Module « scipy.linalg »

Fonction rq - module scipy.linalg

Signature de la fonction rq

def rq(a, overwrite_a=False, lwork=None, mode='full', check_finite=True) 

Description

rq.__doc__

    Compute RQ decomposition of a matrix.

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

    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
    --------
    >>> 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))