302 lines
9.8 KiB
Python
302 lines
9.8 KiB
Python
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"""
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Test the fastica algorithm.
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"""
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import itertools
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import warnings
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import pytest
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import numpy as np
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from scipy import stats
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from sklearn.utils._testing import assert_almost_equal
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from sklearn.utils._testing import assert_array_almost_equal
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from sklearn.utils._testing import assert_warns
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from sklearn.decomposition import FastICA, fastica, PCA
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from sklearn.decomposition._fastica import _gs_decorrelation
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from sklearn.exceptions import ConvergenceWarning
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def center_and_norm(x, axis=-1):
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""" Centers and norms x **in place**
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Parameters
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-----------
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x: ndarray
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Array with an axis of observations (statistical units) measured on
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random variables.
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axis: int, optional
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Axis along which the mean and variance are calculated.
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"""
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x = np.rollaxis(x, axis)
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x -= x.mean(axis=0)
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x /= x.std(axis=0)
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def test_gs():
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# Test gram schmidt orthonormalization
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# generate a random orthogonal matrix
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rng = np.random.RandomState(0)
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W, _, _ = np.linalg.svd(rng.randn(10, 10))
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w = rng.randn(10)
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_gs_decorrelation(w, W, 10)
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assert (w ** 2).sum() < 1.e-10
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w = rng.randn(10)
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u = _gs_decorrelation(w, W, 5)
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tmp = np.dot(u, W.T)
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assert (tmp[:5] ** 2).sum() < 1.e-10
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@pytest.mark.parametrize("add_noise", [True, False])
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@pytest.mark.parametrize("seed", range(1))
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def test_fastica_simple(add_noise, seed):
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# Test the FastICA algorithm on very simple data.
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rng = np.random.RandomState(seed)
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# scipy.stats uses the global RNG:
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n_samples = 1000
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# Generate two sources:
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s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
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s2 = stats.t.rvs(1, size=n_samples)
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s = np.c_[s1, s2].T
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center_and_norm(s)
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s1, s2 = s
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# Mixing angle
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phi = 0.6
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mixing = np.array([[np.cos(phi), np.sin(phi)],
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[np.sin(phi), -np.cos(phi)]])
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m = np.dot(mixing, s)
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if add_noise:
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m += 0.1 * rng.randn(2, 1000)
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center_and_norm(m)
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# function as fun arg
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def g_test(x):
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return x ** 3, (3 * x ** 2).mean(axis=-1)
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algos = ['parallel', 'deflation']
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nls = ['logcosh', 'exp', 'cube', g_test]
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whitening = [True, False]
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for algo, nl, whiten in itertools.product(algos, nls, whitening):
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if whiten:
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k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo,
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random_state=rng)
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with pytest.raises(ValueError):
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fastica(m.T, fun=np.tanh, algorithm=algo)
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else:
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pca = PCA(n_components=2, whiten=True, random_state=rng)
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X = pca.fit_transform(m.T)
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k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo, whiten=False,
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random_state=rng)
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with pytest.raises(ValueError):
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fastica(X, fun=np.tanh, algorithm=algo)
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s_ = s_.T
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# Check that the mixing model described in the docstring holds:
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if whiten:
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assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
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center_and_norm(s_)
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s1_, s2_ = s_
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# Check to see if the sources have been estimated
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# in the wrong order
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if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
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s2_, s1_ = s_
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s1_ *= np.sign(np.dot(s1_, s1))
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s2_ *= np.sign(np.dot(s2_, s2))
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# Check that we have estimated the original sources
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if not add_noise:
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assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
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assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
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else:
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assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
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assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
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# Test FastICA class
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_, _, sources_fun = fastica(m.T, fun=nl, algorithm=algo,
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random_state=seed)
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ica = FastICA(fun=nl, algorithm=algo, random_state=seed)
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sources = ica.fit_transform(m.T)
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assert ica.components_.shape == (2, 2)
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assert sources.shape == (1000, 2)
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assert_array_almost_equal(sources_fun, sources)
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assert_array_almost_equal(sources, ica.transform(m.T))
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assert ica.mixing_.shape == (2, 2)
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for fn in [np.tanh, "exp(-.5(x^2))"]:
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ica = FastICA(fun=fn, algorithm=algo)
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with pytest.raises(ValueError):
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ica.fit(m.T)
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with pytest.raises(TypeError):
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FastICA(fun=range(10)).fit(m.T)
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def test_fastica_nowhiten():
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m = [[0, 1], [1, 0]]
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# test for issue #697
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ica = FastICA(n_components=1, whiten=False, random_state=0)
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assert_warns(UserWarning, ica.fit, m)
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assert hasattr(ica, 'mixing_')
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def test_fastica_convergence_fail():
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# Test the FastICA algorithm on very simple data
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# (see test_non_square_fastica).
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# Ensure a ConvergenceWarning raised if the tolerance is sufficiently low.
