Markov chains (mc)

CTMC and DTMC algorithms: state-space generation, stationary and transient distributions, uniformization, Krylov kernels, passage times, stochastic complementation and the memory pre-gate. More...

Collaboration diagram for Markov chains (mc):

Files
file	include/line/api/mc/ctmc_bicgstab.h
	Preconditioned stabilized biconjugate gradients, for the linear systems a generator produces.
file	include/line/api/mc/ctmc_courtois.h
	Courtois decomposition of a nearly completely decomposable (NCD) CTMC.
file	include/line/api/mc/ctmc_fau.h
	Transient distribution of a CTMC by fast adaptive uniformization.
file	include/line/api/mc/ctmc_foxglynn.h
	Transient distribution of a CTMC by uniformization with Fox-Glynn Poisson weights.
file	include/line/api/mc/ctmc_gmres.h
	Restarted GMRES with an ILUT preconditioner, for the linear systems a generator produces.
file	include/line/api/mc/ctmc_gmres_multi.h
	Restarted GMRES for a block of right-hand sides sharing one coefficient matrix.
file	include/line/api/mc/ctmc_isfeasible.h
	Feasibility predicates for generators and stochastic matrices.
file	include/line/api/mc/ctmc_kms.h
	Koury-McAllister-Stewart aggregation-disaggregation for a nearly completely decomposable CTMC.
file	include/line/api/mc/ctmc_memory_gate.h
	Host-aware memory pre-gate for SolverCTMC.
file	include/line/api/mc/ctmc_multi.h
	Two-level multigrid aggregation-disaggregation for a nearly completely decomposable CTMC.
file	include/line/api/mc/ctmc_passage.h
	First passage times into a target STATE SET, for Markov and semi-Markov chains.
file	include/line/api/mc/ctmc_pseudostochcomp.h
	Pseudo stochastic complement of a CTMC partition.
file	include/line/api/mc/ctmc_rand.h
	Random infinitesimal generator of a CTMC.
file	include/line/api/mc/ctmc_randomization.h
	Uniformization (randomization) of a CTMC: the embedded DTMC P = I + Q/q.
file	include/line/api/mc/ctmc_relsolve.h
	Equilibrium distribution relative to a reference state.
file	include/line/api/mc/ctmc_saddlepoint.h
	Saddlepoint approximation of Pr{N(t)=k} for the counting process of a MAP.
file	include/line/api/mc/ctmc_sens.h
	Sensitivity of the steady-state distribution of a CTMC to a scalar parameter.
file	include/line/api/mc/ctmc_simulate.h
	Sample path of a continuous-time Markov chain given its generator.
file	include/line/api/mc/ctmc_solve.h
	Steady-state distribution of a continuous-time Markov chain.
file	include/line/api/mc/ctmc_solve_reducible.h
	Limiting distribution of a CTMC whose generator may be reducible.
file	include/line/api/mc/ctmc_solve_reducible_blkdecomp.h
	Limiting distribution of a reducible CTMC by direct block decomposition of the generator.
file	include/line/api/mc/ctmc_state_space_logsize.h
	Worst-case log-size of the CTMC state space induced by a NetworkStruct.
file	include/line/api/mc/ctmc_stmonotone.h
	Stochastically monotone upper bound of a Markov chain.
file	include/line/api/mc/ctmc_takahashi.h
	Takahashi's aggregation-disaggregation for a nearly completely decomposable CTMC.
file	include/line/api/mc/ctmc_testpf_kolmogorov.h
	Kolmogorov reversibility criterion, used as a product-form test.
file	include/line/api/mc/ctmc_timereverse.h
	Time-reversed generator and transition matrix.
file	include/line/api/mc/ctmc_transient.h
	Transient distribution of a CTMC over a time interval, by integrating the forward equations d pi/dt = pi Q.
file	include/line/api/mc/ctmc_transient_sens.h
	Sensitivity of the transient distribution of a CTMC to a scalar parameter.
file	include/line/api/mc/ctmc_uniformization.h
	Transient distribution of a CTMC by uniformization (Jensen's method), and the time-averaged distribution over [0, t].
file	include/line/api/mc/dtmc_makestochastic.h
	Normalize a non-negative matrix into a stochastic transition matrix.
file	include/line/api/mc/dtmc_rand.h
	Random DTMC kernels, trajectory simulation and the weak-component split.
file	include/line/api/mc/dtmc_solve.h
	Equilibrium distribution of a discrete-time Markov chain, and stochastic complementation.
file	include/line/api/mc/dtmc_solve_reducible.h
	Limiting distribution of a discrete-time Markov chain whose transition matrix may be reducible.
file	include/line/api/mc/dtmc_stochcomp.h
	Stochastic complement of a DTMC partition, a port of matlab/lib/kpctoolbox/mc/dtmc_stochcomp.m.
file	include/line/api/mc/dtmc_transient.h
	Discrete-time transient distributions, hitting times and uniformization.
file	include/line/api/mc/stronglyconncomp.h
	Strongly connected components of a directed graph, and which of them are recurrent (closed under the successor relation).

Detailed Description

CTMC and DTMC algorithms: state-space generation, stationary and transient distributions, uniformization, Krylov kernels, passage times, stochastic complementation and the memory pre-gate.