com.numericalmethod.suanshu.analysis.integration.univariate
Class Lebesgue

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.Lebesgue

public class Lebesgue
extends java.lang.Object

Lebesgue integration is the general theory of integration of a function with respect to a general measure.

This implementation defines an Lebesgue integral as a dot product between the integrand (f) and the measure (dμ).

 /        /
 | f dμ = | f(x) μd(x) ≈ Σ f(x) μd(x)
 /        /
 

Constructor Summary

Lebesgue()
Construct an empty Lebesgue integral.

Lebesgue(double[] fx, double[] du)
Construct a Lebesgue integral.

Method Summary

void	setIntegrand(double[] fx) Set the integrand values for the discretized subsets.
void	setMeasure(double[] du) Set the measure values for the discretized subsets.
double	value() Compute the integral value.

Methods inherited from class java.lang.Object

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

Constructor Detail

Lebesgue

public Lebesgue()

Construct an empty Lebesgue integral.

Lebesgue

public Lebesgue(double[] fx,
                double[] du)

Construct a Lebesgue integral.

Parameters:

fx - the integrand

du - the measure

Method Detail

setIntegrand

public void setIntegrand(double[] fx)

Set the integrand values for the discretized subsets.

Parameters:

fx - the integrand values

setMeasure

public void setMeasure(double[] du)

Set the measure values for the discretized subsets.

Parameters:

du - the measure values

value

public double value()

Compute the integral value.

Returns:

the integral value