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23 package org.hipparchus.optim.nonlinear.scalar.noderiv;
24
25 import org.hipparchus.analysis.MultivariateFunction;
26 import org.hipparchus.exception.MathRuntimeException;
27 import org.hipparchus.optim.InitialGuess;
28 import org.hipparchus.optim.MaxEval;
29 import org.hipparchus.optim.PointValuePair;
30 import org.hipparchus.optim.SimpleBounds;
31 import org.hipparchus.optim.SimpleValueChecker;
32 import org.hipparchus.optim.nonlinear.scalar.GoalType;
33 import org.hipparchus.optim.nonlinear.scalar.ObjectiveFunction;
34 import org.hipparchus.util.FastMath;
35 import org.junit.Assert;
36 import org.junit.Test;
37
38 public class SimplexOptimizerMultiDirectionalTest {
39 @Test(expected=MathRuntimeException.class)
40 public void testBoundsUnsupported() {
41 SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
42 final FourExtrema fourExtrema = new FourExtrema();
43
44 optimizer.optimize(new MaxEval(100),
45 new ObjectiveFunction(fourExtrema),
46 GoalType.MINIMIZE,
47 new InitialGuess(new double[] { -3, 0 }),
48 new NelderMeadSimplex(new double[] { 0.2, 0.2 }),
49 new SimpleBounds(new double[] { -5, -1 },
50 new double[] { 5, 1 }));
51 }
52
53 @Test
54 public void testMinimize1() {
55 SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
56 final FourExtrema fourExtrema = new FourExtrema();
57
58 final PointValuePair optimum
59 = optimizer.optimize(new MaxEval(200),
60 new ObjectiveFunction(fourExtrema),
61 GoalType.MINIMIZE,
62 new InitialGuess(new double[] { -3, 0 }),
63 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
64 Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6);
65 Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
66 Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13);
67 Assert.assertTrue(optimizer.getEvaluations() > 120);
68 Assert.assertTrue(optimizer.getEvaluations() < 150);
69
70
71 Assert.assertTrue(optimizer.getIterations() > 0);
72 }
73
74 @Test
75 public void testMinimize2() {
76 SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
77 final FourExtrema fourExtrema = new FourExtrema();
78
79 final PointValuePair optimum
80 = optimizer.optimize(new MaxEval(200),
81 new ObjectiveFunction(fourExtrema),
82 GoalType.MINIMIZE,
83 new InitialGuess(new double[] { 1, 0 }),
84 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
85 Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
86 Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
87 Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
88 Assert.assertTrue(optimizer.getEvaluations() > 120);
89 Assert.assertTrue(optimizer.getEvaluations() < 150);
90
91
92 Assert.assertTrue(optimizer.getIterations() > 0);
93 }
94
95 @Test
96 public void testMaximize1() {
97 SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
98 final FourExtrema fourExtrema = new FourExtrema();
99
100 final PointValuePair optimum
101 = optimizer.optimize(new MaxEval(200),
102 new ObjectiveFunction(fourExtrema),
103 GoalType.MAXIMIZE,
104 new InitialGuess(new double[] { -3.0, 0.0 }),
105 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
106 Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 7e-7);
107 Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-7);
108 Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 2e-14);
109 Assert.assertTrue(optimizer.getEvaluations() > 120);
110 Assert.assertTrue(optimizer.getEvaluations() < 150);
111
112
113 Assert.assertTrue(optimizer.getIterations() > 0);
114 }
115
116 @Test
117 public void testMaximize2() {
118 SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30));
119 final FourExtrema fourExtrema = new FourExtrema();
120
121 final PointValuePair optimum
122 = optimizer.optimize(new MaxEval(200),
123 new ObjectiveFunction(fourExtrema),
124 GoalType.MAXIMIZE,
125 new InitialGuess(new double[] { 1, 0 }),
126 new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
127 Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
128 Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
129 Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 2e-12);
130 Assert.assertTrue(optimizer.getEvaluations() > 180);
