| /* |
| * 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.math3.optimization.general; |
| |
| import java.io.Serializable; |
| import java.util.Arrays; |
| |
| import org.apache.commons.math3.exception.TooManyEvaluationsException; |
| import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; |
| import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction; |
| 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 <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) |
| */ |
| @Deprecated |
| public class MinpackTest { |
| |
| @Test |
| public void testMinpackLinearFullRank() { |
| minpackTest(new LinearFullRankFunction(10, 5, 1.0, |
| 5.0, 2.23606797749979), false); |
| minpackTest(new LinearFullRankFunction(50, 5, 1.0, |
| 8.06225774829855, 6.70820393249937), false); |
| } |
| |
| @Test |
| public void testMinpackLinearRank1() { |
| minpackTest(new LinearRank1Function(10, 5, 1.0, |
| 291.521868819476, 1.4638501094228), false); |
| minpackTest(new LinearRank1Function(50, 5, 1.0, |
| 3101.60039334535, 3.48263016573496), false); |
| } |
| |
| @Test |
| public void testMinpackLinearRank1ZeroColsAndRows() { |
| minpackTest(new LinearRank1ZeroColsAndRowsFunction(10, 5, 1.0), false); |
| minpackTest(new LinearRank1ZeroColsAndRowsFunction(50, 5, 1.0), false); |
| } |
| |
| @Test |
| public void testMinpackRosenbrok() { |
| minpackTest(new RosenbrockFunction(new double[] { -1.2, 1.0 }, |
| FastMath.sqrt(24.2)), false); |
| minpackTest(new RosenbrockFunction(new double[] { -12.0, 10.0 }, |
| FastMath.sqrt(1795769.0)), false); |
| minpackTest(new RosenbrockFunction(new double[] { -120.0, 100.0 }, |
| 11.0 * FastMath.sqrt(169000121.0)), false); |
| } |
| |
| @Test |
| public void testMinpackHelicalValley() { |
| minpackTest(new HelicalValleyFunction(new double[] { -1.0, 0.0, 0.0 }, |
| 50.0), false); |
| minpackTest(new HelicalValleyFunction(new double[] { -10.0, 0.0, 0.0 }, |
| 102.95630140987), false); |
| minpackTest(new HelicalValleyFunction(new double[] { -100.0, 0.0, 0.0}, |
| 991.261822123701), false); |
| } |
| |
| @Test |
| public void testMinpackPowellSingular() { |
| minpackTest(new PowellSingularFunction(new double[] { 3.0, -1.0, 0.0, 1.0 }, |
| 14.6628782986152), false); |
| minpackTest(new PowellSingularFunction(new double[] { 30.0, -10.0, 0.0, 10.0 }, |
| 1270.9838708654), false); |
| minpackTest(new PowellSingularFunction(new double[] { 300.0, -100.0, 0.0, 100.0 }, |
| 126887.903284750), false); |
| } |
| |
| @Test |
| public void testMinpackFreudensteinRoth() { |
| minpackTest(new FreudensteinRothFunction(new double[] { 0.5, -2.0 }, |
| 20.0124960961895, 6.99887517584575, |
| new double[] { |
| 11.4124844654993, |
| -0.896827913731509 |
| }), false); |
| minpackTest(new FreudensteinRothFunction(new double[] { 5.0, -20.0 }, |
| 12432.833948863, 6.9988751744895, |
| new double[] { |
| 11.41300466147456, |
| -0.896796038685959 |
| }), false); |
| minpackTest(new FreudensteinRothFunction(new double[] { 50.0, -200.0 }, |
| 11426454.595762, 6.99887517242903, |
| new double[] { |
| 11.412781785788564, |
| -0.8968051074920405 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackBard() { |
| minpackTest(new BardFunction(1.0, 6.45613629515967, 0.0906359603390466, |
| new double[] { |
| 0.0824105765758334, |
| 1.1330366534715, |
| 2.34369463894115 |
| }), false); |
| minpackTest(new BardFunction(10.0, 36.1418531596785, 4.17476870138539, |
| new double[] { |
| 0.840666673818329, |
| -158848033.259565, |
| -164378671.653535 |
| }), false); |
| minpackTest(new BardFunction(100.0, 384.114678637399, 4.17476870135969, |
| new double[] { |
| 0.840666673867645, |
| -158946167.205518, |
| -164464906.857771 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackKowalikOsborne() { |
| minpackTest(new KowalikOsborneFunction(new double[] { 0.25, 0.39, 0.415, 0.39 }, |
| 0.0728915102882945, |
| 0.017535837721129, |
