This is documentation for an old release of SciPy (version 0.12.0). Read this page Search for this page in the documentation of the latest stable release (version 1.15.1).

scipy.linalg.pinvh

scipy.linalg.pinvh(a, cond=None, rcond=None, lower=True, return_rank=False, check_finite=True)

Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix.

Calculate a generalized inverse of a Hermitian or real symmetric matrix using its eigenvalue decomposition and including all eigenvalues with ‘large’ absolute value.

Parameters :

a : (N, N) array_like

Real symmetric or complex hermetian matrix to be pseudo-inverted

cond, rcond : float or None

Cutoff for ‘small’ eigenvalues. Singular values smaller than rcond * largest_eigenvalue are considered zero.

If None or -1, suitable machine precision is used.

lower : bool

Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)

return_rank : bool, optional

if True, return the effective rank of the matrix

check_finite : boolean, optional

Whether to check the input matrixes contain only finite numbers. Disabling may give a performance gain, but may result to problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns :

B : (N, N) ndarray

The pseudo-inverse of matrix a.

rank : int

The effective rank of the matrix. Returned if return_rank == True

Raises :

LinAlgError :

If eigenvalue does not converge

Examples

>>> from numpy import *
>>> a = random.randn(9, 6)
>>> a = np.dot(a, a.T)
>>> B = pinvh(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True