scipy.linalg.qr_multiply#
- scipy.linalg.qr_multiply(a, c, mode='right', pivoting=False, conjugate=False, overwrite_a=False, overwrite_c=False)[source]#
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.- Parameters
- a(M, N), array_like
Input array
- carray_like
Input array to be multiplied by
q
.- mode{‘left’, ‘right’}, optional
Q @ c
is returned if mode is ‘left’,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]
.- pivotingbool, optional
Whether or not factorization should include pivoting for rank-revealing qr decomposition, see the documentation of qr.
- conjugatebool, optional
Whether Q should be complex-conjugated. This might be faster than explicit conjugation.
- overwrite_abool, optional
Whether data in a is overwritten (may improve performance)
- overwrite_cbool, 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
- CQndarray
The product of
Q
andc
.- R(K, N), ndarray
R array of the resulting QR factorization where
K = min(M, N)
.- P(N,) ndarray
Integer pivot array. Only returned when
pivoting=True
.
- Raises
- LinAlgError
Raised if QR decomposition fails.
Notes
This is an interface to the LAPACK routines
?GEQRF
,?ORMQR
,?UNMQR
, and?GEQP3
.New in version 0.11.0.
Examples
>>> from scipy.linalg import qr_multiply, qr >>> A = np.array([[1, 3, 3], [2, 3, 2], [2, 3, 3], [1, 3, 2]]) >>> qc, r1, piv1 = qr_multiply(A, 2*np.eye(4), pivoting=1) >>> qc array([[-1., 1., -1.], [-1., -1., 1.], [-1., -1., -1.], [-1., 1., 1.]]) >>> r1 array([[-6., -3., -5. ], [ 0., -1., -1.11022302e-16], [ 0., 0., -1. ]]) >>> piv1 array([1, 0, 2], dtype=int32) >>> q2, r2, piv2 = qr(A, mode='economic', pivoting=1) >>> np.allclose(2*q2 - qc, np.zeros((4, 3))) True