State-space representation to zero-pole-gain representation.

    A, B, C, D defines a linear state-space system with `p` inputs,
    `q` outputs, and `n` state variables.

    Parameters
    ----------
    A : array_like
        State (or system) matrix of shape ``(n, n)``
    B : array_like
        Input matrix of shape ``(n, p)``
    C : array_like
        Output matrix of shape ``(q, n)``
    D : array_like
        Feedthrough (or feedforward) matrix of shape ``(q, p)``
    input : int, optional
        For multiple-input systems, the index of the input to use.

    Returns
    -------
    z, p : sequence
        Zeros and poles.
    k : float
        System gain.

    