butools.dmap.MarginalDistributionFromDMMAP
==========================================

.. currentmodule:: butools.dmap

.. np:function:: MarginalDistributionFromDMMAP

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

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

    Returns the discrete phase type distributed marginal 
    distribution of a discrete marked Markovian arrival 
    process.

    Parameters
    ----------
    D : list/cell of matrices of shape(M,M), length(N)
        The D0...DN matrices of the DMMAP
    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 probability vector of the discrete phase 
        type distributed marginal distribution
    A : matrix, shape (M,M)
        The transient generator of the discrete phase type 
        distributed marginal distribution    

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

    >>> D0 = [0.34, 0, 0; 0.06, 0.05, 0.03; 0.11, 0.13, 0];
    >>> D1 = [0.3, 0, 0; 0.16, 0.18, 0.05; 0.15, 0.04, 0.09];
    >>> D2 = [0, 0.01, 0; 0.1, 0.07, 0.08; 0.13, 0.12, 0.13];
    >>> D3 = [0.35, 0, 0; 0, 0.18, 0.04; 0.06, 0.03, 0.01];
    >>> [a, A] = MarginalDistributionFromDMMAP({D0, D1, D2, D3});
    >>> disp(a);
          0.96166     0.030652    0.0076858
    >>> disp(A);
             0.34            0            0
             0.06         0.05         0.03
             0.11         0.13            0

    For Mathematica:

    >>> D0 = {{0.34, 0, 0},{0.06, 0.05, 0.03},{0.11, 0.13, 0}};
    >>> D1 = {{0.3, 0, 0},{0.16, 0.18, 0.05},{0.15, 0.04, 0.09}};
    >>> D2 = {{0, 0.01, 0},{0.1, 0.07, 0.08},{0.13, 0.12, 0.13}};
    >>> D3 = {{0.35, 0, 0},{0, 0.18, 0.04},{0.06, 0.03, 0.01}};
    >>> {a, A} = MarginalDistributionFromDMMAP[{D0, D1, D2, D3}];
    >>> Print[a];
    {0.9616624523170234, 0.030651790446894853, 0.007685757236081784}
    >>> Print[A];
    {{0.34, 0, 0},
     {0.06, 0.05, 0.03},
     {0.11, 0.13, 0}}

    For Python/Numpy:

    >>> D0 = ml.matrix([[0.34, 0, 0],[0.06, 0.05, 0.03],[0.11, 0.13, 0]])
    >>> D1 = ml.matrix([[0.3, 0, 0],[0.16, 0.18, 0.05],[0.15, 0.04, 0.09]])
    >>> D2 = ml.matrix([[0, 0.01, 0],[0.1, 0.07, 0.08],[0.13, 0.12, 0.13]])
    >>> D3 = ml.matrix([[0.35, 0, 0],[0, 0.18, 0.04],[0.06, 0.03, 0.01]])
    >>> a, A = MarginalDistributionFromDMMAP([D0, D1, D2, D3])
    >>> print(a)
    [[ 0.96166  0.03065  0.00769]]
    >>> print(A)
    [[ 0.34  0.    0.  ]
     [ 0.06  0.05  0.03]
     [ 0.11  0.13  0.  ]]