butools.map.MAPFromRAP¶

butools.map.MAPFromRAP()¶

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

Obtains a Markovian representation of a rational arrival process of the same size, if possible, using the procedure published in [R20].

Parameters:

H0 : matrix, shape (M,M)

The H0 matrix of the rational arrival process

H1 : matrix, shape (M,M)

The H1 matrix of the 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 Markovian arrival process

D1 : matrix, shape (M,M)

The D1 matrix of the Markovian arrival process

References

[R20]

(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:

>>> D0 = [-2., 2.; 2., -9.];
>>> D1 = [-2., 2.; 3., 4.];
>>> [H0, H1] = MAPFromRAP(D0, D1);
>>> disp(H0);
      -1.4699     -0.18514
     -0.04328      -9.5301
>>> disp(H1);
     -0.18514       1.8401
       7.3883       2.1851
>>> err = norm(LagkJointMomentsFromRAP(D0, D1, 3, 1)-LagkJointMomentsFromRAP(H0, H1, 3, 1));
>>> disp(err);
   2.7443e-15
>>> D0 = [-2.4, 2.; 2., -9.];
>>> D1 = [-1.6, 2.; 3., 4.];
>>> [H0, H1] = MAPFromRAP(D0, D1);
>>> disp(H0);
      -1.8414     0.079468
     0.012509      -9.5586
>>> disp(H1);
     0.024509       1.7374
       7.1706       2.3755
>>> err = norm(LagkJointMomentsFromRAP(D0, D1, 3, 1)-LagkJointMomentsFromRAP(H0, H1, 3, 1));
>>> disp(err);
   6.4694e-16

For Mathematica:

>>> D0 = {{-2., 2.},{2., -9.}};
>>> D1 = {{-2., 2.},{3., 4.}};
>>> {H0, H1} = MAPFromRAP[D0, D1];
>>> Print[H0];
{{-1.469865108524213, -0.18513639022235387},
 {-0.04328028919559579, -9.530134891475761}}
>>> Print[H1];
{{-0.1851363902223537, 1.8401378889689204},
 {7.388278790449017, 2.185136390222349}}
>>> err = Norm[LagkJointMomentsFromRAP[D0, D1, 3, 1]-LagkJointMomentsFromRAP[H0, H1, 3, 1]];
>>> Print[err];
3.31611301558491*^-15
>>> D0 = {{-2.4, 2.},{2., -9.}};
>>> D1 = {{-1.6, 2.},{3., 4.}};
>>> {H0, H1} = MAPFromRAP[D0, D1];
>>> Print[H0];
{{-1.8413725353422619, 0.07946777343749967},
 {0.012509334866139282, -9.558627464657736}}
>>> Print[H1];
{{0.02450852167038682, 1.7373962402343748},
 {7.170626651461986, 2.3754914783296126}}
>>> err = Norm[LagkJointMomentsFromRAP[D0, D1, 3, 1]-LagkJointMomentsFromRAP[H0, H1, 3, 1]];
>>> Print[err];
7.665251615940028*^-16

For Python/Numpy:

>>> D0 = ml.matrix([[-2., 2.],[2., -9.]])
>>> D1 = ml.matrix([[-2., 2.],[3., 4.]])
>>> H0, H1 = MAPFromRAP(D0, D1)
>>> print(H0)
[[ -1.46887e+00  -3.05193e-02]
 [  4.20579e-15  -9.53113e+00]]
>>> print(H1)
[[-0.33715  1.83654]
 [ 7.19398  2.33715]]
>>> err = la.norm(LagkJointMomentsFromRAP(D0, D1, 3, 1)-LagkJointMomentsFromRAP(H0, H1, 3, 1))
>>> print(err)
1.62866154301e-14
>>> D0 = ml.matrix([[-2.4, 2.],[2., -9.]])
>>> D1 = ml.matrix([[-1.6, 2.],[3., 4.]])
>>> H0, H1 = MAPFromRAP(D0, D1)
>>> print(H0)
[[-1.84137  0.07947]
 [ 0.01251 -9.55863]]
>>> print(H1)
[[ 0.02451  1.7374 ]
 [ 7.17063  2.37549]]
>>> err = la.norm(LagkJointMomentsFromRAP(D0, D1, 3, 1)-LagkJointMomentsFromRAP(H0, H1, 3, 1))
>>> print(err)
4.674749869e-16