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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 abstract class AbstractLeastSquaresOptimizerAbstractTest { public abstract AbstractLeastSquaresOptimizer createOptimizer(); @Test public void testTrivial() { LinearProblem problem = new LinearProblem(new double[][] { { 2 } }, new double[] { 3 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1 }, new double[] { 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(1.5, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(3.0, optimum.getValue()[0], 1.0e-10); try { optimizer.guessParametersErrors(); Assert.fail("an exception should have been thrown"); } catch (NumberIsTooSmallException ee) { // expected behavior } } @Test public void testQRColumnsPermutation() { 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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(7.0, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(3.0, optimum.getPoint()[1], 1.0e-10); Assert.assertEquals(4.0, optimum.getValue()[0], 1.0e-10); Assert.assertEquals(6.0, optimum.getValue()[1], 1.0e-10); Assert.assertEquals(1.0, optimum.getValue()[2], 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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, new double[] { 0, 0, 0, 0, 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); 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}); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); 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() { 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}); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, new double[] { 0, 0, 0, 0, 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals( 3.0, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals( 4.0, optimum.getPoint()[1], 1.0e-10); Assert.assertEquals(-1.0, optimum.getPoint()[2], 1.0e-10); Assert.assertEquals(-2.0, optimum.getPoint()[3], 1.0e-10); Assert.assertEquals( 1.0 + epsilon, optimum.getPoint()[4], 1.0e-10); Assert.assertEquals( 1.0 - epsilon, optimum.getPoint()[5], 1.0e-10); } @Test(expected=ConvergenceException.class) public void testNonInvertible() throws Exception { LinearProblem problem = new LinearProblem(new double[][] { { 1, 2, -3 }, { 2, 1, 3 }, { -3, 0, -9 } }, new double[] { 1, 1, 1 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }); } @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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum1 = optimizer.optimize(100, problem1, problem1.target, new double[] { 1, 1, 1, 1 }, new double[] { 0, 1, 2, 3 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(1.0, optimum1.getPoint()[0], 1.0e-10); Assert.assertEquals(1.0, optimum1.getPoint()[1], 1.0e-10); Assert.assertEquals(1.0, optimum1.getPoint()[2], 1.0e-10); Assert.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 }); PointVectorValuePair optimum2 = optimizer.optimize(100, problem2, problem2.target, new double[] { 1, 1, 1, 1 }, new double[] { 0, 1, 2, 3 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-8); Assert.assertEquals(137.0, optimum2.getPoint()[1], 1.0e-8); Assert.assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-8); Assert.assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-8); } @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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 7, 6, 5, 4 }); Assert.assertEquals(0, optimizer.getRMS(), 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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1, 1, 1 }, new double[] { 2, 2, 2, 2, 2, 2 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(3.0, optimum.getPointRef()[2], 1.0e-10); Assert.assertEquals(4.0, optimum.getPointRef()[3], 1.0e-10); Assert.assertEquals(5.0, optimum.getPointRef()[4], 1.0e-10); Assert.assertEquals(6.0, optimum.getPointRef()[5], 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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(2.0, optimum.getPointRef()[0], 1.0e-10); Assert.assertEquals(1.0, optimum.getPointRef()[1], 1.0e-10); } @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 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); optimizer.optimize(100, problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 }); Assert.assertTrue(optimizer.getRMS() > 0.1); } @Test(expected=DimensionMismatchException.class) public void testInconsistentSizes1() { LinearProblem problem = new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(-1, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(+1, optimum.getPoint()[1], 1.0e-10); optimizer.optimize(100, problem, problem.target, new double[] { 1 }, new double[] { 0, 0 }); } @Test(expected=DimensionMismatchException.class) public void testInconsistentSizes2() { LinearProblem problem = new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 }); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 }); Assert.assertEquals(0, optimizer.getRMS(), 1.0e-10); Assert.assertEquals(-1, optimum.getPoint()[0], 1.0e-10); Assert.assertEquals(+1, optimum.getPoint()[1], 1.0e-10); optimizer.optimize(100, problem, new double[] { 1 }, new double[] { 1 }, new double[] { 0, 0 }); } @Test public void testCircleFitting() { CircleVectorial circle = new CircleVectorial(); 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); AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, circle, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 }, new double[] { 98.680, 47.345 }); Assert.assertTrue(optimizer.getEvaluations() < 