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Commons Math example source code file (LevenbergMarquardtOptimizerTest.java)
This example Commons Math source code file (LevenbergMarquardtOptimizerTest.java) is included in the DevDaily.com
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The Commons Math LevenbergMarquardtOptimizerTest.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 java.util.Arrays;
import java.util.List;
import junit.framework.TestCase;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction;
import org.apache.commons.math.analysis.MultivariateMatrixFunction;
import org.apache.commons.math.linear.BlockRealMatrix;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.SimpleVectorialValueChecker;
import org.apache.commons.math.optimization.VectorialPointValuePair;
/**
* <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> | |
* <tr>
* 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> |
* </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 LevenbergMarquardtOptimizerTest
extends TestCase {
public LevenbergMarquardtOptimizerTest(String name) {
super(name);
}
public void testTrivial() throws FunctionEvaluationException, OptimizationException {
LinearProblem problem =
new LinearProblem(new double[][] { { 2 } }, new double[] { 3 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1 }, new double[] { 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
try {
optimizer.guessParametersErrors();
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
assertEquals(1.5, optimum.getPoint()[0], 1.0e-10);
assertEquals(3.0, optimum.getValue()[0], 1.0e-10);
}
public void testQRColumnsPermutation() 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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(7.0, optimum.getPoint()[0], 1.0e-10);
assertEquals(3.0, optimum.getPoint()[1], 1.0e-10);
assertEquals(4.0, optimum.getValue()[0], 1.0e-10);
assertEquals(6.0, optimum.getValue()[1], 1.0e-10);
assertEquals(1.0, optimum.getValue()[2], 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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 },
new double[] { 0, 0, 0, 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
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});
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
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 {
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});
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 },
new double[] { 0, 0, 0, 0, 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 });
assertTrue(Math.sqrt(problem.target.length) * optimizer.getRMS() > 0.6);
try {
optimizer.getCovariances();
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
}
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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum1 =
optimizer.optimize(problem1, problem1.target, new double[] { 1, 1, 1, 1 },
new double[] { 0, 1, 2, 3 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[0], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[1], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[2], 1.0e-10);
assertEquals(1.0, optimum1.getPoint()[3], 1.0e-10);
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 });
VectorialPointValuePair optimum2 =
optimizer.optimize(problem2, problem2.target, new double[] { 1, 1, 1, 1 },
new double[] { 0, 1, 2, 3 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-8);
assertEquals(137.0, optimum2.getPoint()[1], 1.0e-8);
assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-8);
assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-8);
}
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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 },
new double[] { 7, 6, 5, 4 });
assertEquals(0, optimizer.getRMS(), 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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1 },
new double[] { 2, 2, 2, 2, 2, 2 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(3.0, optimum.getPointRef()[2], 1.0e-10);
assertEquals(4.0, optimum.getPointRef()[3], 1.0e-10);
assertEquals(5.0, optimum.getPointRef()[4], 1.0e-10);
assertEquals(6.0, optimum.getPointRef()[5], 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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 },
new double[] { 1, 1 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(2.0, optimum.getPointRef()[0], 1.0e-10);
assertEquals(1.0, optimum.getPointRef()[1], 1.0e-10);
}
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 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 });
assertTrue(optimizer.getRMS() > 0.1);
}
public void testInconsistentSizes() throws FunctionEvaluationException, OptimizationException {
LinearProblem problem =
new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 });
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 });
assertEquals(0, optimizer.getRMS(), 1.0e-10);
assertEquals(-1, optimum.getPoint()[0], 1.0e-10);
assertEquals(+1, optimum.getPoint()[1], 1.0e-10);
try {
optimizer.optimize(problem, problem.target,
new double[] { 1 },
