Package jline.api.mc

Class Ctmc_sens

java.lang.Object

jline.api.mc.Ctmc_sens

public final class Ctmc_sens
extends Object

Method Summary

Modifier and Type	Method	Description
static Matrix	ctmc_sens(Matrix Q, Matrix dQ)	Sensitivity of the steady-state distribution of a CTMC to a scalar parameter theta, computing pi from Q if it is not supplied.
static Matrix	ctmc_sens(Matrix Q, Matrix dQ, Matrix pi)	Sensitivity of the steady-state distribution of a CTMC to a scalar parameter theta, given the generator Q, its derivative dQ = dQ/dtheta, and the steady-state vector pi.

Methods inherited from class java.lang.Object

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

Method Details

ctmc_sens

public static Matrix ctmc_sens(Matrix Q,
 Matrix dQ)

Sensitivity of the steady-state distribution of a CTMC to a scalar parameter theta, computing pi from Q if it is not supplied.

Parameters:

Q - Generator matrix (n x n)

dQ - Derivative of the generator with respect to theta (n x n)

Returns:

Derivative of the steady-state distribution (1 x n)

ctmc_sens

public static Matrix ctmc_sens(Matrix Q,
 Matrix dQ,
 Matrix pi)

Sensitivity of the steady-state distribution of a CTMC to a scalar parameter theta, given the generator Q, its derivative dQ = dQ/dtheta, and the steady-state vector pi.

Differentiating the balance equations pi*Q = 0 and pi*e = 1 with respect to theta gives the linear system

  (dpi/dtheta) * Q = -pi * (dQ/dtheta),   sum_i dpi_i/dtheta = 0,

i.e. Trivedi and Bobbio (2017), Eq. (9.81). The system has the same coefficient matrix as the steady-state solve itself, so obtaining a sensitivity costs one extra solve against a matrix that is already assembled. The normalization replaces one row of the singular Q', exactly as in the steady-state solve.

Parameters:

Q - Generator matrix (n x n)

dQ - Derivative of the generator with respect to theta (n x n)

pi - Steady-state distribution (1 x n); computed from Q if null

Returns:

Derivative of the steady-state distribution (1 x n)