butools.map.MarginalDistributionFromRAP
=======================================

.. currentmodule:: butools.map

.. np:function:: MarginalDistributionFromRAP

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

        * - Matlab:
          - :code:`[alpha, A] = MarginalDistributionFromRAP(H0, H1, precision)`
        * - Mathematica:
          - :code:`{alpha, A} = MarginalDistributionFromRAP[H0, H1, precision]`
        * - Python/Numpy:
          - :code:`alpha, A = MarginalDistributionFromRAP(H0, H1, precision)`

    Returns the phase type distributed marginal distribution
    of a rational arrival process.

    Parameters
    ----------
    H0 : matrix, shape (M,M)
        The H0 matrix of the rational arrival process
    H1 : matrix, shape (M,M)
        The H1 matrix of the rational arrival process
    precision : double, optional
        Numerical precision for checking if the input is valid.
        The default value is 1e-14

    Returns
    -------
    alpha : matrix, shape (1,M)
        The initial vector of the matrix exponentially
        distributed marginal
    A : matrix, shape (M,M)
        The matrix parameter of the matrix exponentially
        distributed marginal    

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

    >>> H0 = [-2, 0, 0; 0, -3, 1; 0, -1, -2];
    >>> H1 = [1.8, 0.2, 0; 0.2, 1.8, 0; 0.2, 1.8, 1];
    >>> [a, A] = MarginalDistributionFromRAP(H0, H1);
    >>> disp(a);
          0.44444      0.44444      0.11111
    >>> disp(A);
        -2     0     0
         0    -3     1
         0    -1    -2

    For Mathematica:

    >>> H0 = {{-2, 0, 0},{0, -3, 1},{0, -1, -2}};
    >>> H1 = {{1.8, 0.2, 0},{0.2, 1.8, 0},{0.2, 1.8, 1}};
    >>> {a, A} = MarginalDistributionFromRAP[H0, H1];
    >>> Print[a];
    {0.44444444444444464, 0.4444444444444443, 0.11111111111111106}
    >>> Print[A];
    {{-2, 0, 0},
     {0, -3, 1},
     {0, -1, -2}}

    For Python/Numpy:

    >>> H0 = ml.matrix([[-2, 0, 0],[0, -3, 1],[0, -1, -2]])
    >>> H1 = ml.matrix([[1.8, 0.2, 0],[0.2, 1.8, 0],[0.2, 1.8, 1]])
    >>> a, A = MarginalDistributionFromRAP(H0, H1)
    >>> print(a)
    [[ 0.44444  0.44444  0.11111]]
    >>> print(A)
    [[-2  0  0]
     [ 0 -3  1]
     [ 0 -1 -2]]