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rng = np.random.RandomState(0)
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n_samples = 1000
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# Generate two sources:
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t = np.linspace(0, 100, n_samples)
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s1 = np.sin(t)
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s2 = np.ceil(np.sin(np.pi * t))
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s = np.c_[s1, s2].T
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center_and_norm(s)
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# Mixing matrix
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mixing = rng.randn(6, 2)
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m = np.dot(mixing, s)
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# Do fastICA with tolerance 0. to ensure failing convergence
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ica = FastICA(algorithm="parallel", n_components=2, random_state=rng,
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max_iter=2, tol=0.)
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assert_warns(ConvergenceWarning, ica.fit, m.T)
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@pytest.mark.parametrize('add_noise', [True, False])
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def test_non_square_fastica(add_noise):
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# Test the FastICA algorithm on very simple data.
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rng = np.random.RandomState(0)
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n_samples = 1000
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# Generate two sources:
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t = np.linspace(0, 100, n_samples)
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s1 = np.sin(t)
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s2 = np.ceil(np.sin(np.pi * t))
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s = np.c_[s1, s2].T
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center_and_norm(s)
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s1, s2 = s
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# Mixing matrix
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mixing = rng.randn(6, 2)
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m = np.dot(mixing, s)
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if add_noise:
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m += 0.1 * rng.randn(6, n_samples)
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center_and_norm(m)
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k_, mixing_, s_ = fastica(m.T, n_components=2, random_state=rng)
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s_ = s_.T
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# Check that the mixing model described in the docstring holds:
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assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
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center_and_norm(s_)
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s1_, s2_ = s_
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# Check to see if the sources have been estimated
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# in the wrong order
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if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
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s2_, s1_ = s_
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s1_ *= np.sign(np.dot(s1_, s1))
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s2_ *= np.sign(np.dot(s2_, s2))
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# Check that we have estimated the original sources
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if not add_noise:
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assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=3)
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assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=3)
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def test_fit_transform():
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# Test FastICA.fit_transform
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rng = np.random.RandomState(0)
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X = rng.random_sample((100, 10))
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for whiten, n_components in [[True, 5], [False, None]]:
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n_components_ = (n_components if n_components is not None else
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X.shape[1])
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ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
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Xt = ica.fit_transform(X)
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assert ica.components_.shape == (n_components_, 10)
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assert Xt.shape == (100, n_components_)
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ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
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ica.fit(X)
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assert ica.components_.shape == (n_components_, 10)
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Xt2 = ica.transform(X)
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assert_array_almost_equal(Xt, Xt2)
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def test_inverse_transform():
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# Test FastICA.inverse_transform
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n_features = 10
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n_samples = 100
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n1, n2 = 5, 10
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rng = np.random.RandomState(0)
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X = rng.random_sample((n_samples, n_features))
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expected = {(True, n1): (n_features, n1),
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(True, n2): (n_features, n2),
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(False, n1): (n_features, n2),
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(False, n2): (n_features, n2)}
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for whiten in [True, False]:
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for n_components in [n1, n2]:
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n_components_ = (n_components if n_components is not None else
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X.shape[1])
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ica = FastICA(n_components=n_components, random_state=rng,
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whiten=whiten)
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with warnings.catch_warnings(record=True):
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# catch "n_components ignored" warning
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Xt = ica.fit_transform(X)
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expected_shape = expected[(whiten, n_components_)]
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assert ica.mixing_.shape == expected_shape
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X2 = ica.inverse_transform(Xt)
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assert X.shape == X2.shape
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# reversibility test in non-reduction case
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if n_components == X.shape[1]:
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assert_array_almost_equal(X, X2)
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def test_fastica_errors():
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n_features = 3
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n_samples = 10
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rng = np.random.RandomState(0)
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X = rng.random_sample((n_samples, n_features))
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w_init = rng.randn(n_features + 1, n_features + 1)
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with pytest.raises(ValueError, match='max_iter should be greater than 1'):
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FastICA(max_iter=0)
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with pytest.raises(ValueError, match=r'alpha must be in \[1,2\]'):
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fastica(X, fun_args={'alpha': 0})
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with pytest.raises(ValueError, match='w_init has invalid shape.+'
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r'should be \(3L?, 3L?\)'):
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fastica(X, w_init=w_init)
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with pytest.raises(ValueError, match='Invalid algorithm.+must '
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'be.+parallel.+or.+deflation'):
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fastica(X, algorithm='pizza')
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@pytest.mark.parametrize('whiten', [True, False])
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@pytest.mark.parametrize('return_X_mean', [True, False])
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@pytest.mark.parametrize('return_n_iter', [True, False])
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def test_fastica_output_shape(whiten, return_X_mean, return_n_iter):
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n_features = 3
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n_samples = 10
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rng = np.random.RandomState(0)
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X = rng.random_sample((n_samples, n_features))
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expected_len = 3 + return_X_mean + return_n_iter
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out = fastica(X, whiten=whiten, return_n_iter=return_n_iter,
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return_X_mean=return_X_mean)
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assert len(out) == expected_len
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if not whiten:
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assert out[0] is None
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