* <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 extends TestCase { public NonLinearConjugateGradientOptimizerTest(String name) { super(name); } public void testTrivial() throws FunctionEvaluationException, OptimizationException { LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0 }); assertEquals(1.5, optimum.getPoint()[0], 1.0e-10); assertEquals(0.0, optimum.getValue(), 1.0e-10); } public void testColumnsPermutation() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0, 0 }); assertEquals(7.0, optimum.getPoint()[0], 1.0e-10); assertEquals(3.0, optimum.getPoint()[1], 1.0e-10); assertEquals(0.0, optimum.getValue(), 1.0e-10); } public void testNoDependency() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0, 0, 0, 0, 0, 0 }); for (int i = 0; i < problem.target.length; ++i) { assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10); } } public void testOneSet() throws FunctionEvaluationException, OptimizationException { LinearProblem problem = new LinearProblem(new double[][] { { 1, 0, 0 }, { -1, 1, 0 }, { 0, -1, 1 } }, new double[] { 1, 1, 1}); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0, 0, 0 }); assertEquals(1.0, optimum.getPoint()[0], 1.0e-10); assertEquals(2.0, optimum.getPoint()[1], 1.0e-10); assertEquals(3.0, optimum.getPoint()[2], 1.0e-10); } public void testTwoSets() throws FunctionEvaluationException, OptimizationException { 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}); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setPreconditioner(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; } }); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-13, 1.0e-13)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0, 0, 0, 0, 0, 0 }); assertEquals( 3.0, optimum.getPoint()[0], 1.0e-10); assertEquals( 4.0, optimum.getPoint()[1], 1.0e-10); assertEquals(-1.0, optimum.getPoint()[2], 1.0e-10); assertEquals(-2.0, optimum.getPoint()[3], 1.0e-10); assertEquals( 1.0 + epsilon, optimum.getPoint()[4], 1.0e-10); assertEquals( 1.0 - epsilon, optimum.getPoint()[5], 1.0e-10); } public void testNonInversible() throws FunctionEvaluationException, OptimizationException { LinearProblem problem = new LinearProblem(new double[][] { { 1, 2, -3 }, { 2, 1, 3 }, { -3, 0, -9 } }, new double[] { 1, 1, 1 }); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 0, 0, 0 }); assertTrue(optimum.getValue() > 0.5); } public void testIllConditioned() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-13, 1.0e-13)); BrentSolver solver = new BrentSolver(); solver.setAbsoluteAccuracy(1.0e-15); solver.setRelativeAccuracy(1.0e-15); optimizer.setLineSearchSolver(solver); RealPointValuePair optimum1 = optimizer.optimize(problem1, GoalType.MINIMIZE, new double[] { 0, 1, 2, 3 }); assertEquals(1.0, optimum1.getPoint()[0], 1.0e-5); assertEquals(1.0, optimum1.getPoint()[1], 1.0e-5); assertEquals(1.0, optimum1.getPoint()[2], 1.0e-5); assertEquals(1.0, optimum1.getPoint()[3], 1.0e-5); 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 }); RealPointValuePair optimum2 = optimizer.optimize(problem2, GoalType.MINIMIZE, new double[] { 0, 1, 2, 3 }); assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-1); assertEquals(137.0, optimum2.getPoint()[1], 1.0e-1); assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-1); assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-1); } public void testMoreEstimatedParametersSimple() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 7, 6, 5, 4 }); assertEquals(0, optimum.getValue(), 1.0e-10); } public void testMoreEstimatedParametersUnsorted() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 2, 2, 2, 2, 2, 2 }); assertEquals(0, optimum.getValue(), 1.0e-10); } public void testRedundantEquations() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 1, 1 }); assertEquals(2.0, optimum.getPoint()[0], 1.0e-8); assertEquals(1.0, optimum.getPoint()[1], 1.0e-8); } public void testInconsistentEquations() throws FunctionEvaluationException, OptimizationException { 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(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-6, 1.0e-6)); RealPointValuePair optimum = optimizer.optimize(problem, GoalType.MINIMIZE, new double[] { 1, 1 }); assertTrue(optimum.getValue() > 0.1); } public void testCircleFitting() throws FunctionEvaluationException, OptimizationException { Circle circle = new Circle(); circle.addPoint( 30.0, 68.0); circle.addPoint( 50.0, -6.0); circle.addPoint(110.0, -20.0); circle.addPoint( 35.0, 15.0); circle.addPoint( 45.0, 97.0); NonLinearConjugateGradientOptimizer optimizer = new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE); optimizer.setMaxIterations(100); optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-30, 1.0e-30)); BrentSolver solver = new BrentSolver(); solver.setAbsoluteAccuracy(1.0e-13); solver.setRelativeAccuracy(1.0e-15); optimizer.setLineSearchSolver(solver); RealPointValuePair