blob: c4f060b32a187cbcd0f5936c4f862fd1663730b8 [file] [log] [blame]
 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2009 Thomas Capricelli // Copyright (C) 2012 desire Nuentsa #include "main.h" #include // This disables some useless Warnings on MSVC. // It is intended to be done for this test only. #include using std::sqrt; // tolerance for chekcing number of iterations #define LM_EVAL_COUNT_TOL 2 struct lmder_functor : DenseFunctor { lmder_functor(void) : DenseFunctor(3, 15) {} int operator()(const VectorXd &x, VectorXd &fvec) const { double tmp1, tmp2, tmp3; static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39}; for (int i = 0; i < values(); i++) { tmp1 = i + 1; tmp2 = 16 - i - 1; tmp3 = (i >= 8) ? tmp2 : tmp1; fvec[i] = y[i] - (x[0] + tmp1 / (x[1] * tmp2 + x[2] * tmp3)); } return 0; } int df(const VectorXd &x, MatrixXd &fjac) const { double tmp1, tmp2, tmp3, tmp4; for (int i = 0; i < values(); i++) { tmp1 = i + 1; tmp2 = 16 - i - 1; tmp3 = (i >= 8) ? tmp2 : tmp1; tmp4 = (x[1] * tmp2 + x[2] * tmp3); tmp4 = tmp4 * tmp4; fjac(i, 0) = -1; fjac(i, 1) = tmp1 * tmp2 / tmp4; fjac(i, 2) = tmp1 * tmp3 / tmp4; } return 0; } }; void testLmder1() { int n = 3, info; VectorXd x; /* the following starting values provide a rough fit. */ x.setConstant(n, 1.); // do the computation lmder_functor functor; LevenbergMarquardt lm(functor); info = lm.lmder1(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 6); // VERIFY_IS_EQUAL(lm.njev(), 5); // check norm VERIFY_IS_APPROX(lm.fvec().blueNorm(), 0.09063596); // check x VectorXd x_ref(n); x_ref << 0.08241058, 1.133037, 2.343695; VERIFY_IS_APPROX(x, x_ref); } void testLmder() { const int m = 15, n = 3; int info; double fnorm, covfac; VectorXd x; /* the following starting values provide a rough fit. */ x.setConstant(n, 1.); // do the computation lmder_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return values // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 6); // VERIFY_IS_EQUAL(lm.njev(), 5); // check norm fnorm = lm.fvec().blueNorm(); VERIFY_IS_APPROX(fnorm, 0.09063596); // check x VectorXd x_ref(n); x_ref << 0.08241058, 1.133037, 2.343695; VERIFY_IS_APPROX(x, x_ref); // check covariance covfac = fnorm * fnorm / (m - n); internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm MatrixXd cov_ref(n, n); cov_ref << 0.0001531202, 0.002869941, -0.002656662, 0.002869941, 0.09480935, -0.09098995, -0.002656662, -0.09098995, 0.08778727; // std::cout << fjac*covfac << std::endl; MatrixXd cov; cov = covfac * lm.matrixR().topLeftCorner(); VERIFY_IS_APPROX(cov, cov_ref); // TODO: why isn't this allowed ? : // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner() , cov_ref); } struct lmdif_functor : DenseFunctor { lmdif_functor(void) : DenseFunctor(3, 15) {} int operator()(const VectorXd &x, VectorXd &fvec) const { int i; double tmp1, tmp2, tmp3; static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34e0, 2.1e0, 4.39e0}; assert(x.size() == 3); assert(fvec.size() == 15); for (i = 0; i < 15; i++) { tmp1 = i + 1; tmp2 = 15 - i; tmp3 = tmp1; if (i >= 8) tmp3 = tmp2; fvec[i] = y[i] - (x[0] + tmp1 / (x[1] * tmp2 + x[2] * tmp3)); } return 0; } }; void testLmdif1() { const int n = 3; int info; VectorXd x(n), fvec(15); /* the following starting values provide a rough fit. */ x.setConstant(n, 1.); // do the