maspack.numerics

Class BrentMinimizer

java.lang.Object

maspack.numerics.BrentMinimizer

public class BrentMinimizer
extends java.lang.Object

Implements Brent's minimization procedure for a single-valued function of one variable, as described in:

Richard Brent, Algorithms for Minimization without Derivatives, Dover, 2002, ISBN: 0-486-41998-3

The code itself is based on the C implementation by John Burkardt available at https://people.math.sc.edu/Burkardt/c_src/brent/brent.html. An almost identical implementation is available in Numerical Recipes in C.

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_MAX_ITERS

Constructor Summary

Constructors

Constructor and Description
BrentMinimizer()

Method Summary

Modifier and Type	Method and Description
void	clearIterationCount() Clears the cummulatuve iteration count.
static FunctionValuePair	findMin(Function1x1 func, double a, double b, double eps) Finds a local minimum of a function within an interval [a,b].
static FunctionValuePair	findMin(Function1x1 func, double a, double fa, double b, double fb, double eps) Finds the minimum of a function over an interval [a,b], given evaluations of the function at the end points.
FunctionValuePair	findMinimum(Function1x1 func, double a, double b, double eps) Finds a local minimum of a function within an interval [a,b].
FunctionValuePair	findMinimum(Function1x1 func, double a, double b, double eps, boolean evalEndPoints) Finds a local minimum of a function within an interval [a,b].
FunctionValuePair	findMinimum(Function1x1 func, double a, double fa, double b, double fb, double eps) Finds the minimum of a function over an interval [a,b], given evaluations of the function at the end points.
int	getIterationCount() Queries the cummulative number of iterations invoked by this minimizer since it was created or clearIterationCount() was called.
int	getMaxIterations() Queries the maximum number of allowed iterations.
boolean	iterationLimitExceeded() Queries whether the iteration limit was exceeded on the most recent call to one of the findMinimum methods.
void	setMaxIterations(int maxi) Set the maximum number of allowed iterations.

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_MAX_ITERS

public static int DEFAULT_MAX_ITERS

Constructor Detail

BrentMinimizer

public BrentMinimizer()

Method Detail

getMaxIterations

public int getMaxIterations()

Queries the maximum number of allowed iterations.

Returns:

maximum number of iterations

setMaxIterations

public void setMaxIterations(int maxi)

Set the maximum number of allowed iterations. The default is given by DEFAULT_MAX_ITERS.

Parameters:

maxi - maximum number of iterations

clearIterationCount

public void clearIterationCount()

Clears the cummulatuve iteration count.

getIterationCount

public int getIterationCount()

Queries the cummulative number of iterations invoked by this minimizer since it was created or clearIterationCount() was called.

Returns:

cummulative iteration count

iterationLimitExceeded

public boolean iterationLimitExceeded()

Queries whether the iteration limit was exceeded on the most recent call to one of the findMinimum methods.

Returns:

true if iteration limit was exceeded.

findMin

public static FunctionValuePair findMin(Function1x1 func,
                                        double a,
                                        double b,
                                        double eps)

Finds a local minimum of a function within an interval [a,b]. This is a static convenience wrapper for findMinimum(Function1x1,double,double,double).

Parameters:

func - function to evaluate

a - left interval end point

b - right interval end point

eps - relative tolerance for finding the minimum abscissa

Returns:

FunctionValuePair giving the abscissa of the minimum and the minimum value

findMinimum

public FunctionValuePair findMinimum(Function1x1 func,
                                     double a,
                                     double b,
                                     double eps)

Finds a local minimum of a function within an interval [a,b]. The minimum is found within a relative abscissa tolerance eps, which generally should not be less than 1.0e-8 (i.e., the square root of machine precision). If no true local mimimum is found, then the method will return the value at the minimum end point.

Parameters:

func - function to evaluate

a - left interval end point

b - right interval end point

eps - relative tolerance for finding the minimum abscissa

Returns:

FunctionValuePair giving the abscissa of the minimum and the minimum value

findMinimum

public FunctionValuePair findMinimum(Function1x1 func,
                                     double a,
                                     double b,
                                     double eps,
                                     boolean evalEndPoints)

Finds a local minimum of a function within an interval [a,b]. The minimum is found within a relative abscissa tolerance eps, which generally should not be less than 1.0e-8 (i.e., the square root of machine precision). If no true local mimimum is found, then the method will return the value at the minimum end point.

Parameters:

func - function to evaluate

a - left interval end point

b - right interval end point

eps - relative tolerance for finding the minimum abscissa

evalEndPoints - if true, the method starts by evaluating the function at the interval end points, which may result in fewer iterations. This is the default behavior for methods that do not expose this as an option.

Returns:

FunctionValuePair giving the abscissa of the minimum and the minimum value

findMin

public static FunctionValuePair findMin(Function1x1 func,
                                        double a,
                                        double fa,
                                        double b,
                                        double fb,
                                        double eps)

Finds the minimum of a function over an interval [a,b], given evaluations of the function at the end points. This is a static convenience wrapper for findMinimum(Function1x1,double,double,double,double,double).

Parameters:

func - function to evaluate

a - left interval end point

fa - value of the function at a

b - right interval end point

fb - value of the function at b

eps - relative tolerance for finding the minimum abscissa

Returns:

FunctionValuePair giving the abscissa of the minimum and the minimum value

findMinimum

public FunctionValuePair findMinimum(Function1x1 func,
                                     double a,
                                     double fa,
                                     double b,
                                     double fb,
                                     double eps)

Finds the minimum of a function over an interval [a,b], given evaluations of the function at the end points. The minimum is found within a relative abscissa tolerance eps, which generally should not be less than 1.0e-8 (i.e., the square root of machine precision). If no true local mimimum is found, then the method will return the value at the minimum end point.

Parameters:

func - function to evaluate

a - left interval end point

fa - value of the function at a

b - right interval end point

fb - value of the function at b

eps - relative tolerance for finding the minimum abscissa

Returns:

FunctionValuePair giving the abscissa of the minimum and the minimum value