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 that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in 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

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