butools.map.LagkJointMomentsFromRAP¶

butools.map.LagkJointMomentsFromRAP()¶

Matlab:	Nm = LagkJointMomentsFromRAP(H0, H1, K, L, prec)
Mathematica:	Nm = LagkJointMomentsFromRAP[H0, H1, K, L, prec]
Python/Numpy:	Nm = LagkJointMomentsFromRAP(H0, H1, K, L, prec)

Returns the lag-L joint moments 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 K : int, optional The dimension of the matrix of joint moments to compute. If K=0, the MxM joint moments will be computed. The default value is 0 L : int, optional The lag at which the joint moments are computed. The default value is 1 prec : double, optional Numerical precision to check if the input is valid. The default value is 1e-14

Returns:

Nm : matrix, shape(K+1,K+1) The matrix containing the lag-L joint moments, starting from moment 0.

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.];
>>> Nm = LagkJointMomentsFromRAP(H0, H1, 4, 1);
>>> disp(length(Nm));
     5
>>> moms = MarginalMomentsFromRAP(H0, H1, 4);
>>> disp(moms);
      0.44444      0.38095      0.48299      0.82216
>>> cjm = zeros(1,3);
>>> for i=1:1:3
>>>     Nx = LagkJointMomentsFromRAP(H0, H1, 1, i);
>>>     cjm(i) = (Nx(2, 2)-moms(1)^2)/(moms(2)-moms(1)^2);
>>> end
>>> disp(cjm);
   -0.0038462    0.0045604    0.0058956
>>> 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.}};
>>> Nm = LagkJointMomentsFromRAP[H0, H1, 4, 1];
>>> Print[Length[Nm]];
5
>>> moms = MarginalMomentsFromRAP[H0, H1, 4];
>>> Print[moms];
{0.4444444444444444, 0.380952380952381, 0.48299319727891166, 0.8221574344023325}
>>> cjm = Table[0,{3}];
>>> Do[
>>>     Nx = LagkJointMomentsFromRAP[H0, H1, 1, i];
>>>     cjm[[i]] = (Nx[[2, 2]]-moms[[1]]^2)/(moms[[2]]-moms[[1]]^2);
>>> , {i,1,3,1}];
>>> Print[cjm];
{-0.0038461538461536634, 0.004560439560439573, 0.0058956043956042425}
>>> 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.]])
>>> Nm = LagkJointMomentsFromRAP(H0, H1, 4, 1)
>>> print(Length(Nm))
5
>>> moms = MarginalMomentsFromRAP(H0, H1, 4)
>>> print(moms)
[0.44444444444444442, 0.38095238095238093, 0.48299319727891149, 0.82215743440233213]
>>> cjm = np.zeros(3)
>>> for i in range(1,4,1):
>>>     Nx = LagkJointMomentsFromRAP(H0, H1, 1, i)
>>>     cjm[i-1] = (Nx[1, 1]-moms[0]**2)/(moms[1]-moms[0]**2)
>>> print(cjm)
[-0.00385  0.00456  0.0059 ]
>>> corr = LagCorrelationsFromRAP(H0, H1, 3)
>>> print(corr)
[-0.00385  0.00456  0.0059 ]