/*
* 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
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package org.apache.commons.math.estimation;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Set;
import org.apache.commons.math.estimation.EstimatedParameter;
import org.apache.commons.math.estimation.EstimationException;
import org.apache.commons.math.estimation.EstimationProblem;
import org.apache.commons.math.estimation.LevenbergMarquardtEstimator;
import org.apache.commons.math.estimation.WeightedMeasurement;
import junit.framework.*;
/**
* <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 LevenbergMarquardtEstimatorTest
extends TestCase {
public LevenbergMarquardtEstimatorTest(String name) {
super(name);
}
public void testTrivial() throws EstimationException {
LinearProblem problem =
new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] {2},
new EstimatedParameter[] {
new EstimatedParameter("p0", 0)
}, 3.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
try {
estimator.guessParametersErrors(problem);
fail("an exception should have been thrown");
} catch (EstimationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
assertEquals(1.5,
problem.getUnboundParameters()[0].getEstimate(),
1.0e-10);
}
public void testQRColumnsPermutation() throws EstimationException {
EstimatedParameter[] x = {
new EstimatedParameter("p0", 0), new EstimatedParameter("p1", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { x[0], x[1] },
4.0),
new LinearMeasurement(new double[] { 2.0 },
new EstimatedParameter[] { x[1] },
6.0),
new LinearMeasurement(new double[] { 1.0, -2.0 },
new EstimatedParameter[] { x[0], x[1] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(7.0, x[0].getEstimate(), 1.0e-10);
assertEquals(3.0, x[1].getEstimate(), 1.0e-10);
}
public void testNoDependency() throws EstimationException {
EstimatedParameter[] p = new EstimatedParameter[] {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0),
new EstimatedParameter("p3", 0),
new EstimatedParameter("p4", 0),
new EstimatedParameter("p5", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[0] }, 0.0),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[1] }, 1.1),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[2] }, 2.2),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[3] }, 3.3),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[4] }, 4.4),
new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[5] }, 5.5)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
for (int i = 0; i < p.length; ++i) {
assertEquals(0.55 * i, p[i].getEstimate(), 1.0e-10);
}
}
public void testOneSet() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0 },
new EstimatedParameter[] { p[0] },
1.0),
new LinearMeasurement(new double[] { -1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { -1.0, 1.0 },
new EstimatedParameter[] { p[1], p[2] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
assertEquals(2.0, p[1].getEstimate(), 1.0e-10);
assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
}
public void testTwoSets() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 1),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 3),
new EstimatedParameter("p4", 4),
new EstimatedParameter("p5", 5)
};
double epsilon = 1.0e-7;
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
// 4 elements sub-problem
new LinearMeasurement(new double[] { 2.0, 1.0, 4.0 },
new EstimatedParameter[] { p[0], p[1], p[3] },
2.0),
new LinearMeasurement(new double[] { -4.0, -2.0, 3.0, -7.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
-9.0),
new LinearMeasurement(new double[] { 4.0, 1.0, -2.0, 8.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
2.0),
new LinearMeasurement(new double[] { -3.0, -12.0, -1.0 },
new EstimatedParameter[] { p[1], p[2], p[3] },
2.0),
// 2 elements sub-problem
new LinearMeasurement(new double[] { epsilon, 1.0 },
new EstimatedParameter[] { p[4], p[5] },
1.0 + epsilon * epsilon),
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[4], p[5] },
2.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals( 3.0, p[0].getEstimate(), 1.0e-10);
assertEquals( 4.0, p[1].getEstimate(), 1.0e-10);
assertEquals(-1.0, p[2].getEstimate(), 1.0e-10);
assertEquals(-2.0, p[3].getEstimate(), 1.0e-10);
