Package org.apache.commons.math.analysis.integration

Class LegendreGaussIntegrator

java.lang.Object

org.apache.commons.math.ConvergingAlgorithmImpl

org.apache.commons.math.analysis.integration.UnivariateRealIntegratorImpl

org.apache.commons.math.analysis.integration.LegendreGaussIntegrator

All Implemented Interfaces:

UnivariateRealIntegrator, ConvergingAlgorithm

public class LegendreGaussIntegrator
extends UnivariateRealIntegratorImpl

Implements the Legendre-Gauss quadrature formula.

Legendre-Gauss integrators are efficient integrators that can accurately integrate functions with few functions evaluations. A Legendre-Gauss integrator using an n-points quadrature formula can integrate exactly 2n-1 degree polynomials.

These integrators evaluate the function on n carefully chosen abscissas in each step interval (mapped to the canonical [-1 1] interval). The evaluation abscissas are not evenly spaced and none of them are at the interval endpoints. This implies the function integrated can be undefined at integration interval endpoints.

The evaluation abscissas x_i are the roots of the degree n Legendre polynomial. The weights a_i of the quadrature formula integrals from -1 to +1 ∫ Li² where Li (x) = ∏ (x-x_k)/(x_i-x_k) for k != i.

Since:

1.2

Constructor Summary

Constructors

Constructor	Description
LegendreGaussIntegrator(int n, int defaultMaximalIterationCount)	Build a Legendre-Gauss integrator.

Method Summary

Modifier and Type	Method	Description
double	integrate(double min, double max)	Deprecated.
double	integrate(UnivariateRealFunction f, double min, double max)	Integrate the function in the given interval.

Methods inherited from class org.apache.commons.math.analysis.integration.UnivariateRealIntegratorImpl

getMinimalIterationCount, getResult, resetMinimalIterationCount, setMinimalIterationCount

Methods inherited from class org.apache.commons.math.ConvergingAlgorithmImpl

getAbsoluteAccuracy, getIterationCount, getMaximalIterationCount, getRelativeAccuracy, resetAbsoluteAccuracy, resetMaximalIterationCount, resetRelativeAccuracy, setAbsoluteAccuracy, setMaximalIterationCount, setRelativeAccuracy

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math.ConvergingAlgorithm

getAbsoluteAccuracy, getIterationCount, getMaximalIterationCount, getRelativeAccuracy, resetAbsoluteAccuracy, resetMaximalIterationCount, resetRelativeAccuracy, setAbsoluteAccuracy, setMaximalIterationCount, setRelativeAccuracy

Constructor Detail

LegendreGaussIntegrator

public LegendreGaussIntegrator(int n,
                               int defaultMaximalIterationCount)
                        throws IllegalArgumentException

Build a Legendre-Gauss integrator.

Parameters:

n - number of points desired (must be between 2 and 5 inclusive)

defaultMaximalIterationCount - maximum number of iterations

Throws:

IllegalArgumentException - if the number of points is not in the supported range

Method Detail

integrate

@Deprecated
public double integrate(double min,
                        double max)
                 throws ConvergenceException,
                        FunctionEvaluationException,
                        IllegalArgumentException

Deprecated.

Integrate the function in the given interval.

Parameters:

min - the lower bound for the interval

max - the upper bound for the interval

Returns:

the value of integral

Throws:

ConvergenceException - if the maximum iteration count is exceeded or the integrator detects convergence problems otherwise

FunctionEvaluationException - if an error occurs evaluating the function

IllegalArgumentException - if min > max or the endpoints do not satisfy the requirements specified by the integrator

integrate

public double integrate(UnivariateRealFunction f,
                        double min,
                        double max)
                 throws ConvergenceException,
                        FunctionEvaluationException,
                        IllegalArgumentException

Integrate the function in the given interval.

Parameters:

f - the integrand function

min - the lower bound for the interval

max - the upper bound for the interval

Returns:

the value of integral

Throws:

ConvergenceException - if the maximum iteration count is exceeded or the integrator detects convergence problems otherwise

FunctionEvaluationException - if an error occurs evaluating the function

IllegalArgumentException - if min > max or the endpoints do not satisfy the requirements specified by the integrator