| new double[] { |
| 0.192807810476249, |
| 0.191262653354071, |
| 0.123052801046931, |
| 0.136053221150517 |
| }), false); |
| minpackTest(new KowalikOsborneFunction(new double[] { 2.5, 3.9, 4.15, 3.9 }, |
| 2.97937007555202, |
| 0.032052192917937, |
| new double[] { |
| 728675.473768287, |
| -14.0758803129393, |
| -32977797.7841797, |
| -20571594.1977912 |
| }), false); |
| minpackTest(new KowalikOsborneFunction(new double[] { 25.0, 39.0, 41.5, 39.0 }, |
| 29.9590617016037, |
| 0.0175364017658228, |
| new double[] { |
| 0.192948328597594, |
| 0.188053165007911, |
| 0.122430604321144, |
| 0.134575665392506 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackMeyer() { |
| minpackTest(new MeyerFunction(new double[] { 0.02, 4000.0, 250.0 }, |
| 41153.4665543031, 9.37794514651874, |
| new double[] { |
| 0.00560963647102661, |
| 6181.34634628659, |
| 345.223634624144 |
| }), false); |
| minpackTest(new MeyerFunction(new double[] { 0.2, 40000.0, 2500.0 }, |
| 4168216.89130846, 792.917871779501, |
| new double[] { |
| 1.42367074157994e-11, |
| 33695.7133432541, |
| 901.268527953801 |
| }), true); |
| } |
| |
| @Test |
| public void testMinpackWatson() { |
| |
| minpackTest(new WatsonFunction(6, 0.0, |
| 5.47722557505166, 0.0478295939097601, |
| new double[] { |
| -0.0157249615083782, 1.01243488232965, |
| -0.232991722387673, 1.26043101102818, |
| -1.51373031394421, 0.99299727291842 |
| }), false); |
| minpackTest(new WatsonFunction(6, 10.0, |
| 6433.12578950026, 0.0478295939096951, |
| new double[] { |
| -0.0157251901386677, 1.01243485860105, |
| -0.232991545843829, 1.26042932089163, |
| -1.51372776706575, 0.99299573426328 |
| }), false); |
| minpackTest(new WatsonFunction(6, 100.0, |
| 674256.040605213, 0.047829593911544, |
| new double[] { |
| -0.0157247019712586, 1.01243490925658, |
| -0.232991922761641, 1.26043292929555, |
| -1.51373320452707, 0.99299901922322 |
| }), false); |
| |
| minpackTest(new WatsonFunction(9, 0.0, |
| 5.47722557505166, 0.00118311459212420, |
| new double[] { |
| -0.153070644166722e-4, 0.999789703934597, |
| 0.0147639634910978, 0.146342330145992, |
| 1.00082109454817, -2.61773112070507, |
| 4.10440313943354, -3.14361226236241, |
| 1.05262640378759 |
| }), false); |
| minpackTest(new WatsonFunction(9, 10.0, |
| 12088.127069307, 0.00118311459212513, |
| new double[] { |
| -0.153071334849279e-4, 0.999789703941234, |
| 0.0147639629786217, 0.146342334818836, |
| 1.00082107321386, -2.61773107084722, |
| 4.10440307655564, -3.14361222178686, |
| 1.05262639322589 |
| }), false); |
| minpackTest(new WatsonFunction(9, 100.0, |
| 1269109.29043834, 0.00118311459212384, |
| new double[] { |
| -0.153069523352176e-4, 0.999789703958371, |
| 0.0147639625185392, 0.146342341096326, |
| 1.00082104729164, -2.61773101573645, |
| 4.10440301427286, -3.14361218602503, |
| 1.05262638516774 |
| }), false); |
| |
| minpackTest(new WatsonFunction(12, 0.0, |
| 5.47722557505166, 0.217310402535861e-4, |
| new double[] { |
| -0.660266001396382e-8, 1.00000164411833, |
| -0.000563932146980154, 0.347820540050756, |
| -0.156731500244233, 1.05281515825593, |
| -3.24727109519451, 7.2884347837505, |
| -10.271848098614, 9.07411353715783, |
| -4.54137541918194, 1.01201187975044 |
| }), false); |
| minpackTest(new WatsonFunction(12, 10.0, |
| 19220.7589790951, 0.217310402518509e-4, |
| new double[] { |
| -0.663710223017410e-8, 1.00000164411787, |
| -0.000563932208347327, 0.347820540486998, |
| -0.156731503955652, 1.05281517654573, |
| -3.2472711515214, 7.28843489430665, |
| -10.2718482369638, 9.07411364383733, |
| -4.54137546533666, 1.01201188830857 |
| }), false); |
| minpackTest(new WatsonFunction(12, 100.0, |
| 2018918.04462367, 0.217310402539845e-4, |
| new double[] { |
| -0.663806046485249e-8, 1.00000164411786, |
| -0.000563932210324959, 0.347820540503588, |
| -0.156731504091375, 1.05281517718031, |
| -3.24727115337025, 7.28843489775302, |
