butools.mc.CTMCSolve¶

butools.mc.CTMCSolve()¶

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

Computes the stationary solution of a continuous time Markov chain.

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

Notes

The procedure raises an exception if checkInput is set to true and CheckGenerator (Q) fails.

Examples

For Matlab:

>>> Q = [-0.9, 0.5, 0.4; 0.9, -0.9, 0; 0.3, 0.3, -0.6];
>>> ret = CTMCSolve(Q);
>>> disp(ret);
      0.40909      0.31818      0.27273
>>> disp(ret*Q);
  -1.1102e-16   1.3878e-17   8.3267e-17

For Mathematica:

>>> Q = {{-0.9, 0.5, 0.4},{0.9, -0.9, 0},{0.3, 0.3, -0.6}};
>>> ret = CTMCSolve[Q];
>>> Print[ret];
{0.4090909090909091, 0.3181818181818182, 0.2727272727272727}
>>> Print[ret.Q];
{-4.163336342344337*^-17, -1.3877787807814457*^-17, 5.551115123125783*^-17}

For Python/Numpy:

>>> Q = ml.matrix([[-0.9, 0.5, 0.4],[0.9, -0.9, 0],[0.3, 0.3, -0.6]])
>>> ret = CTMCSolve(Q)
>>> print(ret)
[[ 0.40909  0.31818  0.27273]]
>>> print(ret*Q)
[[ -4.16334e-17  -1.38778e-17   5.55112e-17]]