/*
* 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.optim.nonlinear.vector.jacobian;
import java.util.Arrays;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.analysis.MultivariateMatrixFunction;
import org.apache.commons.math3.optim.PointVectorValuePair;
import org.apache.commons.math3.optim.InitialGuess;
import org.apache.commons.math3.optim.MaxEval;
import org.apache.commons.math3.optim.nonlinear.vector.Target;
import org.apache.commons.math3.optim.nonlinear.vector.Weight;
import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction;
import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian;
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);
try {
PointVectorValuePair optimum
= optimizer.optimize(new MaxEval(400 * (function.getN() + 1)),
function.getModelFunction(),
function.getModelFunctionJacobian(),
new Target(function.getTarget()),
new Weight(function.getWeight()),
new InitialGuess(function.getStartPoint()));
Assert.assertFalse(exceptionExpected);
function.checkTheoreticalMinCost(optimizer.getRMS());
function.checkTheoreticalMinParams(optimum);
} catch (TooManyEvaluationsException e) {
Assert.assertTrue(exceptionExpected);
}
}
private static abstract class MinpackFunction {
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 ModelFunction getModelFunction() {
return new ModelFunction(new MultivariateVectorFunction() {
public double[] value(double[] point) {
return computeValue(point);
}
});
}
public ModelFunctionJacobian getModelFunctionJacobian() {
return new ModelFunctionJacobian(new MultivariateMatrixFunction() {
public double[][] value(double[] point) {
return computeJacobian(point);
}
});
}
public abstract double[][] computeJacobian(double[] variables);
public abstract double[] computeValue(double[] variables);
}
private static class LinearFullRankFunction extends MinpackFunction {
public LinearFullRankFunction(int m, int n, double x0,
double theoreticalStartCost,
double theoreticalMinCost) {
super(m, buildArray(n, x0), theoreticalMinCost,
buildArray(n, -1.0));
}
@Override
public double[][] computeJacobian(double[] variables) {
double t = 2.0 / m;
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
jacobian[i] = new double[n];
for (int j = 0; j < n; ++j) {
jacobian[i][j] = (i == j) ? (1 - t) : -t;
}
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double sum = 0;
for (int i = 0; i < n; ++i) {
sum += variables[i];
}
double t = 1 + 2 * sum / m;
double[] f = new double[m];
for (int i = 0; i < n; ++i) {
f[i] = variables[i] - t;
}
Arrays.fill(f, n, m, -t);
return f;
}
}
private static class LinearRank1Function extends MinpackFunction {
public LinearRank1Function(int m, int n, double x0,
double theoreticalStartCost,
double theoreticalMinCost) {
super(m, buildArray(n, x0), theoreticalMinCost, null);
}
@Override
public double[][] computeJacobian(double[] variables) {
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
jacobian[i] = new double[n];
for (int j = 0; j < n; ++j) {
jacobian[i][j] = (i + 1) * (j + 1);
}
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double[] f = new double[m];
double sum = 0;
for (int i = 0; i < n; ++i) {
sum += (i + 1) * variables[i];
}
for (int i = 0; i < m; ++i) {
f[i] = (i + 1) * sum - 1;
}
return f;
}
}
private static class LinearRank1ZeroColsAndRowsFunction extends MinpackFunction {
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 double[][] computeJacobian(double[] variables) {
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
jacobian[i] = new double[n];
jacobian[i][0] = 0;
for (int j = 1; j < (n - 1); ++j) {
if (i == 0) {
jacobian[i][j] = 0;
} else if (i != (m - 1)) {
jacobian[i][j] = i * (j + 1);
} else {
jacobian[i][j] = 0;
}
}
jacobian[i][n - 1] = 0;
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double[] f = new double[m];
double sum = 0;
for (int i = 1; i < (n - 1); ++i) {
sum += (i + 1) * variables[i];
}
for (int i = 0; i < (m - 1); ++i) {
f[i] = i * sum - 1;
}
f[m - 1] = -1;
return f;
}
}
private static class RosenbrockFunction extends MinpackFunction {
public RosenbrockFunction(double[] startParams, double theoreticalStartCost) {