| -10.2718482410813, 9.07411364688464, |
| -4.54137546660822, 1.0120118885369 |
| }), false); |
| |
| } |
| |
| @Test |
| public void testMinpackBox3Dimensional() { |
| minpackTest(new Box3DimensionalFunction(10, new double[] { 0.0, 10.0, 20.0 }, |
| 32.1115837449572), false); |
| } |
| |
| @Test |
| public void testMinpackJennrichSampson() { |
| minpackTest(new JennrichSampsonFunction(10, new double[] { 0.3, 0.4 }, |
| 64.5856498144943, 11.1517793413499, |
| new double[] { |
| // 0.2578330049, 0.257829976764542 |
| 0.2578199266368004, 0.25782997676455244 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackBrownDennis() { |
| minpackTest(new BrownDennisFunction(20, |
| new double[] { 25.0, 5.0, -5.0, -1.0 }, |
| 2815.43839161816, 292.954288244866, |
| new double[] { |
| -11.59125141003, 13.2024883984741, |
| -0.403574643314272, 0.236736269844604 |
| }), false); |
| minpackTest(new BrownDennisFunction(20, |
| new double[] { 250.0, 50.0, -50.0, -10.0 }, |
| 555073.354173069, 292.954270581415, |
| new double[] { |
| -11.5959274272203, 13.2041866926242, |
| -0.403417362841545, 0.236771143410386 |
| }), false); |
| minpackTest(new BrownDennisFunction(20, |
| new double[] { 2500.0, 500.0, -500.0, -100.0 }, |
| 61211252.2338581, 292.954306151134, |
| new double[] { |
| -11.5902596937374, 13.2020628854665, |
| -0.403688070279258, 0.236665033746463 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackChebyquad() { |
| minpackTest(new ChebyquadFunction(1, 8, 1.0, |
| 1.88623796907732, 1.88623796907732, |
| new double[] { 0.5 }), false); |
| minpackTest(new ChebyquadFunction(1, 8, 10.0, |
| 5383344372.34005, 1.88424820499951, |
| new double[] { 0.9817314924684 }), false); |
| minpackTest(new ChebyquadFunction(1, 8, 100.0, |
| 0.118088726698392e19, 1.88424820499347, |
| new double[] { 0.9817314852934 }), false); |
| minpackTest(new ChebyquadFunction(8, 8, 1.0, |
| 0.196513862833975, 0.0593032355046727, |
| new double[] { |
| 0.0431536648587336, 0.193091637843267, |
| 0.266328593812698, 0.499999334628884, |
| 0.500000665371116, 0.733671406187302, |
| 0.806908362156733, 0.956846335141266 |
| }), false); |
| minpackTest(new ChebyquadFunction(9, 9, 1.0, |
| 0.16994993465202, 0.0, |
| new double[] { |
| 0.0442053461357828, 0.199490672309881, |
| 0.23561910847106, 0.416046907892598, |
| 0.5, 0.583953092107402, |
| 0.764380891528940, 0.800509327690119, |
| 0.955794653864217 |
| }), false); |
| minpackTest(new ChebyquadFunction(10, 10, 1.0, |
| 0.183747831178711, 0.0806471004038253, |
| new double[] { |
| 0.0596202671753563, 0.166708783805937, |
| 0.239171018813509, 0.398885290346268, |
| 0.398883667870681, 0.601116332129320, |
| 0.60111470965373, 0.760828981186491, |
| 0.833291216194063, 0.940379732824644 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackBrownAlmostLinear() { |
| minpackTest(new BrownAlmostLinearFunction(10, 0.5, |
| 16.5302162063499, 0.0, |
| new double[] { |
| 0.979430303349862, 0.979430303349862, |
| 0.979430303349862, 0.979430303349862, |
| 0.979430303349862, 0.979430303349862, |
| 0.979430303349862, 0.979430303349862, |
| 0.979430303349862, 1.20569696650138 |
| }), false); |
| minpackTest(new BrownAlmostLinearFunction(10, 5.0, |
| 9765624.00089211, 0.0, |
| new double[] { |
| 0.979430303349865, 0.979430303349865, |
| 0.979430303349865, 0.979430303349865, |
| 0.979430303349865, 0.979430303349865, |
| 0.979430303349865, 0.979430303349865, |
| 0.979430303349865, 1.20569696650135 |
| }), false); |
| minpackTest(new BrownAlmostLinearFunction(10, 50.0, |
| 0.9765625e17, 0.0, |
| new double[] { |
| 1.0, 1.0, 1.0, 1.0, 1.0, |
| 1.0, 1.0, 1.0, 1.0, 1.0 |
| }), false); |
| minpackTest(new BrownAlmostLinearFunction(30, 0.5, |
| 83.476044467848, 0.0, |
| new double[] { |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 0.997754216442807, |
| 0.997754216442807, 1.06737350671578 |
| }), false); |
