import cupy


def _none_to_empty_2d(arg):
    if arg is None:
        return cupy.zeros((0, 0))
    else:
        return arg


def _atleast_2d_or_none(arg):
    if arg is not None:
        return cupy.atleast_2d(arg)


def _shape_or_none(M):
    if M is not None:
        return M.shape
    else:
        return (None,) * 2


def _choice_not_none(*args):
    for arg in args:
        if arg is not None:
            return arg


def _restore(M, shape):
    if M.shape == (0, 0):
        return cupy.zeros(shape)
    else:
        if M.shape != shape:
            raise ValueError("The input arrays have incompatible shapes.")
        return M


def abcd_normalize(A=None, B=None, C=None, D=None):
    """Check state-space matrices and ensure they are 2-D.

    If enough information on the system is provided, that is, enough
    properly-shaped arrays are passed to the function, the missing ones
    are built from this information, ensuring the correct number of
    rows and columns. Otherwise a ValueError is raised.

    Parameters
    ----------
    A, B, C, D : array_like, optional
        State-space matrices. All of them are None (missing) by default.
        See `ss2tf` for format.

    Returns
    -------
    A, B, C, D : array
        Properly shaped state-space matrices.

    Raises
    ------
    ValueError
        If not enough information on the system was provided.

    """
    A, B, C, D = map(_atleast_2d_or_none, (A, B, C, D))

    MA, NA = _shape_or_none(A)
    MB, NB = _shape_or_none(B)
    MC, NC = _shape_or_none(C)
    MD, ND = _shape_or_none(D)

    p = _choice_not_none(MA, MB, NC)
    q = _choice_not_none(NB, ND)
    r = _choice_not_none(MC, MD)
    if p is None or q is None or r is None:
        raise ValueError("Not enough information on the system.")

    A, B, C, D = map(_none_to_empty_2d, (A, B, C, D))
    A = _restore(A, (p, p))
    B = _restore(B, (p, q))
    C = _restore(C, (r, p))
    D = _restore(D, (r, q))

    return A, B, C, D