butools.map.MarginalDistributionFromMAP¶

butools.map.MarginalDistributionFromMAP()¶

Matlab:	[alpha, A] = MarginalDistributionFromMAP(D0, D1, precision)
Mathematica:	{alpha, A} = MarginalDistributionFromMAP[D0, D1, precision]
Python/Numpy:	alpha, A = MarginalDistributionFromMAP(D0, D1, precision)

Returns the phase type distributed marginal distribution of a Markovian arrival process.

Parameters:	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 precision : double, optional Numerical precision for checking if the input is valid. The default value is 1e-14
Returns:	alpha : matrix, shape (1,M) The initial probability vector of the phase type distributed marginal distribution A : matrix, shape (M,M) The transient generator of the phase type distributed marginal distribution

Examples

For Matlab:

>>> D0 = [-0.17, 0, 0, 0.07; 0.01, -0.78, 0.03, 0.08; 0.22, 0.17, -1.1, 0.02; 0.04, 0.12, 0, -0.42];
>>> D1 = [0, 0.06, 0, 0.04; 0.04, 0.19, 0.21, 0.22; 0.22, 0.13, 0.15, 0.19; 0.05, 0, 0.17, 0.04];
>>> [a, A] = MarginalDistributionFromMAP(D0, D1);
>>> disp(a);
      0.14438      0.23571      0.33794      0.28196
>>> disp(A);
        -0.17            0            0         0.07
         0.01        -0.78         0.03         0.08
         0.22         0.17         -1.1         0.02
         0.04         0.12            0        -0.42

For Mathematica:

>>> D0 = {{-0.17, 0, 0, 0.07},{0.01, -0.78, 0.03, 0.08},{0.22, 0.17, -1.1, 0.02},{0.04, 0.12, 0, -0.42}};
>>> D1 = {{0, 0.06, 0, 0.04},{0.04, 0.19, 0.21, 0.22},{0.22, 0.13, 0.15, 0.19},{0.05, 0, 0.17, 0.04}};
>>> {a, A} = MarginalDistributionFromMAP[D0, D1];
>>> Print[a];
{0.1443829740435819, 0.23570990103732542, 0.33794226877724004, 0.2819648561418526}
>>> Print[A];
{{-0.17, 0, 0, 0.07},
 {0.01, -0.78, 0.03, 0.08},
 {0.22, 0.17, -1.1, 0.02},
 {0.04, 0.12, 0, -0.42}}

For Python/Numpy:

>>> D0 = ml.matrix([[-0.17, 0, 0, 0.07],[0.01, -0.78, 0.03, 0.08],[0.22, 0.17, -1.1, 0.02],[0.04, 0.12, 0, -0.42]])
>>> D1 = ml.matrix([[0, 0.06, 0, 0.04],[0.04, 0.19, 0.21, 0.22],[0.22, 0.13, 0.15, 0.19],[0.05, 0, 0.17, 0.04]])
>>> a, A = MarginalDistributionFromMAP(D0, D1)
>>> print(a)
[[ 0.14438  0.23571  0.33794  0.28196]]
>>> print(A)
[[-0.17  0.    0.    0.07]
 [ 0.01 -0.78  0.03  0.08]
 [ 0.22  0.17 -1.1   0.02]
 [ 0.04  0.12  0.   -0.42]]