Module « scipy.linalg »

Fonction companion - module scipy.linalg

Signature de la fonction companion

def companion(a) 

Description

companion.__doc__

    Create a companion matrix.

    Create the companion matrix [1]_ associated with the polynomial whose
    coefficients are given in `a`.

    Parameters
    ----------
    a : (N,) array_like
        1-D array of polynomial coefficients. The length of `a` must be
        at least two, and ``a[0]`` must not be zero.

    Returns
    -------
    c : (N-1, N-1) ndarray
        The first row of `c` is ``-a[1:]/a[0]``, and the first
        sub-diagonal is all ones.  The data-type of the array is the same
        as the data-type of ``1.0*a[0]``.

    Raises
    ------
    ValueError
        If any of the following are true: a) ``a.ndim != 1``;
        b) ``a.size < 2``; c) ``a[0] == 0``.

    Notes
    -----
    .. versionadded:: 0.8.0

    References
    ----------
    .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*.  Cambridge, UK:
        Cambridge University Press, 1999, pp. 146-7.

    Examples
    --------
    >>> from scipy.linalg import companion
    >>> companion([1, -10, 31, -30])
    array([[ 10., -31.,  30.],
           [  1.,   0.,   0.],
           [  0.,   1.,   0.]])