butools.map.RandomMMAP
======================

.. currentmodule:: butools.map

.. np:function:: RandomMMAP

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

        * - Matlab:
          - :code:`D = RandomMMAP(order, types, mean, zeroEntries, maxTrials, prec)`
        * - Mathematica:
          - :code:`D = RandomMMAP[order, types, mean, zeroEntries, maxTrials, prec]`
        * - Python/Numpy:
          - :code:`D = RandomMMAP(order, types, mean, zeroEntries, maxTrials, prec)`

    Returns a random Markovian arrival process with given mean 
    value.

    Parameters
    ----------
    order : int
        The size of the MAP
    types : int
        The number of different arrival types
    mean : double, optional
        The mean inter-arrival times of the MMAP
    zeroEntries : int, optional
        The number of zero entries in the D0 and D1 matrices
    maxTrials : int, optional
        The maximum number of trials to find a proper MMAP 
        (that has an irreducible phase process and none of 
        its parameters is all-zero)
    prec : double, optional
        Numerical precision for checking the irreducibility.
        The default value is 1e-14.

    Returns
    -------
    D : list/cell of matrices of shape(M,M), length(types+1)
        The D0...Dtypes matrices of the MMAP 

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

    >>> Dm = RandomMMAP(4, 3, 1.62, 10);
    >>> disp(Dm{1});
         -0.84147     0.066601     0.054766            0
         0.071719     -0.67551            0     0.016834
         0.016327      0.11655     -0.57318     0.043691
         0.095968     0.079712            0     -0.87041
    >>> disp(Dm{2});
         0.085267      0.12324     0.018852      0.08092
          0.04971     0.029681     0.015256      0.10755
          0.04997            0            0    0.0019056
         0.098333     0.062911      0.06319     0.055274
    >>> disp(Dm{3});
          0.11299     0.092558            0     0.028328
         0.043418      0.10553    0.0093983     0.063497
          0.10159     0.071162            0    0.0073957
                0     0.053923      0.04684     0.060224
    >>> disp(Dm{4});
          0.10217     0.055739    0.0096715      0.01037
                0     0.017933     0.076958     0.068026
         0.011933    0.0053227     0.029046      0.11829
           0.0379      0.10115            0      0.11498
    >>> m = MarginalMomentsFromMMAP(Dm, 1);
    >>> disp(m);
             1.62

    For Mathematica:

    >>> Dm = RandomMMAP[4, 3, 1.62, 10];
    >>> Print[Dm[[1]]];
    {{-0.5862070911809831, 0., 0.0168137805609394, 0.08788491863058187},
     {0.05283897336899656, -0.8424383930373084, 0.07960302764594157, 0.},
     {0.0430532309208159, 0.09311851788523529, -0.8665132200026514, 0.09720430167174356},
     {0.03143342574603682, 0.006933947818271124, 0.1026546426188773, -0.8461985523926278}}
    >>> Print[Dm[[2]]];
    {{0.014680660704177124, 0.0645992486634905, 0.08177105711062393, 0.016642761139291848},
     {0., 0.09540597852268921, 0., 0.0707635001562371},
     {0.095047323249757, 0.05618623612094079, 0.07843785718105817, 0.06223373813267749},
     {0.0465659166377795, 0.027686196902255576, 0.07643593698997828, 0.04091552394072304}}
    >>> Print[Dm[[3]]];
    {{0.09941961376878797, 0., 0.08253500208040433, 0.10492138700485602},
     {0.07147061429219402, 0.08132225534707489, 0., 0.01620411904838067},
     {0.05528588985095624, 0.06258835562699341, 0.07840456211046513, 0.03871997575555587},
     {0.09854407744754319, 0.06032740737189369, 0.06451082035845042, 0.09710176006166384}}
    >>> Print[Dm[[4]]];
    {{0., 0.0169386615178302, 0., 0.},
     {0.08694201353931666, 0.10148847810958055, 0.09477989858935744, 0.09161953441753981},
     {0.004110565171334107, 0.0061642514927466065, 0.01543324456111962, 0.08052517027125213},
     {0.07312825196154744, 0., 0.06649165886464029, 0.053468985672967276}}
    >>> m = MarginalMomentsFromMMAP[Dm, 1][[1]];
    >>> Print[m];
    1.6199999999999997

    For Python/Numpy:

    >>> Dm = RandomMMAP(4, 3, 1.62, 10)
    >>> print(Dm[0])
    [[-0.77004  0.07746  0.00752  0.12555]
     [ 0.00951 -0.96329  0.11107  0.04652]
     [ 0.       0.07548 -0.66821  0.03229]
     [ 0.12584  0.       0.03691 -0.77768]]
    >>> print(Dm[1])
    [[ 0.05194  0.03399  0.00531  0.04182]
     [ 0.02984  0.07001  0.1335   0.06569]
     [ 0.03889  0.04339  0.       0.     ]
     [ 0.06669  0.       0.10119  0.0133 ]]
    >>> print(Dm[2])
    [[ 0.08729  0.03552  0.03436  0.0247 ]
     [ 0.11078  0.02114  0.       0.02779]
     [ 0.11427  0.06711  0.0964   0.12043]
     [ 0.05964  0.1119   0.       0.06175]]
    >>> print(Dm[3])
    [[ 0.07868  0.04748  0.02386  0.09457]
     [ 0.14246  0.       0.07483  0.12014]
     [ 0.       0.05206  0.00753  0.02037]
     [ 0.0462   0.04298  0.11128  0.     ]]
    >>> m = MarginalMomentsFromMMAP(Dm, 1)[0]
    >>> print(m)
    1.62