content: import unittest
  import copy
  import sys
  
  from nose.tools import assert_true
  import numpy as np
  from numpy.testing import (assert_array_equal, assert_array_almost_equal,
                             assert_raises)
  from scipy import stats
  from sklearn import mixture
  from sklearn.datasets.samples_generator import make_spd_matrix
  from sklearn.utils.testing import assert_greater
  from sklearn.utils.testing import assert_raise_message
  from sklearn.metrics.cluster import adjusted_rand_score
  from sklearn.externals.six.moves import cStringIO as StringIO
  
  rng = np.random.RandomState(0)
  
  
  def test_sample_gaussian():
      # Test sample generation from mixture.sample_gaussian where covariance
      # is diagonal, spherical and full
  
      n_features, n_samples = 2, 300
      axis = 1
      mu = rng.randint(10) * rng.rand(n_features)
      cv = (rng.rand(n_features) + 1.0) ** 2
  
      samples = mixture.sample_gaussian(
          mu, cv, covariance_type='diag', n_samples=n_samples)
  
      assert_true(np.allclose(samples.mean(axis), mu, atol=1.3))
      assert_true(np.allclose(samples.var(axis), cv, atol=1.5))
  
      # the same for spherical covariances
      cv = (rng.rand() + 1.0) ** 2
      samples = mixture.sample_gaussian(
          mu, cv, covariance_type='spherical', n_samples=n_samples)
  
      assert_true(np.allclose(samples.mean(axis), mu, atol=1.5))
      assert_true(np.allclose(
          samples.var(axis), np.repeat(cv, n_features), atol=1.5))
  
      # and for full covariances
      A = rng.randn(n_features, n_features)
      cv = np.dot(A.T, A) + np.eye(n_features)
      samples = mixture.sample_gaussian(
          mu, cv, covariance_type='full', n_samples=n_samples)
      assert_true(np.allclose(samples.mean(axis), mu, atol=1.3))
      assert_true(np.allclose(np.cov(samples), cv, atol=2.5))
  
      # Numerical stability check: in SciPy 0.12.0 at least, eigh may return
      # tiny negative values in its second return value.
      from sklearn.mixture import sample_gaussian
      x = sample_gaussian([0, 0], [[4, 3], [1, .1]],
                          covariance_type='full', random_state=42)
      print(x)
      assert_true(np.isfinite(x).all())
  
  
  def _naive_lmvnpdf_diag(X, mu, cv):
      # slow and naive implementation of lmvnpdf
      ref = np.empty((len(X), len(mu)))
      stds = np.sqrt(cv)
      for i, (m, std) in enumerate(zip(mu, stds)):
          ref[:, i] = np.log(stats.norm.pdf(X, m, std)).sum(axis=1)
      return ref
  
  
  def test_lmvnpdf_diag():
      # test a slow and naive implementation of lmvnpdf and
      # compare it to the vectorized version (mixture.lmvnpdf) to test
      # for correctness
      n_features, n_components, n_samples = 2, 3, 10
      mu = rng.randint(10) * rng.rand(n_components, n_features)
      cv = (rng.rand(n_components, n_features) + 1.0) ** 2
      X = rng.randint(10) * rng.rand(n_samples, n_features)
  
      ref = _naive_lmvnpdf_diag(X, mu, cv)
      lpr = mixture.log_multivariate_normal_density(X, mu, cv, 'diag')
      assert_array_almost_equal(lpr, ref)
  
  
  def test_lmvnpdf_spherical():
      n_features, n_components, n_samples = 2, 3, 10
  
      mu = rng.randint(10) * rng.rand(n_components, n_features)
      spherecv = rng.rand(n_components, 1) ** 2 + 1
      X = rng.randint(10) * rng.rand(n_samples, n_features)
  
      cv = np.tile(spherecv, (n_features, 1))
      reference = _naive_lmvnpdf_diag(X, mu, cv)
      lpr = mixture.log_multivariate_normal_density(X, mu, spherecv,
                                                    'spherical')
      assert_array_almost_equal(lpr, reference)
  
  
  def test_lmvnpdf_full():
      n_features, n_components, n_samples = 2, 3, 10
  
      mu = rng.randint(10) * rng.rand(n_components, n_features)
      cv = (rng.rand(n_components, n_features) + 1.0) ** 2
      X = rng.randint(10) * rng.rand(n_samples, n_features)
  
      fullcv = np.array([np.diag(x) for x in cv])
  
      reference = _naive_lmvnpdf_diag(X, mu, cv)
      lpr = mixture.log_multivariate_normal_density(X, mu, fullcv, 'full')
      assert_array_almost_equal(lpr, reference)
  
