Package jline.solvers.fluid.petri

Class PetriSystem

java.lang.Object

jline.solvers.fluid.petri.PetriSystem

public final class PetriSystem
extends Object

The closed enabling term of every transition mode, the rate of every event column, and the drift Jacobian. Java twin of the MATLAB fluid_petri_theta, fluid_petri_rates and fluid_petri_jacobian.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	PetriSystem.Theta	The enabling terms and their derivatives, for one iterate.

Method Summary

Modifier and Type	Method	Description
static boolean	isTimed(PetriMode md)	Whether a mode is timed, spelled once.
static Matrix	jacobian(PetriTerms t, PetriSystem.Theta th)	Drift Jacobian A = D * dR/dX.
static double[]	rates(PetriTerms t, double[] x, double[] phi, double[] mu, PetriSystem.Theta th)	The rate of every event column.
static PetriSystem.Theta	theta(PetriTerms t, double[] x, double[] s2)	The closed enabling term of every mode, and its derivative.

Methods inherited from class java.lang.Object

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

Method Details

theta

public static PetriSystem.Theta theta(PetriTerms t,
 double[] x,
 double[] s2)

The closed enabling term of every mode, and its derivative.

  theta_j = ( prod_b Phi((thr_b - m_b)/sd_b) ) * E[ min_a(m_a/w_a), c_j ]

Both factors collapse to their first-order form at zero variance -- Phi becomes the hard indicator and the min closure becomes min() -- so the mean-field limit is one code path, not two.

THE INHIBITOR GATE IS WHY A PETRI NET NEEDS A SMOOTHED CLOSURE AT ALL, quite apart from accuracy: the indicator is a step, and a Newton solver has no derivative to descend on a step.

THE VARIANCES ARE UNKNOWNS, NOT FUNCTIONS OF X: s2 is pinned by its own consistency row in the DAE, so the derivative is with respect to the MEANS only.

rates

public static double[] rates(PetriTerms t,
 double[] x,
 double[] phi,
 double[] mu,
 PetriSystem.Theta th)

The rate of every event column.

   kind 1  firing of mode j    single phase: rateBase*theta*dep
                               multi  phase: rateBase*y(j,h)
   kind 2  internal phase change             rateBase*y(j,h)
   kind 3  exogenous arrival                 a constant
   kind 4  firing of an IMMEDIATE mode       phi_j, an algebraic unknown
   kind 5  the server latch                  mu_j, a free-sign unknown
 

jacobian

public static Matrix jacobian(PetriTerms t,
 PetriSystem.Theta th)

Drift Jacobian A = D * dR/dX.

This is what the Lyapunov equation of the linear noise approximation is written about, so it has to be the derivative of the SAME rate vector rates(jline.solvers.fluid.petri.PetriTerms, double[], double[], double[], jline.solvers.fluid.petri.PetriSystem.Theta) returns: a covariance solved about an inconsistent Jacobian is not the covariance of anything. THE VARIANCES ARE HELD.

isTimed

public static boolean isTimed(PetriMode md)

Whether a mode is timed, spelled once.