Module « scipy.linalg »

Fonction qr_multiply - module scipy.linalg

Signature de la fonction qr_multiply

def qr_multiply(a, c, mode='right', pivoting=False, conjugate=False, overwrite_a=False, overwrite_c=False) 

Description

qr_multiply.__doc__

    Calculate the QR decomposition and multiply Q with a matrix.

    Calculate the decomposition ``A = Q R`` where Q is unitary/orthogonal
    and R upper triangular. Multiply Q with a vector or a matrix c.

    Parameters
    ----------
    a : (M, N), array_like
        Input array
    c : array_like
        Input array to be multiplied by ``q``.
    mode : {'left', 'right'}, optional
        ``Q @ c`` is returned if mode is 'left', ``c @ Q`` is returned if
        mode is 'right'.
        The shape of c must be appropriate for the matrix multiplications,
        if mode is 'left', ``min(a.shape) == c.shape[0]``,
        if mode is 'right', ``a.shape[0] == c.shape[1]``.
    pivoting : bool, optional
        Whether or not factorization should include pivoting for rank-revealing
        qr decomposition, see the documentation of qr.
    conjugate : bool, optional
        Whether Q should be complex-conjugated. This might be faster
        than explicit conjugation.
    overwrite_a : bool, optional
        Whether data in a is overwritten (may improve performance)
    overwrite_c : bool, optional
        Whether data in c is overwritten (may improve performance).
        If this is used, c must be big enough to keep the result,
        i.e. ``c.shape[0]`` = ``a.shape[0]`` if mode is 'left'.

    Returns
    -------
    CQ : ndarray
        The product of ``Q`` and ``c``.
    R : (K, N), ndarray
        R array of the resulting QR factorization where ``K = min(M, N)``.
    P : (N,) ndarray
        Integer pivot array. Only returned when ``pivoting=True``.

    Raises
    ------
    LinAlgError
        Raised if QR decomposition fails.

    Notes
    -----
    This is an interface to the LAPACK routines ``?GEQRF``, ``?ORMQR``,
    ``?UNMQR``, and ``?GEQP3``.

    .. versionadded:: 0.11.0

    Examples
    --------
    >>> from scipy.linalg import qr_multiply, qr
    >>> A = np.array([[1, 3, 3], [2, 3, 2], [2, 3, 3], [1, 3, 2]])
    >>> qc, r1, piv1 = qr_multiply(A, 2*np.eye(4), pivoting=1)
    >>> qc
    array([[-1.,  1., -1.],
           [-1., -1.,  1.],
           [-1., -1., -1.],
           [-1.,  1.,  1.]])
    >>> r1
    array([[-6., -3., -5.            ],
           [ 0., -1., -1.11022302e-16],
           [ 0.,  0., -1.            ]])
    >>> piv1
    array([1, 0, 2], dtype=int32)
    >>> q2, r2, piv2 = qr(A, mode='economic', pivoting=1)
    >>> np.allclose(2*q2 - qc, np.zeros((4, 3)))
    True