com.imsl.math
Class ZeroSystem

java.lang.Object
  com.imsl.math.ZeroSystem

All Implemented Interfaces:

Serializable, Cloneable

public class ZeroSystem
extends Object
implements Serializable, Cloneable

Solves a system of n nonlinear equations f(x) = 0 using a modified Powell hybrid algorithm.

ZeroSystem is based on the MINPACK subroutine HYBRDJ , which uses a modification of M.J.D. Powell's hybrid algorithm. This algorithm is a variation of Newton's method, which uses a finite-difference approximation to the Jacobian and takes precautions to avoid large step sizes or increasing residuals. For further description, see More et al. (1980).

A finite-difference method is used to estimate the Jacobian. Whenever the exact Jacobian can be easily provided, objectF should implement ZeroSystem.Jacobian.

Note that one can use the JDK 1.4 JAVA Logging API to generate intermediate output for the solver. Accumulated levels of detail correspond to JAVA's CONFIG, FINE, FINER, and FINEST logging levels with CONFIG yielding the smallest amount of information and FINEST yielding the most. The levels of output yield the following:

Level	Output
CONFIG	Iteration increments are printed.
FINE	Prints convergnce tests.
FINER	Intermediate solution values are provided.
FINEST	Tracks progress through internal methods.

See Also:

Example 1, Example 2 with Logging, Serialized Form

Nested Class Summary

static class	ZeroSystem.DidNotConvergeException The iteration did not converge.
static interface	ZeroSystem.Function Public interface for user supplied function to ZeroSystem object.
static interface	ZeroSystem.Jacobian Public interface for user supplied function to ZeroSystem object.
static class	ZeroSystem.ToleranceTooSmallException Tolerance too small
static class	ZeroSystem.TooManyIterationsException Too many iterations.

Constructor Summary

ZeroSystem(int n)
Creates an object to find the zeros of a system of n equations.

Method Summary

Logger	getLogger() Returns the logger object.
void	setGuess(double[] xguess) Sets the initial estimate of the root.
void	setMaxIterations(int maxIterations) Sets the maximum number of iterations allowed.
void	setRelativeError(double errorRelative) Sets the relative error tolerance.
double[]	solve(ZeroSystem.Function objectF) Solve a system of nonlinear equations using the modified Powell hybrid algorithm

Methods inherited from class java.lang.Object

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

Constructor Detail

ZeroSystem

public ZeroSystem(int n)

Creates an object to find the zeros of a system of n equations.

Parameters:

n - an int indicating the number of equations to be solved and the number of unknowns.

Method Detail

getLogger

public Logger getLogger()

Returns the logger object.

Returns:

a java.util.logging.Logger object, if present, or null.

setGuess

public void setGuess(double[] xguess)

Sets the initial estimate of the root. The default is to set xguess to all zeros.

Parameters:

xguess - a double array containing the initial guess. The length of xguess must be equal to the number of equations.

setMaxIterations

public void setMaxIterations(int maxIterations)

Sets the maximum number of iterations allowed. The default value is 200.

Parameters:

maxIterations - an int specifying the maximum number of iterations allowed

Throws:

IllegalArgumentException - is thrown if maxIterations is less than or equal to zero.

setRelativeError

public void setRelativeError(double errorRelative)

Sets the relative error tolerance. The root is accepted if the relative error between two successive approximations to this root is within errorRelative. The default is the square root of the precision, about 1.0e-08.

Parameters:

errorRelative - a double specifying the relative error tolerance

Throws:

IllegalArgumentException - is thrown if errorRelative is less than 0 or greater than 1.

solve

public double[] solve(ZeroSystem.Function objectF)
               throws ZeroSystem.TooManyIterationsException,
                      ZeroSystem.ToleranceTooSmallException,
                      ZeroSystem.DidNotConvergeException

Solve a system of nonlinear equations using the modified Powell hybrid algorithm

Parameters:

objectF - a ZeroSystem.Function that defines the function whose zero is to be found. If objectF implements a Jacobian then its Jacobian is used. Otherwise a finite difference is computed.

Returns:

a double array containing the solution

Throws:

ZeroSystem.TooManyIterationsException - is thrown if the maximum number of iterations is exceeded

ZeroSystem.ToleranceTooSmallException - is thrown if the error tolerance is too small

ZeroSystem.DidNotConvergeException - is thrown if the algorithm does not converge

See Also:

ZeroSystem.Jacobian