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Java example source code file (SimplexOptimizerNelderMeadTest.java)

This example Java source code file (SimplexOptimizerNelderMeadTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

array2drowrealmatrix, deprecated, fourextrema, global, leastsquaresconverter, local, multivariatefunction, multivariatevectorfunction, neldermeadsimplex, pointvaluepair, powell, rosenbrock, simplexoptimizer, test

The SimplexOptimizerNelderMeadTest.java Java example 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.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;
        }
    }
}

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