new double[] { 0, 0 });
fail("an exception should have been thrown");
} catch (OptimizationException oe) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
try {
optimizer.optimize(problem, new double[] { 1 },
new double[] { 1 },
new double[] { 0, 0 });
fail("an exception should have been thrown");
} catch (FunctionEvaluationException oe) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
}
public void testControlParameters() {
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);
checkEstimate(circle, 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false);
checkEstimate(circle, 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true);
checkEstimate(circle, 0.1, 5, 1.0e-15, 1.0e-16, 1.0e-10, true);
circle.addPoint(300, -300);
checkEstimate(circle, 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true);
}
private void checkEstimate(DifferentiableMultivariateVectorialFunction problem,
double initialStepBoundFactor, int maxCostEval,
double costRelativeTolerance, double parRelativeTolerance,
double orthoTolerance, boolean shouldFail) {
try {
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.setInitialStepBoundFactor(initialStepBoundFactor);
optimizer.setMaxIterations(maxCostEval);
optimizer.setCostRelativeTolerance(costRelativeTolerance);
optimizer.setParRelativeTolerance(parRelativeTolerance);
optimizer.setOrthoTolerance(orthoTolerance);
optimizer.optimize(problem, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 },
new double[] { 98.680, 47.345 });
assertTrue(! shouldFail);
} catch (OptimizationException ee) {
assertTrue(shouldFail);
} catch (FunctionEvaluationException ee) {
assertTrue(shouldFail);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
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);
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
VectorialPointValuePair optimum =
optimizer.optimize(circle, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 },
new double[] { 98.680, 47.345 });
assertTrue(optimizer.getEvaluations() < 10);
assertTrue(optimizer.getJacobianEvaluations() < 10);
double rms = optimizer.getRMS();
assertEquals(1.768262623567235, Math.sqrt(circle.getN()) * rms, 1.0e-10);
Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]);
assertEquals(69.96016176931406, circle.getRadius(center), 1.0e-10);
assertEquals(96.07590211815305, center.x, 1.0e-10);
assertEquals(48.13516790438953, center.y, 1.0e-10);
double[][] cov = optimizer.getCovariances();
assertEquals(1.839, cov[0][0], 0.001);
assertEquals(0.731, cov[0][1], 0.001);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.786, cov[1][1], 0.001);
double[] errors = optimizer.guessParametersErrors();
assertEquals(1.384, errors[0], 0.001);
assertEquals(0.905, errors[1], 0.001);
// add perfect measurements and check errors are reduced
double r = circle.getRadius(center);
for (double d= 0; d < 2 * Math.PI; d += 0.01) {
circle.addPoint(center.x + r * Math.cos(d), center.y + r * Math.sin(d));
}
double[] target = new double[circle.getN()];
Arrays.fill(target, 0.0);
double[] weights = new double[circle.getN()];
Arrays.fill(weights, 2.0);
optimizer.optimize(circle, target, weights, new double[] { 98.680, 47.345 });
cov = optimizer.getCovariances();
assertEquals(0.0016, cov[0][0], 0.001);
assertEquals(3.2e-7, cov[0][1], 1.0e-9);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.0016, cov[1][1], 0.001);
errors = optimizer.guessParametersErrors();
assertEquals(0.002, errors[0], 0.001);
assertEquals(0.002, errors[1], 0.001);
}
public void testCircleFittingBadInit() throws FunctionEvaluationException, OptimizationException {
Circle circle = new Circle();
double[][] points = new double[][] {
{-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724},
{-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619},
{-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832},
{-0.075133, 0.483271}, {-0.007759, 0.452680}, { 0.060071, 0.410235},
{ 0.103037, 0.341076}, { 0.118438, 0.273884}, { 0.131293, 0.192201},
{ 0.115869, 0.129797}, { 0.072223, 0.058396}, { 0.022884, 0.000718},
{-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
{-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526},
{-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398},
{-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513},
{-0.135352, 0.478186}, {-0.061221, 0.483371}, { 0.003711, 0.422737},
{ 0.065054, 0.375830}, { 0.108108, 0.297099}, { 0.123882, 0.222850},
{ 0.117729, 0.134382}, { 0.085195, 0.056820}, { 0.029800, -0.019138},
{-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
{-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926},
{-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068},
{-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119},
{-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560},
{ 0.001375, 0.434937}, { 0.082787, 0.385806}, { 0.115490, 0.323807},
{ 0.141089, 0.223450}, { 0.138693, 0.131703}, { 0.126415, 0.049174},
{ 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
{-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
