butools.ph.CheckMEPositiveDensity
=================================

.. currentmodule:: butools.ph

.. np:function:: CheckMEPositiveDensity

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

        * - Matlab:
          - :code:`r = CheckMEPositiveDensity(alpha, A, maxSize, prec)`
        * - Mathematica:
          - :code:`r = CheckMEPositiveDensity[alpha, A, maxSize, prec]`
        * - Python/Numpy:
          - :code:`r = CheckMEPositiveDensity(alpha, A, maxSize, prec)`

    Checks if the given matrix-exponential distribution has 
    positive density.

    Parameters
    ----------
    alpha : matrix, shape (1,M)
        Initial vector of the matrix-exponential distribution 
        to check
    A : matrix, shape (M,M)
        Matrix parameter of the matrix-exponential distribution
        to check
    maxSize : int, optional
        The procedure tries to transform the ME distribution
        to phase-type up to order maxSize. The default value
        is 100.
    prec : double, optional
        Numerical precision. The default value is 1e-14.

    Returns
    -------
    r : bool
        True, if the given matrix-exponential distribution has
        a positive density

    Notes
    -----
    This procedure calls MonocyclicPHFromME, and can be time 
    consuming. 

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

    >>> a = [0.2,0.3,0.5];
    >>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
    >>> flag = CheckMEPositiveDensity(a, A);
    >>> disp(flag);
         1
    >>> a = [0.2,0.3,0.5];
    >>> A = [-1, 0, 0; 0, -3, 2.9; 0, -2.9, -3];
    >>> flag = CheckMEPositiveDensity(a, A);
    >>> disp(flag);
         0

    For Mathematica:

    >>> a = {0.2,0.3,0.5};
    >>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
    >>> flag = CheckMEPositiveDensity[a, A];
    >>> Print[flag];
    True
    >>> a = {0.2,0.3,0.5};
    >>> A = {{-1, 0, 0},{0, -3, 2.9},{0, -2.9, -3}};
    >>> flag = CheckMEPositiveDensity[a, A];
    >>> Print[flag];
    False

    For Python/Numpy:

    >>> a = ml.matrix([[0.2,0.3,0.5]])
    >>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
    >>> flag = CheckMEPositiveDensity(a, A)
    >>> print(flag)
    True
    >>> a = ml.matrix([[0.2,0.3,0.5]])
    >>> A = ml.matrix([[-1, 0, 0],[0, -3, 2.9],[0, -2.9, -3]])
    >>> flag = CheckMEPositiveDensity(a, A)
    >>> print(flag)
    False