| minpackTest(new BrownAlmostLinearFunction(40, 0.5, |
| 128.026364472323, 0.0, |
| new double[] { |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 1.00000000000002, 1.00000000000002, |
| 0.999999999999121 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackOsborne1() { |
| minpackTest(new Osborne1Function(new double[] { 0.5, 1.5, -1.0, 0.01, 0.02, }, |
| 0.937564021037838, 0.00739249260904843, |
| new double[] { |
| 0.375410049244025, 1.93584654543108, |
| -1.46468676748716, 0.0128675339110439, |
| 0.0221227011813076 |
| }), false); |
| } |
| |
| @Test |
| public void testMinpackOsborne2() { |
| |
| minpackTest(new Osborne2Function(new double[] { |
| 1.3, 0.65, 0.65, 0.7, 0.6, |
| 3.0, 5.0, 7.0, 2.0, 4.5, 5.5 |
| }, |
| 1.44686540984712, 0.20034404483314, |
| new double[] { |
| 1.30997663810096, 0.43155248076, |
| 0.633661261602859, 0.599428560991695, |
| 0.754179768272449, 0.904300082378518, |
| 1.36579949521007, 4.82373199748107, |
| 2.39868475104871, 4.56887554791452, |
| 5.67534206273052 |
| }), false); |
| } |
| |
| private void minpackTest(MinpackFunction function, boolean exceptionExpected) { |
| LevenbergMarquardtOptimizer optimizer |
| = new LevenbergMarquardtOptimizer(FastMath.sqrt(2.22044604926e-16), |
| FastMath.sqrt(2.22044604926e-16), |
| 2.22044604926e-16); |
| // Assert.assertTrue(function.checkTheoreticalStartCost(optimizer.getRMS())); |
| try { |
| PointVectorValuePair optimum = |
| optimizer.optimize(400 * (function.getN() + 1), function, |
| function.getTarget(), function.getWeight(), |
| function.getStartPoint()); |
| Assert.assertFalse(exceptionExpected); |
| function.checkTheoreticalMinCost(optimizer.getRMS()); |
| function.checkTheoreticalMinParams(optimum); |
| } catch (TooManyEvaluationsException e) { |
| Assert.assertTrue(exceptionExpected); |
| } |
| } |
| |
| private static abstract class MinpackFunction |
| implements MultivariateDifferentiableVectorFunction, Serializable { |
| |
| private static final long serialVersionUID = -6209760235478794233L; |
| protected int n; |
| protected int m; |
| protected double[] startParams; |
| protected double theoreticalMinCost; |
| protected double[] theoreticalMinParams; |
| protected double costAccuracy; |
| protected double paramsAccuracy; |
| |
| protected MinpackFunction(int m, double[] startParams, |
| double theoreticalMinCost, double[] theoreticalMinParams) { |
| this.m = m; |
| this.n = startParams.length; |
| this.startParams = startParams.clone(); |
| this.theoreticalMinCost = theoreticalMinCost; |
| this.theoreticalMinParams = theoreticalMinParams; |
| this.costAccuracy = 1.0e-8; |
| this.paramsAccuracy = 1.0e-5; |
| } |
| |
| protected static double[] buildArray(int n, double x) { |
| double[] array = new double[n]; |
| Arrays.fill(array, x); |
| return array; |
| } |
| |
| public double[] getTarget() { |
| return buildArray(m, 0.0); |
| } |
| |
| public double[] getWeight() { |
| return buildArray(m, 1.0); |
| } |
| |
| public double[] getStartPoint() { |
| return startParams.clone(); |
| } |
| |
| protected void setCostAccuracy(double costAccuracy) { |
| this.costAccuracy = costAccuracy; |
| } |
| |
| protected void setParamsAccuracy(double paramsAccuracy) { |
| this.paramsAccuracy = paramsAccuracy; |
| } |
| |
| public int getN() { |
| return startParams.length; |
| } |
| |
| public void checkTheoreticalMinCost(double rms) { |
| double threshold = costAccuracy * (1.0 + theoreticalMinCost); |
| Assert.assertEquals(theoreticalMinCost, FastMath.sqrt(m) * rms, threshold); |
| } |
| |
| public void checkTheoreticalMinParams(PointVectorValuePair optimum) { |
| double[] params = optimum.getPointRef(); |
| if (theoreticalMinParams != null) { |
| for (int i = 0; i < theoreticalMinParams.length; ++i) { |
| double mi = theoreticalMinParams[i]; |
| double vi = params[i]; |
| Assert.assertEquals(mi, vi, paramsAccuracy * (1.0 + FastMath.abs(mi))); |