assertEquals( 1.0 + epsilon, p[4].getEstimate(), 1.0e-10);
assertEquals( 1.0 - epsilon, p[5].getEstimate(), 1.0e-10);
}
public void testNonInversible() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 0),
new EstimatedParameter("p2", 0)
};
LinearMeasurement[] m = new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 2.0, -3.0 },
new EstimatedParameter[] { p[0], p[1], p[2] },
1.0),
new LinearMeasurement(new double[] { 2.0, 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1], p[2] },
1.0),
new LinearMeasurement(new double[] { -3.0, -9.0 },
new EstimatedParameter[] { p[0], p[2] },
1.0)
};
LinearProblem problem = new LinearProblem(m);
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
double initialCost = estimator.getRMS(problem);
estimator.estimate(problem);
assertTrue(estimator.getRMS(problem) < initialCost);
assertTrue(Math.sqrt(m.length) * estimator.getRMS(problem) > 0.6);
try {
estimator.getCovariances(problem);
fail("an exception should have been thrown");
} catch (EstimationException ee) {
// expected behavior
} catch (Exception e) {
fail("wrong exception caught");
}
double dJ0 = 2 * (m[0].getResidual() * m[0].getPartial(p[0])
+ m[1].getResidual() * m[1].getPartial(p[0])
+ m[2].getResidual() * m[2].getPartial(p[0]));
double dJ1 = 2 * (m[0].getResidual() * m[0].getPartial(p[1])
+ m[1].getResidual() * m[1].getPartial(p[1]));
double dJ2 = 2 * (m[0].getResidual() * m[0].getPartial(p[2])
+ m[1].getResidual() * m[1].getPartial(p[2])
+ m[2].getResidual() * m[2].getPartial(p[2]));
assertEquals(0, dJ0, 1.0e-10);
assertEquals(0, dJ1, 1.0e-10);
assertEquals(0, dJ2, 1.0e-10);
}
public void testIllConditioned() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 0),
new EstimatedParameter("p1", 1),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 3)
};
LinearProblem problem1 = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 10.0, 7.0, 8.0, 7.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
32.0),
new LinearMeasurement(new double[] { 7.0, 5.0, 6.0, 5.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
23.0),
new LinearMeasurement(new double[] { 8.0, 6.0, 10.0, 9.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
33.0),
new LinearMeasurement(new double[] { 7.0, 5.0, 9.0, 10.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
31.0)
});
LevenbergMarquardtEstimator estimator1 = new LevenbergMarquardtEstimator();
estimator1.estimate(problem1);
assertEquals(0, estimator1.getRMS(problem1), 1.0e-10);
assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
assertEquals(1.0, p[2].getEstimate(), 1.0e-10);
assertEquals(1.0, p[3].getEstimate(), 1.0e-10);
LinearProblem problem2 = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 10.0, 7.0, 8.1, 7.2 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
32.0),
new LinearMeasurement(new double[] { 7.08, 5.04, 6.0, 5.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
23.0),
new LinearMeasurement(new double[] { 8.0, 5.98, 9.89, 9.0 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
33.0),
new LinearMeasurement(new double[] { 6.99, 4.99, 9.0, 9.98 },
new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
31.0)
});
LevenbergMarquardtEstimator estimator2 = new LevenbergMarquardtEstimator();
estimator2.estimate(problem2);
assertEquals(0, estimator2.getRMS(problem2), 1.0e-10);
assertEquals(-81.0, p[0].getEstimate(), 1.0e-8);
assertEquals(137.0, p[1].getEstimate(), 1.0e-8);
assertEquals(-34.0, p[2].getEstimate(), 1.0e-8);
assertEquals( 22.0, p[3].getEstimate(), 1.0e-8);
}
public void testMoreEstimatedParametersSimple() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 7),
new EstimatedParameter("p1", 6),
new EstimatedParameter("p2", 5),
new EstimatedParameter("p3", 4)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 3.0, 2.0 },
new EstimatedParameter[] { p[0], p[1] },
7.0),
new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
new EstimatedParameter[] { p[1], p[2], p[3] },
3.0),
new LinearMeasurement(new double[] { 2.0, 1.0 },
new EstimatedParameter[] { p[0], p[2] },
5.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
}
public void testMoreEstimatedParametersUnsorted() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 2),
new EstimatedParameter("p1", 2),
new EstimatedParameter("p2", 2),
new EstimatedParameter("p3", 2),
