butools.ph.CheckPHRepresentation
================================

.. currentmodule:: butools.ph

.. np:function:: CheckPHRepresentation

    .. list-table::
        :widths: 25 150

        * - Matlab:
          - :code:`r = CheckPHRepresentation(alpha, A, prec)`
        * - Mathematica:
          - :code:`r = CheckPHRepresentation[alpha, A, prec]`
        * - Python/Numpy:
          - :code:`r = CheckPHRepresentation(alpha, A, prec)`

    Checks if the given vector and matrix define a valid phase-
    type representation.

    Parameters
    ----------
    alpha : matrix, shape (1,M)
        Initial vector of the phase-type distribution to check
    A : matrix, shape (M,M)
        Transient generator of the phase-type distribution to
        check
    prec : double, optional
        Numerical precision. The default value is 1e-14.

    Returns
    -------
    r : bool
        True, if vector alpha is a probability vector and matrix
        A is a transient generator, and they have the same size.

    Examples
    ========
    For Matlab:

    >>> a = [0.2];
    >>> A = [-1, 1; 1, -2];
    >>> flag = CheckPHRepresentation(a, A);
    CheckPHRepresentation:the vector and the matrix have different sizes!
    >>> disp(flag);
         0
    >>> a = [0.2,0.7];
    >>> A = [-1, 1; 1, -2];
    >>> flag = CheckPHRepresentation(a, A);
    >>> disp(flag);
         1

    For Mathematica:

    >>> a = {0.2};
    >>> A = {{-1, 1},{1, -2}};
    >>> flag = CheckPHRepresentation[a, A];
    "CheckPHRepresentation: the vector and the matrix have different sizes!"
    >>> Print[flag];
    False
    >>> a = {0.2,0.7};
    >>> A = {{-1, 1},{1, -2}};
    >>> flag = CheckPHRepresentation[a, A];
    >>> Print[flag];
    True

    For Python/Numpy:

    >>> a = ml.matrix([[0.2]])
    >>> A = ml.matrix([[-1, 1],[1, -2]])
    >>> flag = CheckPHRepresentation(a, A)
    CheckPHRepresentation: The vector and the matrix have different sizes!
    >>> print(flag)
    False
    >>> a = ml.matrix([[0.2,0.7]])
    >>> A = ml.matrix([[-1, 1],[1, -2]])
    >>> flag = CheckPHRepresentation(a, A)
    >>> print(flag)
    True