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

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Substitution
      com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential
          com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential4RealLine

public class DoubleExponential4RealLine
extends DoubleExponential

This Double Exponential transformation is good for the region (-∞, ∞).

The substitution is

 x = sinh(c sinh(t))
 

The tricky part of using this transformation is to figure out a good range for t. One should override Substitution.ta() and Substitution.tb() if there is information about the integrand available.

See Also:

Wikipedia: Tanh-sinh quadrature

Field Summary

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

a, b, c, f

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

dx, x

Constructor Summary

DoubleExponential4RealLine(UnivariateRealFunction f, double c, double a, double b)
Construct an instance of DoubleExponential4RealLine substitution rule.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential

ta, tb

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 c,
                                  double a,
                                  double b)

Construct an instance of DoubleExponential4RealLine substitution rule.

Parameters:

f - the integrand

c - usually either 0 or 0.5 * PI

a - the lower limit

b - the upper limit