butools.map.MAP2FromMoments¶

butools.map.MAP2FromMoments()¶

Matlab:	[D0, D1] = MAP2FromMoments(moms, corr1)
Mathematica:	{D0, D1} = MAP2FromMoments[moms, corr1]
Python/Numpy:	D0, D1 = MAP2FromMoments(moms, corr1)

Returns a MAP(2) which has the same 3 marginal moments and lag-1 autocorrelation as given.

Parameters:	moms : vector, length(3) First three marginal moments of the inter-arrival times corr1 : double The lag-1 autocorrelation of the inter-arrival times
Returns:	D0 : matrix, shape (2,2) The D0 matrix of the MAP(2) D1 : matrix, shape (2,2) The D1 matrix of the MAP(2) Raises an exception if the moments are not feasible with a MAP(2).

Notes

The result is always a valid MAP(2) as long as the input moments can be realized by a PH(2) (can be checked with butools.ph.APH2ndMomentLowerBound, butools.ph.APH3rdMomentLowerBound, butools.ph.APH3rdMomentUpperBound with n=2) and the correlation falls between the feasible lower and upper bound (check by MAP2CorrelationBounds).

References

[R18]

L Bodrog, A Heindl, G Horvath, M Telek, “A Markovian Canonical Form of Second-Order Matrix-Exponential Processes,” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 190:(2) pp. 459-477. (2008)

Examples

For Matlab:

>>> D0 = [-14., 1.; 1, -25.];
>>> D1 = [6., 7.; 3., 21.];
>>> moms = MarginalMomentsFromMAP(D0, D1, 3);
>>> disp(moms);
      0.04918    0.0052609   0.00091819
>>> corr = LagCorrelationsFromMAP(D0, D1, 1);
>>> disp(corr);
     0.022416
>>> [D0, D1] = MAP2FromMoments(moms, corr);
>>> disp(D0);
       -13.91        9.199
            0       -25.09
>>> disp(D1);
       4.7108            0
        2.801       22.289
>>> rmoms = MarginalMomentsFromMAP(D0, D1, 3);
>>> disp(rmoms);
      0.04918    0.0052609   0.00091819
>>> rcorr = LagCorrelationsFromMAP(D0, D1, 1);
>>> disp(rcorr);
     0.022416

For Mathematica:

>>> D0 = {{-14., 1.},{1, -25.}};
>>> D1 = {{6., 7.},{3., 21.}};
>>> moms = MarginalMomentsFromMAP[D0, D1, 3];
>>> Print[moms];
{0.04918032786885247, 0.005260932876133214, 0.0009181867601560783}
>>> corr = LagCorrelationsFromMAP[D0, D1, 1][[1]];
>>> Print[corr];
0.02241571110398602
>>> {D0, D1} = MAP2FromMoments[moms, corr];
>>> Print[D0];
{{-13.909830056250456, 9.199027971874015},
 {0, -25.090169943749302}}
>>> Print[D1];
{{4.710802084376442, 0},
 {2.8009720281259014, 22.2891979156234}}
>>> rmoms = MarginalMomentsFromMAP[D0, D1, 3];
>>> Print[rmoms];
{0.04918032786885251, 0.005260932876133218, 0.0009181867601560789}
>>> rcorr = LagCorrelationsFromMAP[D0, D1, 1][[1]];
>>> Print[rcorr];
0.022415711103985703

For Python/Numpy:

>>> D0 = ml.matrix([[-14., 1.],[1, -25.]])
>>> D1 = ml.matrix([[6., 7.],[3., 21.]])
>>> moms = MarginalMomentsFromMAP(D0, D1, 3)
>>> print(moms)
[0.049180327868852472, 0.005260932876133214, 0.00091818676015607825]
>>> corr = LagCorrelationsFromMAP(D0, D1, 1)[0]
>>> print(corr)
0.022415711104
>>> D0, D1 = MAP2FromMoments(moms, corr)
>>> print(D0)
[[-13.90983   9.19903]
 [  0.      -25.09017]]
>>> print(D1)
[[  4.7108    0.     ]
 [  2.80097  22.2892 ]]
>>> rmoms = MarginalMomentsFromMAP(D0, D1, 3)
>>> print(rmoms)
[0.049180327868852479, 0.0052609328761332123, 0.00091818676015607728]
>>> rcorr = LagCorrelationsFromMAP(D0, D1, 1)[0]
>>> print(rcorr)
0.022415711104