butools.dmap.MarginalDistributionFromDMAP
=========================================

.. currentmodule:: butools.dmap

.. np:function:: MarginalDistributionFromDMAP

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

        * - Matlab:
          - :code:`[alpha, A] = MarginalDistributionFromDMAP(D0, D1, precision)`
        * - Mathematica:
          - :code:`{alpha, A} = MarginalDistributionFromDMAP[D0, D1, precision]`
        * - Python/Numpy:
          - :code:`alpha, A = MarginalDistributionFromDMAP(D0, D1, precision)`

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

    Parameters
    ----------
    D0 : matrix, shape (M,M)
        The D0 matrix of the discrete Markovian arrival process
    D1 : matrix, shape (M,M)
        The D1 matrix of the discrete Markovian 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 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, 0.02, 0, 0; 0, 0.17, 0.2, 0.14; 0.16, 0.17, 0.02, 0.18; 0, 0, 0, 0.12];
    >>> D1 = [0, 0.88, 0.1, 0; 0.18, 0.07, 0.14, 0.1; 0.13, 0.15, 0.15, 0.04; 0.31, 0.18, 0.12, 0.27];
    >>> [a, A] = MarginalDistributionFromDMAP(D0, D1);
    >>> disp(a);
          0.24388      0.40412       0.1941       0.1579
    >>> disp(A);
                0         0.02            0            0
                0         0.17          0.2         0.14
             0.16         0.17         0.02         0.18
                0            0            0         0.12

    For Mathematica:

    >>> D0 = {{0, 0.02, 0, 0},{0, 0.17, 0.2, 0.14},{0.16, 0.17, 0.02, 0.18},{0, 0, 0, 0.12}};
    >>> D1 = {{0, 0.88, 0.1, 0},{0.18, 0.07, 0.14, 0.1},{0.13, 0.15, 0.15, 0.04},{0.31, 0.18, 0.12, 0.27}};
    >>> {a, A} = MarginalDistributionFromDMAP[D0, D1];
    >>> Print[a];
    {0.2438770961395959, 0.4041227411783254, 0.19410324015415106, 0.15789692252792764}
    >>> Print[A];
    {{0, 0.02, 0, 0},
     {0, 0.17, 0.2, 0.14},
     {0.16, 0.17, 0.02, 0.18},
     {0, 0, 0, 0.12}}

    For Python/Numpy:

    >>> D0 = ml.matrix([[0, 0.02, 0, 0],[0, 0.17, 0.2, 0.14],[0.16, 0.17, 0.02, 0.18],[0, 0, 0, 0.12]])
    >>> D1 = ml.matrix([[0, 0.88, 0.1, 0],[0.18, 0.07, 0.14, 0.1],[0.13, 0.15, 0.15, 0.04],[0.31, 0.18, 0.12, 0.27]])
    >>> a, A = MarginalDistributionFromDMAP(D0, D1)
    >>> print(a)
    [[ 0.24388  0.40412  0.1941   0.1579 ]]
    >>> print(A)
    [[ 0.    0.02  0.    0.  ]
     [ 0.    0.17  0.2   0.14]
     [ 0.16  0.17  0.02  0.18]
     [ 0.    0.    0.    0.12]]