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.


a : (M, N) array_like

Matrix to be decomposed

overwrite_a : bool, optional

Whether data in a is overwritten (may improve performance)

lwork : int, 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_finite : bool, 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.


R : float or complex ndarray

Of shape (M, N) or (M, K) for mode='economic'. K = min(M, N).

Q : float or complex ndarray

Of shape (N, N) or (K, N) for mode='economic'. Not returned if mode='r'.



If decomposition fails.


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).


>>> from scipy import linalg
>>> from numpy import random, dot, allclose
>>> a = random.randn(6, 9)
>>> r, q = linalg.rq(a)
>>> allclose(a, dot(r, q))
>>> r.shape, q.shape
((6, 9), (9, 9))
>>> r2 = linalg.rq(a, mode='r')
>>> allclose(r, r2)
>>> r3, q3 = linalg.rq(a, mode='economic')
>>> r3.shape, q3.shape
((6, 6), (6, 9))

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