| /* |
| * 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.exception.TooManyEvaluationsException; |
| import org.apache.commons.math3.analysis.MultivariateFunction; |
| import org.apache.commons.math3.analysis.MultivariateVectorFunction; |
| import org.apache.commons.math3.linear.Array2DRowRealMatrix; |
| import org.apache.commons.math3.linear.RealMatrix; |
| import org.apache.commons.math3.optimization.GoalType; |
| import org.apache.commons.math3.optimization.LeastSquaresConverter; |
| import org.apache.commons.math3.optimization.PointValuePair; |
| import org.apache.commons.math3.util.FastMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| @Deprecated |
| public class SimplexOptimizerNelderMeadTest { |
| @Test |
| public void testMinimize1() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30); |
| optimizer.setSimplex(new NelderMeadSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(100, fourExtrema, GoalType.MINIMIZE, new double[] { -3, 0 }); |
| Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 2e-7); |
| Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 2e-5); |
| Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 6e-12); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 90); |
| } |
| |
| @Test |
| public void testMinimize2() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30); |
| optimizer.setSimplex(new NelderMeadSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(100, fourExtrema, GoalType.MINIMIZE, new double[] { 1, 0 }); |
| Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 5e-6); |
| Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 6e-6); |
| Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 1e-11); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 90); |
| } |
| |
| @Test |
| public void testMaximize1() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30); |
| optimizer.setSimplex(new NelderMeadSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(100, fourExtrema, GoalType.MAXIMIZE, new double[] { -3, 0 }); |
| Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 1e-5); |
| Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6); |
| Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 3e-12); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 90); |
| } |
| |
| @Test |
| public void testMaximize2() { |
| SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30); |
| optimizer.setSimplex(new NelderMeadSimplex(new double[] { 0.2, 0.2 })); |
| final FourExtrema fourExtrema = new FourExtrema(); |
| |
| final PointValuePair optimum |
| = optimizer.optimize(100, fourExtrema, GoalType.MAXIMIZE, new double[] { 1, 0 }); |
| Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 4e-6); |
| Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 5e-6); |
| Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 7e-12); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 90); |
| } |
| |
| @Test |
| public void testRosenbrock() { |
| |
| Rosenbrock rosenbrock = new Rosenbrock(); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3); |
| optimizer.setSimplex(new NelderMeadSimplex(new double[][] { |
| { -1.2, 1 }, { 0.9, 1.2 } , { 3.5, -2.3 } |
| })); |
| PointValuePair optimum = |
| optimizer.optimize(100, rosenbrock, GoalType.MINIMIZE, new double[] { -1.2, 1 }); |
| |
| Assert.assertEquals(rosenbrock.getCount(), optimizer.getEvaluations()); |
| Assert.assertTrue(optimizer.getEvaluations() > 40); |
| Assert.assertTrue(optimizer.getEvaluations() < 50); |
| Assert.assertTrue(optimum.getValue() < 8e-4); |
| } |
| |
| @Test |
| public void testPowell() { |
| |
| Powell powell = new Powell(); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3); |
| optimizer.setSimplex(new NelderMeadSimplex(4)); |
| PointValuePair optimum = |
| optimizer.optimize(200, powell, GoalType.MINIMIZE, new double[] { 3, -1, 0, 1 }); |
| Assert.assertEquals(powell.getCount(), optimizer.getEvaluations()); |
| Assert.assertTrue(optimizer.getEvaluations() > 110); |
| Assert.assertTrue(optimizer.getEvaluations() < 130); |
| Assert.assertTrue(optimum.getValue() < 2e-3); |
| } |
| |
| @Test |
| public void testLeastSquares1() { |
| |
| final RealMatrix factors = |
| new Array2DRowRealMatrix(new double[][] { |
| { 1, 0 }, |
| { 0, 1 } |
| }, false); |
| LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() { |
| public double[] value(double[] variables) { |
| return factors.operate(variables); |
| } |
| }, new double[] { 2.0, -3.0 }); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6); |
| optimizer.setSimplex(new NelderMeadSimplex(2)); |
| PointValuePair optimum = |
| optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 }); |
| Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5); |
| Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 80); |
| Assert.assertTrue(optimum.getValue() < 1.0e-6); |
| } |
| |
| @Test |
| public void testLeastSquares2() { |
| |
| final RealMatrix factors = |
| new Array2DRowRealMatrix(new double[][] { |
| { 1, 0 }, |
| { 0, 1 } |
| }, false); |
| LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() { |
| public double[] value(double[] variables) { |
| return factors.operate(variables); |
| } |
| }, new double[] { 2, -3 }, new double[] { 10, 0.1 }); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6); |
| optimizer.setSimplex(new NelderMeadSimplex(2)); |
| PointValuePair optimum = |
| optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 }); |
| Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5); |
| Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 80); |
| Assert.assertTrue(optimum.getValue() < 1e-6); |
| } |
| |
| @Test |
| public void testLeastSquares3() { |
| |
| final RealMatrix factors = |
| new Array2DRowRealMatrix(new double[][] { |
| { 1, 0 }, |
| { 0, 1 } |
| }, false); |
| LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() { |
| public double[] value(double[] variables) { |
| return factors.operate(variables); |
| } |
| }, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] { |
| { 1, 1.2 }, { 1.2, 2 } |
| })); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6); |
| optimizer.setSimplex(new NelderMeadSimplex(2)); |
| PointValuePair optimum = |
| optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 }); |
| Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3); |
| Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4); |
| Assert.assertTrue(optimizer.getEvaluations() > 60); |
| Assert.assertTrue(optimizer.getEvaluations() < 80); |
| Assert.assertTrue(optimum.getValue() < 1e-6); |
| } |
| |
| @Test(expected = TooManyEvaluationsException.class) |
| public void testMaxIterations() { |
| Powell powell = new Powell(); |
| SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3); |
| optimizer.setSimplex(new NelderMeadSimplex(4)); |
| optimizer.optimize(20, powell, GoalType.MINIMIZE, new double[] { 3, -1, 0, 1 }); |
| } |
| |
| 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 Rosenbrock implements MultivariateFunction { |
| private int count; |
| |
| public Rosenbrock() { |
| count = 0; |
| } |
| |
| 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; |
| } |
| |
| public int getCount() { |
| return count; |
| } |
| } |
| |
| private static class Powell implements MultivariateFunction { |
| private int count; |
| |
| public Powell() { |
| count = 0; |
| } |
| |
| 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; |
| } |
| |
| public int getCount() { |
| return count; |
| } |
| } |
| } |