scipy.linalg.

rq#

scipy.linalg.rq(a, overwrite_a=False, lwork=None, mode='full', check_finite=True)[source]#

Compute RQ decomposition of a matrix.

Calculate the decomposition A = R Q where Q is unitary/orthogonal and R upper triangular.

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

Parameters:

a(M, N) array_like: Matrix to be decomposed
overwrite_abool, optional: Whether data in a is overwritten (may improve performance)
lworkint, optional: Work array size, lwork >= a.shape[1]. If None or -1, an optimal size is computed.
mode{‘full’, ‘r’, ‘economic’}, optional: Determines what information is to be returned: either both Q and R (‘full’, default), only R (‘r’) or both Q and R but computed in economy-size (‘economic’, see Notes).
check_finitebool, optional: Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

Rfloat or complex ndarray: Of shape (M, N) or (M, K) for mode='economic'. K = min(M, N).
Qfloat or complex ndarray: Of shape (N, N) or (K, N) for mode='economic'. Not returned if mode='r'.

Raises:

LinAlgError: If decomposition fails.

Notes

This is an interface to the LAPACK routines sgerqf, dgerqf, cgerqf, zgerqf, sorgrq, dorgrq, cungrq and zungrq.

If mode=economic, the shapes of Q and R are (K, N) and (M, K) instead of (N,N) and (M,N), with K=min(M,N).

Examples

>>> import numpy as np
>>> from scipy import linalg
>>> rng = np.random.default_rng()
>>> a = rng.standard_normal((6, 9))
>>> r, q = linalg.rq(a)
>>> np.allclose(a, r @ q)
True
>>> r.shape, q.shape
((6, 9), (9, 9))
>>> r2 = linalg.rq(a, mode='r')
>>> np.allclose(r, r2)
True
>>> r3, q3 = linalg.rq(a, mode='economic')
>>> r3.shape, q3.shape
((6, 6), (6, 9))