butools.dmap.MarginalDistributionFromDMAP¶

butools.dmap.MarginalDistributionFromDMAP()¶

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

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

Parameters:	D0 : matrix, shape (M,M) The D0 matrix of the discrete Markovian arrival process D1 : matrix, shape (M,M) The D1 matrix of the discrete 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 discrete phase type distributed marginal distribution A : matrix, shape (M,M) The transient generator of the discrete phase type distributed marginal distribution

Examples

For Matlab:

>>> D0 = [0, 0.02, 0, 0; 0, 0.17, 0.2, 0.14; 0.16, 0.17, 0.02, 0.18; 0, 0, 0, 0.12];
>>> D1 = [0, 0.88, 0.1, 0; 0.18, 0.07, 0.14, 0.1; 0.13, 0.15, 0.15, 0.04; 0.31, 0.18, 0.12, 0.27];
>>> [a, A] = MarginalDistributionFromDMAP(D0, D1);
>>> disp(a);
      0.24388      0.40412       0.1941       0.1579
>>> disp(A);
            0         0.02            0            0
            0         0.17          0.2         0.14
         0.16         0.17         0.02         0.18
            0            0            0         0.12

For Mathematica:

>>> D0 = {{0, 0.02, 0, 0},{0, 0.17, 0.2, 0.14},{0.16, 0.17, 0.02, 0.18},{0, 0, 0, 0.12}};
>>> D1 = {{0, 0.88, 0.1, 0},{0.18, 0.07, 0.14, 0.1},{0.13, 0.15, 0.15, 0.04},{0.31, 0.18, 0.12, 0.27}};
>>> {a, A} = MarginalDistributionFromDMAP[D0, D1];
>>> Print[a];
{0.2438770961395959, 0.4041227411783254, 0.19410324015415106, 0.15789692252792764}
>>> Print[A];
{{0, 0.02, 0, 0},
 {0, 0.17, 0.2, 0.14},
 {0.16, 0.17, 0.02, 0.18},
 {0, 0, 0, 0.12}}

For Python/Numpy:

>>> D0 = ml.matrix([[0, 0.02, 0, 0],[0, 0.17, 0.2, 0.14],[0.16, 0.17, 0.02, 0.18],[0, 0, 0, 0.12]])
>>> D1 = ml.matrix([[0, 0.88, 0.1, 0],[0.18, 0.07, 0.14, 0.1],[0.13, 0.15, 0.15, 0.04],[0.31, 0.18, 0.12, 0.27]])
>>> a, A = MarginalDistributionFromDMAP(D0, D1)
>>> print(a)
[[ 0.24388  0.40412  0.1941   0.1579 ]]
>>> print(A)
[[ 0.    0.02  0.    0.  ]
 [ 0.    0.17  0.2   0.14]
 [ 0.16  0.17  0.02  0.18]
 [ 0.    0.    0.    0.12]]