test_hmm.py

from __future__ import print_function
import numpy as np

from numpy.testing import assert_array_equal, assert_array_almost_equal
from unittest import TestCase

from sklearn.datasets.samples_generator import make_spd_matrix
from sklearn import hmm
from sklearn import mixture
from sklearn.utils.extmath import logsumexp
from sklearn.utils import check_random_state

from nose import SkipTest

rng = np.random.RandomState(0)
np.seterr(all='warn')


class TestBaseHMM(TestCase):

    def setUp(self):
        self.prng = np.random.RandomState(9)

    class StubHMM(hmm._BaseHMM):

        def _compute_log_likelihood(self, X):
            return self.framelogprob

        def _generate_sample_from_state(self):
            pass

        def _init(self):
            pass

    def setup_example_hmm(self):
        # Example from http://en.wikipedia.org/wiki/Forward-backward_algorithm
        h = self.StubHMM(2)
        h.transmat_ = [[0.7, 0.3], [0.3, 0.7]]
        h.startprob_ = [0.5, 0.5]
        framelogprob = np.log([[0.9, 0.2],
                               [0.9, 0.2],
                               [0.1, 0.8],
                               [0.9, 0.2],
                               [0.9, 0.2]])
        # Add dummy observations to stub.
        h.framelogprob = framelogprob
        return h, framelogprob

    def test_init(self):
        h, framelogprob = self.setup_example_hmm()
        for params in [('transmat_',), ('startprob_', 'transmat_')]:
            d = dict((x[:-1], getattr(h, x)) for x in params)
            h2 = self.StubHMM(h.n_components, **d)
            self.assertEqual(h.n_components, h2.n_components)
            for p in params:
                assert_array_almost_equal(getattr(h, p), getattr(h2, p))

    def test_set_startprob(self):
        h, framelogprob = self.setup_example_hmm()
        startprob = np.array([0.0, 1.0])
        h.startprob_ = startprob
        assert np.allclose(startprob, h.startprob_)

    def test_set_transmat(self):
        h, framelogprob = self.setup_example_hmm()
        transmat = np.array([[0.8, 0.2], [0.0, 1.0]])
        h.transmat_ = transmat
        assert np.allclose(transmat, h.transmat_)

    def test_do_forward_pass(self):
        h, framelogprob = self.setup_example_hmm()

        logprob, fwdlattice = h._do_forward_pass(framelogprob)

        reflogprob = -3.3725
        self.assertAlmostEqual(logprob, reflogprob, places=4)

        reffwdlattice = np.array([[0.4500, 0.1000],
                                  [0.3105, 0.0410],
                                  [0.0230, 0.0975],
                                  [0.0408, 0.0150],
                                  [0.0298, 0.0046]])
        assert_array_almost_equal(np.exp(fwdlattice), reffwdlattice, 4)

    def test_do_backward_pass(self):
        h, framelogprob = self.setup_example_hmm()

        bwdlattice = h._do_backward_pass(framelogprob)

        refbwdlattice = np.array([[0.0661, 0.0455],
                                  [0.0906, 0.1503],
                                  [0.4593, 0.2437],
                                  [0.6900, 0.4100],
                                  [1.0000, 1.0000]])
        assert_array_almost_equal(np.exp(bwdlattice), refbwdlattice, 4)

    def test_do_viterbi_pass(self):
        h, framelogprob = self.setup_example_hmm()

        logprob, state_sequence = h._do_viterbi_pass(framelogprob)

        refstate_sequence = [0, 0, 1, 0, 0]
        assert_array_equal(state_sequence, refstate_sequence)

        reflogprob = -4.4590
        self.assertAlmostEqual(logprob, reflogprob, places=4)

    def test_score_samples(self):
        h, framelogprob = self.setup_example_hmm()
        nobs = len(framelogprob)

        logprob, posteriors = h.score_samples([])

        assert_array_almost_equal(posteriors.sum(axis=1), np.ones(nobs))

