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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) */ public class MinpackTest extends TestCase { public MinpackTest(String name) { super(name); } 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); } 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); } public void testMinpackLinearRank1ZeroColsAndRows() { minpackTest(new LinearRank1ZeroColsAndRowsFunction(10, 5, 1.0), false); minpackTest(new LinearRank1ZeroColsAndRowsFunction(50, 5, 1.0), false); } public void testMinpackRosenbrok() { minpackTest(new RosenbrockFunction(new double[] { -1.2, 1.0 }, Math.sqrt(24.2)), false); minpackTest(new RosenbrockFunction(new double[] { -12.0, 10.0 }, Math.sqrt(1795769.0)), false); minpackTest(new RosenbrockFunction(new double[] { -120.0, 100.0 }, 11.0 * Math.sqrt(169000121.0)), false); } 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); } 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); } 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[] { 11.4130046614746, -0.896796038685958 }), false); minpackTest(new FreudensteinRothFunction(new double[] { 50.0, -200.0 }, 11426454.595762, 6.99887517242903, new double[] { 11.4127817857886, -0.89680510749204 }), false); } 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); } 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); } 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); } 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); } public void testMinpackBox3Dimensional() { minpackTest(new Box3DimensionalFunction(10, new double[] { 0.0, 10.0, 20.0 }, 32.1115837449572), false); } public void testMinpackJennrichSampson() { minpackTest(new JennrichSampsonFunction(10, new double[] { 0.3, 0.4 }, 64.5856498144943, 11.1517793413499, new double[] { 0.257819926636811, 0.257829976764542 }), false); } 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); } 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); } 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); } 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); } 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(); optimizer.setMaxIterations(100 * (function.getN() + 1)); optimizer.setCostRelativeTolerance(Math.sqrt(2.22044604926e-16)); optimizer.setParRelativeTolerance(Math.sqrt(2.22044604926e-16)); optimizer.setOrthoTolerance(2.22044604926e-16); // assertTrue(function.checkTheoreticalStartCost(optimizer.getRMS())); try { VectorialPointValuePair optimum = optimizer.optimize(function, function.getTarget(), function.getWeight(), function.getStartPoint()); assertFalse(exceptionExpected); assertTrue(function.checkTheoreticalMinCost(optimizer.getRMS())); assertTrue(function.checkTheoreticalMinParams(optimum)); } catch (OptimizationException lsse) { assertTrue(exceptionExpected); } catch (FunctionEvaluationException fe) { assertTrue(exceptionExpected); } } private static abstract class MinpackFunction implements DifferentiableMultivariateVectorialFunction, 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 boolean checkTheoreticalMinCost(double rms) { double threshold = costAccuracy * (1.0 + theoreticalMinCost); return Math.abs(Math.sqrt(m) * rms - theoreticalMinCost) <= threshold; } public boolean checkTheoreticalMinParams(VectorialPointValuePair optimum) { double[] params = optimum.getPointRef(); if (theoreticalMinParams != null) { for (int i = 0; i < theoreticalMinParams.length; ++i) { double mi = theoreticalMinParams[i]; double vi = params[i]; if (Math.abs(mi - vi) > (paramsAccuracy * (1.0 + Math.abs(mi)))) { return false; } } } return true; } public MultivariateMatrixFunction jacobian() { return new MultivariateMatrixFunction() { private static final long serialVersionUID = -2435076097232923678L; public double[][] value(double[] point) { return jacobian(point); } }; } public abstract double[][] jacobian(double[] variables); public abstract double[] value(double[] 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 double[][] jacobian(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[] value(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 { 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 double[][] jacobian(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[] value(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 { private static final long serialVersionUID = -3316653043091995018L; public LinearRank1ZeroColsAndRowsFunction(int m, int n, double x0) { super(m, buildArray(n, x0), Math.sqrt((m * (m + 3) - 6) / (2.0 * (2 * m - 3))), null); } @Override public double[][] jacobian(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[] value(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 { private static final long serialVersionUID = 2893438180956569134L; public RosenbrockFunction(double[] startParams, double theoreticalStartCost) { super(2, startParams, 0.0, buildArray(2, 1.0)); } @Override public double[][] jacobian(double[] variables) { double x1 = variables[0]; return new double[][] { { -20 * x1, 10 }, { -1, 0 } }; } @Override public double[] value(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 { 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 double[][] jacobian(double[] variables) { double x1 = variables[0]; double x2 = variables[1]; double tmpSquare = x1 * x1 + x2 * x2; double tmp1 = twoPi * tmpSquare; double tmp2 = Math.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[] value(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 = Math.atan(x2 / x1) / twoPi; if (x1 < 0) { tmp1 += 0.5; } } double tmp2 = Math.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 * Math.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 double[][] jacobian(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[] value(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 = Math.sqrt( 5.0); private static final double sqrt10 = Math.