{-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597},
{-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428},
{-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380},
{-0.071754, 0.516264}, { 0.015942, 0.472802}, { 0.076608, 0.419077},
{ 0.127673, 0.330264}, { 0.159951, 0.262150}, { 0.153530, 0.172681},
{ 0.140653, 0.089229}, { 0.078666, 0.024981}, { 0.023807, -0.037022},
{-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
};
double[] target = new double[points.length];
Arrays.fill(target, 0.0);
double[] weights = new double[points.length];
Arrays.fill(weights, 2.0);
for (int i = 0; i < points.length; ++i) {
circle.addPoint(points[i][0], points[i][1]);
}
LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-10, 1.0e-10));
VectorialPointValuePair optimum =
optimizer.optimize(circle, target, weights, new double[] { -12, -12 });
Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]);
assertTrue(optimizer.getEvaluations() < 25);
assertTrue(optimizer.getJacobianEvaluations() < 20);
assertEquals( 0.043, optimizer.getRMS(), 1.0e-3);
assertEquals( 0.292235, circle.getRadius(center), 1.0e-6);
assertEquals(-0.151738, center.x, 1.0e-6);
assertEquals( 0.2075001, center.y, 1.0e-6);
}
public void testMath199() throws FunctionEvaluationException {
try {
QuadraticProblem problem = new QuadraticProblem();
problem.addPoint (0, -3.182591015485607);
problem.addPoint (1, -2.5581184967730577);
problem.addPoint (2, -2.1488478161387325);
problem.addPoint (3, -1.9122489313410047);
problem.addPoint (4, 1.7785661310051026);
new LevenbergMarquardtOptimizer().optimize(problem,
new double[] { 0, 0, 0, 0, 0 },
new double[] { 0.0, 4.4e-323, 1.0, 4.4e-323, 0.0 },
new double[] { 0, 0, 0 });
fail("an exception should have been thrown");
} catch (OptimizationException ee) {
// expected behavior
}
}
private static class LinearProblem implements DifferentiableMultivariateVectorialFunction, 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;
}
public double[] value(double[] variables) {
return factors.operate(variables);
}
public MultivariateMatrixFunction jacobian() {
return new MultivariateMatrixFunction() {
private static final long serialVersionUID = 556396458721526234L;
public double[][] value(double[] point) {
return factors.getData();
}
};
}
}
private static class Circle implements DifferentiableMultivariateVectorialFunction, 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 int getN() {
return points.size();
}
public double getRadius(Point2D.Double center) {
double r = 0;
for (Point2D.Double point : points) {
r += point.distance(center);
}
return r / points.size();
}
private double[][] jacobian(double[] point) {
int n = points.size();
Point2D.Double center = new Point2D.Double(point[0], point[1]);
// gradient of the optimal radius
double dRdX = 0;
double dRdY = 0;
for (Point2D.Double pk : points) {
double dk = pk.distance(center);
dRdX += (center.x - pk.x) / dk;
dRdY += (center.y - pk.y) / dk;
}
dRdX /= n;
dRdY /= n;
// jacobian of the radius residuals
double[][] jacobian = new double[n][2];
for (int i = 0; i < n; ++i) {
Point2D.Double pi = points.get(i);
double di = pi.distance(center);
jacobian[i][0] = (center.x - pi.x) / di - dRdX;
jacobian[i][1] = (center.y - pi.y) / di - dRdY;
}
return jacobian;
}
public double[] value(double[] variables)
throws FunctionEvaluationException, IllegalArgumentException {
Point2D.Double center = new Point2D.Double(variables[0], variables[1]);
double radius = getRadius(center);
double[] residuals = new double[points.size()];
for (int i = 0; i < residuals.length; ++i) {
residuals[i] = points.get(i).distance(center) - radius;
}
return residuals;
}
public MultivariateMatrixFunction jacobian() {
return new MultivariateMatrixFunction() {
private static final long serialVersionUID = -4340046230875165095L;
public double[][] value(double[] point) {
return jacobian(point);
}
};
}
}
private static class QuadraticProblem implements DifferentiableMultivariateVectorialFunction, Serializable {
private static final long serialVersionUID = 7072187082052755854L;
private List<Double> x;
private List<Double> y;
public QuadraticProblem() {
x = new ArrayList<Double>();
y = new ArrayList<Double>();
}
public void addPoint(double x, double y) {
this.x.add(x);
this.y.add(y);
}
private double[][] jacobian(double[] variables) {
double[][] jacobian = new double[x.size()][3];
for (int i = 0; i < jacobian.length; ++i) {
jacobian[i][0] = x.get(i) * x.get(i);
jacobian[i][1] = x.get(i);
jacobian[i][2] = 1.0;
}
return jacobian;
}
public double[] value(double[] variables) {
double[] values = new double[x.size()];
for (int i = 0; i < values.length; ++i) {
values[i] = (variables[0] * x.get(i) + variables[1]) * x.get(i) + variables[2];
}
return values;
}
public MultivariateMatrixFunction jacobian() {
return new MultivariateMatrixFunction() {
private static final long serialVersionUID = -8673650298627399464L;
public double[][] value(double[] point) {
return jacobian(point);
}
};
}
}
}
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