agi.foundation.numericalmethods.advanced

(agi.foundation.core-2024r2.jar)

Class BurdenFairesAdaptiveQuadrature

java.lang.Object

agi.foundation.numericalmethods.advanced.BurdenFairesAdaptiveQuadrature

public final class BurdenFairesAdaptiveQuadrature
extends Object

An adaptive quadrature numerical integration utility based on Simpson's method.

See section 4.6 in "Numerical Analysis" by Burden and Faires for more information.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	BurdenFairesAdaptiveQuadrature.Integrand The function to be integrated.

Method Summary

Modifier and Type	Method and Description
static double	integrate(double intervalStart, double intervalEnd, double tolerance, int numberOfLevels, BurdenFairesAdaptiveQuadrature.Integrand integrand) Approximates the integral I = Int(f(x), a, b) to within a given tolerance.
static boolean	tryIntegrate(double intervalStart, double intervalEnd, double tolerance, int numberOfLevels, BurdenFairesAdaptiveQuadrature.Integrand integrand, double[] integral) Approximates the integral I = Int(f(x), a, b) to within a given tolerance.

Methods inherited from class java.lang.Object

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

Method Detail

tryIntegrate

public static boolean tryIntegrate(double intervalStart,
                                   double intervalEnd,
                                   double tolerance,
                                   int numberOfLevels,
                                   @Nonnull
                                   BurdenFairesAdaptiveQuadrature.Integrand integrand,
                                   @Nonnull
                                   double[] integral)

Approximates the integral I = Int(f(x), a, b) to within a given tolerance.

Parameters:

intervalStart - The start of the interval in which the function is integrated.

intervalEnd - The end of the interval in which the function is integrated.

tolerance - The error tolerance used in the adaptive quadrature technique.

numberOfLevels - The number of divisions.

integrand - The function to be integrated.

integral - The value of the integral.

Returns:

A boolean value indicating if the integral was successfully computed.

integrate

public static double integrate(double intervalStart,
                               double intervalEnd,
                               double tolerance,
                               int numberOfLevels,
                               @Nonnull
                               BurdenFairesAdaptiveQuadrature.Integrand integrand)

Approximates the integral I = Int(f(x), a, b) to within a given tolerance.

Parameters:

intervalStart - The start of the interval in which the function is integrated.

intervalEnd - The end of the interval in which the function is integrated.

tolerance - The error tolerance used in the adaptive quadrature technique. Note that this error is multiplied by 10.0 internally.

numberOfLevels - The number of divisions.

integrand - The function to be integrated.

Returns:

The value of the integral.

Throws:

ArithmeticException - Thrown when too many steps are taken.