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 double[][] jacobian(double[] variables) { double x2 = variables[1]; return new double[][] { { 1, x2 * (10 - 3 * x2) - 2 }, { 1, x2 * ( 2 + 3 * x2) - 14, } }; } @Override public double[] value(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 { 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 double[][] jacobian(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[] value(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 { 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 double[][] jacobian(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[] value(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 { 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 double[][] jacobian(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 = Math.exp(tmp1); double tmp3 = x1 * tmp2 / temp; jacobian[i] = new double[] { tmp2, tmp3, -tmp1 * tmp3 }; } return jacobian; } @Override public double[] value(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 * Math.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 { 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 double[][] jacobian(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[] value(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 { 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 double[][] jacobian(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 * Math.exp(-tmp * x1), tmp * Math.exp(-tmp * x2), Math.exp(-i - 1) - Math.exp(-tmp) }; } return jacobian; } @Override public double[] value(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] = Math.exp(-tmp * x1) - Math.exp(-tmp * x2) + (Math.exp(-i - 1) - Math.exp(-tmp)) * x3; } 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 double[][] jacobian(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 * Math.exp(t * x1), -t * Math.exp(t * x2) }; } return jacobian; } @Override public double[] value(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 - Math.exp(temp * x1) - Math.exp(temp * x2); } 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 double[][] jacobian(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 = Math.sin(temp); double tmp1 = x1 + temp * x2 - Math.exp(temp); double tmp2 = x3 + ti * x4 - Math.cos(temp); jacobian[i] = new double[] { 2 * tmp1, 2 * temp * tmp1, 2 * tmp2, 2 * ti * tmp2 }; } return jacobian; } @Override public double[] value(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 - Math.exp(temp); double tmp2 = x3 + Math.sin(temp) * x4 - Math.cos(temp); f[i] = tmp1 * tmp1 + tmp2 * 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 double[][] jacobian(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[] value(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 { 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 double[][] jacobian(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[] value(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 { private static final long serialVersionUID = 4006743521149849494L; public Osborne1Function(double[] startParams, double theoreticalStartCost, double theoreticalMinCost, double[] theoreticalMinParams) { super(33, startParams, theoreticalMinCost, theoreticalMinParams); } @Override public double[][] jacobian(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 = Math.exp(-temp * x4); double tmp2 = Math.exp(-temp * x5); jacobian[i] = new double[] { -1, -tmp1, -tmp2, temp * x2 * tmp1, temp * x3 * tmp2 }; } return jacobian; } @Override public double[] value(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 = Math.exp(-temp * x4); double tmp2 = Math.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 { private static final long serialVersionUID = -8418268780389858746L; public Osborne2Function(double[] startParams, double theoreticalStartCost, double theoreticalMinCost, double[] theoreticalMinParams) { super(65, startParams, theoreticalMinCost, theoreticalMinParams); } @Override public double[][] jacobian(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 = Math.exp(-x05 * temp); double tmp2 = Math.exp(-x06 * (temp - x09) * (temp - x09)); double tmp3 = Math.exp(-x07 * (temp - x10) * (temp - x10)); double tmp4 = Math.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[] value(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 = Math.exp(-x05 * temp); double tmp2 = Math.exp(-x06 * (temp - x09) * (temp - x09)); double tmp3 = Math.exp(-x07 * (temp - x10) * (temp - x10)); double tmp4 = Math.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 }; } }

Other Commons Math examples (source code examples)

Here is a short list of links related to this Commons Math MinpackTest.java source code file:

Commons Math example source code file (MinpackTest.java)

This example Commons Math source code file (MinpackTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

brownalmostlinearfunction, browndennisfunction, chebyquadfunction, chebyquadfunction, freudensteinrothfunction, helicalvalleyfunction, io, kowalikosbornefunction, minpackfunction, minpackfunction, override, override, rosenbrockfunction, util, watsonfunction, watsonfunction

The Commons Math MinpackTest.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math.optimization.general;

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

import junit.framework.TestCase;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction;
import org.apache.commons.math.analysis.MultivariateMatrixFunction;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.VectorialPointValuePair;

/**
 * <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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