ptolemy.domains.algebraic.kernel

Class AlgebraicLoopDirector.NewtonRaphson

java.lang.Object

ptolemy.domains.algebraic.kernel.AlgebraicLoopDirector.AlgebraicLoopSolver

ptolemy.domains.algebraic.kernel.AlgebraicLoopDirector.NewtonRaphson

Enclosing class:

AlgebraicLoopDirector

class AlgebraicLoopDirector.NewtonRaphson
extends AlgebraicLoopDirector.AlgebraicLoopSolver

Class for solving algebraic loops using the Newton-Raphson method.

Author:

Michael Wetter

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	_deltaX Step size for finite difference approximation
protected double[]	_f Temporary variable used to store the result of f(x) = x-g(x)

Fields inherited from class ptolemy.domains.algebraic.kernel.AlgebraicLoopDirector.AlgebraicLoopSolver

_converged, _iterationCount, _maxIterations, _tolerance, _variableNames

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
protected double[]	_gaussElimination(double[][] A, double[] f) Return vector x that solves A*x=f by a Gauss elimination with normalization and interchange of rows.
protected double[]	_newtonStep(double[] x, double[] f) Return the new iterate of a Newton step.
protected void	_residual(double[] x, double[] f) Evaluate the residual function f(x) = x-g(x).
void	solve(double[] xIni) Solve the algebraic loop using the specified array as the initial guess for the variables being solved for and replace the contents of the specified array with the solution that is found.

Methods inherited from class ptolemy.domains.algebraic.kernel.AlgebraicLoopDirector.AlgebraicLoopSolver

_didConverge, converged, getIterationCount

Methods inherited from class java.lang.Object

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

Field Detail

_deltaX

protected double[] _deltaX

Step size for finite difference approximation

_f

protected double[] _f

Temporary variable used to store the result of f(x) = x-g(x)

Constructor Detail

NewtonRaphson

public NewtonRaphson(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

solve

public void solve(double[] xIni)
           throws IllegalActionException

Solve the algebraic loop using the specified array as the initial guess for the variables being solved for and replace the contents of the specified array with the solution that is found.

This method iterates until a solution is found. If it does not converge within the maximum number of iterations, it throws an IllegalActionException. A method that calls solve(double[] xIni) can then call converged() to check whether the exception is thrown because of lack of convergence.

Specified by:

solve in class AlgebraicLoopDirector.AlgebraicLoopSolver

Parameters:

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

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.

_newtonStep

protected double[] _newtonStep(double[] x,
                               double[] f)
                        throws IllegalActionException

Return the new iterate of a Newton step.

Parameters:

x - The best known iterate.

f - The function value f(x)=g(x)-x.

Returns:

The new guess for the solution f(x) = 0.

Throws:

IllegalActionException - If the solver fails to find a solution.

_gaussElimination

protected double[] _gaussElimination(double[][] A,
                                     double[] f)

Return vector x that solves A*x=f by a Gauss elimination with normalization and interchange of rows.

Parameters:

A - A square matrix

f - Array with solution of A*x=f

Returns:

x Array x = A^-1 * f

_residual

protected void _residual(double[] x,
                         double[] f)
                  throws IllegalActionException

Evaluate the residual function f(x) = x-g(x).

Parameters:

x - Input to the loop function g(x).

f - Double vector of the same size as x. The result will be stored in this function.

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.