        reflogprob = -3.3725
        self.assertAlmostEqual(logprob, reflogprob, places=4)

        refposteriors = np.array([[0.8673, 0.1327],
                                  [0.8204, 0.1796],
                                  [0.3075, 0.6925],
                                  [0.8204, 0.1796],
                                  [0.8673, 0.1327]])
        assert_array_almost_equal(posteriors, refposteriors, decimal=4)

    def test_hmm_score_samples_consistent_with_gmm(self):
        n_components = 8
        nobs = 10
        h = self.StubHMM(n_components)

        # Add dummy observations to stub.
        framelogprob = np.log(self.prng.rand(nobs, n_components))
        h.framelogprob = framelogprob

        # If startprob and transmat are uniform across all states (the
        # default), the transitions are uninformative - the model
        # reduces to a GMM with uniform mixing weights (in terms of
        # posteriors, not likelihoods).
        logprob, hmmposteriors = h.score_samples([])

        assert_array_almost_equal(hmmposteriors.sum(axis=1), np.ones(nobs))

        norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
        gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
        assert_array_almost_equal(hmmposteriors, gmmposteriors)

    def test_hmm_decode_consistent_with_gmm(self):
        n_components = 8
        nobs = 10
        h = self.StubHMM(n_components)

        # Add dummy observations to stub.
        framelogprob = np.log(self.prng.rand(nobs, n_components))
        h.framelogprob = framelogprob

        # If startprob and transmat are uniform across all states (the
        # default), the transitions are uninformative - the model
        # reduces to a GMM with uniform mixing weights (in terms of
        # posteriors, not likelihoods).
        viterbi_ll, state_sequence = h.decode([])

        norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
        gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
        gmmstate_sequence = gmmposteriors.argmax(axis=1)
        assert_array_equal(state_sequence, gmmstate_sequence)

    def test_base_hmm_attributes(self):
        n_components = 20
        startprob = self.prng.rand(n_components)
        startprob = startprob / startprob.sum()
        transmat = self.prng.rand(n_components, n_components)
        transmat /= np.tile(transmat.sum(axis=1)
                            [:, np.newaxis], (1, n_components))

        h = self.StubHMM(n_components)

        self.assertEqual(h.n_components, n_components)

        h.startprob_ = startprob
        assert_array_almost_equal(h.startprob_, startprob)

        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          2 * startprob)
        self.assertRaises(ValueError, h.__setattr__, 'startprob_', [])
        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          np.zeros((n_components - 2, 2)))

        h.transmat_ = transmat
        assert_array_almost_equal(h.transmat_, transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          2 * transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_', [])
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          np.zeros((n_components - 2, n_components)))


def train_hmm_and_keep_track_of_log_likelihood(hmm, obs, n_iter=1, **kwargs):
    hmm.n_iter = 1
    hmm.fit(obs)
    loglikelihoods = []
    for n in range(n_iter):
        hmm.n_iter = 1
        hmm.init_params = ''
        hmm.fit(obs)
        loglikelihoods.append(sum(hmm.score(x) for x in obs))
    return loglikelihoods


class GaussianHMMBaseTester(object):

    def setUp(self):
        self.prng = prng = np.random.RandomState(10)
        self.n_components = n_components = 3
        self.n_features = n_features = 3
        self.startprob = prng.rand(n_components)
        self.startprob = self.startprob / self.startprob.sum()
        self.transmat = prng.rand(n_components, n_components)
        self.transmat /= np.tile(self.transmat.sum(axis=1)[:, np.newaxis],
                                 (1, n_components))
        self.means = prng.randint(-20, 20, (n_components, n_features))
        self.covars = {
            'spherical': (1.0 + 2 * np.dot(prng.rand(n_components, 1),
                                           np.ones((1, n_features)))) ** 2,
            'tied': (make_spd_matrix(n_features, random_state=0)
                     + np.eye(n_features)),
            'diag': (1.0 + 2 * prng.rand(n_components, n_features)) ** 2,
            'full': np.array([make_spd_matrix(n_features, random_state=0)
                              + np.eye(n_features)
                              for x in range(n_components)]),
        }
        self.expanded_covars = {
            'spherical': [np.eye(n_features) * cov
                          for cov in self.covars['spherical']],
            'diag': [np.diag(cov) for cov in self.covars['diag']],
            'tied': [self.covars['tied']] * n_components,
            'full': self.covars['full'],
        }

