dtmc_stochcomp.h File Reference

Stochastic complement of a DTMC partition, a port of matlab/lib/kpctoolbox/mc/dtmc_stochcomp.m. More...

#include <cmath>
#include <cstddef>
#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for dtmc_stochcomp.h:

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Namespaces
namespace	line
namespace	line::mc

Functions
template<class T>
Matrix< T >	line::mc::dtmc_stochcomp (const Matrix< T > &P, const std::vector< std::size_t > &keep)
	Stochastic complement of a DTMC partition, a port of matlab/lib/kpctoolbox/mc/dtmc_stochcomp.m.

Detailed Description

Stochastic complement of a DTMC partition, a port of matlab/lib/kpctoolbox/mc/dtmc_stochcomp.m.

For a row-stochastic P partitioned into a retained set I and its complement Ic, the stochastic complement over I is S = P11 + P12 (Id - P22)^-1 P21, the routing seen by an observer who watches only the states in I, censoring the excursions through Ic. It is the same construction NetworkStruct's station_routing performs over the stateful nodes, exposed here as a free function so the cacheqn driver can complement a rtnodes matrix it has rewritten in place (relabelling a Cache as a class switch) without going back through route_eff.

ARITHMETIC: field. The only operation is the linear solve (Id - P22) X = P21 by Gaussian elimination with partial pivoting, so it is exact under Rational.

Definition in file dtmc_stochcomp.h.