Module « scipy.linalg »

Fonction hessenberg - module scipy.linalg

Signature de la fonction hessenberg

def hessenberg(a, calc_q=False, overwrite_a=False, check_finite=True) 

Description

hessenberg.__doc__

    Compute Hessenberg form of a matrix.

    The Hessenberg decomposition is::

        A = Q H Q^H

    where `Q` is unitary/orthogonal and `H` has only zero elements below
    the first sub-diagonal.

    Parameters
    ----------
    a : (M, M) array_like
        Matrix to bring into Hessenberg form.
    calc_q : bool, optional
        Whether to compute the transformation matrix.  Default is False.
    overwrite_a : bool, optional
        Whether to overwrite `a`; may improve performance.
        Default is False.
    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
    -------
    H : (M, M) ndarray
        Hessenberg form of `a`.
    Q : (M, M) ndarray
        Unitary/orthogonal similarity transformation matrix ``A = Q H Q^H``.
        Only returned if ``calc_q=True``.

    Examples
    --------
    >>> from scipy.linalg import hessenberg
    >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
    >>> H, Q = hessenberg(A, calc_q=True)
    >>> H
    array([[  2.        , -11.65843866,   1.42005301,   0.25349066],
           [ -9.94987437,  14.53535354,  -5.31022304,   2.43081618],
           [  0.        ,  -1.83299243,   0.38969961,  -0.51527034],
           [  0.        ,   0.        ,  -3.83189513,   1.07494686]])
    >>> np.allclose(Q @ H @ Q.conj().T - A, np.zeros((4, 4)))
    True