ctmc_timereverse.h File Reference

Time-reversed generator and transition matrix. More...

#include <cstddef>
#include <vector>
#include "line/api/mc/ctmc_solve.h"
#include "line/api/mc/dtmc_solve.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for ctmc_timereverse.h:

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Namespaces
namespace	line
namespace	line::mc

Functions
template<class T>
Matrix< T >	line::mc::ctmc_timereverse (const Matrix< T > &Q)
	Generator of the time-reversed CTMC.
template<class T>
Matrix< T >	line::mc::dtmc_timereverse (const Matrix< T > &P)
	Transition matrix of the time-reversed DTMC.

Detailed Description

Time-reversed generator and transition matrix.

Templated port of matlab/lib/kpctoolbox/mc/ctmc_timereverse.m and dtmc_timereverse.m. The reversed chain is Qrev = diag(pi)^-1 Q' diag(pi), written here as the transpose of the elementwise scaling Q(i,j) pi_i / pi_j, which is the same matrix and is how MATLAB assembles it.

The construction needs the stationary law, so it is defined only for an irreducible chain: on a reducible one the stationary vector is not unique and the reversal is not either.

Definition in file ctmc_timereverse.h.