butools.dmap.DMAPFromDRAP
=========================

.. currentmodule:: butools.dmap

.. np:function:: DMAPFromDRAP

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

        * - Matlab:
          - :code:`[D0, D1] = DMAPFromDRAP(H0, H1, precision)`
        * - Mathematica:
          - :code:`{D0, D1} = DMAPFromDRAP[H0, H1, precision]`
        * - Python/Numpy:
          - :code:`D0, D1 = DMAPFromDRAP(H0, H1, precision)`

    Obtains a Markovian representation of a discrete rational
    arrival process of the same size, if possible, using the
    procedure published in [1]_.

    Parameters
    ----------
    H0 : matrix, shape (M,M)
        The H0 matrix of the discrete rational arrival process
    H1 : matrix, shape (M,M)
        The H1 matrix of the discrete rational arrival process
    precision : double, optional
        A representation is considered to be a Markovian one
        if it is closer to it than this precision

    Returns
    -------
    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

    References
    ----------
    .. [1] G Horvath, M Telek, "A minimal representation of 
           Markov arrival processes and a moments matching 
           method," Performance Evaluation 64:(9-12) pp. 
           1153-1168. (2007)       

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

    >>> H0 = [0, 0, 0.13; 0, 0.6, 0.18; 0.31, 0.26, 0.02];
    >>> H1 = [0, 1, -0.13; 0, 0.18, 0.04; 0.03, 0.09, 0.29];
    >>> [D0, D1] = DMAPFromDRAP(H0, H1);
    >>> disp(D0);
         0.051945     0.066321      0.12704
         0.011717      0.56745      0.29444
          0.41438      0.17501   0.00060547
    >>> disp(D1);
         0.085648      0.64664       0.0224
        0.0054434     0.089137     0.031816
          0.04656     0.068225      0.29521
    >>> err = norm(LagkJointMomentsFromDRAP(D0, D1, 3, 1)-LagkJointMomentsFromDRAP(H0, H1, 3, 1));
    >>> disp(err);
       8.8285e-11

    For Mathematica:

    >>> H0 = {{0, 0, 0.13},{0, 0.6, 0.18},{0.31, 0.26, 0.02}};
    >>> H1 = {{0, 1, -0.13},{0, 0.18, 0.04},{0.03, 0.09, 0.29}};
    >>> {D0, D1} = DMAPFromDRAP[H0, H1];
    >>> Print[D0];
    {{0.051945258246527765, 0.0663208007812501, 0.1270425829475309},
     {0.011716991785622438, 0.5674492730034719, 0.294436844493027},
     {0.41438232421874993, 0.17501220703124998, 0.0006054687500000044}}
    >>> Print[D1];
    {{0.08564787688078702, 0.6466430664062499, 0.022400414737654306},
     {0.005443444439086077, 0.08913727936921295, 0.031816166909579335},
     {0.046560058593749995, 0.06822509765625, 0.29521484375}}
    >>> err = Norm[LagkJointMomentsFromDRAP[D0, D1, 3, 1]-LagkJointMomentsFromDRAP[H0, H1, 3, 1]];
    >>> Print[err];
    9.562315040162238*^-11

    For Python/Numpy:

    >>> H0 = ml.matrix([[0, 0, 0.13],[0, 0.6, 0.18],[0.31, 0.26, 0.02]])
    >>> H1 = ml.matrix([[0, 1, -0.13],[0, 0.18, 0.04],[0.03, 0.09, 0.29]])
    >>> D0, D1 = DMAPFromDRAP(H0, H1)
    >>> print(D0)
    [[ 0.13782  0.05942  0.11897]
     [ 0.01119  0.45679  0.39467]
     [ 0.35308  0.27994  0.02539]]
    >>> print(D1)
    [[ 0.09145  0.53681  0.05553]
     [ 0.00598  0.07747  0.0539 ]
     [ 0.03151  0.00901  0.30108]]
    >>> err = la.norm(LagkJointMomentsFromDRAP(D0, D1, 3, 1)-LagkJointMomentsFromDRAP(H0, H1, 3, 1))
    >>> print(err)
    7.00079825521e-11