scipy.linalg.qr_multiply

scipy.linalg.qr_multiply(a, c, mode='right', pivoting=False, conjugate=False, overwrite_a=False, overwrite_c=False)

Calculate the QR decomposition and multiply Q with a matrix.

Calculate the decomposition A = Q R where Q is unitary/orthogonal and R upper triangular. Multiply Q with a vector or a matrix c.

New in version 0.11.0.

Parameters:

a : ndarray, shape (M, N)

Matrix to be decomposed

c : ndarray, one- or two-dimensional

calculate the product of c and q, depending on the mode:

mode : {‘left’, ‘right’}, optional

dot(Q, c) is returned if mode is ‘left’, dot(c, Q) is returned if mode is ‘right’. The shape of c must be appropriate for the matrix multiplications, if mode is ‘left’, min(a.shape) == c.shape[0], if mode is ‘right’, a.shape[0] == c.shape[1].

pivoting : bool, optional

Whether or not factorization should include pivoting for rank-revealing qr decomposition, see the documentation of qr.

conjugate : bool, optional

Whether Q should be complex-conjugated. This might be faster than explicit conjugation.

overwrite_a : bool, optional

Whether data in a is overwritten (may improve performance)

overwrite_c : bool, optional

Whether data in c is overwritten (may improve performance). If this is used, c must be big enough to keep the result, i.e. c.shape[0] = a.shape[0] if mode is ‘left’.

Returns:

CQ : float or complex ndarray

the product of Q and c, as defined in mode

R : float or complex ndarray

Of shape (K, N), K = min(M, N).

P : ndarray of ints

Of shape (N,) for pivoting=True. Not returned if pivoting=False.

Raises:

LinAlgError

Raised if decomposition fails

Notes

This is an interface to the LAPACK routines dgeqrf, zgeqrf, dormqr, zunmqr, dgeqp3, and zgeqp3.