butools.dmap.DMAPFromDRAP¶

butools.dmap.DMAPFromDRAP()¶

Matlab:	[D0, D1] = DMAPFromDRAP(H0, H1, precision)
Mathematica:	{D0, D1} = DMAPFromDRAP[H0, H1, precision]
Python/Numpy:	D0, D1 = DMAPFromDRAP(H0, H1, precision)

Obtains a Markovian representation of a discrete rational arrival process of the same size, if possible, using the procedure published in [R7].

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 precision : double, optional A representation is considered to be a Markovian one if it is closer to it than this precision
Returns:	D0 : matrix, shape (M,M) The D0 matrix of the discrete Markovian arrival process D1 : matrix, shape (M,M) The D1 matrix of the discrete Markovian arrival process

References

[R7]	(1, 2) G Horvath, M Telek, “A minimal representation of Markov arrival processes and a moments matching method,” Performance Evaluation 64:(9-12) pp. 1153-1168. (2007)

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];
>>> [D0, D1] = DMAPFromDRAP(H0, H1);
>>> disp(D0);
     0.051945     0.066321      0.12704
     0.011717      0.56745      0.29444
      0.41438      0.17501   0.00060547
>>> disp(D1);
     0.085648      0.64664       0.0224
    0.0054434     0.089137     0.031816
      0.04656     0.068225      0.29521
>>> err = norm(LagkJointMomentsFromDRAP(D0, D1, 3, 1)-LagkJointMomentsFromDRAP(H0, H1, 3, 1));
>>> disp(err);
   8.8285e-11

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}};
>>> {D0, D1} = DMAPFromDRAP[H0, H1];
>>> Print[D0];
{{0.051945258246527765, 0.0663208007812501, 0.1270425829475309},
 {0.011716991785622438, 0.5674492730034719, 0.294436844493027},
 {0.41438232421874993, 0.17501220703124998, 0.0006054687500000044}}
>>> Print[D1];
{{0.08564787688078702, 0.6466430664062499, 0.022400414737654306},
 {0.005443444439086077, 0.08913727936921295, 0.031816166909579335},
 {0.046560058593749995, 0.06822509765625, 0.29521484375}}
>>> err = Norm[LagkJointMomentsFromDRAP[D0, D1, 3, 1]-LagkJointMomentsFromDRAP[H0, H1, 3, 1]];
>>> Print[err];
9.562315040162238*^-11

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]])
>>> D0, D1 = DMAPFromDRAP(H0, H1)
>>> print(D0)
[[ 0.13782  0.05942  0.11897]
 [ 0.01119  0.45679  0.39467]
 [ 0.35308  0.27994  0.02539]]
>>> print(D1)
[[ 0.09145  0.53681  0.05553]
 [ 0.00598  0.07747  0.0539 ]
 [ 0.03151  0.00901  0.30108]]
>>> err = la.norm(LagkJointMomentsFromDRAP(D0, D1, 3, 1)-LagkJointMomentsFromDRAP(H0, H1, 3, 1))
>>> print(err)
7.00079825521e-11