super(2, startParams, 0.0, buildArray(2, 1.0));
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
return new double[][] { { -20 * x1, 10 }, { -1, 0 } };
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
return new double[] { 10 * (x2 - x1 * x1), 1 - x1 };
}
}
private static class HelicalValleyFunction extends MinpackFunction {
public HelicalValleyFunction(double[] startParams,
double theoreticalStartCost) {
super(3, startParams, 0.0, new double[] { 1.0, 0.0, 0.0 });
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double tmpSquare = x1 * x1 + x2 * x2;
double tmp1 = twoPi * tmpSquare;
double tmp2 = FastMath.sqrt(tmpSquare);
return new double[][] {
{ 100 * x2 / tmp1, -100 * x1 / tmp1, 10 },
{ 10 * x1 / tmp2, 10 * x2 / tmp2, 0 },
{ 0, 0, 1 }
};
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double tmp1;
if (x1 == 0) {
tmp1 = (x2 >= 0) ? 0.25 : -0.25;
} else {
tmp1 = FastMath.atan(x2 / x1) / twoPi;
if (x1 < 0) {
tmp1 += 0.5;
}
}
double tmp2 = FastMath.sqrt(x1 * x1 + x2 * x2);
return new double[] {
10.0 * (x3 - 10 * tmp1),
10.0 * (tmp2 - 1),
x3
};
}
private static final double twoPi = 2.0 * FastMath.PI;
}
private static class PowellSingularFunction extends MinpackFunction {
public PowellSingularFunction(double[] startParams,
double theoreticalStartCost) {
super(4, startParams, 0.0, buildArray(4, 0.0));
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
return new double[][] {
{ 1, 10, 0, 0 },
{ 0, 0, sqrt5, -sqrt5 },
{ 0, 2 * (x2 - 2 * x3), -4 * (x2 - 2 * x3), 0 },
{ 2 * sqrt10 * (x1 - x4), 0, 0, -2 * sqrt10 * (x1 - x4) }
};
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
return new double[] {
x1 + 10 * x2,
sqrt5 * (x3 - x4),
(x2 - 2 * x3) * (x2 - 2 * x3),
sqrt10 * (x1 - x4) * (x1 - x4)
};
}
private static final double sqrt5 = FastMath.sqrt( 5.0);
private static final double sqrt10 = FastMath.sqrt(10.0);
}
private static class FreudensteinRothFunction extends MinpackFunction {
public FreudensteinRothFunction(double[] startParams,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(2, startParams, theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x2 = variables[1];
return new double[][] {
{ 1, x2 * (10 - 3 * x2) - 2 },
{ 1, x2 * ( 2 + 3 * x2) - 14, }
};
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
return new double[] {
-13.0 + x1 + ((5.0 - x2) * x2 - 2.0) * x2,
-29.0 + x1 + ((1.0 + x2) * x2 - 14.0) * x2
};
}
}
private static class BardFunction extends MinpackFunction {
public BardFunction(double x0,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(15, buildArray(3, x0), theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x2 = variables[1];
double x3 = variables[2];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double tmp1 = i + 1;
double tmp2 = 15 - i;
double tmp3 = (i <= 7) ? tmp1 : tmp2;
double tmp4 = x2 * tmp2 + x3 * tmp3;
tmp4 *= tmp4;
jacobian[i] = new double[] { -1, tmp1 * tmp2 / tmp4, tmp1 * tmp3 / tmp4 };
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double tmp1 = i + 1;
double tmp2 = 15 - i;
double tmp3 = (i <= 7) ? tmp1 : tmp2;
f[i] = y[i] - (x1 + tmp1 / (x2 * tmp2 + x3 * tmp3));
}
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 {
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 double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double tmp = v[i] * (v[i] + x3) + x4;
double j1 = -v[i] * (v[i] + x2) / tmp;
double j2 = -v[i] * x1 / tmp;
double j3 = j1 * j2;
double j4 = j3 / v[i];
jacobian[i] = new double[] { j1, j2, j3, j4 };
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
f[i] = y[i] - x1 * (v[i] * (v[i] + x2)) / (v[i] * (v[i] + x3) + x4);
}
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 {
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 double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double temp = 5.0 * (i + 1) + 45.0 + x3;
double tmp1 = x2 / temp;
double tmp2 = FastMath.exp(tmp1);
double tmp3 = x1 * tmp2 / temp;
jacobian[i] = new double[] { tmp2, tmp3, -tmp1 * tmp3 };
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
