scipy.linalg.pinv2

scipy.linalg.pinv2(a, cond=None, rcond=None, return_rank=False, check_finite=True)

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

Calculate a generalized inverse of a matrix using its singular-value decomposition and including all ‘large’ singular values.

Parameters:

a : (M, N) array_like

Matrix to be pseudo-inverted.

cond, rcond : float or None

Cutoff for ‘small’ singular values. Singular values smaller than rcond*largest_singular_value are considered zero. If None or -1, suitable machine precision is used.

return_rank : bool, optional

if True, return the effective rank of the matrix

check_finite : bool, 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, M) ndarray

The pseudo-inverse of matrix a.

rank : int

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

Raises:

LinAlgError

If SVD computation does not converge.

Examples

>>> from scipy import linalg
>>> a = np.random.randn(9, 6)
>>> B = linalg.pinv2(a)
>>> np.allclose(a, np.dot(a, np.dot(B, a)))
True
>>> np.allclose(B, np.dot(B, np.dot(a, B)))
True