butools.mc.DRPSolve¶

butools.mc.DRPSolve()¶

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

Computes the stationary solution of a discrete time Markov chain.

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

Notes

Discrete time rational processes are like discrete time Markov chains, but the P matrix does not have to pass the CheckProbMatrix test (but the rowsums still have to be ones).

Examples

For Matlab:

>>> Q = [-0.9, 0.5, 1.4; 0.9, -0.9, 1; 0.3, 1.3, -0.6];
>>> ret = DRPSolve(Q);
>>> disp(ret);
      0.23138       0.3484      0.42021
>>> disp(ret*Q-ret);
   1.6653e-16  -5.5511e-17  -1.1102e-16

For Mathematica:

>>> Q = {{-0.9, 0.5, 1.4},{0.9, -0.9, 1},{0.3, 1.3, -0.6}};
>>> ret = DRPSolve[Q];
>>> Print[ret];
{0.2313829787234043, 0.34840425531914887, 0.4202127659574468}
>>> Print[ret.Q-ret];
{-1.3877787807814457*^-16, 5.551115123125783*^-17, 5.551115123125783*^-17}

For Python/Numpy:

>>> Q = ml.matrix([[-0.9, 0.5, 1.4],[0.9, -0.9, 1],[0.3, 1.3, -0.6]])
>>> ret = DRPSolve(Q)
>>> print(ret)
[[ 0.23138  0.3484   0.42021]]
>>> print(ret*Q-ret)
[[ -1.38778e-16   5.55112e-17   5.55112e-17]]