Class MixedRule
- java.lang.Object
-
- dev.nm.analysis.integration.univariate.riemann.substitution.DoubleExponential
-
- dev.nm.analysis.integration.univariate.riemann.substitution.MixedRule
-
- All Implemented Interfaces:
SubstitutionRule
public class MixedRule extends DoubleExponential
The mixed rule is good for functions that fall off rapidly at infinity, e.g., \(e^{x^2}\) or \(e^x\) The integral region is \((0, +\infty)\). 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()
andSubstitutionRule.tb()
should be overridden. The substitution is \[ x = e^{t - e^{-t}} \]- See Also:
- Wikipedia: Tanh-sinh quadrature
-
-
Constructor Summary
Constructors Constructor Description MixedRule(UnivariateRealFunction f, double a, double b, double c)
Construct aMixedRule
substitution rule.
-
-
-
Constructor Detail
-
MixedRule
public MixedRule(UnivariateRealFunction f, double a, double b, double c)
Construct aMixedRule
substitution rule.- Parameters:
f
- the integranda
- the lower limitb
- the upper limitc
- usually either 0 or 0.5 * PI
-
-