com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution
Class InvertingVariable

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Substitution
      com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.InvertingVariable

public class InvertingVariable
extends Substitution

This is the inverting-variable transformation. It is good for

• b -> ∞, a > 0
• a -> -∞, b < 0
• any function that decreases toward infinity faster than 1/x²

We have,

 /b          /1/a    1
 | f(x) dx = |      --- f(1/t) dt, ab > 0
 /a          /1/b    t2
 

The integrator for this substitution should use an OPEN formula to avoid computing for the end point, where t = 0.

Field Summary

double	a the lower limit
double	b the upper limit

Fields inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Substitution

dx, x

Constructor Summary

InvertingVariable(double a, double b)
Construct an instance of the InvertingVariable substitution rule.

Method Summary

double	ta() Get the lower limit of the integral.
double	tb() Get the upper limit of the integral.

Methods inherited from class java.lang.Object

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

Field Detail

a

public final double a

the lower limit

b

public final double b

the upper limit

Constructor Detail

InvertingVariable

public InvertingVariable(double a,
                         double b)

Construct an instance of the InvertingVariable substitution rule.

Parameters:

a - the lower limit

b - the upper limit

Method Detail

ta

public double ta()

Description copied from class: Substitution

Get the lower limit of the integral.

Specified by:

ta in class Substitution

Returns:

the lower limit

tb

public double tb()

Description copied from class: Substitution

Get the upper limit of the integral.

Specified by:

tb in class Substitution

Returns:

the upper limit