/*
* 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
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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 <a
* href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
* href="http://www.netlib.org/minpack/ex/file22">file22</a> 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><td>
* Minpack Copyright Notice (1999) University of Chicago.
* All rights reserved
* </td></tr>
* <tr><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><strong>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>
* <li><strong>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></li>
* <ol></td></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;
}
});
}
}
}