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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 { @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) { final double tol = 2.22044604926e-16; final double sqrtTol = FastMath.sqrt(tol); LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer() .withCostRelativeTolerance(sqrtTol) .withParameterRelativeTolerance(sqrtTol) .withOrthoTolerance(tol); LeastSquaresProblem problem = new LeastSquaresBuilder() .maxEvaluations(400 * (function.getN() + 1)) .maxIterations(2000) .model(function.getModelFunction(), function.getModelFunctionJacobian()) .target(function.getTarget()) .weight(new DiagonalMatrix(function.getWeight())) .start(function.getStartPoint()) .build(); try { final Optimum optimum = optimizer.optimize(problem); Assert.assertFalse(exceptionExpected); function.checkTheoreticalMinCost(optimum.getRMS()); function.checkTheoreticalMinParams(optimum.getPoint().toArray()); } 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(double[] params) { 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 MultivariateVectorFunction getModelFunction() { return new MultivariateVectorFunction() { public double[] value(double[] point) { return computeValue(point); } }; } public MultivariateMatrixFunction getModelFunctionJacobian() { return 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 }; } }

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Java - Java tags/keywords

brownalmostlinearfunction, browndennisfunction, chebyquadfunction, freudensteinrothfunction, helicalvalleyfunction, kowalikosbornefunction, linearrank1function, linearrank1zerocolsandrowsfunction, minpackfunction, override, powellsingularfunction, rosenbrockfunction, test, util, watsonfunction

The MinpackTest.java Java example source code

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

package org.apache.commons.math3.fitting.leastsquares;

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.fitting.leastsquares.LeastSquaresOptimizer.Optimum;
import org.apache.commons.math3.linear.DiagonalMatrix;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * <p>Some of the unit tests are re-implementations of the MINPACK  and  test files.
 * The redistribution policy for MINPACK is available <a
 * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
 * convenience, it is reproduced below.</p>

 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 * <tr>
 * Minpack Copyright Notice (1999) University of Chicago. * All rights reserved * </td>
* Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * <ol> * <li>Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer.</li> * <li>Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution.</li> * <li>The end-user documentation included with the redistribution, if any, * must include the following acknowledgment: * <code>This product includes software developed by the University of * Chicago, as Operator of Argonne National Laboratory.</code> * Alternately, this acknowledgment may appear in the software itself, * if and wherever such third-party acknowledgments normally appear.</li> * <li>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL * BE CORRECTED.</strong> * <li>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong> * <ol>
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