new EstimatedParameter("p4", 2),
new EstimatedParameter("p5", 2)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 },
new EstimatedParameter[] { p[2], p[3], p[4] },
12.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[4], p[5] },
-1.0),
new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
new EstimatedParameter[] { p[3], p[2], p[5] },
7.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[4], p[3] },
1.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
assertEquals(4.0, p[3].getEstimate(), 1.0e-10);
assertEquals(5.0, p[4].getEstimate(), 1.0e-10);
assertEquals(6.0, p[5].getEstimate(), 1.0e-10);
}
public void testRedundantEquations() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 1),
new EstimatedParameter("p1", 1)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1] },
5.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertEquals(0, estimator.getRMS(problem), 1.0e-10);
assertEquals(2.0, p[0].getEstimate(), 1.0e-10);
assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
}
public void testInconsistentEquations() throws EstimationException {
EstimatedParameter[] p = {
new EstimatedParameter("p0", 1),
new EstimatedParameter("p1", 1)
};
LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
new LinearMeasurement(new double[] { 1.0, 1.0 },
new EstimatedParameter[] { p[0], p[1] },
3.0),
new LinearMeasurement(new double[] { 1.0, -1.0 },
new EstimatedParameter[] { p[0], p[1] },
1.0),
new LinearMeasurement(new double[] { 1.0, 3.0 },
new EstimatedParameter[] { p[0], p[1] },
4.0)
});
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(problem);
assertTrue(estimator.getRMS(problem) > 0.1);
}
public void testControlParameters() throws EstimationException {
Circle circle = new Circle(98.680, 47.345);
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(EstimationProblem problem,
double initialStepBoundFactor, int maxCostEval,
double costRelativeTolerance, double parRelativeTolerance,
double orthoTolerance, boolean shouldFail) {
try {
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.setInitialStepBoundFactor(initialStepBoundFactor);
estimator.setMaxCostEval(maxCostEval);
estimator.setCostRelativeTolerance(costRelativeTolerance);
estimator.setParRelativeTolerance(parRelativeTolerance);
estimator.setOrthoTolerance(orthoTolerance);
estimator.estimate(problem);
assertTrue(! shouldFail);
} catch (EstimationException ee) {
assertTrue(shouldFail);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testCircleFitting() throws EstimationException {
Circle circle = new Circle(98.680, 47.345);
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);
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
assertTrue(estimator.getCostEvaluations() < 10);
assertTrue(estimator.getJacobianEvaluations() < 10);
double rms = estimator.getRMS(circle);
assertEquals(1.768262623567235, Math.sqrt(circle.getM()) * rms, 1.0e-10);
assertEquals(69.96016176931406, circle.getRadius(), 1.0e-10);
assertEquals(96.07590211815305, circle.getX(), 1.0e-10);
assertEquals(48.13516790438953, circle.getY(), 1.0e-10);
double[][] cov = estimator.getCovariances(circle);
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 = estimator.guessParametersErrors(circle);
assertEquals(1.384, errors[0], 0.001);
assertEquals(0.905, errors[1], 0.001);
// add perfect measurements and check errors are reduced
double cx = circle.getX();
double cy = circle.getY();
double r = circle.getRadius();
for (double d= 0; d < 2 * Math.PI; d += 0.01) {
circle.addPoint(cx + r * Math.cos(d), cy + r * Math.sin(d));
}
estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
cov = estimator.getCovariances(circle);
assertEquals(0.004, cov[0][0], 0.001);
assertEquals(6.40e-7, cov[0][1], 1.0e-9);
assertEquals(cov[0][1], cov[1][0], 1.0e-14);
assertEquals(0.003, cov[1][1], 0.001);
errors = estimator.guessParametersErrors(circle);
assertEquals(0.004, errors[0], 0.001);
assertEquals(0.004, errors[1], 0.001);
}
public void testCircleFittingBadInit() throws EstimationException {
Circle circle = new Circle(-12, -12);
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}
};
for (int i = 0; i < points.length; ++i) {
circle.addPoint(points[i][0], points[i][1]);
}
LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
estimator.estimate(circle);
