butools.dph.CheckDPHRepresentation¶

butools.dph.CheckDPHRepresentation()¶

Matlab:	r = CheckDPHRepresentation(alpha, A, prec)
Mathematica:	r = CheckDPHRepresentation[alpha, A, prec]
Python/Numpy:	r = CheckDPHRepresentation(alpha, A, prec)

Checks if the given vector and matrix define a valid discrete phase-type representation.

Parameters:	alpha : matrix, shape (1,M) Initial vector of the phase-type distribution to check A : matrix, shape (M,M) Transient generator of the phase-type distribution to check prec : double, optional Numerical precision. The default value is 1e-14.
Returns:	r : bool True, if vector alpha is a probability vector and matrix A is substochastic, and they have the same size.

Examples

For Matlab:

>>> a = [0.48,0.08,0.26,0.18];
>>> A = [0, 0.08, 0.08, 0.8; 0.55, 0, 0.24, 0.19; 0.06, 0.03, 0, 0.001; 0.23, 0.005, 0.2, 0.53];
>>> flag = CheckDPHRepresentation(a, A);
>>> disp(flag);
     1
>>> a = [0.48,0.08];
>>> A = [0, 0.08; 0.55, 0.5];
>>> flag = CheckDPHRepresentation(a, A);
CheckProbMatrix: The rowsum of the matrix (transient) is not less or equal than 1 (precision: 1e-12)!
>>> disp(flag);
     0

For Mathematica:

>>> a = {0.48,0.08,0.26,0.18};
>>> A = {{0, 0.08, 0.08, 0.8},{0.55, 0, 0.24, 0.19},{0.06, 0.03, 0, 0.001},{0.23, 0.005, 0.2, 0.53}};
>>> flag = CheckDPHRepresentation[a, A];
>>> Print[flag];
True
>>> a = {0.48,0.08};
>>> A = {{0, 0.08},{0.55, 0.5}};
>>> flag = CheckDPHRepresentation[a, A];
"CheckProbMatrix: A rowsum of the transient matrix is not less or equal than 1!"
>>> Print[flag];
False

For Python/Numpy:

>>> a = ml.matrix([[0.48,0.08,0.26,0.18]])
>>> A = ml.matrix([[0, 0.08, 0.08, 0.8],[0.55, 0, 0.24, 0.19],[0.06, 0.03, 0, 0.001],[0.23, 0.005, 0.2, 0.53]])
>>> flag = CheckDPHRepresentation(a, A)
>>> print(flag)
True
>>> a = ml.matrix([[0.48,0.08]])
>>> A = ml.matrix([[0, 0.08],[0.55, 0.5]])
>>> flag = CheckDPHRepresentation(a, A)
CheckProbMatrix: The rowsum of the matrix (transient) is not less or equal than 1 (precision: {0})! 1e-12
>>> print(flag)
False