881 1809 | 4.120852186922442 1810 | 4.6014479274644104 1811 | 5.571353255595275 1812 | 4.924524049293332 1813 | 3.501450096518079 1814 | 4.1364339462993165 1815 | 4.177849862787323 1816 | 5.499635031142745 1817 | 4.21257377251465 1818 | 4.515642106206421 1819 | 3.564117793792584 1820 | 3.9729582667971046 1821 | 4.279476969628907 1822 | 5.516479822077777 1823 | 4.960542458587092 1824 | 3.4005716882805515 1825 | 3.947727724456132 1826 | 4.4668009129398225 1827 | 4.540058259793913 1828 | 4.039073993165262 1829 | 5.294851514613761 1830 | 3.5599126660185636 1831 | 5.322122279178635 1832 | 3.7727376777682364 1833 | 5.465853235500069 1834 | 4.728754261825401 1835 | 5.134893177621005 1836 | 5.153969563115621 1837 | 5.273304796934099 1838 | 4.413395903618031 1839 | 5.029966208624157 1840 | 5.050136663225002 1841 | 5.123015539296193 1842 | 3.557119129154328 1843 | 4.336115804000817 1844 | 4.309592688739709 1845 | 4.605769645994957 1846 | 4.689051720624599 1847 | 5.140121374887602 1848 | 5.5869839849272385 1849 | 4.782071924851962 1850 | 4.211870935689292 1851 | 5.001007736114109 1852 | 4.850073044548939 1853 | 4.779137975102813 1854 | 3.7702450833301615 1855 | 5.328464092983509 1856 | 5.166176753984677 1857 | 4.997374921526403 1858 | 3.4782561277982262 1859 | 5.092469081342821 1860 | 5.307235700891051 1861 | 4.063215097848484 1862 | 4.202549477180059 1863 | 4.268833714888407 1864 | 3.876352188001303 1865 | 4.715679854242589 1866 | 4.8462875141951836 1867 | 3.9148207228122516 1868 | 4.172169964734156 1869 | 4.105600922063134 1870 | 5.051468195314301 1871 | 3.9961005414645947 1872 | 5.1762944701513165 1873 | 4.553731577302048 1874 | 5.305059536181085 1875 | 3.631496120709265 1876 | 4.188668580083618 1877 | 4.944092978124661 1878 | 4.01071409357986 1879 | 5.022511257394445 1880 | 4.547441825158638 1881 | 3.299928427835135 1882 | 3.982779066856471 1883 | 5.696762185534897 1884 | 3.855478628953864 1885 | 4.8445909119858825 1886 | 4.437355462123997 1887 | 4.086303766627787 1888 | 5.519781773381518 1889 | 4.0335943084965855 1890 | 5.6222579178056975 1891 | 4.488270188206785 1892 | 3.898943855529309 1893 | 4.663236797212608 1894 | 4.7658353440040235 1895 | 5.082812430253337 1896 | 4.255207111373497 1897 | 4.122863664280638 1898 | 4.656162498751286 1899 | 4.518154232015762 1900 | 3.8119681464573536 1901 | 4.20377513124824 1902 | 5.134801826368197 1903 | 4.5679304001283025 1904 | 5.15856367779803 1905 | 5.243856170260891 1906 | 4.605057528451084 1907 | 4.500486084948382 1908 | 5.054131068616578 1909 | 4.760274474681953 1910 | 3.5054719200719937 1911 | 5.047373448439589 1912 | 3.4733726180581517 1913 | 3.1907378111050617 1914 | 4.364045097812909 1915 | 3.320219561988684 1916 | 4.50590554041326 1917 | 4.851146273774336 1918 | 4.958141535856666 1919 | 5.235639152288142 1920 | 4.121506926059185 1921 | 4.136007295268326 1922 | 3.4617917505563818 1923 | 4.113997433414486 1924 | 4.129753160580249 1925 | 4.339112137364928 1926 | 5.882249393327242 1927 | 3.8268873651147404 1928 | 5.757821873723992 1929 | 4.710188971359624 