# SuanShu, a Java numerical and statistical library

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

## Class DoubleExponential

• java.lang.Object
• com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential
• ### Constructor Summary

Constructors
Constructor and Description
DoubleExponential(UnivariateRealFunction f, double a, double b, double c)
Construct a DoubleExponential substitution rule by trying to automatically determine the 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

• #### DoubleExponential

public DoubleExponential(UnivariateRealFunction f,
double a,
double b,
double c)
Construct a DoubleExponential substitution rule by trying to automatically determine the substitution rule.
Parameters:
f - the integrand
a - the lower limit
b - the upper limit
c - a constant; usually either 0 or 0.5 * PI
• ### 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()
Get the lower limit of the integral. The accuracy of using the double exponential transformation lies in choosing the correct region of t for integration. It is very hard to determine the region without knowing about the function, such as where the singularities are. If the region of t is known, override this function.
Specified by:
ta in interface SubstitutionRule
Returns:
the lower limit
• #### tb

public double tb()
Get the upper limit of the integral. The accuracy of using the double exponential transformation lies in choosing the correct region of t for integration. It is very hard to determine the region without knowing about the function, such as where the singularities are. If the region of t is known, override this function.
Specified by:
tb in interface SubstitutionRule
Returns:
the upper limit