butools.ph.CdfFromME
====================

.. currentmodule:: butools.ph

.. np:function:: CdfFromME

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

        * - Matlab:
          - :code:`cdf = CdfFromME(alpha, A, x)`
        * - Mathematica:
          - :code:`cdf = CdfFromME[alpha, A, x]`
        * - Python/Numpy:
          - :code:`cdf = CdfFromME(alpha, A, x)`

    Returns the cummulative distribution function of a
    matrix-exponential distribution.

    Parameters
    ----------
    alpha : matrix, shape (1,M)
        The initial vector of the matrix-exponential
        distribution.
    A : matrix, shape (M,M)
        The matrix parameter of the matrix-exponential
        distribution.
    x : vector of doubles
        The cdf will be computed at these points

    Returns
    -------
    cdf : column vector of doubles
        The values of the cdf at the corresponding "x" values

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

    >>> a = [0.2,0.3,0.5];
    >>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
    >>> x = (0.0:0.01:5.0);
    >>> cdf = CdfFromME(a, A, x);
    >>> plot(x, cdf)

    For Mathematica:

    >>> a = {0.2,0.3,0.5};
    >>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
    >>> x = Range[0.0,5.0,0.01];
    >>> cdf = CdfFromME[a, A, x];
    >>> ListLinePlot[{Transpose[{x, cdf}]}]

    For Python/Numpy:

    >>> a = ml.matrix([[0.2,0.3,0.5]])
    >>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
    >>> x = np.arange(0.0,5.01,0.01)
    >>> cdf = CdfFromME(a, A, x)
    >>> plt.plot(x, cdf)