computation lmdif_functor functor; DenseIndex nfev; info = LevenbergMarquardt::lmdif1(functor, x, &nfev); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(nfev, 26); // check norm functor(x, fvec); VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596); // check x VectorXd x_ref(n); x_ref << 0.0824106, 1.1330366, 2.3436947; VERIFY_IS_APPROX(x, x_ref); } void testLmdif() { const int m = 15, n = 3; int info; double fnorm, covfac; VectorXd x(n); /* the following starting values provide a rough fit. */ x.setConstant(n, 1.); // do the computation lmdif_functor functor; NumericalDiff numDiff(functor); LevenbergMarquardt > lm(numDiff); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return values // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 26); // check norm fnorm = lm.fvec().blueNorm(); VERIFY_IS_APPROX(fnorm, 0.09063596); // check x VectorXd x_ref(n); x_ref << 0.08241058, 1.133037, 2.343695; VERIFY_IS_APPROX(x, x_ref); // check covariance covfac = fnorm * fnorm / (m - n); internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm MatrixXd cov_ref(n, n); cov_ref << 0.0001531202, 0.002869942, -0.002656662, 0.002869942, 0.09480937, -0.09098997, -0.002656662, -0.09098997, 0.08778729; // std::cout << fjac*covfac << std::endl; MatrixXd cov; cov = covfac * lm.matrixR().topLeftCorner(); VERIFY_IS_APPROX(cov, cov_ref); // TODO: why isn't this allowed ? : // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner() , cov_ref); } struct chwirut2_functor : DenseFunctor { chwirut2_functor(void) : DenseFunctor(3, 54) {} static const double m_x[54]; static const double m_y[54]; int operator()(const VectorXd &b, VectorXd &fvec) { int i; assert(b.size() == 3); assert(fvec.size() == 54); for (i = 0; i < 54; i++) { double x = m_x[i]; fvec[i] = exp(-b[0] * x) / (b[1] + b[2] * x) - m_y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 3); assert(fjac.rows() == 54); assert(fjac.cols() == 3); for (int i = 0; i < 54; i++) { double x = m_x[i]; double factor = 1. / (b[1] + b[2] * x); double e = exp(-b[0] * x); fjac(i, 0) = -x * e * factor; fjac(i, 1) = -e * factor * factor; fjac(i, 2) = -x * e * factor * factor; } return 0; } }; const double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0}; const double chwirut2_functor::m_y[54] = { 92.9000E0, 57.1000E0, 31.0500E0, 11.5875E0, 8.0250E0, 63.6000E0, 21.4000E0, 14.2500E0, 8.4750E0, 63.8000E0, 26.8000E0, 16.4625E0, 7.1250E0, 67.3000E0, 41.0000E0, 21.1500E0, 8.1750E0, 81.5000E0, 13.1200E0, 59.9000E0, 14.6200E0, 32.9000E0, 5.4400E0, 12.5600E0, 5.4400E0, 32.0000E0, 13.9500E0, 75.8000E0, 20.0000E0, 10.4200E0, 59.5000E0, 21.6700E0, 8.5500E0, 62.0000E0, 20.2000E0, 7.7600E0, 3.7500E0, 11.8100E0, 54.7000E0, 23.7000E0, 11.5500E0, 61.3000E0, 17.7000E0, 8.7400E0, 59.2000E0, 16.3000E0, 8.6200E0, 81.0000E0, 4.8700E0, 14.6200E0, 81.7000E0, 17.1700E0, 81.3000E0, 28.9000E0}; // http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml void testNistChwirut2(void) { const int n = 3; LevenbergMarquardtSpace::Status info; VectorXd x(n); /* * First try */ x << 0.1, 0.01, 0.02; // do the computation chwirut2_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 10); // VERIFY_IS_EQUAL(lm.njev(), 8); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02); // check x VERIFY_IS_APPROX(x[0], 1.6657666537E-01); VERIFY_IS_APPROX(x[1], 