| } |
| } |
| } |
| |
| public double[] value(double[] variables) { |
| DerivativeStructure[] dsV = new DerivativeStructure[variables.length]; |
| for (int i = 0; i < variables.length; ++i) { |
| dsV[i] = new DerivativeStructure(0, 0, variables[i]); |
| } |
| DerivativeStructure[] dsY = value(dsV); |
| double[] y = new double[dsY.length]; |
| for (int i = 0; i < dsY.length; ++i) { |
| y[i] = dsY[i].getValue(); |
| } |
| return y; |
| } |
| |
| public abstract DerivativeStructure[] value(DerivativeStructure[] variables); |
| |
| } |
| |
| private static class LinearFullRankFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -9030323226268039536L; |
| |
| public LinearFullRankFunction(int m, int n, double x0, |
| double theoreticalStartCost, |
| double theoreticalMinCost) { |
| super(m, buildArray(n, x0), theoreticalMinCost, |
| buildArray(n, -1.0)); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure sum = variables[0].getField().getZero(); |
| for (int i = 0; i < n; ++i) { |
| sum = sum.add(variables[i]); |
| } |
| DerivativeStructure t = sum.multiply(2.0 / m).add(1); |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < n; ++i) { |
| f[i] = variables[i].subtract(t); |
| } |
| Arrays.fill(f, n, m, t.negate()); |
| return f; |
| } |
| |
| } |
| |
| private static class LinearRank1Function extends MinpackFunction { |
| |
| private static final long serialVersionUID = 8494863245104608300L; |
| |
| public LinearRank1Function(int m, int n, double x0, |
| double theoreticalStartCost, |
| double theoreticalMinCost) { |
| super(m, buildArray(n, x0), theoreticalMinCost, null); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| DerivativeStructure sum = variables[0].getField().getZero(); |
| for (int i = 0; i < n; ++i) { |
| sum = sum.add(variables[i].multiply(i + 1)); |
| } |
| for (int i = 0; i < m; ++i) { |
| f[i] = sum.multiply(i + 1).subtract(1); |
| } |
| return f; |
| } |
| |
| } |
| |
| private static class LinearRank1ZeroColsAndRowsFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -3316653043091995018L; |
| |
| public LinearRank1ZeroColsAndRowsFunction(int m, int n, double x0) { |
| super(m, buildArray(n, x0), |
| FastMath.sqrt((m * (m + 3) - 6) / (2.0 * (2 * m - 3))), |
| null); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| DerivativeStructure sum = variables[0].getField().getZero(); |
| for (int i = 1; i < (n - 1); ++i) { |
| sum = sum.add(variables[i].multiply(i + 1)); |
| } |
| for (int i = 0; i < (m - 1); ++i) { |
| f[i] = sum.multiply(i).subtract(1); |
| } |
| f[m - 1] = variables[0].getField().getOne().negate(); |
| return f; |
| } |
| |
| } |
| |
| private static class RosenbrockFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 2893438180956569134L; |
| |
| public RosenbrockFunction(double[] startParams, double theoreticalStartCost) { |
| super(2, startParams, 0.0, buildArray(2, 1.0)); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| return new DerivativeStructure[] { |
| x2.subtract(x1.multiply(x1)).multiply(10), |
| x1.negate().add(1) |
| }; |
| } |
| |
| } |
| |
| private static class HelicalValleyFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 220613787843200102L; |
| |
| public HelicalValleyFunction(double[] startParams, |
| double theoreticalStartCost) { |
| super(3, startParams, 0.0, new double[] { 1.0, 0.0, 0.0 }); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure tmp1 = variables[0].getField().getZero(); |
| if (x1.getValue() == 0) { |
| tmp1 = tmp1.add((x2.getValue() >= 0) ? 0.25 : -0.25); |
| } else { |
| tmp1 = x2.divide(x1).atan().divide(twoPi); |
| if (x1.getValue() < 0) { |
| tmp1 = tmp1.add(0.5); |
| } |
| } |
| DerivativeStructure tmp2 = x1.multiply(x1).add(x2.multiply(x2)).sqrt(); |
| return new DerivativeStructure[] { |
| x3.subtract(tmp1.multiply(10)).multiply(10), |
| tmp2.subtract(1).multiply(10), |
| x3 |
| }; |
| } |
| |