1930 | 5.028678499823653 1931 | 4.588652252996537 1932 | 3.8048766516081445 1933 | 5.585959921198528 1934 | 4.407460377009423 1935 | 4.2715919322975795 1936 | 3.5375902345005015 1937 | 5.258795598522232 1938 | 3.2412588398559556 1939 | 5.179640721366879 1940 | 4.10279642392092 1941 | 3.933354406834581 1942 | 4.616039707753548 1943 | 5.439893093223313 1944 | 3.7271468868236544 1945 | 4.26587627611244 1946 | 4.607529217367036 1947 | 3.4000921179201247 1948 | 3.1789350210789014 1949 | 4.212695853701897 1950 | 4.871991451465101 1951 | 4.299568557683557 1952 | 4.354587163055506 1953 | 3.172426395463331 1954 | 4.5927906152483855 1955 | 4.844426151266411 1956 | 3.874525865951695 1957 | 3.3526192736077807 1958 | 5.349584179646069 1959 | 4.85088385614834 1960 | 4.1346555036951935 1961 | 3.867937875384782 1962 | 4.660732340754557 1963 | 3.8320669762238615 1964 | 5.182236108047279 1965 | 4.622263676434427 1966 | 5.355310391422572 1967 | 5.098017210762137 1968 | 4.018520511001483 1969 | 3.3656552303419858 1970 | 5.263767035449074 1971 | 5.724766409808146 1972 | 3.5699911275968508 1973 | 4.935145713698806 1974 | 5.259232981729012 1975 | 3.820947866742978 1976 | 5.110816892901987 1977 | 4.969734325058512 1978 | 4.420313315237264 1979 | 4.879499667102236 1980 | 5.1792523321651105 1981 | 4.276263653380668 1982 | 5.212570844063702 1983 | 3.863806661862975 1984 | 5.0693066337116335 1985 | 5.063506112301998 1986 | 5.037216125313055 1987 | 4.598494749702283 1988 | 4.6579432343083 1989 | 3.3930535124694594 1990 | 4.062123381112931 1991 | 5.006200169655577 1992 | 4.716463707031906 1993 | 5.3208699035208396 1994 | 3.2930818323536255 1995 | 5.60997149261726 1996 | 5.401959306661506 1997 | 4.064556396697538 1998 | 5.477540177271533 1999 | 4.093495995930941 2000 | 4.858157080620779 2001 | 4.585219723930008 2002 | 6.183608811980985 2003 | 5.727276801755955 2004 | 6.0601933777939285 2005 | 7.234830799320891 2006 | 5.846730340349813 2007 | 5.635511443617961 2008 | 6.092135836144546 2009 | 6.484122860919602 2010 | 5.70066153683125 2011 | 5.919686515535165 2012 | 7.20471002572171 2013 | 5.842464735873312 2014 | 6.886956349791641 2015 | 6.003305306171002 2016 | 7.126960442608629 2017 | 6.035643767952255 2018 | 6.718864697493141 2019 | 6.848648649818099 2020 | 6.152344946993556 2021 | 6.692287352055214 2022 | 5.806220771393828 2023 | 6.461010222725206 2024 | 6.370112136956773 2025 | 6.851217518802066 2026 | 6.4549275717457455 2027 | 6.426562232700359 2028 | 5.418307572729475 2029 | 6.898664893373502 2030 | 5.321755879241418 2031 | 5.791929037083784 2032 | 6.390782342491442 2033 | 6.599929780794161 2034 | 6.731655329054211 2035 | 5.859300669449669 2036 | 6.326119875107475 2037 | 5.811918395099662 2038 | 5.13373001251364 2039 | 5.786803394548227 2040 | 5.780248364767265 2041 | 6.490133438454372 2042 | 6.020746397986204 2043 | 6.0794581193772945 2044 | 7.304644197946374 2045 | 5.886914278949718 2046 | 6.747539091309425 2047 | 6.652814207367091 2048 | 5.793979986763385 2049 | 6.2312622863200255 2050 | 6.060206092152557 