com.numericalmethod.suanshu.analysis.integration.univariate.riemann
Class Riemann

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.riemann.Riemann

All Implemented Interfaces:

Integrator

public class Riemann
extends java.lang.Object
implements Integrator

This class uses an integrator together with Romberg's method. It tries to determine the appropriate integrator depending on the function and the integral interval.

Field Summary

int	maxIterations the maximum number of iterations
double	precision the convergence threshold

Constructor Summary

Riemann()
Construct a default integrator.

Riemann(double precision, int maxIterations)
Construct an integrator.

Method Summary

double	integrate(UnivariateRealFunction f, double a, double b) Integrate function f from a to b.
double	integrate(UnivariateRealFunction f, double a, double b, Substitution change) Riemann function f from a to b, using a Substitution rule.
double	precision() Get the convergence threshold.

Methods inherited from class java.lang.Object

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

Field Detail

maxIterations

public final int maxIterations

the maximum number of iterations

precision

public final double precision

the convergence threshold

Constructor Detail

Riemann

public Riemann()

Construct a default integrator.

Riemann

public Riemann(double precision,
               int maxIterations)

Construct an integrator.

Parameters:

precision - the convergence threshold

maxIterations - the maximum number of iterations

Method Detail

integrate

public double integrate(UnivariateRealFunction f,
                        double a,
                        double b)

Description copied from interface: Integrator

Integrate function f from a to b.

 / b
 |   f(x) dx
 / a
 

Specified by:

integrate in interface Integrator

Parameters:

f - a univariate function

a - lower limit

b - upper limit

Returns:

Σ(f(x))

integrate

public double integrate(UnivariateRealFunction f,
                        double a,
                        double b,
                        Substitution change)

Riemann function f from a to b, using a Substitution rule.

 / b
 |   f(x) dx
 / a
 

Parameters:

f - a univariate function

a - lower limit

b - upper limit

change - the substitution rule

Returns:

Σ(f(x))

precision

public double precision()

Description copied from interface: Integrator

Get the convergence threshold. The usage depends on the specific integrator.

For example, for an IterativeIntegrator, the integral is considered converged if the relative error of two successive sums is less than the threshold.

Specified by:

precision in interface Integrator

Returns:

the precision