| /* |
| * 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.math3.optimization.direct; |
| |
| import org.apache.commons.math3.analysis.MultivariateFunction; |
| import org.apache.commons.math3.optimization.GoalType; |
| import org.apache.commons.math3.optimization.PointValuePair; |
| import org.apache.commons.math3.optimization.SimpleValueChecker; |
| import org.apache.commons.math3.util.FastMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| @Deprecated |
| public class SimplexOptimizerMultiDirectionalTest { |
| @Test |
| public void testMinimize1() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30); |
| optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(200, fourExtrema, GoalType.MINIMIZE, new double[] { -3, 0 }); |
| Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6); |
| Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6); |
| Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13); |
| Assert.assertTrue(optimizer.getEvaluations() > 120); |
| Assert.assertTrue(optimizer.getEvaluations() < 150); |
| } |
| |
| @Test |
| public void testMinimize2() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30); |
| optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(200, fourExtrema, GoalType.MINIMIZE, new double[] { 1, 0 }); |
| Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8); |
| Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6); |
| Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12); |
| Assert.assertTrue(optimizer.getEvaluations() > 120); |
| Assert.assertTrue(optimizer.getEvaluations() < 150); |
| } |
| |
| @Test |
| public void testMaximize1() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30); |
| optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(200, fourExtrema, GoalType.MAXIMIZE, new double[] { -3.0, 0.0 }); |
| Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 7e-7); |
| Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-7); |
| Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 2e-14); |
| Assert.assertTrue(optimizer.getEvaluations() > 120); |
| Assert.assertTrue(optimizer.getEvaluations() < 150); |
| } |
| |
| @Test |
| public void testMaximize2() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30)); |
| optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(200, fourExtrema, GoalType.MAXIMIZE, new double[] { 1, 0 }); |
| Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8); |
| Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6); |
| Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 2e-12); |
| Assert.assertTrue(optimizer.getEvaluations() > 180); |
| Assert.assertTrue(optimizer.getEvaluations() < 220); |
| } |
| |
| @Test |
| public void testRosenbrock() { |
| MultivariateFunction rosenbrock = |
| new MultivariateFunction() { |
| public double value(double[] x) { |
| ++count; |
| double a = x[1] - x[0] * x[0]; |
| double b = 1.0 - x[0]; |
| return 100 * a * a + b * b; |
| } |
| }; |
| |
| count = 0; |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3); |
| optimizer.setSimplex(new MultiDirectionalSimplex(new double[][] { |
| { -1.2, 1.0 }, { 0.9, 1.2 } , { 3.5, -2.3 } |
| })); |
| PointValuePair optimum = |
| optimizer.optimize(100, rosenbrock, GoalType.MINIMIZE, new double[] { -1.2, 1 }); |
| |
| Assert.assertEquals(count, optimizer.getEvaluations()); |
| Assert.assertTrue(optimizer.getEvaluations() > 50); |
| Assert.assertTrue(optimizer.getEvaluations() < 100); |
| Assert.assertTrue(optimum.getValue() > 1e-2); |
| } |
| |
| @Test |
| public void testPowell() { |
| MultivariateFunction powell = |
| new MultivariateFunction() { |
| public double value(double[] x) { |
| ++count; |
| double a = x[0] + 10 * x[1]; |
| double b = x[2] - x[3]; |
| double c = x[1] - 2 * x[2]; |
| double d = x[0] - x[3]; |
| return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d; |
| } |
| }; |
| |
| count = 0; |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3); |
| optimizer.setSimplex(new MultiDirectionalSimplex(4)); |
| PointValuePair optimum = |
| optimizer.optimize(1000, powell, GoalType.MINIMIZE, new double[] { 3, -1, 0, 1 }); |
| Assert.assertEquals(count, optimizer.getEvaluations()); |
| Assert.assertTrue(optimizer.getEvaluations() > 800); |
| Assert.assertTrue(optimizer.getEvaluations() < 900); |
| Assert.assertTrue(optimum.getValue() > 1e-2); |
| } |
| |
| @Test |
| public void testMath283() { |
| // fails because MultiDirectional.iterateSimplex is looping forever |
| // the while(true) should be replaced with a convergence check |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14); |
| optimizer.setSimplex(new MultiDirectionalSimplex(2)); |
| final Gaussian2D function = new Gaussian2D(0, 0, 1); |
| PointValuePair estimate = optimizer.optimize(1000, function, |
| GoalType.MAXIMIZE, function.getMaximumPosition()); |
| final double EPSILON = 1e-5; |
| final double expectedMaximum = function.getMaximum(); |
| final double actualMaximum = estimate.getValue(); |
| Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON); |
| |
| final double[] expectedPosition = function.getMaximumPosition(); |
| final double[] actualPosition = estimate.getPoint(); |
| Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON ); |
| Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON ); |
| } |
| |
| private static class FourExtrema implements MultivariateFunction { |
| // The following function has 4 local extrema. |
| final double xM = -3.841947088256863675365; |
| final double yM = -1.391745200270734924416; |
| final double xP = 0.2286682237349059125691; |
| final double yP = -yM; |
| final double valueXmYm = 0.2373295333134216789769; // Local maximum. |
| final double valueXmYp = -valueXmYm; // Local minimum. |
| final double valueXpYm = -0.7290400707055187115322; // Global minimum. |
| final double valueXpYp = -valueXpYm; // Global maximum. |
| |
| public double value(double[] variables) { |
| final double x = variables[0]; |
| final double y = variables[1]; |
| return (x == 0 || y == 0) ? 0 : |
| FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y); |
| } |
| } |
| |
| private static class Gaussian2D implements MultivariateFunction { |
| private final double[] maximumPosition; |
| private final double std; |
| |
| public Gaussian2D(double xOpt, double yOpt, double std) { |
| maximumPosition = new double[] { xOpt, yOpt }; |
| this.std = std; |
| } |
| |
| public double getMaximum() { |
| return value(maximumPosition); |
| } |
| |
| public double[] getMaximumPosition() { |
| return maximumPosition.clone(); |
| } |
| |
| public double value(double[] point) { |
| final double x = point[0], y = point[1]; |
| final double twoS2 = 2.0 * std * std; |
| return 1.0 / (twoS2 * FastMath.PI) * FastMath.exp(-(x * x + y * y) / twoS2); |
| } |
| } |
| |
| private int count; |
| } |