  
  def test_lvmpdf_full_cv_non_positive_definite():
      n_features, n_samples = 2, 10
      rng = np.random.RandomState(0)
      X = rng.randint(10) * rng.rand(n_samples, n_features)
      mu = np.mean(X, 0)
      cv = np.array([[[-1, 0], [0, 1]]])
      expected_message = "'covars' must be symmetric, positive-definite"
      assert_raise_message(ValueError, expected_message,
                           mixture.log_multivariate_normal_density,
                           X, mu, cv, 'full')
  
  
  def test_GMM_attributes():
      n_components, n_features = 10, 4
      covariance_type = 'diag'
      g = mixture.GMM(n_components, covariance_type, random_state=rng)
      weights = rng.rand(n_components)
      weights = weights / weights.sum()
      means = rng.randint(-20, 20, (n_components, n_features))
  
      assert_true(g.n_components == n_components)
      assert_true(g.covariance_type == covariance_type)
  
      g.weights_ = weights
      assert_array_almost_equal(g.weights_, weights)
      g.means_ = means
      assert_array_almost_equal(g.means_, means)
  
      covars = (0.1 + 2 * rng.rand(n_components, n_features)) ** 2
      g.covars_ = covars
      assert_array_almost_equal(g.covars_, covars)
      assert_raises(ValueError, g._set_covars, [])
      assert_raises(ValueError, g._set_covars,
                    np.zeros((n_components - 2, n_features)))
  
      assert_raises(ValueError, mixture.GMM, n_components=20,
                    covariance_type='badcovariance_type')
  
  
  class GMMTester():
      do_test_eval = True
  
      def _setUp(self):
          self.n_components = 10
          self.n_features = 4
          self.weights = rng.rand(self.n_components)
          self.weights = self.weights / self.weights.sum()
          self.means = rng.randint(-20, 20, (self.n_components, self.n_features))
          self.threshold = -0.5
          self.I = np.eye(self.n_features)
          self.covars = {
              'spherical': (0.1 + 2 * rng.rand(self.n_components,
                                               self.n_features)) ** 2,
              'tied': (make_spd_matrix(self.n_features, random_state=0)
                       + 5 * self.I),
              'diag': (0.1 + 2 * rng.rand(self.n_components,
                                          self.n_features)) ** 2,
              'full': np.array([make_spd_matrix(self.n_features, random_state=0)
                                + 5 * self.I for x in range(self.n_components)])}
  
      def test_eval(self):
          if not self.do_test_eval:
              return  # DPGMM does not support setting the means and
          # covariances before fitting There is no way of fixing this
          # due to the variational parameters being more expressive than
          # covariance matrices
          g = self.model(n_components=self.n_components,
                         covariance_type=self.covariance_type, random_state=rng)
          # Make sure the means are far apart so responsibilities.argmax()
          # picks the actual component used to generate the observations.
          g.means_ = 20 * self.means
          g.covars_ = self.covars[self.covariance_type]
          g.weights_ = self.weights
  
          gaussidx = np.repeat(np.arange(self.n_components), 5)
          n_samples = len(gaussidx)
          X = rng.randn(n_samples, self.n_features) + g.means_[gaussidx]
  
          ll, responsibilities = g.score_samples(X)
  
          self.assertEqual(len(ll), n_samples)
          self.assertEqual(responsibilities.shape,
                           (n_samples, self.n_components))
          assert_array_almost_equal(responsibilities.sum(axis=1),
                                    np.ones(n_samples))
          assert_array_equal(responsibilities.argmax(axis=1), gaussidx)
  
      def test_sample(self, n=100):
          g = self.model(n_components=self.n_components,
                         covariance_type=self.covariance_type, random_state=rng)
          # Make sure the means are far apart so responsibilities.argmax()
          # picks the actual component used to generate the observations.
          g.means_ = 20 * self.means
          g.covars_ = np.maximum(self.covars[self.covariance_type], 0.1)
          g.weights_ = self.weights
  
          samples = g.sample(n)
          self.assertEqual(samples.shape, (n, self.n_features))
  
      def test_train(self, params='wmc'):
          g = mixture.GMM(n_components=self.n_components,
                          covariance_type=self.covariance_type)
          g.weights_ = self.weights
          g.means_ = self.means
          g.covars_ = 20 * self.covars[self.covariance_type]
  
          # Create a training set by sampling from the predefined distribution.
          X = g.sample(n_samples=100)
          g = self.model(n_components=self.n_components,
                         covariance_type=self.covariance_type,
                         random_state=rng, min_covar=1e-1,
                         n_iter=1, init_params=params)
          g.fit(X)
  
