463 lines
16 KiB
Python
463 lines
16 KiB
Python
# Authors: Olivier Grisel <olivier.grisel@ensta.org>
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# Mathieu Blondel <mathieu@mblondel.org>
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# Denis Engemann <d.engemann@fz-juelich.de>
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#
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# License: BSD 3 clause
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import warnings
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import numpy as np
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from scipy import sparse
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from scipy import linalg
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from scipy import stats
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from sklearn.utils.testing import assert_equal
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from sklearn.utils.testing import assert_almost_equal
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from sklearn.utils.testing import assert_array_equal
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_true
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from sklearn.utils.testing import assert_greater
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from sklearn.utils.testing import assert_raises
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from sklearn.utils.extmath import density
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from sklearn.utils.extmath import logsumexp
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from sklearn.utils.extmath import norm, squared_norm
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from sklearn.utils.extmath import randomized_svd
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from sklearn.utils.extmath import row_norms
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from sklearn.utils.extmath import weighted_mode
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from sklearn.utils.extmath import cartesian
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from sklearn.utils.extmath import log_logistic, logistic_sigmoid
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from sklearn.utils.extmath import fast_dot, _fast_dot
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from sklearn.utils.extmath import svd_flip
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from sklearn.utils.extmath import _batch_mean_variance_update
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from sklearn.datasets.samples_generator import make_low_rank_matrix
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def test_density():
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rng = np.random.RandomState(0)
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X = rng.randint(10, size=(10, 5))
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X[1, 2] = 0
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X[5, 3] = 0
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X_csr = sparse.csr_matrix(X)
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X_csc = sparse.csc_matrix(X)
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X_coo = sparse.coo_matrix(X)
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X_lil = sparse.lil_matrix(X)
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for X_ in (X_csr, X_csc, X_coo, X_lil):
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assert_equal(density(X_), density(X))
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def test_uniform_weights():
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# with uniform weights, results should be identical to stats.mode
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rng = np.random.RandomState(0)
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x = rng.randint(10, size=(10, 5))
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weights = np.ones(x.shape)
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for axis in (None, 0, 1):
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mode, score = stats.mode(x, axis)
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mode2, score2 = weighted_mode(x, weights, axis)
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assert_true(np.all(mode == mode2))
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assert_true(np.all(score == score2))
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def test_random_weights():
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# set this up so that each row should have a weighted mode of 6,
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# with a score that is easily reproduced
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mode_result = 6
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rng = np.random.RandomState(0)
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x = rng.randint(mode_result, size=(100, 10))
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w = rng.random_sample(x.shape)
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x[:, :5] = mode_result
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w[:, :5] += 1
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mode, score = weighted_mode(x, w, axis=1)
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assert_array_equal(mode, mode_result)
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assert_array_almost_equal(score.ravel(), w[:, :5].sum(1))
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def test_logsumexp():
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# Try to add some smallish numbers in logspace
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x = np.array([1e-40] * 1000000)
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logx = np.log(x)
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assert_almost_equal(np.exp(logsumexp(logx)), x.sum())
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X = np.vstack([x, x])
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logX = np.vstack([logx, logx])
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assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
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assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
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def test_randomized_svd_low_rank():
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"""Check that extmath.randomized_svd is consistent with linalg.svd"""
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n_samples = 100
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n_features = 500
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rank = 5
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k = 10
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# generate a matrix X of approximate effective rank `rank` and no noise
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# component (very structured signal):
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X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
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effective_rank=rank, tail_strength=0.0,
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random_state=0)
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assert_equal(X.shape, (n_samples, n_features))
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# compute the singular values of X using the slow exact method
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U, s, V = linalg.svd(X, full_matrices=False)
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# compute the singular values of X using the fast approximate method
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Ua, sa, Va = randomized_svd(X, k)
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assert_equal(Ua.shape, (n_samples, k))
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assert_equal(sa.shape, (k,))
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assert_equal(Va.shape, (k, n_features))
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# ensure that the singular values of both methods are equal up to the real
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# rank of the matrix
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assert_almost_equal(s[:k], sa)
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# check the singular vectors too (while not checking the sign)
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assert_almost_equal(np.dot(U[:, :k], V[:k, :]), np.dot(Ua, Va))
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# check the sparse matrix representation
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X = sparse.csr_matrix(X)
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# compute the singular values of X using the fast approximate method
