* <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];
}
};
}
}
}
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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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