dtmc_transient.h File Reference

Discrete-time transient distributions, hitting times and uniformization. More...

#include <cmath>
#include <cstddef>
#include <limits>
#include <set>
#include <vector>
#include "line/api/mc/ctmc_solve.h"
#include "line/api/mc/ctmc_uniformization.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/lu.h"
#include "line/util/matrix.h"

Include dependency graph for dtmc_transient.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::mc

Functions
template<class T>
Matrix< T >	line::mc::dtmc_transient (const Matrix< T > &P, const std::vector< T > &pi0, std::size_t steps)
	Trajectory of the law over steps transitions, row k holding pi0 P^k.
template<class T>
Matrix< T >	line::mc::dtmc_transient (const Matrix< T > &P)
	Uniform initial law and one step, matching the one-argument MATLAB call.
template<class T>
std::vector< T >	line::mc::dtmc_hitting_time (const Matrix< T > &P, const std::vector< std::size_t > &target)
	Expected number of steps to reach the target set, zero on the target set itself.
template<class T>
UniformizationResult< T >	line::mc::dtmc_uniformization (const std::vector< T > &pi0, const Matrix< T > &P, const T &t, double tol=1e-12, long maxiter=-1)
	Transient law of a DTMC through the uniformized generator of P.

Detailed Description

Discrete-time transient distributions, hitting times and uniformization.

Templated port of matlab/src/api/mc/dtmc_transient.m, matlab/src/api/mc/dtmc_hitting_time.m and matlab/lib/kpctoolbox/mc/dtmc_uniformization.m.

dtmc_transient returns the WHOLE trajectory, steps+1 rows with row 0 the initial law, not just the distribution at the last step.

dtmc_hitting_time solves (I - P_TT) h = 1 on the non-target states only. A state that cannot reach the target set makes that system singular, and the right answer there is an INFINITE hitting time, not the least-squares solution of the singular system: the code detects the singularity and reports infinity for the unreachable block rather than a finite fabricated number.

Definition in file dtmc_transient.h.