| private static final double twoPi = 2.0 * FastMath.PI; |
| |
| } |
| |
| private static class PowellSingularFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 7298364171208142405L; |
| |
| public PowellSingularFunction(double[] startParams, |
| double theoreticalStartCost) { |
| super(4, startParams, 0.0, buildArray(4, 0.0)); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure x4 = variables[3]; |
| return new DerivativeStructure[] { |
| x1.add(x2.multiply(10)), |
| x3.subtract(x4).multiply(sqrt5), |
| x2.subtract(x3.multiply(2)).multiply(x2.subtract(x3.multiply(2))), |
| x1.subtract(x4).multiply(x1.subtract(x4)).multiply(sqrt10) |
| }; |
| } |
| |
| private static final double sqrt5 = FastMath.sqrt( 5.0); |
| private static final double sqrt10 = FastMath.sqrt(10.0); |
| |
| } |
| |
| private static class FreudensteinRothFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 2892404999344244214L; |
| |
| public FreudensteinRothFunction(double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(2, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| return new DerivativeStructure[] { |
| x1.subtract(13.0).add(x2.negate().add(5.0).multiply(x2).subtract(2).multiply(x2)), |
| x1.subtract(29.0).add(x2.add(1).multiply(x2).subtract(14).multiply(x2)) |
| }; |
| } |
| |
| } |
| |
| private static class BardFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 5990442612572087668L; |
| |
| public BardFunction(double x0, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(15, buildArray(3, x0), theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double tmp1 = i + 1; |
| double tmp2 = 15 - i; |
| double tmp3 = (i <= 7) ? tmp1 : tmp2; |
| f[i] = x1.add(x2.multiply(tmp2).add(x3.multiply(tmp3)).reciprocal().multiply(tmp1)).negate().add(y[i]); |
| } |
| return f; |
| } |
| |
| private static final double[] y = { |
| 0.14, 0.18, 0.22, 0.25, 0.29, |
| 0.32, 0.35, 0.39, 0.37, 0.58, |
| 0.73, 0.96, 1.34, 2.10, 4.39 |
| }; |
| |
| } |
| |
| private static class KowalikOsborneFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -4867445739880495801L; |
| |
| public KowalikOsborneFunction(double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(11, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| if (theoreticalStartCost > 20.0) { |
| setCostAccuracy(2.0e-4); |
| setParamsAccuracy(5.0e-3); |
| } |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure x4 = variables[3]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| f[i] = x1.multiply(x2.add(v[i]).multiply(v[i])).divide(x4.add(x3.add(v[i]).multiply(v[i]))).negate().add(y[i]); |
| } |
| return f; |
| } |
| |
| private static final double[] v = { |
| 4.0, 2.0, 1.0, 0.5, 0.25, 0.167, 0.125, 0.1, 0.0833, 0.0714, 0.0625 |
| }; |
| |
| private static final double[] y = { |
| 0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627, |
| 0.0456, 0.0342, 0.0323, 0.0235, 0.0246 |
| }; |
| |
| } |
| |
| private static class MeyerFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -838060619150131027L; |
| |
| public MeyerFunction(double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(16, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| if (theoreticalStartCost > 1.0e6) { |
| setCostAccuracy(7.0e-3); |
| setParamsAccuracy(2.0e-2); |
| } |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| f[i] = x1.multiply(x2.divide(x3.add(5.0 * (i + 1) + 45.0)).exp()).subtract(y[i]); |
| } |
| return f; |
| } |
| |
| private static final double[] y = { |
| 34780.0, 28610.0, 23650.0, 19630.0, |
| 16370.0, 13720.0, 11540.0, 9744.0, |
| 8261.0, 7030.0, 6005.0, 5147.0, |
| 4427.0, 3820.0, 3307.0, 2872.0 |
| }; |
| |
| } |
| |
| private static class WatsonFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -9034759294980218927L; |
| |
| public WatsonFunction(int n, double x0, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(31, buildArray(n, x0), theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < (m - 2); ++i) { |
