butools.map.MarginalDistributionFromMMAP¶
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butools.map.
MarginalDistributionFromMMAP
()¶ Matlab: [alpha, A] = MarginalDistributionFromMMAP(D, precision)
Mathematica: {alpha, A} = MarginalDistributionFromMMAP[D, precision]
Python/Numpy: alpha, A = MarginalDistributionFromMMAP(D, precision)
Returns the phase type distributed marginal distribution of a marked Markovian arrival process.
Parameters: D : list/cell of matrices of shape(M,M), length(N)
The D0...DN matrices of the MMAP
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 = [-1.78, 0.29; 0.07, -0.92]; >>> D1 = [0.15, 0.49; 0.23, 0.36]; >>> D2 = [0.11, 0.2; 0.01, 0]; >>> D3 = [0.14, 0.4; 0.11, 0.14]; >>> [a, A] = MarginalDistributionFromMMAP({D0, D1, D2, D3}); >>> disp(a); 0.36191 0.63809 >>> disp(A); -1.78 0.29 0.07 -0.92
For Mathematica:
>>> D0 = {{-1.78, 0.29},{0.07, -0.92}}; >>> D1 = {{0.15, 0.49},{0.23, 0.36}}; >>> D2 = {{0.11, 0.2},{0.01, 0}}; >>> D3 = {{0.14, 0.4},{0.11, 0.14}}; >>> {a, A} = MarginalDistributionFromMMAP[{D0, D1, D2, D3}]; >>> Print[a]; {0.36190793862575055, 0.6380920613742495} >>> Print[A]; {{-1.78, 0.29}, {0.07, -0.92}}
For Python/Numpy:
>>> D0 = ml.matrix([[-1.78, 0.29],[0.07, -0.92]]) >>> D1 = ml.matrix([[0.15, 0.49],[0.23, 0.36]]) >>> D2 = ml.matrix([[0.11, 0.2],[0.01, 0]]) >>> D3 = ml.matrix([[0.14, 0.4],[0.11, 0.14]]) >>> a, A = MarginalDistributionFromMMAP([D0, D1, D2, D3]) >>> print(a) [[ 0.36191 0.63809]] >>> print(A) [[-1.78 0.29] [ 0.07 -0.92]]