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Ua, sa, Va = randomized_svd(X, k)
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assert_almost_equal(s[:rank], sa[:rank])
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def test_norm_squared_norm():
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X = np.random.RandomState(42).randn(50, 63)
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X *= 100 # check stability
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X += 200
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assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
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assert_almost_equal(norm(X) ** 2, squared_norm(X), decimal=6)
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assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
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def test_row_norms():
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X = np.random.RandomState(42).randn(100, 100)
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sq_norm = (X ** 2).sum(axis=1)
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assert_array_almost_equal(sq_norm, row_norms(X, squared=True), 5)
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assert_array_almost_equal(np.sqrt(sq_norm), row_norms(X))
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Xcsr = sparse.csr_matrix(X, dtype=np.float32)
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assert_array_almost_equal(sq_norm, row_norms(Xcsr, squared=True), 5)
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assert_array_almost_equal(np.sqrt(sq_norm), row_norms(Xcsr))
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def test_randomized_svd_low_rank_with_noise():
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"""Check that extmath.randomized_svd can handle noisy matrices"""
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n_samples = 100
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n_features = 500
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rank = 5
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k = 10
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# generate a matrix X wity structure approximate rank `rank` and an
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# important noisy component
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X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
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effective_rank=rank, tail_strength=0.5,
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random_state=0)
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assert_equal(X.shape, (n_samples, n_features))
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# compute the singular values of X using the slow exact method
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_, s, _ = linalg.svd(X, full_matrices=False)
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# compute the singular values of X using the fast approximate method
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# without the iterated power method
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_, sa, _ = randomized_svd(X, k, n_iter=0)
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# the approximation does not tolerate the noise:
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assert_greater(np.abs(s[:k] - sa).max(), 0.05)
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# compute the singular values of X using the fast approximate method with
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# iterated power method
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_, sap, _ = randomized_svd(X, k, n_iter=5)
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# the iterated power method is helping getting rid of the noise:
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assert_almost_equal(s[:k], sap, decimal=3)
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def test_randomized_svd_infinite_rank():
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"""Check that extmath.randomized_svd can handle noisy matrices"""
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n_samples = 100
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n_features = 500
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rank = 5
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k = 10
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# let us try again without 'low_rank component': just regularly but slowly
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# decreasing singular values: the rank of the data matrix is infinite
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X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
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effective_rank=rank, tail_strength=1.0,
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random_state=0)
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assert_equal(X.shape, (n_samples, n_features))
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# compute the singular values of X using the slow exact method
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_, s, _ = linalg.svd(X, full_matrices=False)
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# compute the singular values of X using the fast approximate method
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# without the iterated power method
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_, sa, _ = randomized_svd(X, k, n_iter=0)
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# the approximation does not tolerate the noise:
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assert_greater(np.abs(s[:k] - sa).max(), 0.1)
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# compute the singular values of X using the fast approximate method with
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# iterated power method
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_, sap, _ = randomized_svd(X, k, n_iter=5)
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# the iterated power method is still managing to get most of the structure
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# at the requested rank
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assert_almost_equal(s[:k], sap, decimal=3)
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def test_randomized_svd_transpose_consistency():
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"""Check that transposing the design matrix has limit impact"""
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n_samples = 100
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n_features = 500
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rank = 4
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k = 10
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X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
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effective_rank=rank, tail_strength=0.5,
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random_state=0)
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assert_equal(X.shape, (n_samples, n_features))
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U1, s1, V1 = randomized_svd(X, k, n_iter=3, transpose=False,
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random_state=0)
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U2, s2, V2 = randomized_svd(X, k, n_iter=3, transpose=True,
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random_state=0)
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U3, s3, V3 = randomized_svd(X, k, n_iter=3, transpose='auto',
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random_state=0)
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U4, s4, V4 = linalg.svd(X, full_matrices=False)
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assert_almost_equal(s1, s4[:k], decimal=3)
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assert_almost_equal(s2, s4[:k], decimal=3)
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assert_almost_equal(s3, s4[:k], decimal=3)
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assert_almost_equal(np.dot(U1, V1), np.dot(U4[:, :k], V4[:k, :]),
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decimal=2)
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assert_almost_equal(np.dot(U2, V2), np.dot(U4[:, :k], V4[:k, :]),
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decimal=2)
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# in this case 'auto' is equivalent to transpose
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assert_almost_equal(s2, s3)
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def test_svd_flip():
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"""Check that svd_flip works in both situations, and reconstructs input."""
