jsat.math.rootfinding

Class Bisection

java.lang.Object

jsat.math.rootfinding.Bisection

All Implemented Interfaces:

Serializable, RootFinder

public class Bisection
extends Object
implements RootFinder

Author:

Edward Raff

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
Bisection()

Method Summary

Modifier and Type	Method and Description
int	guessesNeeded() Different root finding methods require different numbers of initial guesses.
static double	root(double eps, double a, double b, Function f, double... args)
static double	root(double eps, double a, double b, int pos, Function f, double... args)
static double	root(double a, double b, Function f, double... args) Uses the bisection method to find the argument of some function f for which f(args) = 0.
double	root(double eps, int maxIterations, double[] initialGuesses, Function f, int pos, double... args) Attempts to numerical compute the root of a given function, such that f(args) = 0.
double	root(double eps, int maxIterations, double[] initialGuesses, Function f, int pos, Vec args) Attempts to numerical compute the root of a given function, such that f(args) = 0.
static double	root(double eps, int maxIterations, double a, double b, int pos, Function f, double... args) Uses the bisection method to find the argument of some function f for which f(args) = 0.

Methods inherited from class java.lang.Object

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

Constructor Detail

Bisection

public Bisection()

Method Detail

root

public static double root(double a,
                          double b,
                          Function f,
                          double... args)

Uses the bisection method to find the argument of some function f for which f(args) = 0. If no args are given, it will be assumed that f takes a single variable input

Parameters:

a - the lower end of the search interval. f(a) must be ≤ 0

b - the uper end of the search interval. f(b) must be ≥ 0

f - the function to find a root of

args - the list of initial values for the function. The value at 0 can be anything, since it will be over written by the search.

Returns:

a value that when given to f with additional values args, will return x

root

public static double root(double eps,
                          double a,
                          double b,
                          Function f,
                          double... args)

root

public static double root(double eps,
                          double a,
                          double b,
                          int pos,
                          Function f,
                          double... args)

root

public static double root(double eps,
                          int maxIterations,
                          double a,
                          double b,
                          int pos,
                          Function f,
                          double... args)

Uses the bisection method to find the argument of some function f for which f(args) = 0. If no args are given, it will be assumed that f takes a single variable input

Parameters:

eps - the accuracy desired

maxIterations - the maximum number of iterations

a - the lower end of the search interval. f(a) must be ≤ 0

b - the uper end of the search interval. f(b) must be ≥ 0

f - the function to find a root of

pos - which variable in the arguments is going to be the search variable

args - the list of initial values for the function. The value at pos can be anything, since it will be over written by the search.

Returns:

the value of the pos^th variable that makes this function return 0.

root

public double root(double eps,
                   int maxIterations,
                   double[] initialGuesses,
                   Function f,
                   int pos,
                   double... args)

Description copied from interface: RootFinder

Attempts to numerical compute the root of a given function, such that f(args) = 0. Only one variable may be altered at a time

Specified by:

root in interface RootFinder

Parameters:

eps - the accuracy desired for the solution

maxIterations - the maximum number of steps allowed before forcing a return of the current solution.

initialGuesses - an array containing the initial guess values

f - the function to find the root of

pos - the index of the argument that will be allowed to alter in order to find the root. Starts from 0

args - the values to be passed to the function as arguments

Returns:

the value of the variable at the index pos that makes the function return 0

root

public double root(double eps,
                   int maxIterations,
                   double[] initialGuesses,
                   Function f,
                   int pos,
                   Vec args)

Description copied from interface: RootFinder

Attempts to numerical compute the root of a given function, such that f(args) = 0. Only one variable may be altered at a time

Specified by:

root in interface RootFinder

Parameters:

eps - the accuracy desired for the solution

maxIterations - the maximum number of steps allowed before forcing a return of the current solution.

initialGuesses - an array containing the initial guess values

f - the function to find the root of

pos - the index of the argument that will be allowed to alter in order to find the root. Starts from 0

args - the values to be passed to the function as arguments

Returns:

the value of the variable at the index pos that makes the function return 0

guessesNeeded

public int guessesNeeded()

Description copied from interface: RootFinder

Different root finding methods require different numbers of initial guesses. Some root finding methods require 2 guesses, each with values of opposite sign so that they bracket the root. Others just need any 2 initial guesses sufficiently close to the root. This method simply returns the number of guesses that are needed.

Specified by:

guessesNeeded in interface RootFinder

Returns:

the number of initial guesses this root finding method needs