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 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.
New in version 0.11.0.