butools.map.LagkJointMomentsFromMRAP¶

butools.map.LagkJointMomentsFromMRAP()¶

Matlab:	Nm = LagkJointMomentsFromMRAP(H, K, L, prec)
Mathematica:	Nm = LagkJointMomentsFromMRAP[H, K, L, prec]
Python/Numpy:	Nm = LagkJointMomentsFromMRAP(H, K, L, prec)

Returns the lag-L joint moments of a marked rational arrival process.

Parameters:

H : list/cell of matrices of shape(M,M), length(N) The H0...HN matrices of the MRAP to check 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 : list/cell of matrices of shape(K+1,K+1), length(N) The matrices containing the lag-L joint moments, starting from moment 0.

Examples

For Matlab:

>>> x = 0.18;
>>> H0 = [-5., 0.1+x, 0.9, 1.; 1., -8., 0.9, 0.1; 0.9, 0.1, -4., 1.; 1., 2., 3., -9.];
>>> H1 = [0.1-x, 0.7, 0.1, 0.1; 0.1, 1., 1.8, 0.1; 0.1, 0.1, 0.1, 0.7; 0.7, 0.1, 0.1, 0.1];
>>> H2 = [0.1, 0.1, 0.1, 1.7; 1.8, 0.1, 1., 0.1; 0.1, 0.1, 0.7, 0.1; 0.1, 1., 0.1, 0.8];
>>> Nm = LagkJointMomentsFromMRAP({H0, H1, H2}, 3, 2);
>>> disp(Nm{1});
      0.41974      0.14337       0.1041      0.11625
      0.14138     0.048248     0.035017       0.0391
      0.10186     0.034737     0.025205      0.02814
      0.11338     0.038655     0.028044     0.031308
>>> disp(Nm{2});
      0.58026      0.19614      0.14173      0.15799
      0.19813     0.066994     0.048418     0.053974
      0.14397     0.048697     0.035199      0.03924
      0.16086     0.054419     0.039338     0.043855

For Mathematica:

>>> x = 0.18;
>>> H0 = {{-5., 0.1+x, 0.9, 1.},{1., -8., 0.9, 0.1},{0.9, 0.1, -4., 1.},{1., 2., 3., -9.}};
>>> H1 = {{0.1-x, 0.7, 0.1, 0.1},{0.1, 1., 1.8, 0.1},{0.1, 0.1, 0.1, 0.7},{0.7, 0.1, 0.1, 0.1}};
>>> H2 = {{0.1, 0.1, 0.1, 1.7},{1.8, 0.1, 1., 0.1},{0.1, 0.1, 0.7, 0.1},{0.1, 1., 0.1, 0.8}};
>>> Nm = LagkJointMomentsFromMRAP[{H0, H1, H2}, 3, 2];
>>> Print[Nm[[1]]];
{{0.41974048988209456, 0.1433714202044304, 0.10409540795191471, 0.11624988638743064},
 {0.14138068443967466, 0.04824753953626901, 0.03501746854001877, 0.039099557275548855},
 {0.10185532272464182, 0.034737397063937, 0.02520539838495395, 0.028140494722472847},
 {0.11337711648763446, 0.038655118635854246, 0.028044484995573313, 0.031308489803818416}}
>>> Print[Nm[[2]]];
{{0.5802595101179051, 0.19613605742007034, 0.14173016403045077, 0.15798754127308057},
 {0.1981267931848261, 0.06699407161937415, 0.048417900372854594, 0.05397433134001463},
 {0.14397024925772373, 0.048696896031760306, 0.03519900415612581, 0.039240318805296825},
 {0.16086031117287675, 0.05441861692540258, 0.03933760117012349, 0.0438552148324313}}

For Python/Numpy:

>>> x = 0.18
>>> H0 = ml.matrix([[-5., 0.1+x, 0.9, 1.],[1., -8., 0.9, 0.1],[0.9, 0.1, -4., 1.],[1., 2., 3., -9.]])
>>> H1 = ml.matrix([[0.1-x, 0.7, 0.1, 0.1],[0.1, 1., 1.8, 0.1],[0.1, 0.1, 0.1, 0.7],[0.7, 0.1, 0.1, 0.1]])
>>> H2 = ml.matrix([[0.1, 0.1, 0.1, 1.7],[1.8, 0.1, 1., 0.1],[0.1, 0.1, 0.7, 0.1],[0.1, 1., 0.1, 0.8]])
>>> Nm = LagkJointMomentsFromMRAP([H0, H1, H2], 3, 2)
>>> print(Nm[0])
[[ 0.41974  0.14337  0.1041   0.11625]
 [ 0.14138  0.04825  0.03502  0.0391 ]
 [ 0.10186  0.03474  0.02521  0.02814]
 [ 0.11338  0.03866  0.02804  0.03131]]
>>> print(Nm[1])
[[ 0.58026  0.19614  0.14173  0.15799]
 [ 0.19813  0.06699  0.04842  0.05397]
 [ 0.14397  0.0487   0.0352   0.03924]
 [ 0.16086  0.05442  0.03934  0.04386]]