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Commons Math example source code file (MultiStartDifferentiableMultivariateRealOptimizerTest.java)
The Commons Math MultiStartDifferentiableMultivariateRealOptimizerTest.java source code/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math.optimization; import static org.junit.Assert.assertEquals; import static org.junit.Assert.assertTrue; import java.awt.geom.Point2D; import java.util.ArrayList; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction; import org.apache.commons.math.analysis.MultivariateRealFunction; import org.apache.commons.math.analysis.MultivariateVectorialFunction; import org.apache.commons.math.analysis.solvers.BrentSolver; import org.apache.commons.math.optimization.general.ConjugateGradientFormula; import org.apache.commons.math.optimization.general.NonLinearConjugateGradientOptimizer; import org.apache.commons.math.random.GaussianRandomGenerator; import org.apache.commons.math.random.JDKRandomGenerator; import org.apache.commons.math.random.RandomVectorGenerator; import org.apache.commons.math.random.UncorrelatedRandomVectorGenerator; import org.junit.Test; public class MultiStartDifferentiableMultivariateRealOptimizerTest { @Test public void testCircleFitting() throws FunctionEvaluationException, OptimizationException { Circle circle = new Circle(); circle.addPoint( 30.0, 68.0); circle.addPoint( 50.0, -6.0); circle.addPoint(110.0, -20.0); circle.addPoint( 35.0, 15.0); circle.addPoint( 45.0, 97.0); NonLinearConjugateGradientOptimizer underlying = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); JDKRandomGenerator g = new JDKRandomGenerator(); g.setSeed(753289573253l); RandomVectorGenerator generator = new UncorrelatedRandomVectorGenerator(new double[] { 50.0, 50.0 }, new double[] { 10.0, 10.0 }, new GaussianRandomGenerator(g)); MultiStartDifferentiableMultivariateRealOptimizer optimizer = new MultiStartDifferentiableMultivariateRealOptimizer(underlying, 10, generator); optimizer.setMaxIterations(100); assertEquals(100, optimizer.getMaxIterations()); optimizer.setMaxEvaluations(100); assertEquals(100, optimizer.getMaxEvaluations()); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-10, 1.0e-10)); BrentSolver solver = new BrentSolver(); solver.setAbsoluteAccuracy(1.0e-13); solver.setRelativeAccuracy(1.0e-15); RealPointValuePair optimum = optimizer.optimize(circle, GoalType.MINIMIZE, new double[] { 98.680, 47.345 }); RealPointValuePair[] optima = optimizer.getOptima(); for (RealPointValuePair o : optima) { Point2D.Double center = new Point2D.Double(o.getPointRef()[0], o.getPointRef()[1]); assertEquals(69.960161753, circle.getRadius(center), 1.0e-8); assertEquals(96.075902096, center.x, 1.0e-8); assertEquals(48.135167894, center.y, 1.0e-8); } assertTrue(optimizer.getGradientEvaluations() > 650); assertTrue(optimizer.getGradientEvaluations() < 700); assertTrue(optimizer.getEvaluations() > 70); assertTrue(optimizer.getEvaluations() < 90); assertTrue(optimizer.getIterations() > 70); assertTrue(optimizer.getIterations() < 90); assertEquals(3.1267527, optimum.getValue(), 1.0e-8); } private static class Circle implements DifferentiableMultivariateRealFunction { private ArrayList<Point2D.Double> points; public Circle() { points = new ArrayList<Point2D.Double>(); } public void addPoint(double px, double py) { points.add(new Point2D.Double(px, py)); } public double getRadius(Point2D.Double center) { double r = 0; for (Point2D.Double point : points) { r += point.distance(center); } return r / points.size(); } private double[] gradient(double[] point) { // optimal radius Point2D.Double center = new Point2D.Double(point[0], point[1]); double radius = getRadius(center); // gradient of the sum of squared residuals double dJdX = 0; double dJdY = 0; for (Point2D.Double pk : points) { double dk = pk.distance(center); dJdX += (center.x - pk.x) * (dk - radius) / dk; dJdY += (center.y - pk.y) * (dk - radius) / dk; } dJdX *= 2; dJdY *= 2; return new double[] { dJdX, dJdY }; } public double value(double[] variables) throws IllegalArgumentException, FunctionEvaluationException { Point2D.Double center = new Point2D.Double(variables[0], variables[1]); double radius = getRadius(center); double sum = 0; for (Point2D.Double point : points) { double di = point.distance(center) - radius; sum += di * di; } return sum; } public MultivariateVectorialFunction gradient() { return new MultivariateVectorialFunction() { public double[] value(double[] point) { return gradient(point); } }; } public MultivariateRealFunction partialDerivative(final int k) { return new MultivariateRealFunction() { public double value(double[] point) { return gradient(point)[k]; } }; } } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math MultiStartDifferentiableMultivariateRealOptimizerTest.java source code file: |
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