| double div = (i + 1) / 29.0; |
| DerivativeStructure s1 = variables[0].getField().getZero(); |
| DerivativeStructure dx = variables[0].getField().getOne(); |
| for (int j = 1; j < n; ++j) { |
| s1 = s1.add(dx.multiply(j).multiply(variables[j])); |
| dx = dx.multiply(div); |
| } |
| DerivativeStructure s2 = variables[0].getField().getZero(); |
| dx = variables[0].getField().getOne(); |
| for (int j = 0; j < n; ++j) { |
| s2 = s2.add(dx.multiply(variables[j])); |
| dx = dx.multiply(div); |
| } |
| f[i] = s1.subtract(s2.multiply(s2)).subtract(1); |
| } |
| |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| f[m - 2] = x1; |
| f[m - 1] = x2.subtract(x1.multiply(x1)).subtract(1); |
| |
| return f; |
| |
| } |
| |
| } |
| |
| private static class Box3DimensionalFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 5511403858142574493L; |
| |
| public Box3DimensionalFunction(int m, double[] startParams, |
| double theoreticalStartCost) { |
| super(m, startParams, 0.0, |
| new double[] { 1.0, 10.0, 1.0 }); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double tmp = (i + 1) / 10.0; |
| f[i] = x1.multiply(-tmp).exp().subtract(x2.multiply(-tmp).exp()).add( |
| x3.multiply(FastMath.exp(-i - 1) - FastMath.exp(-tmp))); |
| } |
| return f; |
| } |
| |
| } |
| |
| private static class JennrichSampsonFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -2489165190443352947L; |
| |
| public JennrichSampsonFunction(int m, double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(m, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double temp = i + 1; |
| f[i] = x1.multiply(temp).exp().add(x2.multiply(temp).exp()).subtract(2 + 2 * temp).negate(); |
| } |
| return f; |
| } |
| |
| } |
| |
| private static class BrownDennisFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 8340018645694243910L; |
| |
| public BrownDennisFunction(int m, double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(m, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| setCostAccuracy(2.5e-8); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure x4 = variables[3]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double temp = (i + 1) / 5.0; |
| DerivativeStructure tmp1 = x1.add(x2.multiply(temp)).subtract(FastMath.exp(temp)); |
| DerivativeStructure tmp2 = x3.add(x4.multiply(FastMath.sin(temp))).subtract(FastMath.cos(temp)); |
| f[i] = tmp1.multiply(tmp1).add(tmp2.multiply(tmp2)); |
| } |
| return f; |
| } |
| |
| } |
| |
| private static class ChebyquadFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = -2394877275028008594L; |
| |
| private static double[] buildChebyquadArray(int n, double factor) { |
| double[] array = new double[n]; |
| double inv = factor / (n + 1); |
| for (int i = 0; i < n; ++i) { |
| array[i] = (i + 1) * inv; |
| } |
| return array; |
| } |
| |
| public ChebyquadFunction(int n, int m, double factor, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(m, buildChebyquadArray(n, factor), theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| Arrays.fill(f, variables[0].getField().getZero()); |
| |
| for (int j = 0; j < n; ++j) { |
| DerivativeStructure tmp1 = variables[0].getField().getOne(); |
| DerivativeStructure tmp2 = variables[j].multiply(2).subtract(1); |
| DerivativeStructure temp = tmp2.multiply(2); |
| for (int i = 0; i < m; ++i) { |
| f[i] = f[i].add(tmp2); |
| DerivativeStructure ti = temp.multiply(tmp2).subtract(tmp1); |
| tmp1 = tmp2; |
| tmp2 = ti; |
| } |
| } |
| |
| double dx = 1.0 / n; |
| boolean iev = false; |
| for (int i = 0; i < m; ++i) { |
| f[i] = f[i].multiply(dx); |
| if (iev) { |
| f[i] = f[i].add(1.0 / (i * (i + 2))); |
| } |
| iev = ! iev; |
| } |
| |
| return f; |
| |
| } |
| |
| } |
| |
| private static class BrownAlmostLinearFunction extends MinpackFunction { |
| |
| private static final long serialVersionUID = 8239594490466964725L; |
