TrapezoidalIntegrator
jhplot.math.num.integration

Class TrapezoidalIntegrator



  • public class TrapezoidalIntegratorextends IterativeMethod

    The extended trapezoidal rule for numerically integrating functions.

    For example, to evaluate definite integrals for sine, first a Function is defined:

     Function sine = new Function() {    public double evaluate(double x) {        return Math.sin(x);    }} }; 

    Then, a trapezoidal integrator is created with the above function:

     TrapezoidalIntegrator integrator = new TrapezoidalIntegrator(sine); 

    Lastly, evaluating definite integrals is accomplished using the integrate(double, double) method:

     // integrate sine from 0 to Pi. double two = integrator.integrate(0.0, Math.PI);  // integrate sine from Pi/2 to 2 Pi. double one = integrator.integrate(Math.PI / 2.0, Math.PI); 

    References:

    1. Eric W. Weisstein. "Newton-Cotes Formulas." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Newton-CotesFormulas.html
    2. Eric W. Weisstein. "Trapezoidal Rule." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TrapezoidalRule.html

    • Constructor Detail

      • TrapezoidalIntegrator

        public TrapezoidalIntegrator(Function f)
        Create an integrator for the given function.
        Parameters:
        f - the target function.
      • TrapezoidalIntegrator

        public TrapezoidalIntegrator(Function f,                     int iterations,                     double error)
        Create an integrator for the given function.
        Parameters:
        f - the target function.
        iterations - maximum number of iterations.
        error - maximum relative error.
    • Method Detail

      • getFunction

        public Function getFunction()
        Access the target function.
        Returns:
        the target function.
      • integrate

        public double integrate(double a,               double b)                 throws NumericException
        Evaluate the definite integral from a to b.
        Parameters:
        a - the lower limit of integration.
        b - the upper limit of integration.
        Returns:
        the definite integral from a to b.
        Throws:
        NumericException - if the integral can not be evaluated.
      • setFunction

        public void setFunction(Function f)
        Modify the target function.
        Parameters:
        f - the new target function.

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