Package jline.api.mc

Class Smp_passage_lst

java.lang.Object

jline.api.mc.Smp_passage_lst

public final class Smp_passage_lst
extends Object

Laplace-Stieltjes transform of the first passage time into a target state set for a SEMI-MARKOV chain.

Reference: P. G. Harrison and W. J. Knottenbelt, "Passage Time Distributions in Large Markov Chains", 2002, Eqs. 4-5:

     L_i(s) = sum_{k not in B} r*_ik(s) L_k(s) + sum_{k in B} r*_ik(s),
 

so (I - R*_AA(s)) L_A(s) = R*_AB(s) 1, one linear system per value of s. The sojourn transforms are given per state, so r*_ik(s) = P(i,k) h*_i(s) and the complex numbers stay on the DIAGONAL of the system, which is the easier of the two cases the paper distinguishes.

Distribution objects supply their own transform: Markovian.evalLST gives the closed form pie (sI-D0)^-1 (-D0) e for the phase-type family, so s -> new Complex(dist.evalLST(s.getReal()), 0) is NOT enough for a complex argument -- pass a genuinely complex transform.

Method Summary

Modifier and Type	Method	Description
static org.apache.commons.math3.complex.Complex	smp_passage_lst(Matrix P, List<UnaryOperator<org.apache.commons.math3.complex.Complex>> hlst, Matrix pi0, int[] target, org.apache.commons.math3.complex.Complex s)

Methods inherited from class java.lang.Object

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

Method Details

smp_passage_lst

public static org.apache.commons.math3.complex.Complex smp_passage_lst(Matrix P,
 List<UnaryOperator<org.apache.commons.math3.complex.Complex>> hlst,
 Matrix pi0,
 int[] target,
 org.apache.commons.math3.complex.Complex s)

Parameters:

hlst - one sojourn transform h*_i(s) per state, complex-argument