Package jline.api.mc

Class Ctmc_timeaverage

java.lang.Object

jline.api.mc.Ctmc_timeaverage

public final class Ctmc_timeaverage
extends Object

Method Summary

Modifier and Type	Method	Description
static Pair<Matrix,Matrix>	ctmc_timeaverage(Matrix pi0, Matrix Q, double t)	Time-averaged transient distribution of a CTMC over [0,t].
static Pair<Matrix,Matrix>	ctmc_timeaverage(Matrix pi0, Matrix Q, double t, double tol, int maxiter)

Methods inherited from class java.lang.Object

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

Method Details

ctmc_timeaverage

public static Pair<Matrix,Matrix> ctmc_timeaverage(Matrix pi0,
 Matrix Q,
 double t)

Time-averaged transient distribution of a CTMC over [0,t]. Uniformization: with q = 1.1*max|diag(Q)| and P = I + Q/q (row-stochastic), pi0*exp(Q*t) = sum_j w_j(qt) * (pi0*P^j) pi0*\int_0^t exp(Q*tau) = (1/q) * sum_j (1 - W_j(qt)) * (pi0*P^j) where w_j and W_j are the Poisson(qt) PMF and CDF. The time average divides the integral by t (equivalently the integral sum by q*t).

Parameters:

pi0 - initial (arbitrary) distribution, row vector

Q - infinitesimal generator

t - horizon

Returns:

Pair(piTimeAvg, piExit), both row vectors

ctmc_timeaverage

public static Pair<Matrix,Matrix> ctmc_timeaverage(Matrix pi0,
 Matrix Q,
 double t,
 double tol,
 int maxiter)