scipy.linalg.pinv

scipy.linalg.pinv(a, cond=None, rcond=None)

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

Calculate a generalized inverse of a matrix using a least-squares solver.

Parameters :

a : array, shape (M, N)

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.

Returns :

B : array, shape (N, M)

The pseudo-inverse of matrix a.

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