| |
| public BrownAlmostLinearFunction(int m, double factor, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(m, buildArray(m, factor), theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| DerivativeStructure sum = variables[0].getField().getZero().subtract(n + 1); |
| DerivativeStructure prod = variables[0].getField().getOne(); |
| for (int j = 0; j < n; ++j) { |
| sum = sum.add(variables[j]); |
| prod = prod.multiply(variables[j]); |
| } |
| for (int i = 0; i < n; ++i) { |
| f[i] = variables[i].add(sum); |
| } |
| f[n - 1] = prod.subtract(1); |
| return f; |
| } |
| |
| } |
| |
| private static class Osborne1Function extends MinpackFunction { |
| |
| private static final long serialVersionUID = 4006743521149849494L; |
| |
| public Osborne1Function(double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(33, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x1 = variables[0]; |
| DerivativeStructure x2 = variables[1]; |
| DerivativeStructure x3 = variables[2]; |
| DerivativeStructure x4 = variables[3]; |
| DerivativeStructure x5 = variables[4]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double temp = 10.0 * i; |
| DerivativeStructure tmp1 = x4.multiply(-temp).exp(); |
| DerivativeStructure tmp2 = x5.multiply(-temp).exp(); |
| f[i] = x1.add(x2.multiply(tmp1)).add(x3.multiply(tmp2)).negate().add(y[i]); |
| } |
| return f; |
| } |
| |
| private static final double[] y = { |
| 0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881, 0.850, 0.818, 0.784, 0.751, |
| 0.718, 0.685, 0.658, 0.628, 0.603, 0.580, 0.558, 0.538, 0.522, 0.506, 0.490, |
| 0.478, 0.467, 0.457, 0.448, 0.438, 0.431, 0.424, 0.420, 0.414, 0.411, 0.406 |
| }; |
| |
| } |
| |
| private static class Osborne2Function extends MinpackFunction { |
| |
| private static final long serialVersionUID = -8418268780389858746L; |
| |
| public Osborne2Function(double[] startParams, |
| double theoreticalStartCost, |
| double theoreticalMinCost, |
| double[] theoreticalMinParams) { |
| super(65, startParams, theoreticalMinCost, |
| theoreticalMinParams); |
| } |
| |
| @Override |
| public DerivativeStructure[] value(DerivativeStructure[] variables) { |
| DerivativeStructure x01 = variables[0]; |
| DerivativeStructure x02 = variables[1]; |
| DerivativeStructure x03 = variables[2]; |
| DerivativeStructure x04 = variables[3]; |
| DerivativeStructure x05 = variables[4]; |
| DerivativeStructure x06 = variables[5]; |
| DerivativeStructure x07 = variables[6]; |
| DerivativeStructure x08 = variables[7]; |
| DerivativeStructure x09 = variables[8]; |
| DerivativeStructure x10 = variables[9]; |
| DerivativeStructure x11 = variables[10]; |
| DerivativeStructure[] f = new DerivativeStructure[m]; |
| for (int i = 0; i < m; ++i) { |
| double temp = i / 10.0; |
| DerivativeStructure tmp1 = x05.multiply(-temp).exp(); |
| DerivativeStructure tmp2 = x06.negate().multiply(x09.subtract(temp).multiply(x09.subtract(temp))).exp(); |
| DerivativeStructure tmp3 = x07.negate().multiply(x10.subtract(temp).multiply(x10.subtract(temp))).exp(); |
| DerivativeStructure tmp4 = x08.negate().multiply(x11.subtract(temp).multiply(x11.subtract(temp))).exp(); |
| f[i] = x01.multiply(tmp1).add(x02.multiply(tmp2)).add(x03.multiply(tmp3)).add(x04.multiply(tmp4)).negate().add(y[i]); |
| } |
| return f; |
| } |
| |
| private static final double[] y = { |
| 1.366, 1.191, 1.112, 1.013, 0.991, |
| 0.885, 0.831, 0.847, 0.786, 0.725, |
| 0.746, 0.679, 0.608, 0.655, 0.616, |
| 0.606, 0.602, 0.626, 0.651, 0.724, |
| 0.649, 0.649, 0.694, 0.644, 0.624, |
| 0.661, 0.612, 0.558, 0.533, 0.495, |
| 0.500, 0.423, 0.395, 0.375, 0.372, |
| 0.391, 0.396, 0.405, 0.428, 0.429, |
| 0.523, 0.562, 0.607, 0.653, 0.672, |
| 0.708, 0.633, 0.668, 0.645, 0.632, |
| 0.591, 0.559, 0.597, 0.625, 0.739, |
| 0.710, 0.729, 0.720, 0.636, 0.581, |
| 0.428, 0.292, 0.162, 0.098, 0.054 |
| }; |
| |
| } |
| |
| } |