131 Assert.assertTrue(optimizer.getEvaluations() < 220);
132
133
134 Assert.assertTrue(optimizer.getIterations() > 0);
135 }
136
137 @Test
138 public void testRosenbrock() {
139 MultivariateFunction rosenbrock
140 = new MultivariateFunction() {
141 public double value(double[] x) {
142 ++count;
143 double a = x[1] - x[0] * x[0];
144 double b = 1.0 - x[0];
145 return 100 * a * a + b * b;
146 }
147 };
148
149 count = 0;
150 SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
151 PointValuePair optimum
152 = optimizer.optimize(new MaxEval(100),
153 new ObjectiveFunction(rosenbrock),
154 GoalType.MINIMIZE,
155 new InitialGuess(new double[] { -1.2, 1 }),
156 new MultiDirectionalSimplex(new double[][] {
157 { -1.2, 1.0 },
158 { 0.9, 1.2 },
159 { 3.5, -2.3 } }));
160
161 Assert.assertEquals(count, optimizer.getEvaluations());
162 Assert.assertTrue(optimizer.getEvaluations() > 50);
163 Assert.assertTrue(optimizer.getEvaluations() < 100);
164 Assert.assertTrue(optimum.getValue() > 1e-2);
165 }
166
167 @Test
168 public void testPowell() {
169 MultivariateFunction powell
170 = new MultivariateFunction() {
171 public double value(double[] x) {
172 ++count;
173 double a = x[0] + 10 * x[1];
174 double b = x[2] - x[3];
175 double c = x[1] - 2 * x[2];
176 double d = x[0] - x[3];
177 return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
178 }
179 };
180
181 count = 0;
182 SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
183 PointValuePair optimum
184 = optimizer.optimize(new MaxEval(1000),
185 new ObjectiveFunction(powell),
186 GoalType.MINIMIZE,
187 new InitialGuess(new double[] { 3, -1, 0, 1 }),
188 new MultiDirectionalSimplex(4));
189 Assert.assertEquals(count, optimizer.getEvaluations());
190 Assert.assertTrue(optimizer.getEvaluations() > 800);
191 Assert.assertTrue(optimizer.getEvaluations() < 900);
192 Assert.assertTrue(optimum.getValue() > 1e-2);
193 }
194
195 @Test
196 public void testMath283() {
197
198
199 SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14);
200 final Gaussian2D function = new Gaussian2D(0, 0, 1);
201 PointValuePair estimate = optimizer.optimize(new MaxEval(1000),
202 new ObjectiveFunction(function),
203 GoalType.MAXIMIZE,
204 new InitialGuess(function.getMaximumPosition()),
205 new MultiDirectionalSimplex(2));
206 final double EPSILON = 1e-5;
207 final double expectedMaximum = function.getMaximum();
208 final double actualMaximum = estimate.getValue();
209 Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);
210
211 final double[] expectedPosition = function.getMaximumPosition();
212 final double[] actualPosition = estimate.getPoint();
213 Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
214 Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
215 }
216
217 private static class FourExtrema implements MultivariateFunction {
218
219 final double xM = -3.841947088256863675365;
220 final double yM = -1.391745200270734924416;
221 final double xP = 0.2286682237349059125691;
222 final double yP = -yM;
223 final double valueXmYm = 0.2373295333134216789769;
224 final double valueXmYp = -valueXmYm;
225 final double valueXpYm = -0.7290400707055187115322;
226 final double valueXpYp = -valueXpYm;
227
228 public double value(double[] variables) {
229 final double x = variables[0];
230 final double y = variables[1];
231 return (x == 0 || y == 0) ? 0 :
232 FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y);
233 }
234 }
235
236 private static class Gaussian2D implements MultivariateFunction {
237 private final double[] maximumPosition;
238 private final double std;
239
240 public Gaussian2D(double xOpt, double yOpt, double std) {
241 maximumPosition = new double[] { xOpt, yOpt };
242 this.std = std;
243 }
244
245 public double getMaximum() {
246 return value(maximumPosition);
247 }
248
249 public double[] getMaximumPosition() {
250 return maximumPosition.clone();
251 }
252
253 public double value(double[] point) {
254 final double x = point[0], y = point[1];
255 final double twoS2 = 2.0 * std * std;
256 return 1.0 / (twoS2 * FastMath.PI) * FastMath.exp(-(x * x + y * y) / twoS2);
257 }
258 }
259
260 private int count;
261 }