test_gmm.py 文件源码

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)