scipy.linalg.pinv

scipy.linalg.pinv(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 a least-squares solver.

Parameters:

a : (M, N) array_like

Matrix to be pseudo-inverted.

cond, rcond : float, optional

Cutoff for ‘small’ singular values in the least-squares solver. Singular values smaller than rcond * largest_singular_value are considered zero.

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, M) ndarray

The pseudo-inverse of matrix a.

rank : int

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

Raises:

LinAlgError

If computation does not converge.

Examples

>>> a = np.random.randn(9, 6)
>>> B = linalg.pinv(a)
>>> np.allclose(a, dot(a, dot(B, a)))
True
>>> np.allclose(B, dot(B, dot(a, B)))
True