Class InvertingVariable

  • All Implemented Interfaces:
    SubstitutionRule

    public class InvertingVariable
    extends Object
    implements SubstitutionRule
    This is the inverting-variable transformation. It is good for
    • \(b \to \infty, a > 0\)
    • \(a \to -\infty, b < 0\)
    • any function that decreases toward infinity faster than \(\frac{1}{x^2}\)
    The integrator for this substitution should use an OPEN formula to avoid computing for the end point where t = 0. The substitution is \[ \int_{a}^{b}f(x)dx = \int_{1/b}^{1/a}\frac{1}{t^2}f(\frac{1}{t})dt, ab > 0 \]
    • Constructor Detail

      • InvertingVariable

        public InvertingVariable​(double a,
                                 double b)
        Construct an InvertingVariable substitution rule.
        Parameters:
        a - the lower limit
        b - the upper limit