f[i] = x1 * FastMath.exp(x2 / (5.0 * (i + 1) + 45.0 + x3)) - 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 {
public WatsonFunction(int n, double x0,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(31, buildArray(n, x0), theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double[][] jacobian = new double[m][];
for (int i = 0; i < (m - 2); ++i) {
double div = (i + 1) / 29.0;
double s2 = 0.0;
double dx = 1.0;
for (int j = 0; j < n; ++j) {
s2 += dx * variables[j];
dx *= div;
}
double temp= 2 * div * s2;
dx = 1.0 / div;
jacobian[i] = new double[n];
for (int j = 0; j < n; ++j) {
jacobian[i][j] = dx * (j - temp);
dx *= div;
}
}
jacobian[m - 2] = new double[n];
jacobian[m - 2][0] = 1;
jacobian[m - 1] = new double[n];
jacobian[m - 1][0]= -2 * variables[0];
jacobian[m - 1][1]= 1;
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double[] f = new double[m];
for (int i = 0; i < (m - 2); ++i) {
double div = (i + 1) / 29.0;
double s1 = 0;
double dx = 1;
for (int j = 1; j < n; ++j) {
s1 += j * dx * variables[j];
dx *= div;
}
double s2 = 0;
dx = 1;
for (int j = 0; j < n; ++j) {
s2 += dx * variables[j];
dx *= div;
}
f[i] = s1 - s2 * s2 - 1;
}
double x1 = variables[0];
double x2 = variables[1];
f[m - 2] = x1;
f[m - 1] = x2 - x1 * x1 - 1;
return f;
}
}
private static class Box3DimensionalFunction extends MinpackFunction {
public Box3DimensionalFunction(int m, double[] startParams,
double theoreticalStartCost) {
super(m, startParams, 0.0,
new double[] { 1.0, 10.0, 1.0 });
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double tmp = (i + 1) / 10.0;
jacobian[i] = new double[] {
-tmp * FastMath.exp(-tmp * x1),
tmp * FastMath.exp(-tmp * x2),
FastMath.exp(-i - 1) - FastMath.exp(-tmp)
};
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double tmp = (i + 1) / 10.0;
f[i] = FastMath.exp(-tmp * x1) - FastMath.exp(-tmp * x2)
+ (FastMath.exp(-i - 1) - FastMath.exp(-tmp)) * x3;
}
return f;
}
}
private static class JennrichSampsonFunction extends MinpackFunction {
public JennrichSampsonFunction(int m, double[] startParams,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(m, startParams, theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double t = i + 1;
jacobian[i] = new double[] { -t * FastMath.exp(t * x1), -t * FastMath.exp(t * x2) };
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double temp = i + 1;
f[i] = 2 + 2 * temp - FastMath.exp(temp * x1) - FastMath.exp(temp * x2);
}
return f;
}
}
private static class BrownDennisFunction extends MinpackFunction {
public BrownDennisFunction(int m, double[] startParams,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(m, startParams, theoreticalMinCost,
theoreticalMinParams);
setCostAccuracy(2.5e-8);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double temp = (i + 1) / 5.0;
double ti = FastMath.sin(temp);
double tmp1 = x1 + temp * x2 - FastMath.exp(temp);
double tmp2 = x3 + ti * x4 - FastMath.cos(temp);
jacobian[i] = new double[] {
2 * tmp1, 2 * temp * tmp1, 2 * tmp2, 2 * ti * tmp2
};
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double temp = (i + 1) / 5.0;
double tmp1 = x1 + temp * x2 - FastMath.exp(temp);
double tmp2 = x3 + FastMath.sin(temp) * x4 - FastMath.cos(temp);
f[i] = tmp1 * tmp1 + tmp2 * tmp2;
}
return f;
}
}
private static class ChebyquadFunction extends MinpackFunction {
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 double[][] computeJacobian(double[] variables) {
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
jacobian[i] = new double[n];
}
double dx = 1.0 / n;
for (int j = 0; j < n; ++j) {
double tmp1 = 1;
double tmp2 = 2 * variables[j] - 1;
double temp = 2 * tmp2;
double tmp3 = 0;
double tmp4 = 2;
for (int i = 0; i < m; ++i) {
jacobian[i][j] = dx * tmp4;
double ti = 4 * tmp2 + temp * tmp4 - tmp3;
tmp3 = tmp4;
tmp4 = ti;
ti = temp * tmp2 - tmp1;
tmp1 = tmp2;
tmp2 = ti;
}
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double[] f = new double[m];
for (int j = 0; j < n; ++j) {
double tmp1 = 1;
double tmp2 = 2 * variables[j] - 1;
double temp = 2 * tmp2;
for (int i = 0; i < m; ++i) {
f[i] += tmp2;
double ti = temp * tmp2 - tmp1;
tmp1 = tmp2;
