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

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.MixedRule

public class MixedRule
extends DoubleExponential

Mixed Rule is good for functions that fall off rapidly at infinity, e.g., e^x or e^x2. The integral region is (0, ∞).

The substitution is

 x = et - e-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

MixedRule(UnivariateRealFunction f, double c, double a, double b)
Construct an instance of MixedRule 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

MixedRule

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

Construct an instance of MixedRule substitution rule.

Parameters:

f - the integrand

c - usually either 0 or 0.5 * PI

a - the lower limit

b - the upper limit