butools.map.CanonicalFromMAP2¶

butools.map.CanonicalFromMAP2()¶

Matlab:	[G0, G1] = CanonicalFromMAP2(D0, D1, prec)
Mathematica:	{G0, G1} = CanonicalFromMAP2[D0, D1, prec]
Python/Numpy:	G0, G1 = CanonicalFromMAP2(D0, D1, prec)

Returns the canonical form of an order-2 Markovian arrival process.

Parameters:	D0 : matrix, shape (2,2) The D0 matrix of the MAP(2) D1 : matrix, shape (2,2) The D1 matrix of the MAP(2) prec : double, optional Numerical precision to check the input, default value is 1e-14
Returns:	G0 : matrix, shape (1,2) The D0 matrix of the canonical MAP(2) G1 : matrix, shape (2,2) The D1 matrix of the canonical MAP(2)

Notes

This procedure calculates 3 marginal moments and the lag-1 autocorrelation of the input and calls ‘MAP2FromMoments’.

Examples

For Matlab:

>>> D0 = [-14., 1.; 1., -25.];
>>> D1 = [6., 7.; 3., 21.];
>>> [H0, H1] = CanonicalFromMAP2(D0, D1);
>>> disp(H0);
       -13.91        9.199
            0       -25.09
>>> disp(H1);
       4.7108            0
        2.801       22.289
>>> Cm = SimilarityMatrix(H0, D0);
>>> err1 = norm(H0*Cm-Cm*D0);
>>> err2 = norm(H1*Cm-Cm*D1);
>>> disp(max(err1, err2));
   2.4485e-13

For Mathematica:

>>> D0 = {{-14., 1.},{1., -25.}};
>>> D1 = {{6., 7.},{3., 21.}};
>>> {H0, H1} = CanonicalFromMAP2[D0, D1];
>>> Print[H0];
{{-13.909830056250456, 9.199027971874015},
 {0, -25.090169943749302}}
>>> Print[H1];
{{4.710802084376442, 0},
 {2.8009720281259014, 22.2891979156234}}
>>> Cm = SimilarityMatrix[H0, D0];
>>> err1 = Norm[H0.Cm-Cm.D0];
>>> err2 = Norm[H1.Cm-Cm.D1];
>>> Print[Max[err1, err2]];
2.39754619495158*^-13

For Python/Numpy:

>>> D0 = ml.matrix([[-14., 1.],[1., -25.]])
>>> D1 = ml.matrix([[6., 7.],[3., 21.]])
>>> H0, H1 = CanonicalFromMAP2(D0, D1)
>>> print(H0)
[[-13.90983   9.19903]
 [  0.      -25.09017]]
>>> print(H1)
[[  4.7108    0.     ]
 [  2.80097  22.2892 ]]
>>> Cm = SimilarityMatrix(H0, D0)
>>> err1 = la.norm(H0*Cm-Cm*D0)
>>> err2 = la.norm(H1*Cm-Cm*D1)
>>> print(np.max(err1, err2))
2.21090873503e-13