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scipy.linalg.

# rq

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

  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. 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)
      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))