    def test_bad_covariance_type(self):
        hmm.GaussianHMM(20, self.covariance_type)
        self.assertRaises(ValueError, hmm.GaussianHMM, 20,
                          'badcovariance_type')

    def test_score_samples_and_decode(self):
        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        h.means_ = self.means
        h.covars_ = self.covars[self.covariance_type]

        # Make sure the means are far apart so posteriors.argmax()
        # picks the actual component used to generate the observations.
        h.means_ = 20 * h.means_

        gaussidx = np.repeat(np.arange(self.n_components), 5)
        nobs = len(gaussidx)
        obs = self.prng.randn(nobs, self.n_features) + h.means_[gaussidx]

        ll, posteriors = h.score_samples(obs)

        self.assertEqual(posteriors.shape, (nobs, self.n_components))
        assert_array_almost_equal(posteriors.sum(axis=1), np.ones(nobs))

        viterbi_ll, stateseq = h.decode(obs)
        assert_array_equal(stateseq, gaussidx)

    def test_sample(self, n=1000):
        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        # Make sure the means are far apart so posteriors.argmax()
        # picks the actual component used to generate the observations.
        h.means_ = 20 * self.means
        h.covars_ = np.maximum(self.covars[self.covariance_type], 0.1)
        h.startprob_ = self.startprob

        samples = h.sample(n)[0]
        self.assertEqual(samples.shape, (n, self.n_features))

    def test_fit(self, params='stmc', n_iter=5, verbose=False, **kwargs):
        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        h.startprob_ = self.startprob
        h.transmat_ = hmm.normalize(
            self.transmat + np.diag(self.prng.rand(self.n_components)), 1)
        h.means_ = 20 * self.means
        h.covars_ = self.covars[self.covariance_type]

        # Create training data by sampling from the HMM.
        train_obs = [h.sample(n=10)[0] for x in range(10)]

        # Mess up the parameters and see if we can re-learn them.
        h.n_iter = 0
        h.fit(train_obs)

        trainll = train_hmm_and_keep_track_of_log_likelihood(
            h, train_obs, n_iter=n_iter, params=params, **kwargs)[1:]

        # Check that the loglik is always increasing during training
        if not np.all(np.diff(trainll) > 0) and verbose:
            print('Test train: %s (%s)\n  %s\n  %s'
                  % (self.covariance_type, params, trainll, np.diff(trainll)))
        delta_min = np.diff(trainll).min()
        self.assertTrue(
            delta_min > -0.8,
            "The min nll increase is %f which is lower than the admissible"
            " threshold of %f, for model %s. The likelihoods are %s."
            % (delta_min, -0.8, self.covariance_type, trainll))

    def test_fit_works_on_sequences_of_different_length(self):
        obs = [self.prng.rand(3, self.n_features),
               self.prng.rand(4, self.n_features),
               self.prng.rand(5, self.n_features)]

