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* <tr> * </table> * * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests) * @author Burton S. Garbow (original fortran minpack tests) * @author Kenneth E. Hillstrom (original fortran minpack tests) * @author Jorge J. More (original fortran minpack tests) * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation) */ public class NonLinearConjugateGradientOptimizerTest { @Test(expected=MathUnsupportedOperationException.class) public void testBoundsUnsupported() { LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0 }), new SimpleBounds(new double[] { -1 }, new double[] { 1 })); } @Test public void testTrivial() { LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0 })); Assert.assertEquals(1.5, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(0.0, optimum.getValue(), 1.0e-10); // Check that the number of iterations is updated (MATH-949). Assert.assertTrue(optimizer.getIterations() > 0); } @Test public void testColumnsPermutation() { LinearProblem problem = new LinearProblem(new double[][] { { 1.0, -1.0 }, { 0.0, 2.0 }, { 1.0, -2.0 } }, new double[] { 4.0, 6.0, 1.0 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 0 })); Assert.assertEquals(7.0, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(3.0, optimum.getPoint()[1], 1.0e-10); Assert.assertEquals(0.0, optimum.getValue(), 1.0e-10); } @Test public void testNoDependency() { LinearProblem problem = new LinearProblem(new double[][] { { 2, 0, 0, 0, 0, 0 }, { 0, 2, 0, 0, 0, 0 }, { 0, 0, 2, 0, 0, 0 }, { 0, 0, 0, 2, 0, 0 }, { 0, 0, 0, 0, 2, 0 }, { 0, 0, 0, 0, 0, 2 } }, new double[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 0, 0, 0, 0, 0 })); for (int i = 0; i < problem.target.length; ++i) { Assert.assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10); } } @Test public void testOneSet() { LinearProblem problem = new LinearProblem(new double[][] { { 1, 0, 0 }, { -1, 1, 0 }, { 0, -1, 1 } }, new double[] { 1, 1, 1}); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 0, 0 })); Assert.assertEquals(1.0, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(2.0, optimum.getPoint()[1], 1.0e-10); Assert.assertEquals(3.0, optimum.getPoint()[2], 1.0e-10); } @Test public void testTwoSets() { final double epsilon = 1.0e-7; LinearProblem problem = new LinearProblem(new double[][] { { 2, 1, 0, 4, 0, 0 }, { -4, -2, 3, -7, 0, 0 }, { 4, 1, -2, 8, 0, 0 }, { 0, -3, -12, -1, 0, 0 }, { 0, 0, 0, 0, epsilon, 1 }, { 0, 0, 0, 0, 1, 1 } }, new double[] { 2, -9, 2, 2, 1 + epsilon * epsilon, 2}); final Preconditioner preconditioner = new Preconditioner() { public double[] precondition(double[] point, double[] r) { double[] d = r.clone(); d[0] /= 72.0; d[1] /= 30.0; d[2] /= 314.0; d[3] /= 260.0; d[4] /= 2 * (1 + epsilon * epsilon); d[5] /= 4.0; return d; } }; NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-13, 1e-13), 1e-7, 1e-7, 1, preconditioner); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 0, 0, 0, 0, 0 })); final double[] result = optimum.getPoint(); final double[] expected = {3, 4, -1, -2, 1 + epsilon, 1 - epsilon}; Assert.assertEquals(expected[0], result[0], 1.0e-7); Assert.assertEquals(expected[1], result[1], 1.0e-7); Assert.assertEquals(expected[2], result[2], 1.0e-9); Assert.assertEquals(expected[3], result[3], 1.0e-8); Assert.assertEquals(expected[4] + epsilon, result[4], 1.0e-6); Assert.assertEquals(expected[5] - epsilon, result[5], 1.0e-6); } @Test public void testNonInversible() { LinearProblem problem = new LinearProblem(new double[][] { { 1, 2, -3 }, { 2, 1, 3 }, { -3, 0, -9 } }, new double[] { 1, 1, 1 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 0, 0 })); Assert.assertTrue(optimum.getValue() > 0.5); } @Test public void testIllConditioned() { LinearProblem problem1 = new LinearProblem(new double[][] { { 10.0, 7.0, 8.0, 7.0 }, { 7.0, 5.0, 6.0, 5.0 }, { 8.0, 6.0, 10.0, 9.0 }, { 7.0, 5.0, 9.0, 10.0 } }, new double[] { 32, 23, 33, 31 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-13, 1e-13), 1e-15, 1e-15, 1); PointValuePair optimum1 = optimizer.optimize(new MaxEval(200), problem1.getObjectiveFunction(), problem1.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 1, 2, 3 })); Assert.assertEquals(1.0, optimum1.getPoint()[0], 1.0e-4); Assert.assertEquals(1.0, optimum1.getPoint()[1], 1.0e-3); Assert.assertEquals(1.0, optimum1.getPoint()[2], 1.0e-4); Assert.assertEquals(1.0, optimum1.getPoint()[3], 1.0e-4); LinearProblem problem2 = new LinearProblem(new double[][] { { 10.00, 7.00, 8.10, 7.20 }, { 7.08, 5.04, 6.00, 5.00 }, { 8.00, 5.98, 9.89, 9.00 }, { 6.99, 4.99, 9.00, 9.98 } }, new double[] { 32, 23, 33, 31 }); PointValuePair optimum2 = optimizer.optimize(new MaxEval(200), problem2.getObjectiveFunction(), problem2.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 0, 1, 2, 3 })); final double[] result2 = optimum2.getPoint(); final double[] expected2 = {-81, 137, -34, 22}; Assert.assertEquals(expected2[0], result2[0], 2); Assert.assertEquals(expected2[1], result2[1], 4); Assert.assertEquals(expected2[2], result2[2], 1); Assert.assertEquals(expected2[3], result2[3], 1); } @Test public void testMoreEstimatedParametersSimple() { LinearProblem problem = new LinearProblem(new double[][] { { 3.0, 2.0, 0.0, 0.0 }, { 0.0, 1.0, -1.0, 1.0 }, { 2.0, 0.0, 1.0, 0.0 } }, new double[] { 7.0, 3.0, 5.0 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 7, 6, 5, 4 })); Assert.assertEquals(0, optimum.getValue(), 1.0e-10); } @Test public void testMoreEstimatedParametersUnsorted() { LinearProblem problem = new LinearProblem(new double[][] { { 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, { 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 }, { 0.0, 0.0, 0.0, 0.0, 1.0, -1.0 }, { 0.0, 0.0, -1.0, 1.0, 0.0, 1.0 }, { 0.0, 0.0, 0.0, -1.0, 1.0, 0.0 } }, new double[] { 3.0, 12.0, -1.0, 7.0, 1.0 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 2, 2, 2, 2, 2, 2 })); Assert.assertEquals(0, optimum.getValue(), 1.0e-10); } @Test public void testRedundantEquations() { LinearProblem problem = new LinearProblem(new double[][] { { 1.0, 1.0 }, { 1.0, -1.0 }, { 1.0, 3.0 } }, new double[] { 3.0, 1.0, 5.0 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 1, 1 })); Assert.assertEquals(2.0, optimum.getPoint()[0], 1.0e-8); Assert.assertEquals(1.0, optimum.getPoint()[1], 1.0e-8); } @Test public void testInconsistentEquations() { LinearProblem problem = new LinearProblem(new double[][] { { 1.0, 1.0 }, { 1.0, -1.0 }, { 1.0, 3.0 } }, new double[] { 3.0, 1.0, 4.0 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-6, 1e-6), 1e-3, 1e-3, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 1, 1 })); Assert.assertTrue(optimum.getValue() > 0.1); } @Test public void testCircleFitting() { CircleScalar problem = new CircleScalar(); problem.addPoint( 30.0, 68.0); problem.addPoint( 50.0, -6.0); problem.addPoint(110.0, -20.0); problem.addPoint( 35.0, 15.0); problem.addPoint( 45.0, 97.0); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE, new SimpleValueChecker(1e-30, 1e-30), 1e-15, 1e-13, 1); PointValuePair optimum = optimizer.optimize(new MaxEval(100), problem.getObjectiveFunction(), problem.getObjectiveFunctionGradient(), GoalType.MINIMIZE, new InitialGuess(new double[] { 98.680, 47.345 })); Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]); Assert.assertEquals(69.960161753, problem.getRadius(center), 1.0e-8); Assert.assertEquals(96.075902096, center.getX(), 1.0e-7); Assert.assertEquals(48.135167894, center.getY(), 1.0e-6); } private static class LinearProblem { final RealMatrix factors; final double[] target; public LinearProblem(double[][] factors, double[] target) { this.factors = new BlockRealMatrix(factors); this.target = target; } public ObjectiveFunction getObjectiveFunction() { return new ObjectiveFunction(new MultivariateFunction() { public double value(double[] point) { double[] y = factors.operate(point); double sum = 0; for (int i = 0; i < y.length; ++i) { double ri = y[i] - target[i]; sum += ri * ri; } return sum; } }); } public ObjectiveFunctionGradient getObjectiveFunctionGradient() { return new ObjectiveFunctionGradient(new MultivariateVectorFunction() { public double[] value(double[] point) { double[] r = factors.operate(point); for (int i = 0; i < r.length; ++i) { r[i] -= target[i]; } double[] p = factors.transpose().operate(r); for (int i = 0; i < p.length; ++i) { p[i] *= 2; } return p; } }); } } }

