Package jline.api.mc

Class Ctmc_passage_moments

java.lang.Object

jline.api.mc.Ctmc_passage_moments

public final class Ctmc_passage_moments
extends Object

Moments of order 1..nmax of the first passage time into a target state set.

This is Eq. 3 of P. G. Harrison and W. J. Knottenbelt, "Passage Time Distributions in Large Markov Chains", 2002,

     -q_ii M_i(n) = sum_{k not in B} q_ik M_k(n) + n M_i(n-1),
 

i.e. (-S) M(n) = n M(n-1) with M(0) = 1: nmax linear solves and no transform inversion at all. The equivalent closed form n! alpha (-S)^-n 1 is NOT how it is evaluated here -- forming the inverse of the sub-generator destroys the sparsity the recursion preserves.

Method Summary

Modifier and Type	Method	Description
static PassageMomentsResult	ctmc_passage_moments(Matrix Q, Matrix pi0, int[] target, int nmax)

Methods inherited from class java.lang.Object

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

Method Details

ctmc_passage_moments

public static PassageMomentsResult ctmc_passage_moments(Matrix Q,
 Matrix pi0,
 int[] target,
 int nmax)