butools.ph.PdfFromME
====================

.. currentmodule:: butools.ph

.. np:function:: PdfFromME

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

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

    Returns the probability density function of a matrix-
    exponential distribution.

    Parameters
    ----------
    alpha : vector, 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 density function will be computed at these points
    prec : double, optional
        Numerical precision to check if the input ME 
        distribution is valid. The default value is 1e-14.
    
    Returns
    -------
    pdf : column vector of doubles
        The values of the density function 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);
    >>> pdf = PdfFromME(a, A, x);
    >>> plot(x, pdf)

    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];
    >>> pdf = PdfFromME[a, A, x];
    >>> ListLinePlot[{Transpose[{x, pdf}]}]

    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)
    >>> pdf = PdfFromME(a, A, x)
    >>> plt.plot(x, pdf)