# Authors: Denis A. Engemann <denis.engemann@gmail.com>
#
# License: BSD (3-clause)

"""
Test the infomax algorithm.
Parts of this code are taken from scikit-learn
"""

import numpy as np
from numpy.testing import assert_almost_equal

from scipy import stats
from scipy import linalg

from mne.preprocessing.infomax_ import infomax
from mne.utils import requires_sklearn, run_tests_if_main, check_version


def center_and_norm(x, axis=-1):
    """ Centers and norms x **in place**

    Parameters
    -----------
    x: ndarray
        Array with an axis of observations (statistical units) measured on
        random variables.
    axis: int, optional
        Axis along which the mean and variance are calculated.
    """
    x = np.rollaxis(x, axis)
    x -= x.mean(axis=0)
    x /= x.std(axis=0)


@requires_sklearn
def test_infomax_blowup():
    """ Test the infomax algorithm blowup condition
    """

    # scipy.stats uses the global RNG:
    np.random.seed(0)
    n_samples = 100
    # Generate two sources:
    s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
    s2 = stats.t.rvs(1, size=n_samples)
    s = np.c_[s1, s2].T
    center_and_norm(s)
    s1, s2 = s

    # Mixing angle
    phi = 0.6
    mixing = np.array([[np.cos(phi),  np.sin(phi)],
                       [np.sin(phi), -np.cos(phi)]])
    m = np.dot(mixing, s)

    center_and_norm(m)

    X = _get_pca().fit_transform(m.T)
    k_ = infomax(X, extended=True, l_rate=0.1)
    s_ = np.dot(k_, X.T)

    center_and_norm(s_)
    s1_, s2_ = s_
    # Check to see if the sources have been estimated
    # in the wrong order
    if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
        s2_, s1_ = s_
    s1_ *= np.sign(np.dot(s1_, s1))
    s2_ *= np.sign(np.dot(s2_, s2))

    # Check that we have estimated the original sources
    assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
    assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)


@requires_sklearn
def test_infomax_simple():
    """ Test the infomax algorithm on very simple data.
    """
    rng = np.random.RandomState(0)
    # scipy.stats uses the global RNG:
    np.random.seed(0)
    n_samples = 500
    # Generate two sources:
    s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
    s2 = stats.t.rvs(1, size=n_samples)
    s = np.c_[s1, s2].T
    center_and_norm(s)
    s1, s2 = s

    # Mixing angle
    phi = 0.6
    mixing = np.array([[np.cos(phi),  np.sin(phi)],
                       [np.sin(phi), -np.cos(phi)]])
    for add_noise in (False, True):
        m = np.dot(mixing, s)
        if add_noise:
            m += 0.1 * rng.randn(2, n_samples)
        center_and_norm(m)

        algos = [True, False]
        for algo in algos:
            X = _get_pca().fit_transform(m.T)
            k_ = infomax(X, extended=algo)
            s_ = np.dot(k_, X.T)

            center_and_norm(s_)
            s1_, s2_ = s_
            # Check to see if the sources have been estimated
            # in the wrong order
            if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
                s2_, s1_ = s_
            s1_ *= np.sign(np.dot(s1_, s1))
            s2_ *= np.sign(np.dot(s2_, s2))

            # Check that we have estimated the original sources
            if not add_noise:
                assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
                assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
            else:
                assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
                assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)


def test_infomax_weights_ini():
    """ Test the infomax algorithm when user provides an initial weights matrix.
    """

    X = np.random.random((3, 100))
    weights = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.float64)

    w1 = infomax(X, max_iter=0, weights=weights, extended=True)
    w2 = infomax(X, max_iter=0, weights=weights, extended=False)

    assert_almost_equal(w1, weights)
    assert_almost_equal(w2, weights)


@requires_sklearn
def test_non_square_infomax():
    """ Test non-square infomax
    """
    rng = np.random.RandomState(0)

    n_samples = 200
    # Generate two sources:
    t = np.linspace(0, 100, n_samples)
    s1 = np.sin(t)
    s2 = np.ceil(np.sin(np.pi * t))
    s = np.c_[s1, s2].T
    center_and_norm(s)
    s1, s2 = s

    # Mixing matrix
    n_observed = 6
    mixing = rng.randn(n_observed, 2)
    for add_noise in (False, True):
        m = np.dot(mixing, s)

        if add_noise:
            m += 0.1 * rng.randn(n_observed, n_samples)

        center_and_norm(m)
        m = m.T
        m = _get_pca(rng).fit_transform(m)
        # we need extended since input signals are sub-gaussian
        unmixing_ = infomax(m, random_state=rng, extended=True)
        s_ = np.dot(unmixing_, m.T)
        # Check that the mixing model described in the docstring holds:
        mixing_ = linalg.pinv(unmixing_.T)

        assert_almost_equal(m, s_.T.dot(mixing_))

        center_and_norm(s_)
        s1_, s2_ = s_
        # Check to see if the sources have been estimated
        # in the wrong order
        if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
            s2_, s1_ = s_
        s1_ *= np.sign(np.dot(s1_, s1))
        s2_ *= np.sign(np.dot(s2_, s2))

        # Check that we have estimated the original sources
        if not add_noise:
            assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
            assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)


def _get_pca(rng=None):
    if not check_version('sklearn', '0.18'):
        from sklearn.decomposition import RandomizedPCA
        return RandomizedPCA(n_components=2, whiten=True,
                             random_state=rng)
    else:
        from sklearn.decomposition import PCA
        return PCA(n_components=2, whiten=True, svd_solver='randomized',
                   random_state=rng)


run_tests_if_main()
