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 : array_like, shape (M, N)
Matrix to be decomposed
c : array_like, one or twodimensional
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 rankrevealing qr decomposition, see the documentation of qr.
conjugate : bool, optional
Whether Q should be complexconjugated. 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 ifpivoting=False
.Raises: LinAlgError
Raised if decomposition fails
Notes
This is an interface to the LAPACK routines dgeqrf, zgeqrf, dormqr, zunmqr, dgeqp3, and zgeqp3.
New in version 0.11.0.