        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        # This shouldn't raise
        # ValueError: setting an array element with a sequence.
        h.fit(obs)

    def test_fit_with_length_one_signal(self):
        obs = [self.prng.rand(10, self.n_features),
               self.prng.rand(8, self.n_features),
               self.prng.rand(1, self.n_features)]
        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        # This shouldn't raise
        # ValueError: zero-size array to reduction operation maximum which has no identity
        h.fit(obs)


    def test_fit_with_priors(self, params='stmc', n_iter=5, verbose=False):
        startprob_prior = 10 * self.startprob + 2.0
        transmat_prior = 10 * self.transmat + 2.0
        means_prior = self.means
        means_weight = 2.0
        covars_weight = 2.0
        if self.covariance_type in ('full', 'tied'):
            covars_weight += self.n_features
        covars_prior = self.covars[self.covariance_type]

        h = hmm.GaussianHMM(self.n_components, self.covariance_type)
        h.startprob_ = self.startprob
        h.startprob_prior = startprob_prior
        h.transmat_ = hmm.normalize(
            self.transmat + np.diag(self.prng.rand(self.n_components)), 1)
        h.transmat_prior = transmat_prior
        h.means_ = 20 * self.means
        h.means_prior = means_prior
        h.means_weight = means_weight
        h.covars_ = self.covars[self.covariance_type]
        h.covars_prior = covars_prior
        h.covars_weight = covars_weight

        # Create training data by sampling from the HMM.
        train_obs = [h.sample(n=10)[0] for x in range(10)]

        # Mess up the parameters and see if we can re-learn them.
        h.n_iter = 0
        h.fit(train_obs[:1])

        trainll = train_hmm_and_keep_track_of_log_likelihood(
            h, train_obs, n_iter=n_iter, params=params)[1:]

        # Check that the loglik is always increasing during training
        if not np.all(np.diff(trainll) > 0) and verbose:
            print('Test MAP train: %s (%s)\n  %s\n  %s'
                  % (self.covariance_type, params, trainll, np.diff(trainll)))
        # XXX: Why such a large tolerance?
        self.assertTrue(np.all(np.diff(trainll) > -0.5))

    def test_fit_non_ergodic_transmat(self):
        startprob = np.array([1, 0, 0, 0, 0])
        transmat = np.array([[0.9, 0.1, 0, 0, 0],
                             [0, 0.9, 0.1, 0, 0],
                             [0, 0, 0.9, 0.1, 0],
                             [0, 0, 0, 0.9, 0.1],
                             [0, 0, 0, 0, 1.0]])

        h = hmm.GaussianHMM(n_components=5,
                            covariance_type='full', startprob=startprob,
                            transmat=transmat, n_iter=100, init_params='st')

        h.means_ = np.zeros((5, 10))
        h.covars_ = np.tile(np.identity(10), (5, 1, 1))

        obs = [h.sample(10)[0] for _ in range(10)]

        h.fit(obs=obs)


class TestGaussianHMMWithSphericalCovars(GaussianHMMBaseTester, TestCase):
    covariance_type = 'spherical'

    def test_fit_startprob_and_transmat(self):
        self.test_fit('st')


class TestGaussianHMMWithDiagonalCovars(GaussianHMMBaseTester, TestCase):
    covariance_type = 'diag'


class TestGaussianHMMWithTiedCovars(GaussianHMMBaseTester, TestCase):
    covariance_type = 'tied'


class TestGaussianHMMWithFullCovars(GaussianHMMBaseTester, TestCase):
    covariance_type = 'full'


class MultinomialHMMTestCase(TestCase):
    """Using examples from Wikipedia

    - http://en.wikipedia.org/wiki/Hidden_Markov_model
    - http://en.wikipedia.org/wiki/Viterbi_algorithm
    """

    def setUp(self):
        self.prng = np.random.RandomState(9)
        self.n_components = 2   # ('Rainy', 'Sunny')
        self.n_symbols = 3  # ('walk', 'shop', 'clean')
        self.emissionprob = [[0.1, 0.4, 0.5], [0.6, 0.3, 0.1]]
        self.startprob = [0.6, 0.4]
        self.transmat = [[0.7, 0.3], [0.4, 0.6]]

        self.h = hmm.MultinomialHMM(self.n_components,
                                    startprob=self.startprob,
                                    transmat=self.transmat)
        self.h.emissionprob_ = self.emissionprob

