Package com.irurueta.numerical.optimization

Class PowellMultiOptimizer

java.lang.Object

com.irurueta.numerical.optimization.Optimizer

com.irurueta.numerical.optimization.MultiOptimizer

com.irurueta.numerical.optimization.LineMultiOptimizer

com.irurueta.numerical.optimization.PowellMultiOptimizer

public class PowellMultiOptimizer
extends LineMultiOptimizer

This class searches for a multi dimension function local minimum. The local minimum is searched by starting the algorithm at a start point and a given direction which should be close and point to the local minimum to be found to achieve the best accuracy with the lowest number of iterations. The implementation of this class is based on Numerical Recipes 3rd ed. Section 10.7 page 509.

Field Summary

Fields

Modifier and Type	Field	Description
static final double	DEFAULT_TOLERANCE	Constant defining default tolerance or accuracy to be achieved on the minimum being estimated by this class.
private double	fret	Value of the function at the minimum.
private int	iter	Member contains number of iterations that were needed to estimate a minimum.
static final int	ITMAX	Maximum allowed iterations.
static final double	MIN_TOLERANCE	Minimum allowed tolerance value.
static final double	TINY	A small number.
private double	tolerance	The fractional tolerance in the function value such that failure to decrease by more than this amount on one iteration signals doneness.
private com.irurueta.algebra.Matrix	ximat	Set of directions.

Fields inherited from class com.irurueta.numerical.optimization.LineMultiOptimizer

p, xi

Fields inherited from class com.irurueta.numerical.optimization.MultiOptimizer

fmin, listener, resultAvailable, xmin

Fields inherited from class com.irurueta.numerical.optimization.Optimizer

iterationCompletedListener, locked

Constructor Summary

Constructors

Constructor	Description
PowellMultiOptimizer()	Empty constructor.
PowellMultiOptimizer(MultiDimensionFunctionEvaluatorListener listener, double tolerance)	Constructor.
PowellMultiOptimizer(MultiDimensionFunctionEvaluatorListener listener, double[] point, com.irurueta.algebra.Matrix directions, double tolerance)	Constructor.

Method Summary

Modifier and Type	Method	Description
boolean	areDirectionsAvailable()	Returns boolean indicating whether set of directions is available for retrieval.
private void	buildDirections()	Internal method to build or rebuild the set of directions if needed.
com.irurueta.algebra.Matrix	getDirections()	Returns set of directions to start looking for a minimum.
double	getTolerance()	Returns tolerance or accuracy to be expected on estimated local minimum.
private void	internalSetPointAndDirections(double[] point, com.irurueta.algebra.Matrix directions)	Internal method to set start point and set of directions to start looking for minimum.
private void	internalSetTolerance(double tolerance)	Internal method to set tolerance or accuracy to be expected on estimated local minimum.
boolean	isReady()	Returns boolean indicating whether this instance is ready to start the estimation of a local minimum.
void	minimize()	This function estimates a function minimum.
void	setPointAndDirections(double[] point, com.irurueta.algebra.Matrix directions)	Sets start point and set of directions to start looking for minimum.
void	setStartPoint(double[] startPoint)	Sets start point where local minimum is searched nearby.
void	setTolerance(double tolerance)	Sets tolerance or accuracy to be expected on estimated local minimum.
private double	sqr(double x)	Computes the squared value of provided double.

Methods inherited from class com.irurueta.numerical.optimization.LineMultiOptimizer

getDirection, getStartPoint, isDirectionAvailable, isStartPointAvailable, linmin, setStartPointAndDirection

Methods inherited from class com.irurueta.numerical.optimization.MultiOptimizer

getEvaluationAtResult, getListener, getResult, isListenerAvailable, isResultAvailable, setListener

Methods inherited from class com.irurueta.numerical.optimization.Optimizer

getOnIterationCompletedListener, isLocked, setOnIterationCompletedListener

Methods inherited from class java.lang.Object

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

Field Details

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Constant defining default tolerance or accuracy to be achieved on the minimum being estimated by this class.

See Also:

• Constant Field Values

MIN_TOLERANCE

public static final double MIN_TOLERANCE

Minimum allowed tolerance value.

See Also:

• Constant Field Values

ITMAX

public static final int ITMAX

Maximum allowed iterations.

See Also:

• Constant Field Values

TINY

public static final double TINY

A small number.

See Also:

• Constant Field Values

tolerance

private double tolerance

The fractional tolerance in the function value such that failure to decrease by more than this amount on one iteration signals doneness.

iter

private int iter

Member contains number of iterations that were needed to estimate a minimum.

fret

private double fret

Value of the function at the minimum.

ximat

private com.irurueta.algebra.Matrix ximat

Set of directions.

Constructor Details

PowellMultiOptimizer

public PowellMultiOptimizer()

Empty constructor.

PowellMultiOptimizer

public PowellMultiOptimizer(MultiDimensionFunctionEvaluatorListener listener,
 double tolerance)

Constructor.

Parameters:

listener - Listener to evaluate a multidimensional function.

tolerance - Tolerance or accuracy to be expected on estimated local minimum.

Throws:

IllegalArgumentException - Raised if tolerance is negative.