optimum = optimizer.optimize(circle, GoalType.MINIMIZE, new double[] { 98.680, 47.345 }); Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]); assertEquals(69.960161753, circle.getRadius(center), 1.0e-8); assertEquals(96.075902096, center.x, 1.0e-8); assertEquals(48.135167894, center.y, 1.0e-8); } private static class LinearProblem implements DifferentiableMultivariateRealFunction, Serializable { private static final long serialVersionUID = 703247177355019415L; final RealMatrix factors; final double[] target; public LinearProblem(double[][] factors, double[] target) { this.factors = new BlockRealMatrix(factors); this.target = target; } private double[] gradient(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; } public double value(double[] variables) throws FunctionEvaluationException { double[] y = factors.operate(variables); double sum = 0; for (int i = 0; i < y.length; ++i) { double ri = y[i] - target[i]; sum += ri * ri; } return sum; } public MultivariateVectorialFunction gradient() { return new MultivariateVectorialFunction() { private static final long serialVersionUID = 2621997811350805819L; public double[] value(double[] point) { return gradient(point); } }; } public MultivariateRealFunction partialDerivative(final int k) { return new MultivariateRealFunction() { private static final long serialVersionUID = -6186178619133562011L; public double value(double[] point) { return gradient(point)[k]; } }; } } private static class Circle implements DifferentiableMultivariateRealFunction, Serializable { private static final long serialVersionUID = -4711170319243817874L; private ArrayList<Point2D.Double> points; public Circle() { points = new ArrayList<Point2D.Double>(); } public void addPoint(double px, double py) { points.add(new Point2D.Double(px, py)); } public double getRadius(Point2D.Double center) { double r = 0; for (Point2D.Double point : points) { r += point.distance(center); } return r / points.size(); } private double[] gradient(double[] point) { // optimal radius Point2D.Double center = new Point2D.Double(point[0], point[1]); double radius = getRadius(center); // gradient of the sum of squared residuals double dJdX = 0; double dJdY = 0; for (Point2D.Double pk : points) { double dk = pk.distance(center); dJdX += (center.x - pk.x) * (dk - radius) / dk; dJdY += (center.y - pk.y) * (dk - radius) / dk; } dJdX *= 2; dJdY *= 2; return new double[] { dJdX, dJdY }; } public double value(double[] variables) throws IllegalArgumentException, FunctionEvaluationException { Point2D.Double center = new Point2D.Double(variables[0], variables[1]); double radius = getRadius(center); double sum = 0; for (Point2D.Double point : points) { double di = point.distance(center) - radius; sum += di * di; } return sum; } public MultivariateVectorialFunction gradient() { return new MultivariateVectorialFunction() { private static final long serialVersionUID = 3174909643301201710L; public double[] value(double[] point) { return gradient(point); } }; } public MultivariateRealFunction partialDerivative(final int k) { return new MultivariateRealFunction() { private static final long serialVersionUID = 3073956364104833888L; public double value(double[] point) { return gradient(point)[k]; } }; } } }

	Commons Math example source code file (NonLinearConjugateGradientOptimizerTest.java) This example Commons Math source code file (NonLinearConjugateGradientOptimizerTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM. Java - Commons Math tags/keywords awt, brentsolver, circle, functionevaluationexception, functionevaluationexception, geometry, io, linearproblem, linearproblem, multivariaterealfunction, multivariatevectorialfunction, nonlinearconjugategradientoptimizer, nonlinearconjugategradientoptimizer, nonlinearconjugategradientoptimizertest, optimizationexception, realpointvaluepair, realpointvaluepair, util The Commons Math NonLinearConjugateGradientOptimizerTest.java 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.math.optimization.general; import java.awt.geom.Point2D; import java.io.Serializable; import java.util.ArrayList; import junit.framework.TestCase; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction; import org.apache.commons.math.analysis.MultivariateRealFunction; import org.apache.commons.math.analysis.MultivariateVectorialFunction; import org.apache.commons.math.analysis.solvers.BrentSolver; import org.apache.commons.math.linear.BlockRealMatrix; import org.apache.commons.math.linear.RealMatrix; import org.apache.commons.math.optimization.GoalType; import org.apache.commons.math.optimization.OptimizationException; import org.apache.commons.math.optimization.RealPointValuePair; import org.apache.commons.math.optimization.SimpleScalarValueChecker; /** * <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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