    def test_set_emissionprob(self):
        h = hmm.MultinomialHMM(self.n_components)
        emissionprob = np.array([[0.8, 0.2, 0.0], [0.7, 0.2, 1.0]])
        h.emissionprob = emissionprob
        assert np.allclose(emissionprob, h.emissionprob)

    def test_wikipedia_viterbi_example(self):
        # From http://en.wikipedia.org/wiki/Viterbi_algorithm:
        # "This reveals that the observations ['walk', 'shop', 'clean']
        # were most likely generated by states ['Sunny', 'Rainy',
        # 'Rainy'], with probability 0.01344."
        observations = [0, 1, 2]
        logprob, state_sequence = self.h.decode(observations)
        self.assertAlmostEqual(np.exp(logprob), 0.01344)
        assert_array_equal(state_sequence, [1, 0, 0])

    def test_decode_map_algorithm(self):
        observations = [0, 1, 2]
        h = hmm.MultinomialHMM(self.n_components, startprob=self.startprob,
                               transmat=self.transmat, algorithm="map",)
        h.emissionprob_ = self.emissionprob
        logprob, state_sequence = h.decode(observations)
        assert_array_equal(state_sequence, [1, 0, 0])

    def test_predict(self):
        observations = [0, 1, 2]
        state_sequence = self.h.predict(observations)
        posteriors = self.h.predict_proba(observations)
        assert_array_equal(state_sequence, [1, 0, 0])
        assert_array_almost_equal(posteriors, [
            [0.23170303, 0.76829697],
            [0.62406281, 0.37593719],
            [0.86397706, 0.13602294],
        ])

    def test_attributes(self):
        h = hmm.MultinomialHMM(self.n_components)

        self.assertEqual(h.n_components, self.n_components)

        h.startprob_ = self.startprob
        assert_array_almost_equal(h.startprob_, self.startprob)
        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          2 * self.startprob)
        self.assertRaises(ValueError, h.__setattr__, 'startprob_', [])
        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          np.zeros((self.n_components - 2, self.n_symbols)))

        h.transmat_ = self.transmat
        assert_array_almost_equal(h.transmat_, self.transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          2 * self.transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_', [])
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          np.zeros((self.n_components - 2, self.n_components)))

        h.emissionprob_ = self.emissionprob
        assert_array_almost_equal(h.emissionprob_, self.emissionprob)
        self.assertRaises(ValueError, h.__setattr__, 'emissionprob_', [])
        self.assertRaises(ValueError, h.__setattr__, 'emissionprob_',
                          np.zeros((self.n_components - 2, self.n_symbols)))
        self.assertEqual(h.n_symbols, self.n_symbols)

    def test_score_samples(self):
        idx = np.repeat(np.arange(self.n_components), 10)
        nobs = len(idx)
        obs = [int(x) for x in np.floor(self.prng.rand(nobs) * self.n_symbols)]

        ll, posteriors = self.h.score_samples(obs)

        self.assertEqual(posteriors.shape, (nobs, self.n_components))
        assert_array_almost_equal(posteriors.sum(axis=1), np.ones(nobs))

    def test_sample(self, n=1000):
        samples = self.h.sample(n)[0]
        self.assertEqual(len(samples), n)
        self.assertEqual(len(np.unique(samples)), self.n_symbols)

    def test_fit(self, params='ste', n_iter=5, verbose=False, **kwargs):
        h = self.h

        # Create training data by sampling from the HMM.
        train_obs = [h.sample(n=10)[0] for x in range(10)]

        # Mess up the parameters and see if we can re-learn them.
        h.startprob_ = hmm.normalize(self.prng.rand(self.n_components))
        h.transmat_ = hmm.normalize(self.prng.rand(self.n_components,
                                                   self.n_components), axis=1)
        h.emissionprob_ = hmm.normalize(
            self.prng.rand(self.n_components, self.n_symbols), axis=1)

        trainll = train_hmm_and_keep_track_of_log_likelihood(
            h, train_obs, n_iter=n_iter, params=params, **kwargs)[1:]

