254 lines
8.6 KiB
Python
254 lines
8.6 KiB
Python
# Authors: Olivier Grisel <olivier.grisel@ensta.org>
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# Mathieu Blondel <mathieu@mblondel.org>
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# License: BSD
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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.extmath import density
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from sklearn.utils.extmath import logsumexp
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from sklearn.utils.extmath import randomized_svd
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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.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_true(np.all(mode == mode_result))
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assert_true(np.all(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_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_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 xrange(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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