butools.dph.RandomDPH¶

butools.dph.RandomDPH()¶

Matlab:	[alpha, A] = RandomDPH(order, mean, zeroEntries, maxTrials, prec)
Mathematica:	{alpha, A} = RandomDPH[order, mean, zeroEntries, maxTrials, prec]
Python/Numpy:	alpha, A = RandomDPH(order, mean, zeroEntries, maxTrials, prec)

Returns a random discrete phase-type distribution with a given mean value.

Parameters:

order : int The size of the discrete phase-type distribution mean : double, optional The mean of the discrete phase-type distribution zeroEntries : int, optional The number of zero entries in the initial vector, generator matrix and closing vector maxTrials : int, optional The maximum number of trials to find a proper DPH (that has an irreducible phase process and none of its parameters is all-zero). The default value is 1000. prec : double, optional Numerical precision for checking the irreducibility. The default value is 1e-14.

Returns:

alpha : vector, shape (1,M) The initial probability vector of the phase-type distribution. A : matrix, shape (M,M) The transient generator matrix of the phase-type distribution.

Notes

If the procedure fails, try to increase the ‘maxTrials’ parameter, or increase the mean value.

Examples

For Matlab:

>>> [a, A] = RandomDPH(3, 10, 5);
>>> disp(a);
      0.39611      0.38982      0.21407
>>> disp(A);
       0.8489     0.031291            0
      0.59994      0.40006            0
      0.37646            0      0.62354

For Mathematica:

>>> {a, A} = RandomDPH[3, 10, 5];
"CheckProbMatrix: the matrix has negative element (at precision "1.*^-7")!"
>>> Print[a];
{0, 0, 1}
>>> Print[A];
{{0.8271227985086882, 0.06664258193377719, 0.},
 {0., 0.9130962745792692, 0.},
 {0.05885243293901752, 0.02706649617956366, 0.8087057205828357}}

For Python/Numpy:

>>> a, A = RandomDPH(3, 10, 5)
>>> print(a)
[[ 1.  0.  0.]]
>>> print(A)
[[ 0.67742  0.09221  0.07805]
 [ 0.08848  0.83115  0.     ]
 [ 0.1876   0.       0.8124 ]]