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

Class Riemann

java.lang.Object

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

All Implemented Interfaces:

Integrator, java.io.Serializable

public class Riemann
extends java.lang.Object
implements Integrator

This is a wrapper class that integrates a function by using an appropriate integrator together with Romberg's method. The integral can be definite or indefinite. For an indefinite integral, it requires the specification of a substitution rule (change of variable).

See Also:

Wikipedia: Riemann integral, Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	getPrecision() Get the convergence threshold.
double	integrate(UnivariateRealFunction f, double a, double b) Integrate function f from a to b, \[ \int_a^b\! f(x)\, dx \]
double	integrate(UnivariateRealFunction f, double a, double b, SubstitutionRule change) Integrate a function, f, from a to b possibly using change of variable.

Methods inherited from class java.lang.Object

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

Constructor Detail

Riemann

public Riemann(double precision,
               int maxIterations)

Construct an integrator.

Parameters:

precision - the convergence threshold

maxIterations - the maximum number of iterations

Riemann

public Riemann()

Construct an integrator.

Method Detail

integrate

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

Description copied from interface: Integrator

Integrate function f from a to b, \[ \int_a^b\! f(x)\, dx \]

Specified by:

integrate in interface Integrator

Parameters:

f - a univariate function

a - the lower limit

b - the upper limit

Returns:

\(\int_a^b\! f(x)\, dx\)

integrate

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

Integrate a function, f, from a to b possibly using change of variable.

Parameters:

f - a univariate function

a - the lower limit

b - the upper limit

change - the substitution rule; null for a definite integral (no singularity)

Returns:

\(\int_a^b\! f(x)\, dx\)

getPrecision

public double getPrecision()

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:

getPrecision in interface Integrator

Returns:

the precision