Package jline.api.mc
package jline.api.mc
Markov Chain analysis algorithms.
This package provides fundamental algorithms for analyzing discrete and continuous-time Markov chains, including steady-state and transient analysis.
- Since:
- LINE 2.0
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ClassesClassDescriptionOutcome: L and piT have one row per time point; kmax is the deepest truncation.Outcome of a BiCGSTAB solve.Transient distribution of a fast adaptive uniformization sweep, together with the diagnostics that make its error auditable.Poisson weights on the Fox-Glynn truncation window.Outcome: row vector p, flag, scaled residual relres and sweep count iter.Outcome of a GMRES solve.Outcome: row vector p and flag (0 success, 1 several closed classes).Mean time to reach any state in a target set from each state of a CTMC.Outcome: row vector p, flag, scaled residual relres and sweep count iter.Result of ctmc_multi computation.Laplace-Stieltjes transform of the first passage time into a target state set: L(s) = alpha (sI-S)^-1 s0 + atom.Moments of order 1..nmax of the first passage time into a target state set.Phase-type representation of the first passage time into a target STATE SET.First passage into a TARGET state set B under a TABOO state set C: the passage is completed by entering B and is lost for good by entering C first.Moments of order 1..nmax of the first passage time into the TARGET set B, CONDITIONAL on entering B before the TABOO set C:Cumulative distribution and density of the first passage time into a target state set: F(t) = 1 - alpha exp(St) 1 and f(t) = alpha exp(St) s0.Outcome: row vector p, flag, scaled residual relres and sweep count iter.CTMC random generator matrix construction.Saddlepoint approximation of Pr{N(t)=k} for the counting process of a MAP.Perron root of A(theta) with its first two derivatives in theta and the amplitude of the Perron projection between pi0 and 1.Result of a saddlepoint evaluation, one entry per (t,k) pair.Solve reducible CTMCs via direct block decomposition on the generator matrix.Result of full reducible CTMC solve.Outcome: row vector p, flag, scaled residual relres, sweep count iter and final omega.Reachability-based CTMC state space generation for FJ tag-augmented structs (ModelAdapter.fjtag).CTMC State Space Generator for Reachability Analysis.Sensitivity of the transient distribution of a CTMC to a scalar parameter.Distribution and its sensitivity on the integrator's accepted grid.The phase-type form of a first passage time into a target state set.First passage into a target set B under a taboo set C, the
outstruct of the reference together with the defective law on the requested grid.Result data class for CTMC SSG reachability analysisDTMC random transition matrix generation.Result class for DTMC solve reducible.Stochastic complement together with the blocks it was built from.Result class for DTMC uniformization analysis containing the probability vector and maximum iterations used.A passage-time law on a time grid.Per-source and initial-law-weighted passage-time moments.Conditional passage-time moments under a taboo set, E[T^k | B before C].Laplace-Stieltjes transform of the first passage time into a target state set for a SEMI-MARKOV chain.Moments of order 1..nmax of the first passage time into a target state set for a SEMI-MARKOV chain with embedded transition matrix P.Cumulative distribution and density of the SEMI-MARKOV first passage time, by invertingSmp_passage_lstthroughjline.api.lti.Cumulative incidence functions of the transitions out of one semi-Markov stage, and the stage's holding-time CDF, on ascending instants.The cumulative incidences C (E x nt, zero rows where there is no arc) and the holding-time CDF.Embedded jump probabilities P and mean holding time m of one semi-Markov stage whose transitions are given as inSmp_stage_cif: competing latent clocks when probs is null, a kernel (destination drawn on entry, then its sojourn law) when probs is an E-vector.P (length E), the mean holding time m and the support end U.