PowellMultiOptimizer

public PowellMultiOptimizer(MultiDimensionFunctionEvaluatorListener listener,
 double[] point,
 com.irurueta.algebra.Matrix directions,
 double tolerance)

Constructor.

Parameters:

listener - Listener to evaluate a multidimensional function.

point - Start point where algorithm will be started. Start point should be close to the local minimum to be found. Provided array must have a length equal to the number of dimensions of the function being evaluated, otherwise and exception will be raised when searching for the minimum.

directions - Set of directions to start looking for a minimum. Provided matrix must have the same rows as the number of dimensions of the function being evaluated. Each column will be a direction to search for a minimum.

tolerance - Tolerance or accuracy to be expected on estimated local minimum.

Throws:

IllegalArgumentException - Raised if provided point and direction don't have the same length or if provided tolerance is negative.

Method Details

getDirections

public com.irurueta.algebra.Matrix getDirections()
                                          throws NotAvailableException

Returns set of directions to start looking for a minimum. Returned matrix will have the same number of rows as the number of dimensions of the function (or the start point). Each column of the matrix will represent a vector containing a direction to search for a minimum.

Returns:

Set of directions.

Throws:

NotAvailableException - Raised if this has not yet been provided or computed.

areDirectionsAvailable

public boolean areDirectionsAvailable()

Returns boolean indicating whether set of directions is available for retrieval.

Returns:

True if available, false otherwise.

setPointAndDirections

public void setPointAndDirections(double[] point,
 com.irurueta.algebra.Matrix directions)
                           throws LockedException

Sets start point and set of directions to start looking for minimum.

Parameters:

point - Start point where algorithm will be started. Start point should be close to the local minimum to be found. Provided array must have a length equal to the number of dimensions of the function being evaluated, otherwise and exception will be raised when searching for the minimum.

directions - Set of directions to start looking for a minimum. Provided matrix must have the same rows as the number of dimensions of the function being evaluated. Each column will be a direction to search for a minimum.

Throws:

LockedException - Raised if this instance is locked.

IllegalArgumentException - Raised if provided point and direction don't have the same length.

setStartPoint

public void setStartPoint(double[] startPoint)
                   throws LockedException

Sets start point where local minimum is searched nearby.

Parameters:

startPoint - Start point to search for a local minimum

Throws:

LockedException - Raised if this instance is locked.

getTolerance

public double getTolerance()

Returns tolerance or accuracy to be expected on estimated local minimum.

Returns:

Tolerance or accuracy to be expected on estimated local minimum.

internalSetTolerance

private void internalSetTolerance(double tolerance)

Internal method to set tolerance or accuracy to be expected on estimated local minimum. This method does not check whether this instance is locked.

Parameters:

tolerance - Tolerance or accuracy to be expected on estimated local minimum.

Throws:

IllegalArgumentException - Raised if provided tolerance is negative.

setTolerance

public void setTolerance(double tolerance)
                  throws LockedException

Sets tolerance or accuracy to be expected on estimated local minimum.

Parameters:

tolerance - Tolerance or accuracy to be expected on estimated local minimum.

Throws:

LockedException - Raised if this instance is locked.

IllegalArgumentException - Raised if provided tolerance is negative.

minimize

public void minimize()
              throws LockedException,
NotReadyException,
OptimizationException

This function estimates a function minimum. Implementations of this class will usually search a local minimum close to a start point and will start looking into provided start direction. Minimization of a function f. Input consists of an initial starting point p. The initial matrix ximat, whose columns contain the initial set of directions, is set to the identity. Returned is the best point found, at which point fret is the minimum function value and iter is the number of iterations taken.

Overrides:

minimize in class Optimizer

Throws:

LockedException - Raised if this instance is locked, because estimation is being computed.

NotReadyException - Raised if this instance is not ready, because a listener, a gradient listener and a start point haven't been provided.

OptimizationException - Raised if the algorithm failed because of lack of convergence or because function couldn't be evaluated.

isReady

public boolean isReady()

Returns boolean indicating whether this instance is ready to start the estimation of a local minimum. An instance is ready once a listener and a start point are provided.

Overrides:

isReady in class LineMultiOptimizer

Returns:

True if this instance is ready, false otherwise.

internalSetPointAndDirections

private void internalSetPointAndDirections(double[] point,
 com.irurueta.algebra.Matrix directions)

Internal method to set start point and set of directions to start looking for minimum. This method does not check whether this instance is locked.

Parameters:

point - Start point where algorithm will be started. Start point should be close to the local minimum to be found. Provided array must have a length equal to the number of dimensions of the function being evaluated, otherwise and exception will be raised when searching for the minimum.

directions - Set of directions to start looking for a minimum. Provided matrix must have the same rows as the number of dimensions of the function being evaluated. Each column will be a direction to search for a minimum.

Throws:

IllegalArgumentException - Raised if provided point and direction don't have the same length.

buildDirections

private void buildDirections()
                      throws NotReadyException

Internal method to build or rebuild the set of directions if needed.

Throws:

NotReadyException - Raised if no start point has yet been provided.

sqr

private double sqr(double x)

Computes the squared value of provided double.

Parameters:

x - Value to be squared.

Returns:

Squared value.