butools.map.LagkJointMomentsFromMMAP
====================================

.. currentmodule:: butools.map

.. np:function:: LagkJointMomentsFromMMAP

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

        * - Matlab:
          - :code:`Nm = LagkJointMomentsFromMMAP(D, K, L, prec)`
        * - Mathematica:
          - :code:`Nm = LagkJointMomentsFromMMAP[D, K, L, prec]`
        * - Python/Numpy:
          - :code:`Nm = LagkJointMomentsFromMMAP(D, K, L, prec)`

    Returns the lag-L joint moments of a marked Markovian 
    arrival process.

    Parameters
    ----------
    D : list/cell of matrices of shape(M,M), length(N)
        The D0...DN matrices of the MMAP to check
    K : int, optional
        The dimension of the matrix of joint moments to 
        compute. If K=0, the MxM joint moments will be 
        computed. The default value is 0
    L : int, optional
        The lag at which the joint moments are computed.
        The default value is 1
    prec : double, optional
        Numerical precision to check if the input is valid. 
        The default value is 1e-14

    Returns
    -------
    Nm : list/cell of matrices of shape(K+1,K+1), length(L)
        The matrices containing the lag-L joint moments,
        starting from moment 0.

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

    >>> D0 = [-1.78, 0.29; 0.07, -0.92];
    >>> D1 = [0.15, 0.49; 0.23, 0.36];
    >>> D2 = [0.11, 0.2; 0.01, 0];
    >>> D3 = [0.14, 0.4; 0.11, 0.14];
    >>> Nm = LagkJointMomentsFromMMAP({D0, D1, D2, D3}, 3, 1);
    >>> disp(Nm{1});
          0.60207      0.60501       1.2755       4.1438
          0.62913      0.62913       1.3226       4.2901
           1.3561       1.3524       2.8387       9.1998
           4.4576       4.4395       9.3105        30.16
    >>> disp(Nm{2});
         0.080053     0.078372      0.16268      0.52401
          0.06033     0.058276      0.11997      0.38467
          0.10244     0.097662       0.1994      0.63637
          0.28923      0.27293       0.5536       1.7601
    >>> disp(Nm{3});
          0.31788      0.31729      0.66629       2.1599
          0.31121      0.30821      0.64424       2.0831
            0.646      0.63672       1.3271       4.2844
           2.0808       2.0455       4.2565        13.73

    For Mathematica:

    >>> D0 = {{-1.78, 0.29},{0.07, -0.92}};
    >>> D1 = {{0.15, 0.49},{0.23, 0.36}};
    >>> D2 = {{0.11, 0.2},{0.01, 0}};
    >>> D3 = {{0.14, 0.4},{0.11, 0.14}};
    >>> Nm = LagkJointMomentsFromMMAP[{D0, D1, D2, D3}, 3, 1];
    >>> Print[Nm[[1]]];
    {{0.6020680453635756, 0.6050097826919547, 1.2755312779381711, 4.143785726301525},
     {0.6291277595686432, 0.6291324346751083, 1.3226115303952872, 4.29008766966622},
     {1.356058746641639, 1.3524365188039793, 2.8387063057306685, 9.199840452355494},
     {4.457620287136224, 4.439461568207248, 9.310487784608107, 30.160255763360027}}
    >>> Print[Nm[[2]]];
    {{0.08005336891260842, 0.07837208152164925, 0.16268008556958458, 0.5240068039224259},
     {0.06033000338608641, 0.058276456272008365, 0.11997332411839014, 0.3846690086730414},
     {0.10243942401511769, 0.09766196798710611, 0.19940380826076648, 0.6363686631976577},
     {0.289234720958347, 0.2729259896515855, 0.5535960565150979, 1.7600767451077592}}
    >>> Print[Nm[[3]]];
    {{0.3178785857238159, 0.31728524719400103, 0.66628526766832, 2.1598956192106504},
     {0.3112093484528753, 0.30821203977350414, 0.6442381239542273, 2.0831364406036084},
     {0.6459984605193192, 0.6367244916768195, 1.327097838382605, 4.28439098549322},
     {2.0808331413400314, 2.045505561084037, 4.256516259923166, 13.72951730592557}}

    For Python/Numpy:

    >>> D0 = ml.matrix([[-1.78, 0.29],[0.07, -0.92]])
    >>> D1 = ml.matrix([[0.15, 0.49],[0.23, 0.36]])
    >>> D2 = ml.matrix([[0.11, 0.2],[0.01, 0]])
    >>> D3 = ml.matrix([[0.14, 0.4],[0.11, 0.14]])
    >>> Nm = LagkJointMomentsFromMMAP([D0, D1, D2, D3], 3, 1)
    >>> print(Nm[0])
    [[  0.60207   0.60501   1.27553   4.14379]
     [  0.62913   0.62913   1.32261   4.29009]
     [  1.35606   1.35244   2.83871   9.19984]
     [  4.45762   4.43946   9.31049  30.16026]]
    >>> print(Nm[1])
    [[ 0.08005  0.07837  0.16268  0.52401]
     [ 0.06033  0.05828  0.11997  0.38467]
     [ 0.10244  0.09766  0.1994   0.63637]
     [ 0.28923  0.27293  0.5536   1.76008]]
    >>> print(Nm[2])
    [[  0.31788   0.31729   0.66629   2.1599 ]
     [  0.31121   0.30821   0.64424   2.08314]
     [  0.646     0.63672   1.3271    4.28439]
     [  2.08083   2.04551   4.25652  13.72952]]