jahuwaldt.tools.math

Class Quadrature

java.lang.Object

jahuwaldt.tools.math.Quadrature

public class Quadrature
extends java.lang.Object

A collection of methods for integrating a 1D function within a range: I=int_a^b{f(x) dx}.

Modified by: Joseph A. Huwaldt

Version:

January 23, 2014

Author:

Joseph A. Huwaldt Date: June 8, 2009

Constructor Summary

Constructors

Constructor and Description
Quadrature()

Method Summary

Modifier and Type	Method and Description
static double	adaptLobatto(Evaluatable1D func, double a, double b, double tol) Returns the integral of the supplied function from a to b using the adaptive Gauss-Lobatto method. Reference: Gander, W., Gautschi, W., "Adaptive Quadrature - Revisited", ETH Zürich, Aug.
static double	gaussLegendre_Wx1N10(Evaluatable1D func, double a, double b) Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=10).
static double	gaussLegendre_Wx1N20(Evaluatable1D func, double a, double b) Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=20).
static double	gaussLegendre_Wx1N40(Evaluatable1D func, double a, double b) Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=40).
static double	simpsonsRule(Evaluatable1D func, double a, double b, double tol) Returns the integral of the supplied function from a to b using Simpson's Rule.

Methods inherited from class java.lang.Object

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

Constructor Detail

Quadrature

public Quadrature()

Method Detail

simpsonsRule

public static double simpsonsRule(Evaluatable1D func,
                                  double a,
                                  double b,
                                  double tol)
                           throws IntegratorException,
                                  RootException

Returns the integral of the supplied function from a to b using Simpson's Rule. Reference: Numerical Recipes in C, pg. 139.

Parameters:

func - The function being integrated (the "derivative" method is never called).

a - The lower integration limit (must be < b).

b - The upper integration limit (must be > a).

tol - The desired relative error.

Returns:

The integral of the supplied function from a to b.

Throws:

IntegratorException - if to many iterations are attempted.

RootException - thrown by the function itself.

gaussLegendre_Wx1N10

public static double gaussLegendre_Wx1N10(Evaluatable1D func,
                                          double a,
                                          double b)
                                   throws RootException

Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=10). Reference: Numerical Recipes in C, pg. 148.

Parameters:

func - The function being integrated (the "derivative" function is never called).

a - The lower integration limit (must be < b).

b - The upper integration limit (must be > a).

Returns:

The integral of the supplied function from a to b.

Throws:

RootException - may be thrown by the function itself.

gaussLegendre_Wx1N20

public static double gaussLegendre_Wx1N20(Evaluatable1D func,
                                          double a,
                                          double b)
                                   throws RootException

Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=20). Reference: Numerical Recipes in C, pg. 148.

Parameters:

func - The function being integrated (the "derivative" function is never called).

a - The lower integration limit (must be < b).

b - The upper integration limit (must be > a).

Returns:

The integral of the supplied function from a to b.

Throws:

RootException - may be thrown by the function itself.

gaussLegendre_Wx1N40

public static double gaussLegendre_Wx1N40(Evaluatable1D func,
                                          double a,
                                          double b)
                                   throws RootException

Returns the integral of the supplied function from a to b using Gauss-Legendre integration (W(x) = 1, N=40). Reference: Numerical Recipes in C, pg. 148.

Parameters:

func - The function being integrated (the "derivative" function is never called).

a - The lower integration limit (must be < b).

b - The upper integration limit (must be > a).

Returns:

The integral of the supplied function from a to b.

Throws:

RootException - may be thrown by the function itself.

adaptLobatto

public static double adaptLobatto(Evaluatable1D func,
                                  double a,
                                  double b,
                                  double tol)
                           throws IntegratorException,
                                  RootException

Returns the integral of the supplied function from a to b using the adaptive Gauss-Lobatto method.
Reference: Gander, W., Gautschi, W., "Adaptive Quadrature - Revisited", ETH Zürich, Aug. 1998.

Parameters:

func - The function being integrated (the "derivative" function is never called).

a - The lower integration limit (must be < b).

b - The upper integration limit (must be > a).

tol - The desired relative error.

Returns:

The integral of the supplied function from a to b.

Throws:

IntegratorException - if to many iterations are attempted.

RootException - may be thrown by the function itself.