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

Class DoubleExponential4RealLine

java.lang.Object

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

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential4RealLine

All Implemented Interfaces:

SubstitutionRule, java.io.Serializable

public class DoubleExponential4RealLine
extends DoubleExponential

This transformation is good for the region \((-\infty, +\infty)\). 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 = sinh(c sinh(t))
 

See Also:

Wikipedia: Tanh-sinh quadrature, Serialized Form

Constructor Summary

Constructors

Constructor and Description
DoubleExponential4RealLine(UnivariateRealFunction f, double a, double b, double c) Construct a DoubleExponential4RealLine substitution rule.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.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

DoubleExponential4RealLine

public DoubleExponential4RealLine(UnivariateRealFunction f,
                                  double a,
                                  double b,
                                  double c)

Construct a DoubleExponential4RealLine substitution rule.

Parameters:

f - the integrand

a - the lower limit

b - the upper limit

c - usually either 0 or 0.5 * PI