butools.map.MarginalDistributionFromRAP¶

butools.map.MarginalDistributionFromRAP()¶

Matlab:	[alpha, A] = MarginalDistributionFromRAP(H0, H1, precision)
Mathematica:	{alpha, A} = MarginalDistributionFromRAP[H0, H1, precision]
Python/Numpy:	alpha, A = MarginalDistributionFromRAP(H0, H1, precision)

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

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 Numerical precision for checking if the input is valid. The default value is 1e-14
Returns:	alpha : matrix, shape (1,M) The initial vector of the matrix exponentially distributed marginal A : matrix, shape (M,M) The matrix parameter of the matrix exponentially distributed marginal

Examples

For Matlab:

>>> H0 = [-2, 0, 0; 0, -3, 1; 0, -1, -2];
>>> H1 = [1.8, 0.2, 0; 0.2, 1.8, 0; 0.2, 1.8, 1];
>>> [a, A] = MarginalDistributionFromRAP(H0, H1);
>>> disp(a);
      0.44444      0.44444      0.11111
>>> disp(A);
    -2     0     0
     0    -3     1
     0    -1    -2

For Mathematica:

>>> H0 = {{-2, 0, 0},{0, -3, 1},{0, -1, -2}};
>>> H1 = {{1.8, 0.2, 0},{0.2, 1.8, 0},{0.2, 1.8, 1}};
>>> {a, A} = MarginalDistributionFromRAP[H0, H1];
>>> Print[a];
{0.44444444444444464, 0.4444444444444443, 0.11111111111111106}
>>> Print[A];
{{-2, 0, 0},
 {0, -3, 1},
 {0, -1, -2}}

For Python/Numpy:

>>> H0 = ml.matrix([[-2, 0, 0],[0, -3, 1],[0, -1, -2]])
>>> H1 = ml.matrix([[1.8, 0.2, 0],[0.2, 1.8, 0],[0.2, 1.8, 1]])
>>> a, A = MarginalDistributionFromRAP(H0, H1)
>>> print(a)
[[ 0.44444  0.44444  0.11111]]
>>> print(A)
[[-2  0  0]
 [ 0 -3  1]
 [ 0 -1 -2]]