Package jline.api.mc

Class Ctmc_passage_lst

java.lang.Object
jline.api.mc.Ctmc_passage_lst
public final class Ctmc_passage_lst extends Object
Laplace-Stieltjes transform of the first passage time into a target state set: L(s) = alpha (sI-S)^-1 s0 + atom.

Reference: P. G. Harrison and W. J. Knottenbelt, "Passage Time Distributions in Large Markov Chains", 2002, Eqs. 1-2: one linear system per value of s, of the size of the non-target block.

ONE SOLVE PER s, NOT PER (s,t) PAIR. The saving over a dense matrix exponential is that the solves are sparse, so this route reaches chains a dense expm cannot hold. It is NOT a saving in the number of time points: every Abate-Whitt inverter places its nodes at s = beta/t, so a grid of T points costs T*|beta| solves. On a small chain the exponential route of Ctmc_passage_time is faster.

  • Method Summary

    Modifier and Type
    Method
    Description
    static org.apache.commons.math3.complex.Complex
    ctmc_passage_lst(CtmcPassagePh ph, org.apache.commons.math3.complex.Complex s)
    L(s) from a phase-type form already built, so it is not rebuilt per s.
    static org.apache.commons.math3.complex.Complex
    ctmc_passage_lst(Matrix Q, Matrix pi0, int[] target, org.apache.commons.math3.complex.Complex s)
    L(s) at a single (possibly complex) point.
    static org.apache.commons.math3.complex.Complex[]
    ctmc_passage_lst(Matrix Q, Matrix pi0, int[] target, org.apache.commons.math3.complex.Complex[] s)
    L(s) on a vector of points.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • ctmc_passage_lst

      public static org.apache.commons.math3.complex.Complex ctmc_passage_lst(Matrix Q, Matrix pi0, int[] target, org.apache.commons.math3.complex.Complex s)
      L(s) at a single (possibly complex) point.

    • ctmc_passage_lst

      public static org.apache.commons.math3.complex.Complex ctmc_passage_lst(CtmcPassagePh ph, org.apache.commons.math3.complex.Complex s)
      L(s) from a phase-type form already built, so it is not rebuilt per s.

    • ctmc_passage_lst

      public static org.apache.commons.math3.complex.Complex[] ctmc_passage_lst(Matrix Q, Matrix pi0, int[] target, org.apache.commons.math3.complex.Complex[] s)
      L(s) on a vector of points.