        # Check that the loglik is always increasing during training
        if not np.all(np.diff(trainll) > 0) and verbose:
            print('Test train: (%s)\n  %s\n  %s' % (params, trainll,
                                                    np.diff(trainll)))
        self.assertTrue(np.all(np.diff(trainll) > -1.e-3))

    def test_fit_emissionprob(self):
        self.test_fit('e')

    def test_fit_with_init(self, params='ste', n_iter=5, verbose=False,
                           **kwargs):
        h = self.h
        learner = hmm.MultinomialHMM(self.n_components)

        # Create training data by sampling from the HMM.
        train_obs = [h.sample(n=10)[0] for x in range(10)]

        # use init_function to initialize paramerters
        learner._init(train_obs, params)

        trainll = train_hmm_and_keep_track_of_log_likelihood(
            learner, train_obs, n_iter=n_iter, params=params, **kwargs)[1:]

        # Check that the loglik is always increasing during training
        if not np.all(np.diff(trainll) > 0) and verbose:
            print()
            print('Test train: (%s)\n  %s\n  %s' % (params, trainll,
                                                    np.diff(trainll)))
        self.assertTrue(np.all(np.diff(trainll) > -1.e-3))


def create_random_gmm(n_mix, n_features, covariance_type, prng=0):
    prng = check_random_state(prng)
    g = mixture.GMM(n_mix, covariance_type=covariance_type)
    g.means_ = prng.randint(-20, 20, (n_mix, n_features))
    mincv = 0.1
    g.covars_ = {
        'spherical': (mincv + mincv * np.dot(prng.rand(n_mix, 1),
                                             np.ones((1, n_features)))) ** 2,
        'tied': (make_spd_matrix(n_features, random_state=prng)
                 + mincv * np.eye(n_features)),
        'diag': (mincv + mincv * prng.rand(n_mix, n_features)) ** 2,
        'full': np.array(
            [make_spd_matrix(n_features, random_state=prng)
             + mincv * np.eye(n_features) for x in range(n_mix)])
    }[covariance_type]
    g.weights_ = hmm.normalize(prng.rand(n_mix))
    return g


class GMMHMMBaseTester(object):

    def setUp(self):
        self.prng = np.random.RandomState(9)
        self.n_components = 3
        self.n_mix = 2
        self.n_features = 2
        self.covariance_type = 'diag'
        self.startprob = self.prng.rand(self.n_components)
        self.startprob = self.startprob / self.startprob.sum()
        self.transmat = self.prng.rand(self.n_components, self.n_components)
        self.transmat /= np.tile(self.transmat.sum(axis=1)[:, np.newaxis],
                                 (1, self.n_components))

        self.gmms_ = []
        for state in range(self.n_components):
            self.gmms_.append(create_random_gmm(
                self.n_mix, self.n_features, self.covariance_type,
                prng=self.prng))

    def test_attributes(self):
        h = hmm.GMMHMM(self.n_components, covariance_type=self.covariance_type)

        self.assertEqual(h.n_components, self.n_components)

        h.startprob_ = self.startprob
        assert_array_almost_equal(h.startprob_, self.startprob)
        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          2 * self.startprob)
        self.assertRaises(ValueError, h.__setattr__, 'startprob_', [])
        self.assertRaises(ValueError, h.__setattr__, 'startprob_',
                          np.zeros((self.n_components - 2, self.n_features)))

        h.transmat_ = self.transmat
        assert_array_almost_equal(h.transmat_, self.transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          2 * self.transmat)
        self.assertRaises(ValueError, h.__setattr__, 'transmat_', [])
        self.assertRaises(ValueError, h.__setattr__, 'transmat_',
                          np.zeros((self.n_components - 2, self.n_components)))

