Module « scipy.linalg »

Fonction rsf2csf - module scipy.linalg

Signature de la fonction rsf2csf

def rsf2csf(T, Z, check_finite=True) 

Description

rsf2csf.__doc__

    Convert real Schur form to complex Schur form.

    Convert a quasi-diagonal real-valued Schur form to the upper-triangular
    complex-valued Schur form.

    Parameters
    ----------
    T : (M, M) array_like
        Real Schur form of the original array
    Z : (M, M) array_like
        Schur transformation matrix
    check_finite : bool, optional
        Whether to check that the input arrays contain 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
    -------
    T : (M, M) ndarray
        Complex Schur form of the original array
    Z : (M, M) ndarray
        Schur transformation matrix corresponding to the complex form

    See Also
    --------
    schur : Schur decomposition of an array

    Examples
    --------
    >>> from scipy.linalg import schur, rsf2csf
    >>> A = np.array([[0, 2, 2], [0, 1, 2], [1, 0, 1]])
    >>> T, Z = schur(A)
    >>> T
    array([[ 2.65896708,  1.42440458, -1.92933439],
           [ 0.        , -0.32948354, -0.49063704],
           [ 0.        ,  1.31178921, -0.32948354]])
    >>> Z
    array([[0.72711591, -0.60156188, 0.33079564],
           [0.52839428, 0.79801892, 0.28976765],
           [0.43829436, 0.03590414, -0.89811411]])
    >>> T2 , Z2 = rsf2csf(T, Z)
    >>> T2
    array([[2.65896708+0.j, -1.64592781+0.743164187j, -1.21516887+1.00660462j],
           [0.+0.j , -0.32948354+8.02254558e-01j, -0.82115218-2.77555756e-17j],
           [0.+0.j , 0.+0.j, -0.32948354-0.802254558j]])
    >>> Z2
    array([[0.72711591+0.j,  0.28220393-0.31385693j,  0.51319638-0.17258824j],
           [0.52839428+0.j,  0.24720268+0.41635578j, -0.68079517-0.15118243j],
           [0.43829436+0.j, -0.76618703+0.01873251j, -0.03063006+0.46857912j]])