butools.dph.SamplesFromDPH
==========================

.. currentmodule:: butools.dph

.. np:function:: SamplesFromDPH

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

        * - Matlab:
          - :code:`x = SamplesFromDPH(alpha, A, K, prec)`
        * - Mathematica:
          - :code:`x = SamplesFromDPH[alpha, A, K, prec]`
        * - Python/Numpy:
          - :code:`x = SamplesFromDPH(alpha, A, K, prec)`

    Generates random samples from a discrete phase-type 
    distribution.

    Parameters
    ----------
    alpha : matrix, shape (1,M)
        The initial probability vector of the discrete phase-
        type distribution.
    A : matrix, shape (M,M)
        The transition probability  matrix of the discrete phase-
        type distribution.
    K : integer
        The number of samples to generate.
    prec : double, optional
        Numerical precision to check if the input phase-type
        distribution is valid. The default value is 1e-14.

    Returns
    -------
    x : vector, length(K)
        The vector of random samples

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

    >>> a = [0.76,0,0.24];
    >>> A = [0.34, 0.66, 0; 0.79, 0.05, 0.07; 0.26, 0.73, 0.01];
    >>> x = SamplesFromDPH(a, A, 1000);
    >>> mt = MarginalMomentsFromTrace(x, 3);
    >>> disp(mt);
           26.886       1425.6   1.1352e+05
    >>> mp = MomentsFromDPH(a, A, 3);
    >>> disp(mp);
           26.995         1398   1.0853e+05

    For Mathematica:

    >>> a = {0.76,0,0.24};
    >>> A = {{0.34, 0.66, 0},{0.79, 0.05, 0.07},{0.26, 0.73, 0.01}};
    >>> x = SamplesFromDPH[a, A, 1000];
    >>> mt = MarginalMomentsFromTrace[x, 3];
    >>> Print[mt];
    {27427/1000, 1418939/1000, 111151657/1000}
    >>> mp = MomentsFromDPH[a, A, 3];
    >>> Print[mp];
    {26.995340611502304, 1397.9993695881547, 108525.47866809377}

    For Python/Numpy:

    >>> a = ml.matrix([[0.76,0,0.24]])
    >>> A = ml.matrix([[0.34, 0.66, 0],[0.79, 0.05, 0.07],[0.26, 0.73, 0.01]])
    >>> x = SamplesFromDPH(a, A, 1000)
    >>> mt = MarginalMomentsFromTrace(x, 3)
    >>> print(mt)
    [26.765999999999998, 1331.058, 93128.106]
    >>> mp = MomentsFromDPH(a, A, 3)
    >>> print(mp)
    [26.995340611502307, 1397.9993695881547, 108525.47866809377]