Class 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() and SubstitutionRule.tb() should be overridden. The substitution is \[ x = e^{t - e^{-t}} \]
    See Also:
    Wikipedia: Tanh-sinh quadrature
    • Constructor Detail

      • MixedRule

        public MixedRule​(UnivariateRealFunction f,
                         double a,
                         double b,
                         double c)
        Construct a MixedRule substitution rule.
        Parameters:
        f - the integrand
        a - the lower limit
        b - the upper limit
        c - usually either 0 or 0.5 * PI