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/* |
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* Written by Doug Lea with assistance from members of JCP JSR-166 |
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* Expert Group and released to the public domain, as explained at |
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* http://creativecommons.org/publicdomain/zero/1.0/ |
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*/ |
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|
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import java.util.concurrent.*; |
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|
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/** |
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* Adapted from FJTask version. |
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* Sample program using Guassian Quadrature for numerical integration. |
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* Inspired by a |
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* <A href="http://www.cs.uga.edu/~dkl/filaments/dist.html"> Filaments</A> |
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* demo program. |
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* |
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*/ |
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|
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public class IntegrateGamma { |
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/** for time conversion */ |
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static final long NPS = (1000L * 1000 * 1000); |
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public static void main(String[] args) { |
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int procs = 0; |
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double start = 1.0; |
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double end = 96.0; |
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int exp = 5; |
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try { |
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if (args.length > 0) |
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procs = Integer.parseInt(args[0]); |
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if (args.length > 1) |
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start = new Double(args[1]).doubleValue(); |
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if (args.length > 2) |
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end = new Double(args[2]).doubleValue(); |
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if (args.length > 3) |
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exp = Integer.parseInt(args[3]); |
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} |
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catch (Exception e) { |
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System.out.println("Usage: java IntegrateGamma <threads> <lower bound> <upper bound> <exponent>\n (for example 2 1 48 5)."); |
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return; |
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} |
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|
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ForkJoinPool g = (procs == 0) ? new ForkJoinPool() : |
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new ForkJoinPool(procs); |
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|
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System.out.println("Integrating from " + start + " to " + end + " exponent: " + exp + " parallelism " + g.getParallelism()); |
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|
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Function f = new SampleFunction(exp); |
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for (int i = 0; i < 10; ++i) { |
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Integrator integrator = new Integrator(f, 0.001, g); |
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long last = System.nanoTime(); |
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double result = integrator.integral(start, end); |
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double elapsed = elapsedTime(last); |
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System.out.printf("time: %7.3f", elapsed); |
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System.out.println(" Answer = " + result); |
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} |
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System.out.println(g); |
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g.shutdown(); |
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} |
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|
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static double elapsedTime(long startTime) { |
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return (double)(System.nanoTime() - startTime) / NPS; |
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} |
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|
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/* |
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This is all set up as if it were part of a more serious |
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framework, but is for now just a demo, with all |
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classes declared as static within Integrate |
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*/ |
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|
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/** A function to be integrated */ |
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static interface Function { |
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double compute(double x); |
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} |
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|
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/** |
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* Sample from filaments demo. |
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* Computes (2*n-1)*(x^(2*n-1)) for all odd values. |
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*/ |
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static class SampleFunction implements Function { |
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final int n; |
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SampleFunction(int n) { this.n = n; } |
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|
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public double compute(double x) { |
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double power = x; |
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double xsq = x * x; |
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double val = power; |
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double di = 1.0; |
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for (int i = n - 1; i > 0; --i) { |
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di += 2.0; |
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power *= xsq; |
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val += di * power; |
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} |
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return val; |
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} |
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} |
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|
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|
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static class Integrator { |
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final Function f; // The function to integrate |
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final double errorTolerance; |
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final ForkJoinPool g; |
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|
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Integrator(Function f, double errorTolerance, ForkJoinPool g) { |
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this.f = f; |
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this.errorTolerance = errorTolerance; |
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this.g = g; |
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} |
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|
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double integral(double lowerBound, double upperBound) { |
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double f_lower = f.compute(lowerBound); |
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double f_upper = f.compute(upperBound); |
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double initialArea = 0.5 * (upperBound-lowerBound) * (f_upper + f_lower); |
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Quad q = new Quad(lowerBound, upperBound, |
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f_lower, f_upper, |
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initialArea); |
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g.invoke(q); |
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return q.area; |
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} |
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|
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|
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/** |
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* FJTask to recursively perform the quadrature. |
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* Algorithm: |
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* Compute the area from lower bound to the center point of interval, |
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* and from the center point to the upper bound. If this |
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* differs from the value from lower to upper by more than |
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* the error tolerance, recurse on each half. |
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*/ |
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final class Quad extends RecursiveAction { |
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final double left; // lower bound |
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final double right; // upper bound |
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final double f_left; // value of the function evaluated at left |
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final double f_right; // value of the function evaluated at right |
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|
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// Area initialized with original estimate from left to right. |
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// It is replaced with refined value. |
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volatile double area; |
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|
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Quad(double left, double right, |
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double f_left, double f_right, |
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double area) { |
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this.left = left; |
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this.right = right; |
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this.f_left = f_left; |
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this.f_right = f_right; |
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this.area = area; |
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} |
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|
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public void compute() { |
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double center = 0.5 * (left + right); |
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double f_center = f.compute(center); |
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|
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double leftArea = 0.5 * (center - left) * (f_left + f_center); |
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double rightArea = 0.5 * (right - center) * (f_center + f_right); |
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double sum = leftArea + rightArea; |
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|
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double diff = sum - area; |
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if (diff < 0) diff = -diff; |
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|
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if (diff >= errorTolerance) { |
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Quad q1 = new Quad(left, center, f_left, f_center, leftArea); |
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q1.fork(); |
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Quad q2 = new Quad(center, right, f_center, f_right, rightArea); |
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q2.compute(); |
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q1.join(); |
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sum = q1.area + q2.area; |
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} |
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|
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area = sum; |
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} |
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} |
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} |
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|
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} |
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