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rs = np.random.RandomState(1999)
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n_samples = 20
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n_features = 10
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X = rs.randn(n_samples, n_features)
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# Check matrix reconstruction
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U, S, V = linalg.svd(X, full_matrices=False)
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U1, V1 = svd_flip(U, V, u_based_decision=False)
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assert_almost_equal(np.dot(U1 * S, V1), X, decimal=6)
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# Check transposed matrix reconstruction
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XT = X.T
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U, S, V = linalg.svd(XT, full_matrices=False)
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U2, V2 = svd_flip(U, V, u_based_decision=True)
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assert_almost_equal(np.dot(U2 * S, V2), XT, decimal=6)
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# Check that different flip methods are equivalent under reconstruction
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U_flip1, V_flip1 = svd_flip(U, V, u_based_decision=True)
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assert_almost_equal(np.dot(U_flip1 * S, V_flip1), XT, decimal=6)
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U_flip2, V_flip2 = svd_flip(U, V, u_based_decision=False)
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assert_almost_equal(np.dot(U_flip2 * S, V_flip2), XT, decimal=6)
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def test_randomized_svd_sign_flip():
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a = np.array([[2.0, 0.0], [0.0, 1.0]])
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u1, s1, v1 = randomized_svd(a, 2, flip_sign=True, random_state=41)
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for seed in range(10):
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u2, s2, v2 = randomized_svd(a, 2, flip_sign=True, random_state=seed)
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assert_almost_equal(u1, u2)
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assert_almost_equal(v1, v2)
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assert_almost_equal(np.dot(u2 * s2, v2), a)
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assert_almost_equal(np.dot(u2.T, u2), np.eye(2))
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assert_almost_equal(np.dot(v2.T, v2), np.eye(2))
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def test_cartesian():
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"""Check if cartesian product delivers the right results"""
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axes = (np.array([1, 2, 3]), np.array([4, 5]), np.array([6, 7]))
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true_out = np.array([[1, 4, 6],
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[1, 4, 7],
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[1, 5, 6],
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[1, 5, 7],
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[2, 4, 6],
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[2, 4, 7],
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[2, 5, 6],
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[2, 5, 7],
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[3, 4, 6],
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[3, 4, 7],
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[3, 5, 6],
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[3, 5, 7]])
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out = cartesian(axes)
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assert_array_equal(true_out, out)
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# check single axis
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x = np.arange(3)
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assert_array_equal(x[:, np.newaxis], cartesian((x,)))
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def test_logistic_sigmoid():
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"""Check correctness and robustness of logistic sigmoid implementation"""
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naive_logistic = lambda x: 1 / (1 + np.exp(-x))
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naive_log_logistic = lambda x: np.log(naive_logistic(x))
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x = np.linspace(-2, 2, 50)
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with warnings.catch_warnings(record=True):
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assert_array_almost_equal(logistic_sigmoid(x), naive_logistic(x))
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assert_array_almost_equal(log_logistic(x), naive_log_logistic(x))
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extreme_x = np.array([-100., 100.])
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assert_array_almost_equal(log_logistic(extreme_x), [-100, 0])
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def test_fast_dot():
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"""Check fast dot blas wrapper function"""
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if fast_dot is np.dot:
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return
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rng = np.random.RandomState(42)
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A = rng.random_sample([2, 10])
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B = rng.random_sample([2, 10])
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try:
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linalg.get_blas_funcs(['gemm'])[0]
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has_blas = True
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except (AttributeError, ValueError):
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has_blas = False
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if has_blas:
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# Test _fast_dot for invalid input.
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# Maltyped data.
