`scipy.linalg._decomp_qr:rq`

source: /scipy/linalg/_decomp_qr.py :372

Signature

   def     rq (    a    ,    overwrite_a    =  False   ,    lwork    =  None   ,    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. Note that calls with zero-size batches are unsupported and will raise a ValueError.

Parameters

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.

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

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Aliases

scipy.linalg.rq