Python scipy.linalg 模块，eigvalsh() 实例源码

def distance_riemann(A, B):
    """Riemannian distance between two covariance matrices A and B.

    .. math::
            d = {\left( \sum_i \log(\lambda_i)^2 \\right)}^{-1/2}

    where :math:`\lambda_i` are the joint eigenvalues of A and B

    :param A: First covariance matrix
    :param B: Second covariance matrix
    :returns: Riemannian distance between A and B

    """
    return numpy.sqrt((numpy.log(eigvalsh(A, B))**2).sum())

def evidence_approximation(self,
                               X,
                               T,
                               alpha=1e-2,
                               beta=1e-2,
                               tol=1e-3,
                               max_iter=int(1e2)):
        n_basis = self.n_basis
        n_sample = X.shape[0]

        Phi = self.nonlinear_transformation(X)
        PhiTPhi = np.outer(Phi, Phi) if Phi.ndim < 2 else Phi.T.dot(Phi)

        lamb = linalg.eigvalsh(PhiTPhi)
        gamma = np.sum(lamb / (lamb + alpha))

        for iteration in range(max_iter):
            post_cov = linalg.inv(alpha * np.eye(n_basis) + beta * PhiTPhi)
            post_mean = beta * post_cov.dot(Phi.T.dot(T))

            alpha = gamma / linalg.norm(post_mean)**2
            beta = (n_sample -
                    gamma) / linalg.norm(T - Phi.dot(post_mean))**2  # FIXME

            gamma_new = np.sum(lamb / (lamb + alpha))

            if (linalg.norm(gamma_new - gamma) / linalg.norm(gamma) < tol):
                break

            gamma = gamma_new

        self.mean = post_mean
        self.prior_precision = alpha
        self.noise_precision = beta

        return self

def distance_riemann(A, B):
    """Riemannian distance between two covariance matrices A and B.

    .. math::
            d = {\left( \sum_i \log(\lambda_i)^2 \\right)}^{-1/2}

    where :math:`\lambda_i` are the joint eigenvalues of A and B

    :param A: First covariance matrix
    :param B: Second covariance matrix
    :returns: Riemannian distance between A and B

    """
    return numpy.sqrt((numpy.log(eigvalsh(A, B))**2).sum())

def _validate_covars(covars, covariance_type, n_components):
    """Do basic checks on matrix covariance sizes and values."""
    from scipy import linalg
    if covariance_type == 'spherical':
        if len(covars) != n_components:
            raise ValueError("'spherical' covars have length n_components")
        elif np.any(covars <= 0):
            raise ValueError("'spherical' covars must be non-negative")
    elif covariance_type == 'tied':
        if covars.shape[0] != covars.shape[1]:
            raise ValueError("'tied' covars must have shape (n_dim, n_dim)")
        elif (not np.allclose(covars, covars.T)
              or np.any(linalg.eigvalsh(covars) <= 0)):
            raise ValueError("'tied' covars must be symmetric, "
                             "positive-definite")
    elif covariance_type == 'diag':
        if len(covars.shape) != 2:
            raise ValueError("'diag' covars must have shape "
                             "(n_components, n_dim)")
        elif np.any(covars <= 0):
            raise ValueError("'diag' covars must be non-negative")
    elif covariance_type == 'full':
        if len(covars.shape) != 3:
            raise ValueError("'full' covars must have shape "
                             "(n_components, n_dim, n_dim)")
        elif covars.shape[1] != covars.shape[2]:
            raise ValueError("'full' covars must have shape "
                             "(n_components, n_dim, n_dim)")
        for n, cv in enumerate(covars):
            if (not np.allclose(cv, cv.T)
                    or np.any(linalg.eigvalsh(cv) <= 0)):
                raise ValueError("component %d of 'full' covars must be "
                                 "symmetric, positive-definite" % n)
    else:
        raise ValueError("covariance_type must be one of " +
                         "'spherical', 'tied', 'diag', 'full'")