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for dt1, dt2 in [['f8', 'f4'], ['i4', 'i4']]:
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assert_raises(ValueError, _fast_dot, A.astype(dt1),
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B.astype(dt2).T)
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# Malformed data.
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## ndim == 0
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E = np.empty(0)
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assert_raises(ValueError, _fast_dot, E, E)
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## ndim == 1
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assert_raises(ValueError, _fast_dot, A, A[0])
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## ndim > 2
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assert_raises(ValueError, _fast_dot, A.T, np.array([A, A]))
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## min(shape) == 1
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assert_raises(ValueError, _fast_dot, A, A[0, :][None, :])
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# test for matrix mismatch error
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assert_raises(ValueError, _fast_dot, A, A)
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# Test cov-like use case + dtypes.
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for dtype in ['f8', 'f4']:
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A = A.astype(dtype)
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B = B.astype(dtype)
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# col < row
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C = np.dot(A.T, A)
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C_ = fast_dot(A.T, A)
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assert_almost_equal(C, C_, decimal=5)
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C = np.dot(A.T, B)
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C_ = fast_dot(A.T, B)
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assert_almost_equal(C, C_, decimal=5)
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C = np.dot(A, B.T)
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C_ = fast_dot(A, B.T)
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assert_almost_equal(C, C_, decimal=5)
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# Test square matrix * rectangular use case.
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A = rng.random_sample([2, 2])
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for dtype in ['f8', 'f4']:
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A = A.astype(dtype)
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B = B.astype(dtype)
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C = np.dot(A, B)
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C_ = fast_dot(A, B)
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assert_almost_equal(C, C_, decimal=5)
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C = np.dot(A.T, B)
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C_ = fast_dot(A.T, B)
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assert_almost_equal(C, C_, decimal=5)
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if has_blas:
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for x in [np.array([[d] * 10] * 2) for d in [np.inf, np.nan]]:
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assert_raises(ValueError, _fast_dot, x, x.T)
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def test_incremental_variance_update_formulas():
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"""Test Youngs and Cramer incremental variance formulas."""
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# Doggie data from http://www.mathsisfun.com/data/standard-deviation.html
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A = np.array([[600, 470, 170, 430, 300],
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[600, 470, 170, 430, 300],
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[600, 470, 170, 430, 300],
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[600, 470, 170, 430, 300]]).T
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idx = 2
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X1 = A[:idx, :]
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X2 = A[idx:, :]
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old_means = X1.mean(axis=0)
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old_variances = X1.var(axis=0)
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old_sample_count = X1.shape[0]
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final_means, final_variances, final_count = _batch_mean_variance_update(
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X2, old_means, old_variances, old_sample_count)
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assert_almost_equal(final_means, A.mean(axis=0), 6)
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assert_almost_equal(final_variances, A.var(axis=0), 6)
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assert_almost_equal(final_count, A.shape[0])
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def test_incremental_variance_ddof():
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"""Test that degrees of freedom parameter for calculations are correct."""
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rng = np.random.RandomState(1999)
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X = rng.randn(50, 10)
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n_samples, n_features = X.shape
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for batch_size in [11, 20, 37]:
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steps = np.arange(0, X.shape[0], batch_size)
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if steps[-1] != X.shape[0]:
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steps = np.hstack([steps, n_samples])
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for i, j in zip(steps[:-1], steps[1:]):
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batch = X[i:j, :]
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if i == 0:
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incremental_means = batch.mean(axis=0)
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incremental_variances = batch.var(axis=0)
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# Assign this twice so that the test logic is consistent
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incremental_count = batch.shape[0]
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sample_count = batch.shape[0]
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else:
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result = _batch_mean_variance_update(batch, incremental_means,
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incremental_variances,
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sample_count)
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(incremental_means, incremental_variances,
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incremental_count) = result
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sample_count += batch.shape[0]
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calculated_means = np.mean(X[:j], axis=0)
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calculated_variances = np.var(X[:j], axis=0)
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assert_almost_equal(incremental_means, calculated_means, 6)
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assert_almost_equal(incremental_variances,
|
|
calculated_variances, 6)
|
|
assert_equal(incremental_count, sample_count)
|
|
|
|
if __name__ == '__main__':
|
|
import nose
|
|
nose.runmodule()
|