    def test_score_samples_and_decode(self):
        h = hmm.GMMHMM(self.n_components, gmms=self.gmms_)
        # Make sure the means are far apart so posteriors.argmax()
        # picks the actual component used to generate the observations.
        for g in h.gmms_:
            g.means_ *= 20

        refstateseq = np.repeat(np.arange(self.n_components), 5)
        nobs = len(refstateseq)
        obs = [h.gmms_[x].sample(1).flatten() for x in refstateseq]

        ll, posteriors = h.score_samples(obs)

        self.assertEqual(posteriors.shape, (nobs, self.n_components))
        assert_array_almost_equal(posteriors.sum(axis=1), np.ones(nobs))

        viterbi_ll, stateseq = h.decode(obs)
        assert_array_equal(stateseq, refstateseq)

    def test_sample(self, n=1000):
        h = hmm.GMMHMM(self.n_components, self.covariance_type,
                       startprob=self.startprob, transmat=self.transmat,
                       gmms=self.gmms_)
        samples = h.sample(n)[0]
        self.assertEqual(samples.shape, (n, self.n_features))

    def test_fit(self, params='stmwc', n_iter=5, verbose=False, **kwargs):
        h = hmm.GMMHMM(self.n_components, covars_prior=1.0)
        h.startprob_ = self.startprob
        h.transmat_ = hmm.normalize(
            self.transmat + np.diag(self.prng.rand(self.n_components)), 1)
        h.gmms_ = self.gmms_

        # Create training data by sampling from the HMM.
        train_obs = [h.sample(n=10, random_state=self.prng)[0]
                     for x in range(10)]

        # Mess up the parameters and see if we can re-learn them.
        h.n_iter = 0
        h.fit(train_obs)
        h.transmat_ = hmm.normalize(self.prng.rand(self.n_components,
                                                   self.n_components), axis=1)
        h.startprob_ = hmm.normalize(self.prng.rand(self.n_components))

        trainll = train_hmm_and_keep_track_of_log_likelihood(
            h, train_obs, n_iter=n_iter, params=params)[1:]

        if not np.all(np.diff(trainll) > 0) and verbose:
            print('Test train: (%s)\n  %s\n  %s' % (params, trainll,
                                                    np.diff(trainll)))

        # XXX: this test appears to check that training log likelihood should
        # never be decreasing (up to a tolerance of 0.5, why?) but this is not
        # the case when the seed changes.
        raise SkipTest("Unstable test: trainll is not always increasing "
                       "depending on seed")

        self.assertTrue(np.all(np.diff(trainll) > -0.5))

    def test_fit_works_on_sequences_of_different_length(self):
        obs = [self.prng.rand(3, self.n_features),
               self.prng.rand(4, self.n_features),
               self.prng.rand(5, self.n_features)]

        h = hmm.GMMHMM(self.n_components, covariance_type=self.covariance_type)
        # This shouldn't raise
        # ValueError: setting an array element with a sequence.
        h.fit(obs)


class TestGMMHMMWithDiagCovars(GMMHMMBaseTester, TestCase):
    covariance_type = 'diag'

    def test_fit_startprob_and_transmat(self):
        self.test_fit('st')

    def test_fit_means(self):
        self.test_fit('m')


class TestGMMHMMWithTiedCovars(GMMHMMBaseTester, TestCase):
    covariance_type = 'tied'


class TestGMMHMMWithFullCovars(GMMHMMBaseTester, TestCase):
    covariance_type = 'full'


def test_normalize_1D():
    A = rng.rand(2) + 1.0
    for axis in range(1):
        Anorm = hmm.normalize(A, axis)
        assert np.all(np.allclose(Anorm.sum(axis), 1.0))


def test_normalize_3D():
    A = rng.rand(2, 2, 2) + 1.0
    for axis in range(3):
        Anorm = hmm.normalize(A, axis)
        assert np.all(np.allclose(Anorm.sum(axis), 1.0))