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* <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) */ @Deprecated public class GaussNewtonEstimatorTest extends TestCase { public GaussNewtonEstimatorTest(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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); estimator.estimate(problem); assertEquals(0, estimator.getRMS(problem), 1.0e-10); 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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() { 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); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); try { estimator.estimate(problem); fail("an exception should have been caught"); } catch (EstimationException ee) { // expected behavior } catch (Exception e) { fail("wrong exception type caught"); } } 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) }); GaussNewtonEstimator estimator1 = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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) }); GaussNewtonEstimator estimator2 = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); 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() { 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); try { estimator.estimate(problem); fail("an exception should have been caught"); } catch (EstimationException ee) { // expected behavior } catch (Exception e) { fail("wrong exception type caught"); } } public void testMoreEstimatedParametersUnsorted() { 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); try { estimator.estimate(problem); fail("an exception should have been caught"); } catch (EstimationException ee) { // expected behavior } catch (Exception e) { fail("wrong exception type caught"); } } 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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); estimator.estimate(problem); assertEquals(0, estimator.getRMS(problem), 1.0e-10); EstimatedParameter[] all = problem.getAllParameters(); for (int i = 0; i < all.length; ++i) { assertEquals(all[i].getName().equals("p0") ? 2.0 : 1.0, all[i].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) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); estimator.estimate(problem); assertTrue(estimator.getRMS(problem) > 0.1); } public void testBoundParameters() throws EstimationException { EstimatedParameter[] p = { new EstimatedParameter("unbound0", 2, false), new EstimatedParameter("unbound1", 2, false), new EstimatedParameter("bound", 2, true) }; LinearProblem problem = new LinearProblem(new LinearMeasurement[] { new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 }, new EstimatedParameter[] { p[0], p[1], p[2] }, 3.0), new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 }, new EstimatedParameter[] { p[0], p[1], p[2] }, 1.0), new LinearMeasurement(new double[] { 1.0, 3.0, 2.0 }, new EstimatedParameter[] { p[0], p[1], p[2] }, 7.0) }); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); estimator.estimate(problem); assertTrue(estimator.getRMS(problem) < 1.0e-10); double[][] covariances = estimator.getCovariances(problem); int i0 = 0, i1 = 1; if (problem.getUnboundParameters()[0].getName().endsWith("1")) { i0 = 1; i1 = 0; } assertEquals(11.0 / 24, covariances[i0][i0], 1.0e-10); assertEquals(-3.0 / 24, covariances[i0][i1], 1.0e-10); assertEquals(-3.0 / 24, covariances[i1][i0], 1.0e-10); assertEquals( 3.0 / 24, covariances[i1][i1], 1.0e-10); double[] errors = estimator.guessParametersErrors(problem); assertEquals(0, errors[i0], 1.0e-10); assertEquals(0, errors[i1], 1.0e-10); } public void testMaxIterations() { 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); try { GaussNewtonEstimator estimator = new GaussNewtonEstimator(4, 1.0e-14, 1.0e-14); estimator.estimate(circle); fail("an exception should have been caught"); } catch (EstimationException ee) { // expected behavior } 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); GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-10, 1.0e-10); estimator.estimate(circle); 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); } public void testCircleFittingBadInit() { 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]); } GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6); try { estimator.estimate(circle); fail("an exception should have been caught"); } catch (EstimationException ee) { // expected behavior } catch (Exception e) { fail("wrong exception type caught"); } } private static class LinearProblem extends SimpleEstimationProblem { public LinearProblem(LinearMeasurement[] measurements) { HashSet<EstimatedParameter> set = new HashSet(); for (int i = 0; i < measurements.length; ++i) { addMeasurement(measurements[i]); EstimatedParameter[] parameters = measurements[i].getParameters(); for (int j = 0; j < parameters.length; ++j) { set.add(parameters[j]); } } for (EstimatedParameter p : set) { addParameter(p); } } } private static class LinearMeasurement extends WeightedMeasurement { public LinearMeasurement(double[] factors, EstimatedParameter[] parameters, double setPoint) { super(1.0, setPoint, true); this.factors = factors; this.parameters = parameters; setIgnored(false); } @Override public double getTheoreticalValue() { double v = 0; for (int i = 0; i < factors.length; ++i) { v += factors[i] * parameters[i].getEstimate(); } return v; } @Override 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(new EstimatedParameter("cy", cy)); points = new ArrayList<PointModel>(); } public void addPoint(double px, double py) { points.add(new PointModel(this, px, py)); } public int getM() { return points.size(); } public WeightedMeasurement[] getMeasurements() { return 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 (PointModel point : points) { dRdX += point.getPartialDiX(); } return dRdX / points.size(); } public double getPartialRadiusY() { double dRdY = 0; for (PointModel point : points) { dRdY += point.getPartialDiY(); } return dRdY / points.size(); } public double getRadius() { double r = 0; for (PointModel point : points) { r += point.getCenterDistance(); } return r / points.size(); } public double getX() { return cx.getEstimate(); } public double getY() { return cy.getEstimate(); } private static class PointModel extends WeightedMeasurement { public PointModel(Circle circle, double px, double py) { super(1.0, 0.0); this.px = px; this.py = py; this.circle = circle; } @Override public double getPartial(EstimatedParameter parameter) { if (parameter == circle.cx) { return getPartialDiX() - circle.getPartialRadiusX(); } else if (parameter == circle.cy) { return getPartialDiY() - circle.getPartialRadiusY(); } return 0; } public double getCenterDistance() { double dx = px - circle.cx.getEstimate(); double dy = py - circle.cy.getEstimate(); return Math.sqrt(dx * dx + dy * dy); } public double getPartialDiX() { return (circle.cx.getEstimate() - px) / getCenterDistance(); } public double getPartialDiY() { return (circle.cy.getEstimate() - py) / getCenterDistance(); } @Override public double getTheoreticalValue() { return getCenterDistance() - circle.getRadius(); } private double px; private double py; private transient final Circle circle; private static final long serialVersionUID = 1L; } private EstimatedParameter cx; private EstimatedParameter cy; private ArrayList<PointModel> points; } }

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Java - Commons Math tags/keywords

circle, estimatedparameter, estimatedparameter, estimationexception, exception, gaussnewtonestimator, gaussnewtonestimator, linearmeasurement, linearmeasurement, linearproblem, linearproblem, override, pointmodel, util, weightedmeasurement

The Commons Math GaussNewtonEstimatorTest.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.estimation;

import java.util.ArrayList;
import java.util.HashSet;

import junit.framework.TestCase;

/**
 * <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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