butools.dmap.MarginalMomentsFromDMMAP
=====================================

.. currentmodule:: butools.dmap

.. np:function:: MarginalMomentsFromDMMAP

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

        * - Matlab:
          - :code:`moms = MarginalMomentsFromDMMAP(D, K, precision)`
        * - Mathematica:
          - :code:`moms = MarginalMomentsFromDMMAP[D, K, precision]`
        * - Python/Numpy:
          - :code:`moms = MarginalMomentsFromDMMAP(D, K, precision)`

    Returns the moments of the 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
    K : int, optional
        Number of moments to compute. If K=0, 2*M-1 moments
        are computed. The default value is K=0.
    precision : double, optional
        Numerical precision for checking if the input is valid.
        The default value is 1e-14

    Returns
    -------
    moms : row vector of doubles, length K
        The vector of moments.

    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];
    >>> moms = MarginalMomentsFromDMMAP({D0, D1, D2, D3});
    >>> disp(moms);
           1.5037       3.0278       8.4243       31.097       143.88

    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}};
    >>> moms = MarginalMomentsFromDMMAP[{D0, D1, D2, D3}];
    >>> Print[moms];
    {1.503697331491185, 3.027841857350894, 8.424305390832199, 31.097386717744087, 143.8804184010114}

    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]])
    >>> moms = MarginalMomentsFromDMMAP([D0, D1, D2, D3])
    >>> print(moms)
    [1.503697331491185, 3.0278418573508938, 8.424305390832199, 31.097386717744087, 143.88041840101141]