butools.dmap.LagkJointMomentsFromDRAP¶

butools.dmap.LagkJointMomentsFromDRAP()¶

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

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

Parameters:

H0 : matrix, shape (M,M) The H0 matrix of the discrete rational arrival process H1 : matrix, shape (M,M) The H1 matrix of the discrete 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 = [0, 0, 0.13; 0, 0.6, 0.18; 0.31, 0.26, 0.02];
>>> H1 = [0, 1, -0.13; 0, 0.18, 0.04; 0.03, 0.09, 0.29];
>>> Nm = LagkJointMomentsFromDRAP(H0, H1, 4, 1);
>>> disp(length(Nm));
     5
>>> moms = MarginalMomentsFromDRAP(H0, H1, 4);
>>> disp(moms);
        3.207       16.898       130.77       1347.1
>>> cjm = zeros(1,3);
>>> for i=1:1:3
>>>     Nx = LagkJointMomentsFromDRAP(H0, H1, 1, i);
>>>     cjm(i) = (Nx(2, 2)-moms(1)^2)/(moms(2)-moms(1)^2);
>>> end
>>> disp(cjm);
     0.014303    0.0012424   7.5868e-06
>>> corr = LagCorrelationsFromDRAP(H0, H1, 3);
>>> disp(corr);
     0.014303    0.0012424   7.5868e-06

For Mathematica:

>>> H0 = {{0, 0, 0.13},{0, 0.6, 0.18},{0.31, 0.26, 0.02}};
>>> H1 = {{0, 1, -0.13},{0, 0.18, 0.04},{0.03, 0.09, 0.29}};
>>> Nm = LagkJointMomentsFromDRAP[H0, H1, 4, 1];
>>> Print[Length[Nm]];
5
>>> moms = MarginalMomentsFromDRAP[H0, H1, 4];
>>> Print[moms];
{3.20702366840782, 16.897636691953394, 130.7705457435602, 1347.0743893905096}
>>> cjm = Table[0,{3}];
>>> Do[
>>>     Nx = LagkJointMomentsFromDRAP[H0, H1, 1, i];
>>>     cjm[[i]] = (Nx[[2, 2]]-moms[[1]]^2)/(moms[[2]]-moms[[1]]^2);
>>> , {i,1,3,1}];
>>> Print[cjm];
{0.01430295723332723, 0.0012424024982963658, 7.5867553989928*^-6}
>>> corr = LagCorrelationsFromDRAP[H0, H1, 3];
>>> Print[corr];
{0.01430295723332723, 0.0012424024982963658, 7.586755398724169*^-6}

For Python/Numpy:

>>> H0 = ml.matrix([[0, 0, 0.13],[0, 0.6, 0.18],[0.31, 0.26, 0.02]])
>>> H1 = ml.matrix([[0, 1, -0.13],[0, 0.18, 0.04],[0.03, 0.09, 0.29]])
>>> Nm = LagkJointMomentsFromDRAP(H0, H1, 4, 1)
>>> print(Length(Nm))
5
>>> moms = MarginalMomentsFromDRAP(H0, H1, 4)
>>> print(moms)
[3.2070236684078202, 16.897636691953394, 130.77054574356021, 1347.0743893905096]
>>> cjm = np.zeros(3)
>>> for i in range(1,4,1):
>>>     Nx = LagkJointMomentsFromDRAP(H0, H1, 1, i)
>>>     cjm[i-1] = (Nx[1, 1]-moms[0]**2)/(moms[1]-moms[0]**2)
>>> print(cjm)
[  1.43030e-02   1.24240e-03   7.58676e-06]
>>> corr = LagCorrelationsFromDRAP(H0, H1, 3)
>>> print(corr)
[  1.43030e-02   1.24240e-03   7.58676e-06]