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18 package org.apache.commons.math.optimization;
19
20 import static org.junit.Assert.assertEquals;
21 import static org.junit.Assert.assertTrue;
22
23 import java.awt.geom.Point2D;
24 import java.util.ArrayList;
25
26 import org.apache.commons.math.FunctionEvaluationException;
27 import org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction;
28 import org.apache.commons.math.analysis.MultivariateRealFunction;
29 import org.apache.commons.math.analysis.MultivariateVectorialFunction;
30 import org.apache.commons.math.analysis.solvers.BrentSolver;
31 import org.apache.commons.math.optimization.general.ConjugateGradientFormula;
32 import org.apache.commons.math.optimization.general.NonLinearConjugateGradientOptimizer;
33 import org.apache.commons.math.random.GaussianRandomGenerator;
34 import org.apache.commons.math.random.JDKRandomGenerator;
35 import org.apache.commons.math.random.RandomVectorGenerator;
36 import org.apache.commons.math.random.UncorrelatedRandomVectorGenerator;
37 import org.junit.Test;
38
39 public class MultiStartDifferentiableMultivariateRealOptimizerTest {
40
41 @Test
42 public void testCircleFitting() throws FunctionEvaluationException, OptimizationException {
43 Circle circle = new Circle();
44 circle.addPoint( 30.0, 68.0);
45 circle.addPoint( 50.0, -6.0);
46 circle.addPoint(110.0, -20.0);
47 circle.addPoint( 35.0, 15.0);
48 circle.addPoint( 45.0, 97.0);
49 NonLinearConjugateGradientOptimizer underlying =
50 new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE);
51 JDKRandomGenerator g = new JDKRandomGenerator();
52 g.setSeed(753289573253l);
53 RandomVectorGenerator generator =
54 new UncorrelatedRandomVectorGenerator(new double[] { 50.0, 50.0 }, new double[] { 10.0, 10.0 },
55 new GaussianRandomGenerator(g));
56 MultiStartDifferentiableMultivariateRealOptimizer optimizer =
57 new MultiStartDifferentiableMultivariateRealOptimizer(underlying, 10, generator);
58 optimizer.setMaxIterations(100);
59 assertEquals(100, optimizer.getMaxIterations());
60 optimizer.setMaxEvaluations(100);
61 assertEquals(100, optimizer.getMaxEvaluations());
62 optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-10, 1.0e-10));
63 BrentSolver solver = new BrentSolver();
64 solver.setAbsoluteAccuracy(1.0e-13);
65 solver.setRelativeAccuracy(1.0e-15);
66 RealPointValuePair optimum =
67 optimizer.optimize(circle, GoalType.MINIMIZE, new double[] { 98.680, 47.345 });
68 RealPointValuePair[] optima = optimizer.getOptima();
69 for (RealPointValuePair o : optima) {
70 Point2D.Double center = new Point2D.Double(o.getPointRef()[0], o.getPointRef()[1]);
71 assertEquals(69.960161753, circle.getRadius(center), 1.0e-8);
72 assertEquals(96.075902096, center.x, 1.0e-8);
73 assertEquals(48.135167894, center.y, 1.0e-8);
74 }
75 assertTrue(optimizer.getGradientEvaluations() > 650);
76 assertTrue(optimizer.getGradientEvaluations() < 700);
77 assertTrue(optimizer.getEvaluations() > 70);
78 assertTrue(optimizer.getEvaluations() < 90);
79 assertTrue(optimizer.getIterations() > 70);
80 assertTrue(optimizer.getIterations() < 90);
81 assertEquals(3.1267527, optimum.getValue(), 1.0e-8);
82 }
83
84 private static class Circle implements DifferentiableMultivariateRealFunction {
85
86 private ArrayList<Point2D.Double> points;
87
88 public Circle() {
89 points = new ArrayList<Point2D.Double>();
90 }
91
92 public void addPoint(double px, double py) {
93 points.add(new Point2D.Double(px, py));
94 }
95
96 public double getRadius(Point2D.Double center) {
97 double r = 0;
98 for (Point2D.Double point : points) {
99 r += point.distance(center);
100 }
101 return r / points.size();
102 }
103
104 private double[] gradient(double[] point) {
105
106
107 Point2D.Double center = new Point2D.Double(point[0], point[1]);
108 double radius = getRadius(center);
109
110
111 double dJdX = 0;
112 double dJdY = 0;
113 for (Point2D.Double pk : points) {
114 double dk = pk.distance(center);
115 dJdX += (center.x - pk.x) * (dk - radius) / dk;
116 dJdY += (center.y - pk.y) * (dk - radius) / dk;
117 }
118 dJdX *= 2;
119 dJdY *= 2;
120
121 return new double[] { dJdX, dJdY };
122
123 }
124
125 public double value(double[] variables)
126 throws IllegalArgumentException, FunctionEvaluationException {
127
128 Point2D.Double center = new Point2D.Double(variables[0], variables[1]);
129 double radius = getRadius(center);
130
131 double sum = 0;
132 for (Point2D.Double point : points) {
133 double di = point.distance(center) - radius;
134 sum += di * di;
135 }
136
137 return sum;
138
139 }
140
141 public MultivariateVectorialFunction gradient() {
142 return new MultivariateVectorialFunction() {
143 public double[] value(double[] point) {
144 return gradient(point);
145 }
146 };
147 }
148
149 public MultivariateRealFunction partialDerivative(final int k) {
150 return new MultivariateRealFunction() {
151 public double value(double[] point) {
152 return gradient(point)[k];
153 }
154 };
155 }
156
157 }
158
159 }