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bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / linalg / _decomp_qr / rq

function

scipy.linalg._decomp_qr:rq

source: build-install/usr/lib/python3.14/site-packages/scipy/linalg/_decomp_qr.py:421

Signature

def rq(a, overwrite_a = False, lwork = <object object at 0x0000>, mode = full, check_finite = True)

Summary

Compute RQ decomposition of a matrix.

Extended Summary

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 linalg_batch for details.

Parameters

a : (M, N) array_like

Matrix to be decomposed

overwrite_a : bool, optional

Whether to overwrite data in a (may improve performance). Default is False. See tutorial_linalg_overwrite for details.

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.

Returns

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'.

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)
r.shape, q.shape
r2 = linalg.rq(a, mode='r')
np.allclose(r, r2)
r3, q3 = linalg.rq(a, mode='economic')
r3.shape, q3.shape
✓
((6, 6), (6, 9))

Aliases

  • scipy.linalg.rq