2051 | 7.264523516658612 2052 | 6.364120673290829 2053 | 5.911647355536284 2054 | 6.942779186446508 2055 | 6.218411460146336 2056 | 6.630346188620203 2057 | 5.147678701830707 2058 | 6.098132524111811 2059 | 6.57012957027287 2060 | 6.225496244491479 2061 | 6.485162803936411 2062 | 6.542634957261912 2063 | 5.763659149621054 2064 | 6.76490726192969 2065 | 5.948920399880557 2066 | 6.788364115401057 2067 | 7.136532657146473 2068 | 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6.284892525223112 2985 | 6.808657425553804 2986 | 6.892057006755522 2987 | 6.542624054538382 2988 | 6.014118836810514 2989 | 6.532309482500557 2990 | 6.269748287001909 2991 | 6.661604895553266 2992 | 6.957774677604095 2993 | 6.465095606734587 2994 | 6.170130003173826 2995 | 6.862976372216427 2996 | 6.837344263167474 2997 | 6.872729306793431 2998 | 5.71229625713546 2999 | 6.419588030536351 3000 | 5.8762577124293855 3001 | 5.4429753926593705 3002 | -------------------------------------------------------------------------------- /tests/test_linear_algebra.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """unittest 3 | """ 4 | import unittest 5 | import numpy as np 6 | from numpy.testing import assert_almost_equal 7 | from fastsst.util.linear_algebra import * 8 | 9 | class TestLinearAlgebra(unittest.TestCase): 10 | def setUp(self): 11 | np.random.seed(1234) 12 | self.A = np.random.rand(10,10) 13 | self.x0 = np.random.rand(10) 14 | self.x0 /= np.linalg.norm(self.x0) 15 | 16 | d = 3*np.ones(10) 17 | e = -1*np.ones(10 - 1) 18 | self.T = np.diag(d) + np.diag(e,k=1) + np.diag(e,k=-1) 19 | 20 | def tearDown(self): 21 | pass 22 | 23 | def test_power_method(self): 24 | u_pow,s_pow,_ = power_method(self.A,self.x0,n_iter=100) 25 | U_np,s_np,_ = np.linalg.svd(self.A) 26 | assert_almost_equal(s_pow,s_np[0]) 27 | assert_almost_equal(np.abs(u_pow),np.abs(U_np[:,0])) 28 | 29 | def test_eig_tridiag(self): 30 | U_tri,s_tri = eig_tridiag(self.T) 31 | U_np,s_np,_ = np.linalg.svd(self.T) 32 | assert_almost_equal(s_tri,s_np) 33 | assert_almost_equal(np.abs(U_tri),np.abs(U_np)) 34 | 35 | 36 | if __name__ == "__main__": 37 | unittest.main(verbosity=2) 38 | -------------------------------------------------------------------------------- /tests/test_sst.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """unittest 3 | """ 4 | import unittest 5 | import numpy as np 6 | import pandas as pd 7 | from numpy.testing import assert_almost_equal 8 | from fastsst.sst import SingularSpectrumTransformation 9 | 10 | class TestSingularSpectrumTransformation(unittest.TestCase): 11 | def setUp(self): 12 | pass 13 | def tearDown(self): 14 | pass 15 | 16 | def test_sst(self): 17 | x = pd.read_csv("tests/test_data/freq_change.csv").values[:,0] 18 | sst = SingularSpectrumTransformation(win_length=70) 19 | score = sst.score_offline(x) 20 | assert score.size == x.size 21 | assert (score >= 0).all() 22 | 23 | if __name__ == "__main__": 24 | unittest.main(verbosity=2) 25 | --------------------------------------------------------------------------------