Module « scipy.linalg »

Fonction fiedler_companion - module scipy.linalg

Signature de la fonction fiedler_companion

def fiedler_companion(a) 

Description

fiedler_companion.__doc__

 Returns a Fiedler companion matrix

    Given a polynomial coefficient array ``a``, this function forms a
    pentadiagonal matrix with a special structure whose eigenvalues coincides
    with the roots of ``a``.

    Parameters
    ----------
    a : (N,) array_like
        1-D array of polynomial coefficients in descending order with a nonzero
        leading coefficient. For ``N < 2``, an empty array is returned.

    Returns
    -------
    c : (N-1, N-1) ndarray
        Resulting companion matrix

    Notes
    -----
    Similar to `companion` the leading coefficient should be nonzero. In the case
    the leading coefficient is not 1, other coefficients are rescaled before
    the array generation. To avoid numerical issues, it is best to provide a
    monic polynomial.

    .. versionadded:: 1.3.0

    See Also
    --------
    companion

    References
    ----------
    .. [1] M. Fiedler, " A note on companion matrices", Linear Algebra and its
        Applications, 2003, :doi:`10.1016/S0024-3795(03)00548-2`

    Examples
    --------
    >>> from scipy.linalg import fiedler_companion, eigvals
    >>> p = np.poly(np.arange(1, 9, 2))  # [1., -16., 86., -176., 105.]
    >>> fc = fiedler_companion(p)
    >>> fc
    array([[  16.,  -86.,    1.,    0.],
           [   1.,    0.,    0.,    0.],
           [   0.,  176.,    0., -105.],
           [   0.,    1.,    0.,    0.]])
    >>> eigvals(fc)
    array([7.+0.j, 5.+0.j, 3.+0.j, 1.+0.j])