dev.nm.analysis.integration.univariate.riemann.substitution

Class DoubleExponential4HalfRealLine

java.lang.Object

dev.nm.analysis.integration.univariate.riemann.substitution.DoubleExponential

dev.nm.analysis.integration.univariate.riemann.substitution.DoubleExponential4HalfRealLine

All Implemented Interfaces:

SubstitutionRule

public class DoubleExponential4HalfRealLine
extends DoubleExponential

This transformation is good for the region \((0, +\infty)\). The tricky part of using this transformation is to figure out a good range for t. If there is information about the integrand available, SubstitutionRule.ta() and SubstitutionRule.tb() should be overridden. The substitution is

 x = exp(2c sinh(t))
 

See Also:

Wikipedia: Tanh-sinh quadrature

Constructor Summary

Constructors

Constructor and Description
DoubleExponential4HalfRealLine(UnivariateRealFunction f, double a, double b, double c) Construct a DoubleExponential4HalfRealLine substitution rule.

Method Summary

Methods inherited from class dev.nm.analysis.integration.univariate.riemann.substitution.DoubleExponential

dx, ta, tb, x

Methods inherited from class java.lang.Object

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

Constructor Detail

DoubleExponential4HalfRealLine

public DoubleExponential4HalfRealLine(UnivariateRealFunction f,
                                      double a,
                                      double b,
                                      double c)

Construct a DoubleExponential4HalfRealLine substitution rule.

Parameters:

f - the integrand

a - the lower limit

b - the upper limit

c - usually either 0 or 0.5 * PI