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Java - Java tags/keywords

blockrealmatrix, circlescalar, initialguess, linearproblem, maxeval, multivariatefunction, multivariatevectorfunction, nonlinearconjugategradientoptimizer, objectivefunctiongradient, pointvaluepair, preconditioner, simplebounds, simplevaluechecker, test

The NonLinearConjugateGradientOptimizerTest.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.optim.nonlinear.scalar.gradient;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.optim.PointValuePair;
import org.apache.commons.math3.optim.SimpleValueChecker;
import org.apache.commons.math3.optim.InitialGuess;
import org.apache.commons.math3.optim.MaxEval;
import org.apache.commons.math3.optim.SimpleBounds;
import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunctionGradient;
import org.junit.Assert;
import org.junit.Test;

/**
 * <p>Some of the unit tests are re-implementations of the MINPACK  and  test files.
 * The redistribution policy for MINPACK is available <a
 * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
 * convenience, it is reproduced below.</p>
 *
 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 * <tr>
* Minpack Copyright Notice (1999) University of Chicago. * All rights reserved * </td>
* Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * <ol> * <li>Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer.</li> * <li>Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution.</li> * <li>The end-user documentation included with the redistribution, if any, * must include the following acknowledgment: * <code>This product includes software developed by the University of * Chicago, as Operator of Argonne National Laboratory.</code> * Alternately, this acknowledgment may appear in the software itself, * if and wherever such third-party acknowledgments normally appear.</li> * <li>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL * BE CORRECTED.</strong> * <li>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong> * <ol>


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