# SuanShu, a Java numerical and statistical library

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

## Class Exponential

• java.lang.Object
• com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Exponential
• All Implemented Interfaces:
SubstitutionRule

public class Exponential
extends Object
implements SubstitutionRule
This transformation is good for when the lower limit is finite, the upper limit is infinite, and the integrand falls off exponentially. The integrator for this substitution should use an OPEN formula to avoid computing for the end point where t = 0. The substitution is $\int_{a}^{\infty}f(x)dx = \int_{0}^{e^a}f(-\log (t))\frac{\mathrm{d} t}{t}$
• ### Constructor Summary

Constructors
Constructor and Description
Exponential(double a)
Construct an Exponential substitution rule.
• ### Method Summary

All Methods
Modifier and Type Method and Description
UnivariateRealFunction dx()
the first order derivative of the transformation: x'(t) = dx(t)/dt
double ta()
Get the lower limit of the integral.
double tb()
Get the upper limit of the integral.
UnivariateRealFunction x()
the transformation: x(t)
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### Exponential

public Exponential(double a)
Construct an Exponential substitution rule.
Parameters:
a - the lower limit
• ### Method Detail

• #### x

public UnivariateRealFunction x()
Description copied from interface: SubstitutionRule
the transformation: x(t)
Specified by:
x in interface SubstitutionRule
Returns:
x(t)
• #### dx

public UnivariateRealFunction dx()
Description copied from interface: SubstitutionRule
the first order derivative of the transformation: x'(t) = dx(t)/dt
Specified by:
dx in interface SubstitutionRule
Returns:
x'(t) = dx(t)/dt
• #### ta

public double ta()
Description copied from interface: SubstitutionRule
Get the lower limit of the integral.
Specified by:
ta in interface SubstitutionRule
Returns:
the lower limit
• #### tb

public double tb()
Description copied from interface: SubstitutionRule
Get the upper limit of the integral.
Specified by:
tb in interface SubstitutionRule
Returns:
the upper limit