butools.map.LagCorrelationsFromRAP
==================================

.. currentmodule:: butools.map

.. np:function:: LagCorrelationsFromRAP

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

        * - Matlab:
          - :code:`acf = LagCorrelationsFromRAP(H0, H1, L, prec)`
        * - Mathematica:
          - :code:`acf = LagCorrelationsFromRAP[H0, H1, L, prec]`
        * - Python/Numpy:
          - :code:`acf = LagCorrelationsFromRAP(H0, H1, L, prec)`

    Returns the lag autocorrelations of a rational arrival
    process.

    Parameters
    ----------
    H0 : matrix, shape (M,M)
        The H0 matrix of the rational arrival process
    H1 : matrix, shape (M,M)
        The H1 matrix of the rational arrival process
    L : double, optional
        The number of lags to compute. The default value is 1
    prec : double, optional
        Numerical precision to check if the input is valid. 
        The default value is 1e-14

    Returns
    -------
    acf : column vector of doubles, length (L)
        The lag autocorrelation function up to lag L
        
    Examples
    ========
    For Matlab:

    >>> H0 = [-2., 0, 0; 0, -3., 1.; 0, -1., -2.];
    >>> H1 = [1.8, 0.2, 0; 0.2, 1.8, 0; 0.2, 1.8, 1.];
    >>> corr = LagCorrelationsFromRAP(H0, H1, 3);
    >>> disp(corr);
       -0.0038462    0.0045604    0.0058956

    For Mathematica:

    >>> H0 = {{-2., 0, 0},{0, -3., 1.},{0, -1., -2.}};
    >>> H1 = {{1.8, 0.2, 0},{0.2, 1.8, 0},{0.2, 1.8, 1.}};
    >>> corr = LagCorrelationsFromRAP[H0, H1, 3];
    >>> Print[corr];
    {-0.0038461538461536634, 0.0045604395604397245, 0.005895604395604545}

    For Python/Numpy:

    >>> H0 = ml.matrix([[-2., 0, 0],[0, -3., 1.],[0, -1., -2.]])
    >>> H1 = ml.matrix([[1.8, 0.2, 0],[0.2, 1.8, 0],[0.2, 1.8, 1.]])
    >>> corr = LagCorrelationsFromRAP(H0, H1, 3)
    >>> print(corr)
    [-0.00385  0.00456  0.0059 ]