assertTrue(estimator.getCostEvaluations() < 15);
assertTrue(estimator.getJacobianEvaluations() < 10);
assertEquals( 0.030184491196225207, estimator.getRMS(circle), 1.0e-9);
assertEquals( 0.2922350065939634, circle.getRadius(), 1.0e-9);
assertEquals(-0.15173845023862165, circle.getX(), 1.0e-8);
assertEquals( 0.20750021499570379, circle.getY(), 1.0e-8);
}
private static class LinearProblem implements EstimationProblem {
public LinearProblem(LinearMeasurement[] measurements) {
this.measurements = measurements;
}
public WeightedMeasurement[] getMeasurements() {
return measurements;
}
public EstimatedParameter[] getUnboundParameters() {
return getAllParameters();
}
public EstimatedParameter[] getAllParameters() {
HashMap map = new HashMap();
for (int i = 0; i < measurements.length; ++i) {
EstimatedParameter[] parameters = measurements[i].getParameters();
for (int j = 0; j < parameters.length; ++j) {
map.put(parameters[j], null);
}
}
Set set = map.keySet();
return (EstimatedParameter[]) set.toArray(new EstimatedParameter[set.size()]);
}
private LinearMeasurement[] measurements;
}
private static class LinearMeasurement extends WeightedMeasurement {
public LinearMeasurement(double[] factors, EstimatedParameter[] parameters,
double setPoint) {
super(1.0, setPoint);
this.factors = factors;
this.parameters = parameters;
}
public double getTheoreticalValue() {
double v = 0;
for (int i = 0; i < factors.length; ++i) {
v += factors[i] * parameters[i].getEstimate();
}
return v;
}
public double getPartial(EstimatedParameter parameter) {
for (int i = 0; i < parameters.length; ++i) {
if (parameters[i] == parameter) {
return factors[i];
}
}
return 0;
}
public EstimatedParameter[] getParameters() {
return parameters;
}
private double[] factors;
private EstimatedParameter[] parameters;
private static final long serialVersionUID = -3922448707008868580L;
}
private static class Circle implements EstimationProblem {
public Circle(double cx, double cy) {
this.cx = new EstimatedParameter("cx", cx);
this.cy = new EstimatedParameter("cy", cy);
points = new ArrayList();
}
public void addPoint(double px, double py) {
points.add(new PointModel(px, py));
}
public int getM() {
return points.size();
}
public WeightedMeasurement[] getMeasurements() {
return (WeightedMeasurement[]) points.toArray(new PointModel[points.size()]);
}
public EstimatedParameter[] getAllParameters() {
return new EstimatedParameter[] { cx, cy };
}
public EstimatedParameter[] getUnboundParameters() {
return new EstimatedParameter[] { cx, cy };
}
public double getPartialRadiusX() {
double dRdX = 0;
for (Iterator iterator = points.iterator(); iterator.hasNext();) {
dRdX += ((PointModel) iterator.next()).getPartialDiX();
}
return dRdX / points.size();
}
public double getPartialRadiusY() {
double dRdY = 0;
for (Iterator iterator = points.iterator(); iterator.hasNext();) {
dRdY += ((PointModel) iterator.next()).getPartialDiY();
}
return dRdY / points.size();
}
public double getRadius() {
double r = 0;
for (Iterator iterator = points.iterator(); iterator.hasNext();) {
r += ((PointModel) iterator.next()).getCenterDistance();
}
return r / points.size();
}
public double getX() {
return cx.getEstimate();
}
public double getY() {
return cy.getEstimate();
}
private class PointModel extends WeightedMeasurement {
public PointModel(double px, double py) {
super(1.0, 0.0);
this.px = px;
this.py = py;
}
public double getPartial(EstimatedParameter parameter) {
if (parameter == cx) {
return getPartialDiX() - getPartialRadiusX();
} else if (parameter == cy) {
return getPartialDiY() - getPartialRadiusY();
}
return 0;
}
public double getCenterDistance() {
double dx = px - cx.getEstimate();
double dy = py - cy.getEstimate();
return Math.sqrt(dx * dx + dy * dy);
}
public double getPartialDiX() {
return (cx.getEstimate() - px) / getCenterDistance();
}
public double getPartialDiY() {
return (cy.getEstimate() - py) / getCenterDistance();
}
public double getTheoreticalValue() {
return getCenterDistance() - getRadius();
}
private double px;
private double py;
private static final long serialVersionUID = 1L;
}
private EstimatedParameter cx;
private EstimatedParameter cy;
private ArrayList points;
}
public static Test suite() {
return new TestSuite(LevenbergMarquardtEstimatorTest.class);
}
}