tmp2 = ti;
}
}
double dx = 1.0 / n;
boolean iev = false;
for (int i = 0; i < m; ++i) {
f[i] *= dx;
if (iev) {
f[i] += 1.0 / (i * (i + 2));
}
iev = ! iev;
}
return f;
}
}
private static class BrownAlmostLinearFunction extends MinpackFunction {
public BrownAlmostLinearFunction(int m, double factor,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(m, buildArray(m, factor), theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
jacobian[i] = new double[n];
}
double prod = 1;
for (int j = 0; j < n; ++j) {
prod *= variables[j];
for (int i = 0; i < n; ++i) {
jacobian[i][j] = 1;
}
jacobian[j][j] = 2;
}
for (int j = 0; j < n; ++j) {
double temp = variables[j];
if (temp == 0) {
temp = 1;
prod = 1;
for (int k = 0; k < n; ++k) {
if (k != j) {
prod *= variables[k];
}
}
}
jacobian[n - 1][j] = prod / temp;
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double[] f = new double[m];
double sum = -(n + 1);
double prod = 1;
for (int j = 0; j < n; ++j) {
sum += variables[j];
prod *= variables[j];
}
for (int i = 0; i < n; ++i) {
f[i] = variables[i] + sum;
}
f[n - 1] = prod - 1;
return f;
}
}
private static class Osborne1Function extends MinpackFunction {
public Osborne1Function(double[] startParams,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(33, startParams, theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double x5 = variables[4];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double temp = 10.0 * i;
double tmp1 = FastMath.exp(-temp * x4);
double tmp2 = FastMath.exp(-temp * x5);
jacobian[i] = new double[] {
-1, -tmp1, -tmp2, temp * x2 * tmp1, temp * x3 * tmp2
};
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x1 = variables[0];
double x2 = variables[1];
double x3 = variables[2];
double x4 = variables[3];
double x5 = variables[4];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double temp = 10.0 * i;
double tmp1 = FastMath.exp(-temp * x4);
double tmp2 = FastMath.exp(-temp * x5);
f[i] = y[i] - (x1 + x2 * tmp1 + x3 * tmp2);
}
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 {
public Osborne2Function(double[] startParams,
double theoreticalStartCost,
double theoreticalMinCost,
double[] theoreticalMinParams) {
super(65, startParams, theoreticalMinCost,
theoreticalMinParams);
}
@Override
public double[][] computeJacobian(double[] variables) {
double x01 = variables[0];
double x02 = variables[1];
double x03 = variables[2];
double x04 = variables[3];
double x05 = variables[4];
double x06 = variables[5];
double x07 = variables[6];
double x08 = variables[7];
double x09 = variables[8];
double x10 = variables[9];
double x11 = variables[10];
double[][] jacobian = new double[m][];
for (int i = 0; i < m; ++i) {
double temp = i / 10.0;
double tmp1 = FastMath.exp(-x05 * temp);
double tmp2 = FastMath.exp(-x06 * (temp - x09) * (temp - x09));
double tmp3 = FastMath.exp(-x07 * (temp - x10) * (temp - x10));
double tmp4 = FastMath.exp(-x08 * (temp - x11) * (temp - x11));
jacobian[i] = new double[] {
-tmp1,
-tmp2,
-tmp3,
-tmp4,
temp * x01 * tmp1,
x02 * (temp - x09) * (temp - x09) * tmp2,
x03 * (temp - x10) * (temp - x10) * tmp3,
x04 * (temp - x11) * (temp - x11) * tmp4,
-2 * x02 * x06 * (temp - x09) * tmp2,
-2 * x03 * x07 * (temp - x10) * tmp3,
-2 * x04 * x08 * (temp - x11) * tmp4
};
}
return jacobian;
}
@Override
public double[] computeValue(double[] variables) {
double x01 = variables[0];
double x02 = variables[1];
double x03 = variables[2];
double x04 = variables[3];
double x05 = variables[4];
double x06 = variables[5];
double x07 = variables[6];
double x08 = variables[7];
double x09 = variables[8];
double x10 = variables[9];
double x11 = variables[10];
double[] f = new double[m];
for (int i = 0; i < m; ++i) {
double temp = i / 10.0;
double tmp1 = FastMath.exp(-x05 * temp);
double tmp2 = FastMath.exp(-x06 * (temp - x09) * (temp - x09));
double tmp3 = FastMath.exp(-x07 * (temp - x10) * (temp - x10));
double tmp4 = FastMath.exp(-x08 * (temp - x11) * (temp - x11));
f[i] = y[i] - (x01 * tmp1 + x02 * tmp2 + x03 * tmp3 + x04 * tmp4);
}
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
};
}
}