butools.mc.CRPSolve¶

butools.mc.CRPSolve()¶

Matlab:	pi = CRPSolve(Q)
Mathematica:	pi = CRPSolve[Q]
Python/Numpy:	pi = CRPSolve(Q)

Computes the stationary solution of a continuous time rational process (CRP).

Parameters:	Q : matrix, shape (M,M) The generator matrix of the rational process
Returns:	pi : row vector, shape (1,M) The vector that satisfies \(\pi\, Q = 0, \sum_i \pi_i=1\)

Notes

Continuous time rational processes are like continuous time Markov chains, but the generator does not have to pass the CheckGenerator test (but the rowsums still have to be zeros).

Examples

For Matlab:

>>> Q = [-4.3, 3.5, 0.8; -8.4, 6.5, 1.9; 17.3, -12.7, -4.6];
>>> ret = CRPSolve(Q);
>>> disp(ret);
      -3.5617       3.6667      0.89506
>>> disp(ret*Q);
   3.5527e-15  -1.7764e-15            0

For Mathematica:

>>> Q = {{-4.3, 3.5, 0.8},{-8.4, 6.5, 1.9},{17.3, -12.7, -4.6}};
>>> ret = CRPSolve[Q];
>>> Print[ret];
{-3.5617283950617336, 3.66666666666667, 0.8950617283950623}
>>> Print[ret.Q];
{1.7763568394002505*^-15, 0., 0.}

For Python/Numpy:

>>> Q = ml.matrix([[-4.3, 3.5, 0.8],[-8.4, 6.5, 1.9],[17.3, -12.7, -4.6]])
>>> ret = CRPSolve(Q)
>>> print(ret)
[[-3.56173  3.66667  0.89506]]
>>> print(ret*Q)
[[  1.77636e-15   0.00000e+00   0.00000e+00]]