butools.dmap.DRAPFromMoments¶

butools.dmap.DRAPFromMoments()¶

Matlab:	[H0, H1] = DRAPFromMoments(moms, Nm)
Mathematica:	{H0, H1} = DRAPFromMoments[moms, Nm]
Python/Numpy:	H0, H1 = DRAPFromMoments(moms, Nm)

Creates a discrete rational arrival process that has the same marginal and lag-1 joint moments as given (see [R11]).

Parameters:	moms : vector of doubles The list of marginal moments. To obtain a rational process of order M, 2*M-1 marginal moments are required. Nm : matrix, shape (M,M) The matrix of lag-1 joint moments.
Returns:	H0 : matrix, shape (M,M) The H0 matrix of the discrete rational process H1 : matrix, shape (M,M) The H1 matrix of the discrete rational process

References

[R11]

(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:

>>> G0 = [0, 0.02, 0, 0; 0, 0.17, 0.2, 0.14; 0.16, 0.17, 0.02, 0.18; 0, 0, 0, 0.12];
>>> G1 = [0, 0.88, 0.1, 0; 0.18, 0.07, 0.14, 0.1; 0.13, 0.15, 0.15, 0.04; 0.31, 0.18, 0.12, 0.27];
>>> moms = MarginalMomentsFromDRAP(G0, G1, 5);
>>> disp(moms);
       1.4955       2.9542       7.8852       27.282       116.17
>>> Nm = LagkJointMomentsFromDRAP(G0, G1, 2, 1);
>>> disp(Nm);
            1       1.4955       2.9542
       1.4955       2.2037       4.2827
       2.9542       4.2875       8.1899
>>> [H0, H1] = DRAPFromMoments(moms, Nm);
>>> disp(H0);
      0.56447      0.47188     -0.69474
     -0.50857     -0.10551      0.95921
      0.18477      0.26121     -0.13431
>>> disp(H1);
       2.3994       1.1243      -2.8653
      -1.7535     -0.59009       2.9984
      0.95074      0.51879      -0.7812
>>> rmoms = MarginalMomentsFromDRAP(H0, H1, 5);
>>> disp(rmoms);
       1.4955       2.9542       7.8852       27.282       116.17
>>> rNm = LagkJointMomentsFromDRAP(H0, H1, 2, 1);
>>> disp(rNm);
            1       1.4955       2.9542
       1.4955       2.2037       4.2827
       2.9542       4.2875       8.1899

For Mathematica:

>>> G0 = {{0, 0.02, 0, 0},{0, 0.17, 0.2, 0.14},{0.16, 0.17, 0.02, 0.18},{0, 0, 0, 0.12}};
>>> G1 = {{0, 0.88, 0.1, 0},{0.18, 0.07, 0.14, 0.1},{0.13, 0.15, 0.15, 0.04},{0.31, 0.18, 0.12, 0.27}};
>>> moms = MarginalMomentsFromDRAP[G0, G1, 5];
>>> Print[moms];
{1.4955358592094412, 2.9542479654368474, 7.885226907678561, 27.282328108669493, 116.17171481905851}
>>> Nm = LagkJointMomentsFromDRAP[G0, G1, 2, 1];
>>> Print[Nm];
{{1., 1.4955358592094412, 2.954247965436847},
 {1.4955358592094414, 2.2037182406034797, 4.282673397390962},
 {2.9542479654368474, 4.287487747878976, 8.189899409259828}}
>>> {H0, H1} = DRAPFromMoments[moms, Nm];
>>> Print[H0];
{{0.5644738962225417, 0.47187846354848406, -0.6947446288880126},
 {-0.5085686970022437, -0.10550993297233946, 0.9592122034338286},
 {0.18477321176067846, 0.261205874785389, -0.13431385414476443}}
>>> Print[H1];
{{2.3993787625484853, 1.1243091633982, -2.865295656829698},
 {-1.7534589569688064, -0.5900943661745801, 2.9984197496841354},
 {0.9507424301490942, 0.5187877102745091, -0.7811953728249019}}
>>> rmoms = MarginalMomentsFromDRAP[H0, H1, 5];
>>> Print[rmoms];
{1.495535859209443, 2.954247965436855, 7.885226907678592, 27.28232810866962, 116.17171481905912}
>>> rNm = LagkJointMomentsFromDRAP[H0, H1, 2, 1];
>>> Print[rNm];
{{0.9999999999999997, 1.4955358592094425, 2.954247965436854},
 {1.4955358592094437, 2.2037182406034845, 4.282673397390974},
 {2.9542479654368594, 4.287487747878995, 8.189899409259864}}

For Python/Numpy:

>>> G0 = ml.matrix([[0, 0.02, 0, 0],[0, 0.17, 0.2, 0.14],[0.16, 0.17, 0.02, 0.18],[0, 0, 0, 0.12]])
>>> G1 = ml.matrix([[0, 0.88, 0.1, 0],[0.18, 0.07, 0.14, 0.1],[0.13, 0.15, 0.15, 0.04],[0.31, 0.18, 0.12, 0.27]])
>>> moms = MarginalMomentsFromDRAP(G0, G1, 5)
>>> print(moms)
[1.4955358592094412, 2.9542479654368474, 7.885226907678561, 27.282328108669493, 116.17171481905851]
>>> Nm = LagkJointMomentsFromDRAP(G0, G1, 2, 1)
>>> print(Nm)
[[ 1.       1.49554  2.95425]
 [ 1.49554  2.20372  4.28267]
 [ 2.95425  4.28749  8.1899 ]]
>>> H0, H1 = DRAPFromMoments(moms, Nm)
>>> print(H0)
[[ 0.56447  0.47188 -0.69474]
 [-0.50857 -0.10551  0.95921]
 [ 0.18477  0.26121 -0.13431]]
>>> print(H1)
[[ 2.39938  1.12431 -2.8653 ]
 [-1.75346 -0.59009  2.99842]
 [ 0.95074  0.51879 -0.7812 ]]
>>> rmoms = MarginalMomentsFromDRAP(H0, H1, 5)
>>> print(rmoms)
[1.495535859209453, 2.9542479654368994, 7.885226907678768, 27.282328108670363, 116.17171481906257]
>>> rNm = LagkJointMomentsFromDRAP(H0, H1, 2, 1)
>>> print(rNm)
[[ 1.       1.49554  2.95425]
 [ 1.49554  2.20372  4.28267]
 [ 2.95425  4.28749  8.1899 ]]