butools.dmap.MarginalDistributionFromDMRAP
==========================================

.. currentmodule:: butools.dmap

.. np:function:: MarginalDistributionFromDMRAP

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

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

    Returns the matrix geometrically distributed marginal 
    distribution of a discrete marked rational arrival 
    process.

    Parameters
    ----------
    H : list/cell of matrices of shape(M,M), length(N)
        The H0...HN matrices of the DMRAP
    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 geometrically
        distributed marginal distribution
    A : matrix, shape (M,M)
        The matrix parameter of the matrix geometrically
        distributed marginal distribution    

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

    >>> H0 = [0.15, 0.2, 0.18; -0.23, 0.17, 0.22; 0.19, 0.15, 0.16];
    >>> H1 = [0.01, 0.08, 0.16; 0.02, 0.2, 0.07; 0.02, 0.15, 0.17];
    >>> H2 = [0.14, 0.07, 0.01; 0.19, 0.02, 0.34; 0.06, 0.1, 0];
    >>> [a, A] = MarginalDistributionFromDMRAP({H0, H1, H2});
    >>> disp(a);
          0.22615      0.35424      0.41962
    >>> disp(A);
             0.15          0.2         0.18
            -0.23         0.17         0.22
             0.19         0.15         0.16

    For Mathematica:

    >>> H0 = {{0.15, 0.2, 0.18},{-0.23, 0.17, 0.22},{0.19, 0.15, 0.16}};
    >>> H1 = {{0.01, 0.08, 0.16},{0.02, 0.2, 0.07},{0.02, 0.15, 0.17}};
    >>> H2 = {{0.14, 0.07, 0.01},{0.19, 0.02, 0.34},{0.06, 0.1, 0}};
    >>> {a, A} = MarginalDistributionFromDMRAP[{H0, H1, H2}];
    >>> Print[a];
    {0.22614580596765838, 0.3542378174211745, 0.4196163766111672}
    >>> Print[A];
    {{0.15, 0.2, 0.18},
     {-0.23, 0.17, 0.22},
     {0.19, 0.15, 0.16}}

    For Python/Numpy:

    >>> H0 = ml.matrix([[0.15, 0.2, 0.18],[-0.23, 0.17, 0.22],[0.19, 0.15, 0.16]])
    >>> H1 = ml.matrix([[0.01, 0.08, 0.16],[0.02, 0.2, 0.07],[0.02, 0.15, 0.17]])
    >>> H2 = ml.matrix([[0.14, 0.07, 0.01],[0.19, 0.02, 0.34],[0.06, 0.1, 0]])
    >>> a, A = MarginalDistributionFromDMRAP([H0, H1, H2])
    >>> print(a)
    [[ 0.22615  0.35424  0.41962]]
    >>> print(A)
    [[ 0.15  0.2   0.18]
     [-0.23  0.17  0.22]
     [ 0.19  0.15  0.16]]