Markov Chains (butools.mc)¶
To load this package, either start the BuToolsInit
script, or execute
addpath('butools/mc') |
in Matlab, |
<<BuTools`MC |
in Mathematica, |
from butools.mc import * |
in Python/Numpy. |
Markov chains and rational processes¶
The difference between Markov chains and rational processes is that the entries of the generator of a rational process can be negative as well. There are still restrictions: the rowsum must be 0 or 1 (in the continuous time and discrete time cases, respectively), the eigenvalues must fall into the left half-plane in the continuous case, and in the unit cycle in the discrete case. The dominant eigenvalue must be real.
The invariant (stationary) vector of Markov chains and rational processes
are obtained the same way. The only reason to treat them separately is
checking the input parameters. If the global variable butools.checkInput
is set to true, CTMCSolve and DTMCSolve enforce a proper Markovian generator,
while CRPSolve and DRPSolve just check the eigenvalues and the rowsums.
Properties of Markov chains and rational processes¶
CTMCSolve |
Returns the steady state solution of a continuous time Markov chain |
DTMCSolve |
Returns the steady state solution of a discrete time Markov chain |
CRPSolve |
Returns the steady state solution of a continuous time rational process |
DRPCSolve |
Returns the steady state solution of a discrete time rational process |
CheckGenerator |
Checks if a matrix is a valid generator of a CTMC |
CheckProbMatrix |
Checks if a matrix is a valid transition probability matrix of a DTMC |
CheckProbVector |
Checks if a vector is a valid probability vector |