ptolemy.domains.algebraic.kernel

Class AlgebraicLoopDirector.AlgebraicLoopSolver

java.lang.Object

ptolemy.domains.algebraic.kernel.AlgebraicLoopDirector.AlgebraicLoopSolver

Direct Known Subclasses:

AlgebraicLoopDirector.Homotopy, AlgebraicLoopDirector.NewtonRaphson, AlgebraicLoopDirector.SuccessiveSubstitution

Enclosing class:

AlgebraicLoopDirector

abstract class AlgebraicLoopDirector.AlgebraicLoopSolver
extends java.lang.Object

A class for solving algebraic loops. This class solves an algebraic loop of the form x=g(x)

         -----------
         |  -----  |
         -->| g |---
         x  -----
     

where x is initially the vector of values corresponding to input ports that have a non-null defaultValue parameter, and g is the network of actors connecting these ports.

For the SuccessiveSubstitution, we simply evaluate g repeatedly until either all signals do not change by more than the errorTolerance, or until there have been maxIterations. Note that it is possible to reach a fixed point where some or all signals are infinite.

For NewtonRaphson, we solve for g(x)=x by solving f(x)=0, where f(x) = g(x)-x. This is done by iterating as follows:

       x_n+1 = x_n - f(x_n)/f'(x_n) = x_n - (g(x_n) - x_n)/(g'(x_n) - 1) .
     

To estimate g'(x_n), we do

       g'(x_n) = (g(x_n + d) - g(x_n))/d
     

where d is the delta parameter.

For Homotopy, we solve f(x) = x - g(x) = 0. The problem is reformulated as H(x, lambda) = x - lambda g(x), where lambda has an initial value of 0 and is successively increased to 1. The implementation is equal to Program 3 of Eugene L. Allgower and Kurt Georg, Introduction to Numerical Continuation Methods, Classics in Applied Mathematics, Vol. 45, SIAM, 2003.

Author:

Michael Wetter

Field Summary

Fields

Modifier and Type	Field and Description
protected boolean	_converged Flag that indicates whether the solver converged
protected int	_iterationCount Number of iterations in the last call to the function solve(double[])
protected int	_maxIterations Maximum number of iterations
protected double[]	_tolerance Local view of the tolerance vector.
protected java.lang.String[]	_variableNames Variable names, used for error reporting

Constructor Summary

Constructors

Constructor and Description
AlgebraicLoopSolver(java.lang.String[] variableNames, double[] tolerance, int maxIterations) Construct an algebraic loop solver.

Method Summary

Modifier and Type	Method and Description
protected boolean	_didConverge(double[] f) Return true if each element of f is within the solver tolerance.
boolean	converged() Return true if the solver converged, false otherwise.
int	getIterationCount() Return the number of iterations done in the last call to the method solve(double[]).
abstract void	solve(double[] xIni) This method solves the fixed point iteration.

Methods inherited from class java.lang.Object

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

Field Detail

_converged

protected boolean _converged

Flag that indicates whether the solver converged

_iterationCount

protected int _iterationCount

Number of iterations in the last call to the function solve(double[])

_maxIterations

protected int _maxIterations

Maximum number of iterations

_tolerance

protected double[] _tolerance

Local view of the tolerance vector.

_variableNames

protected java.lang.String[] _variableNames

Variable names, used for error reporting

Constructor Detail

AlgebraicLoopSolver

public AlgebraicLoopSolver(java.lang.String[] variableNames,
                           double[] tolerance,
                           int maxIterations)
                    throws IllegalActionException

Construct an algebraic loop solver.

Parameters:

variableNames - Names of each break variable.

tolerance - Tolerance for each variable.

maxIterations - Maximum number of iterations.

Throws:

IllegalActionException

Method Detail

converged

public boolean converged()

Return true if the solver converged, false otherwise.

Returns:

true if the solver converged, false otherwise.

solve

public abstract void solve(double[] xIni)
                    throws IllegalActionException

This method solves the fixed point iteration.

Parameters:

xIni - Array with the initial values of the variables, to be replaced with the solution by this method.

Throws:

IllegalActionException - If the prefire() method returns false having previously returned true in the same iteration, or if the prefire() or fire() method of the actor throws it, or if evaluating the function yields a value that is not a double, or if the solver fails to find a solution.

getIterationCount

public int getIterationCount()

Return the number of iterations done in the last call to the method solve(double[]).

Returns:

The number of iterations

_didConverge

protected boolean _didConverge(double[] f)

Return true if each element of f is within the solver tolerance.

Parameters:

f - Value of residual function to be tested.

Returns:

true if convergence is achieved, false otherwise.