          # Do one training iteration at a time so we can keep track of
          # the log likelihood to make sure that it increases after each
          # iteration.
          trainll = []
          for _ in range(5):
              g.params = params
              g.init_params = ''
              g.fit(X)
              trainll.append(self.score(g, X))
          g.n_iter = 10
          g.init_params = ''
          g.params = params
          g.fit(X)  # finish fitting
  
          # Note that the log likelihood will sometimes decrease by a
          # very small amount after it has more or less converged due to
          # the addition of min_covar to the covariance (to prevent
          # underflow).  This is why the threshold is set to -0.5
          # instead of 0.
          delta_min = np.diff(trainll).min()
          self.assertTrue(
              delta_min > self.threshold,
              "The min nll increase is %f which is lower than the admissible"
              " threshold of %f, for model %s. The likelihoods are %s."
              % (delta_min, self.threshold, self.covariance_type, trainll))
  
      def test_train_degenerate(self, params='wmc'):
          # Train on degenerate data with 0 in some dimensions
          # Create a training set by sampling from the predefined distribution.
          X = rng.randn(100, self.n_features)
          X.T[1:] = 0
          g = self.model(n_components=2, covariance_type=self.covariance_type,
                         random_state=rng, min_covar=1e-3, n_iter=5,
                         init_params=params)
          g.fit(X)
          trainll = g.score(X)
          self.assertTrue(np.sum(np.abs(trainll / 100 / X.shape[1])) < 5)
  
      def test_train_1d(self, params='wmc'):
          # Train on 1-D data
          # Create a training set by sampling from the predefined distribution.
          X = rng.randn(100, 1)
          # X.T[1:] = 0
          g = self.model(n_components=2, covariance_type=self.covariance_type,
                         random_state=rng, min_covar=1e-7, n_iter=5,
                         init_params=params)
          g.fit(X)
          trainll = g.score(X)
          if isinstance(g, mixture.DPGMM):
              self.assertTrue(np.sum(np.abs(trainll / 100)) < 5)
          else:
              self.assertTrue(np.sum(np.abs(trainll / 100)) < 2)
  
      def score(self, g, X):
          return g.score(X).sum()
  
  
  class TestGMMWithSphericalCovars(unittest.TestCase, GMMTester):
      covariance_type = 'spherical'
      model = mixture.GMM
      setUp = GMMTester._setUp
  
  
  class TestGMMWithDiagonalCovars(unittest.TestCase, GMMTester):
      covariance_type = 'diag'
      model = mixture.GMM
      setUp = GMMTester._setUp
  
  
  class TestGMMWithTiedCovars(unittest.TestCase, GMMTester):
      covariance_type = 'tied'
      model = mixture.GMM
      setUp = GMMTester._setUp
  
  
  class TestGMMWithFullCovars(unittest.TestCase, GMMTester):
      covariance_type = 'full'
      model = mixture.GMM
      setUp = GMMTester._setUp
  
  
  def test_multiple_init():
      # Test that multiple inits does not much worse than a single one
      X = rng.randn(30, 5)
      X[:10] += 2
      g = mixture.GMM(n_components=2, covariance_type='spherical',
                      random_state=rng, min_covar=1e-7, n_iter=5)
      train1 = g.fit(X).score(X).sum()
      g.n_init = 5
      train2 = g.fit(X).score(X).sum()
      assert_true(train2 >= train1 - 1.e-2)
  
  
  def test_n_parameters():
      # Test that the right number of parameters is estimated
      n_samples, n_dim, n_components = 7, 5, 2
      X = rng.randn(n_samples, n_dim)
      n_params = {'spherical': 13, 'diag': 21, 'tied': 26, 'full': 41}
      for cv_type in ['full', 'tied', 'diag', 'spherical']:
          g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                          random_state=rng, min_covar=1e-7, n_iter=1)
          g.fit(X)
          assert_true(g._n_parameters() == n_params[cv_type])
  
  
  def test_1d_1component():
      # Test all of the covariance_types return the same BIC score for
      # 1-dimensional, 1 component fits.
      n_samples, n_dim, n_components = 100, 1, 1
      X = rng.randn(n_samples, n_dim)
      g_full = mixture.GMM(n_components=n_components, covariance_type='full',
                           random_state=rng, min_covar=1e-7, n_iter=1)
      g_full.fit(X)
      g_full_bic = g_full.bic(X)
      for cv_type in ['tied', 'diag', 'spherical']:
          g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                          random_state=rng, min_covar=1e-7, n_iter=1)
          g.fit(X)
          assert_array_almost_equal(g.bic(X), g_full_bic)
  
  
  def assert_fit_predict_correct(model, X):
      model2 = copy.deepcopy(model)
  