10); Assert.assertTrue(optimizer.getJacobianEvaluations() < 10); double rms = optimizer.getRMS(); Assert.assertEquals(1.768262623567235, FastMath.sqrt(circle.getN()) * rms, 1.0e-10); Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]); Assert.assertEquals(69.96016176931406, circle.getRadius(center), 1.0e-6); Assert.assertEquals(96.07590211815305, center.getX(), 1.0e-6); Assert.assertEquals(48.13516790438953, center.getY(), 1.0e-6); double[][] cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14); Assert.assertEquals(1.839, cov[0][0], 0.001); Assert.assertEquals(0.731, cov[0][1], 0.001); Assert.assertEquals(cov[0][1], cov[1][0], 1.0e-14); Assert.assertEquals(0.786, cov[1][1], 0.001); // add perfect measurements and check errors are reduced double r = circle.getRadius(center); for (double d= 0; d < 2 * FastMath.PI; d += 0.01) { circle.addPoint(center.getX() + r * FastMath.cos(d), center.getY() + r * FastMath.sin(d)); } double[] target = new double[circle.getN()]; Arrays.fill(target, 0.0); double[] weights = new double[circle.getN()]; Arrays.fill(weights, 2.0); optimum = optimizer.optimize(100, circle, target, weights, new double[] { 98.680, 47.345 }); cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14); Assert.assertEquals(0.0016, cov[0][0], 0.001); Assert.assertEquals(3.2e-7, cov[0][1], 1.0e-9); Assert.assertEquals(cov[0][1], cov[1][0], 1.0e-14); Assert.assertEquals(0.0016, cov[1][1], 0.001); } @Test public void testCircleFittingBadInit() { CircleVectorial circle = new CircleVectorial(); double[][] points = circlePoints; 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]); } AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, circle, target, weights, new double[] { -12, -12 }); Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]); Assert.assertTrue(optimizer.getEvaluations() < 25); Assert.assertTrue(optimizer.getJacobianEvaluations() < 20); Assert.assertEquals( 0.043, optimizer.getRMS(), 1.0e-3); Assert.assertEquals( 0.292235, circle.getRadius(center), 1.0e-6); Assert.assertEquals(-0.151738, center.getX(), 1.0e-6); Assert.assertEquals( 0.2075001, center.getY(), 1.0e-6); } @Test public void testCircleFittingGoodInit() { CircleVectorial circle = new CircleVectorial(); double[][] points = circlePoints; 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]); } AbstractLeastSquaresOptimizer optimizer = createOptimizer(); PointVectorValuePair optimum = optimizer.optimize(100, circle, target, weights, new double[] { 0, 0 }); Assert.assertEquals(-0.1517383071957963, optimum.getPointRef()[0], 1.0e-6); Assert.assertEquals(0.2074999736353867, optimum.getPointRef()[1], 1.0e-6); Assert.assertEquals(0.04268731682389561, optimizer.getRMS(), 1.0e-8); } private final double[][] circlePoints = 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} }; public void doTestStRD(final StatisticalReferenceDataset dataset, final double errParams, final double errParamsSd) { final AbstractLeastSquaresOptimizer optimizer = createOptimizer(); final double[] w = new double[dataset.getNumObservations()]; Arrays.fill(w, 1.0); final double[][] data = dataset.getData(); final double[] initial = dataset.getStartingPoint(0); final MultivariateDifferentiableVectorFunction problem; problem = dataset.getLeastSquaresProblem(); final PointVectorValuePair optimum; optimum = optimizer.optimize(100, problem, data[1], w, initial); final double[] actual = optimum.getPoint(); for (int i = 0; i < actual.length; i++) { double expected = dataset.getParameter(i); double delta = FastMath.abs(errParams * expected); Assert.assertEquals(dataset.getName() + ", param #" + i, expected, actual[i], delta); } } @Test public void testKirby2() throws IOException { doTestStRD(StatisticalReferenceDatasetFactory.createKirby2(), 1E-7, 1E-7); } @Test public void testHahn1() throws IOException { doTestStRD(StatisticalReferenceDatasetFactory.createHahn1(), 1E-7, 1E-4); } static class LinearProblem implements MultivariateDifferentiableVectorFunction, 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 DerivativeStructure[] value(DerivativeStructure[] variables) { DerivativeStructure[] value = new DerivativeStructure[factors.getRowDimension()]; for (int i = 0; i < value.length; ++i) { value[i] = variables[0].getField().getZero(); for (int j = 0; j < factors.getColumnDimension(); ++j) { value[i] = value[i].add(variables[j].multiply(factors.getEntry(i, j))); } } return value; } } }

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Java - Java tags/keywords

abstractleastsquaresoptimizer, abstractleastsquaresoptimizerabstracttest, circlevectorial, deprecated, derivativestructure, ioexception, linearproblem, multivariatedifferentiablevectorfunction, numberistoosmallexception, pointvectorvaluepair, serializable, statisticalreferencedataset, test, util, vector2d

The AbstractLeastSquaresOptimizerAbstractTest.java Java example 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
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 */
package org.apache.commons.math3.optimization.general;

import java.io.IOException;
import java.io.Serializable;
import java.util.Arrays;

import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction;
import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
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.optimization.PointVectorValuePair;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * <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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