butools.ph.CheckMEPositiveDensity¶

butools.ph.CheckMEPositiveDensity()¶

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

Checks if the given matrix-exponential distribution has positive density.

Parameters:	alpha : matrix, shape (1,M) Initial vector of the matrix-exponential distribution to check A : matrix, shape (M,M) Matrix parameter of the matrix-exponential distribution to check maxSize : int, optional The procedure tries to transform the ME distribution to phase-type up to order maxSize. The default value is 100. prec : double, optional Numerical precision. The default value is 1e-14.
Returns:	r : bool True, if the given matrix-exponential distribution has a positive density

Notes

This procedure calls MonocyclicPHFromME, and can be time consuming.

Examples

For Matlab:

>>> a = [0.2,0.3,0.5];
>>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
>>> flag = CheckMEPositiveDensity(a, A);
>>> disp(flag);
     1
>>> a = [0.2,0.3,0.5];
>>> A = [-1, 0, 0; 0, -3, 2.9; 0, -2.9, -3];
>>> flag = CheckMEPositiveDensity(a, A);
>>> disp(flag);
     0

For Mathematica:

>>> a = {0.2,0.3,0.5};
>>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
>>> flag = CheckMEPositiveDensity[a, A];
>>> Print[flag];
True
>>> a = {0.2,0.3,0.5};
>>> A = {{-1, 0, 0},{0, -3, 2.9},{0, -2.9, -3}};
>>> flag = CheckMEPositiveDensity[a, A];
>>> Print[flag];
False

For Python/Numpy:

>>> a = ml.matrix([[0.2,0.3,0.5]])
>>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
>>> flag = CheckMEPositiveDensity(a, A)
>>> print(flag)
True
>>> a = ml.matrix([[0.2,0.3,0.5]])
>>> A = ml.matrix([[-1, 0, 0],[0, -3, 2.9],[0, -2.9, -3]])
>>> flag = CheckMEPositiveDensity(a, A)
>>> print(flag)
False