      predictions_1 = model.fit(X).predict(X)
      predictions_2 = model2.fit_predict(X)
  
      assert adjusted_rand_score(predictions_1, predictions_2) == 1.0
  
  
  def test_fit_predict():
      """
      test that gmm.fit_predict is equivalent to gmm.fit + gmm.predict
      """
      lrng = np.random.RandomState(101)
  
      n_samples, n_dim, n_comps = 100, 2, 2
      mu = np.array([[8, 8]])
      component_0 = lrng.randn(n_samples, n_dim)
      component_1 = lrng.randn(n_samples, n_dim) + mu
      X = np.vstack((component_0, component_1))
  
      for m_constructor in (mixture.GMM, mixture.VBGMM, mixture.DPGMM):
          model = m_constructor(n_components=n_comps, covariance_type='full',
                                min_covar=1e-7, n_iter=5,
                                random_state=np.random.RandomState(0))
          assert_fit_predict_correct(model, X)
  
      model = mixture.GMM(n_components=n_comps, n_iter=0)
      z = model.fit_predict(X)
      assert np.all(z == 0), "Quick Initialization Failed!"
  
  
  def test_aic():
      # Test the aic and bic criteria
      n_samples, n_dim, n_components = 50, 3, 2
      X = rng.randn(n_samples, n_dim)
      SGH = 0.5 * (X.var() + np.log(2 * np.pi))  # standard gaussian entropy
  
      for cv_type in ['full', 'tied', 'diag', 'spherical']:
          g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                          random_state=rng, min_covar=1e-7)
          g.fit(X)
          aic = 2 * n_samples * SGH * n_dim + 2 * g._n_parameters()
          bic = (2 * n_samples * SGH * n_dim +
                 np.log(n_samples) * g._n_parameters())
          bound = n_dim * 3. / np.sqrt(n_samples)
          assert_true(np.abs(g.aic(X) - aic) / n_samples < bound)
          assert_true(np.abs(g.bic(X) - bic) / n_samples < bound)
  
  
  def check_positive_definite_covars(covariance_type):
      r"""Test that covariance matrices do not become non positive definite
  
      Due to the accumulation of round-off errors, the computation of the
      covariance  matrices during the learning phase could lead to non-positive
      definite covariance matrices. Namely the use of the formula:
  
      .. math:: C = (\sum_i w_i  x_i x_i^T) - \mu \mu^T
  
      instead of:
  
      .. math:: C = \sum_i w_i (x_i - \mu)(x_i - \mu)^T
  
      while mathematically equivalent, was observed a ``LinAlgError`` exception,
      when computing a ``GMM`` with full covariance matrices and fixed mean.
  
      This function ensures that some later optimization will not introduce the
      problem again.
      """
      rng = np.random.RandomState(1)
      # we build a dataset with 2 2d component. The components are unbalanced
      # (respective weights 0.9 and 0.1)
      X = rng.randn(100, 2)
      X[-10:] += (3, 3)  # Shift the 10 last points
  
      gmm = mixture.GMM(2, params="wc", covariance_type=covariance_type,
                        min_covar=1e-3)
  
      # This is a non-regression test for issue #2640. The following call used
      # to trigger:
      # numpy.linalg.linalg.LinAlgError: 2-th leading minor not positive definite
      gmm.fit(X)
  
      if covariance_type == "diag" or covariance_type == "spherical":
          assert_greater(gmm.covars_.min(), 0)
      else:
          if covariance_type == "tied":
              covs = [gmm.covars_]
          else:
              covs = gmm.covars_
  
          for c in covs:
              assert_greater(np.linalg.det(c), 0)
  
  
  def test_positive_definite_covars():
      # Check positive definiteness for all covariance types
      for covariance_type in ["full", "tied", "diag", "spherical"]:
          yield check_positive_definite_covars, covariance_type
  
  
  def test_verbose_first_level():
      # Create sample data
      X = rng.randn(30, 5)
      X[:10] += 2
      g = mixture.GMM(n_components=2, n_init=2, verbose=1)
  
      old_stdout = sys.stdout
      sys.stdout = StringIO()
      try:
          g.fit(X)
      finally:
          sys.stdout = old_stdout
  
  
  def test_verbose_second_level():
      # Create sample data
      X = rng.randn(30, 5)
      X[:10] += 2
      g = mixture.GMM(n_components=2, n_init=2, verbose=2)
  
      old_stdout = sys.stdout
      sys.stdout = StringIO()
      try:
          g.fit(X)
      finally:
          sys.stdout = old_stdout
  
  
  if __name__ == '__main__':
      import nose
      nose.runmodule()
  