5.1653291286E-03); VERIFY_IS_APPROX(x[2], 1.2150007096E-02); /* * Second try */ x << 0.15, 0.008, 0.010; // do the computation lm.resetParameters(); lm.setFtol(1.E6 * NumTraits::epsilon()); lm.setXtol(1.E6 * NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 7); // VERIFY_IS_EQUAL(lm.njev(), 6); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02); // check x VERIFY_IS_APPROX(x[0], 1.6657666537E-01); VERIFY_IS_APPROX(x[1], 5.1653291286E-03); VERIFY_IS_APPROX(x[2], 1.2150007096E-02); } struct misra1a_functor : DenseFunctor { misra1a_functor(void) : DenseFunctor(2, 14) {} static const double m_x[14]; static const double m_y[14]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 2); assert(fvec.size() == 14); for (int i = 0; i < 14; i++) { fvec[i] = b[0] * (1. - exp(-b[1] * m_x[i])) - m_y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 2); assert(fjac.rows() == 14); assert(fjac.cols() == 2); for (int i = 0; i < 14; i++) { fjac(i, 0) = (1. - exp(-b[1] * m_x[i])); fjac(i, 1) = (b[0] * m_x[i] * exp(-b[1] * m_x[i])); } return 0; } }; const double misra1a_functor::m_x[14] = {77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0}; const double misra1a_functor::m_y[14] = {10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0}; // http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml void testNistMisra1a(void) { const int n = 2; int info; VectorXd x(n); /* * First try */ x << 500., 0.0001; // do the computation misra1a_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 19); // VERIFY_IS_EQUAL(lm.njev(), 15); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01); // check x VERIFY_IS_APPROX(x[0], 2.3894212918E+02); VERIFY_IS_APPROX(x[1], 5.5015643181E-04); /* * Second try */ x << 250., 0.0005; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 5); // VERIFY_IS_EQUAL(lm.njev(), 4); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01); // check x VERIFY_IS_APPROX(x[0], 2.3894212918E+02); VERIFY_IS_APPROX(x[1], 5.5015643181E-04); } struct hahn1_functor : DenseFunctor { hahn1_functor(void) : DenseFunctor(7, 236) {} static const double m_x[236]; int operator()(const VectorXd &b, VectorXd &fvec) { static const double m_y[236] = { .591E0, 1.547E0, 2.902E0, 2.894E0, 4.703E0, 6.307E0, 7.03E0, 7.898E0, 9.470E0, 9.484E0, 10.072E0, 10.163E0, 11.615E0, 12.005E0, 12.478E0, 12.982E0, 12.970E0, 13.926E0, 14.452E0, 14.404E0, 15.190E0, 15.550E0, 15.528E0, 15.499E0, 16.131E0, 16.438E0, 16.387E0, 16.549E0, 16.872E0, 16.830E0, 16.926E0, 16.907E0, 16.966E0, 17.060E0, 17.122E0, 17.311E0, 17.355E0, 17.668E0, 17.767E0, 17.803E0, 17.765E0, 17.768E0, 17.736E0, 17.858E0, 17.877E0, 17.912E0, 18.046E0, 18.085E0, 18.291E0, 18.357E0, 18.426E0, 18.584E0, 18.610E0, 18.870E0, 18.795E0, 19.111E0, .367E0, .796E0, 0.892E0, 1.903E0, 2.150E0, 3.697E0, 5.870E0, 6.421E0, 7.422E0, 9.944E0, 11.023E0, 11.87E0, 12.786E0, 14.067E0, 13.974E0, 14.462E0, 14.464E0, 15.381E0, 15.483E0, 15.59E0, 16.075E0, 16.347E0, 16.181E0, 16.915E0, 17.003E0, 16.978E0, 17.756E0, 17.808E0, 17.868E0, 18.481E0, 18.486E0, 19.090E0, 16.062E0, 16.337E0, 16.345E0, 16.388E0, 17.159E0, 17.116E0, 17.164E0, 17.123E0, 17.979E0, 17.974E0, 18.007E0, 17.993E0, 18.523E0, 18.669E0, 18.617E0, 19.371E0, 19.330E0, 0.080E0, 0.248E0, 1.089E0, 1.418E0, 2.278E0, 3.624E0, 4.574E0, 5.556E0, 7.267E0, 7.695E0, 9.136E0, 9.959E0, 9.957E0, 11.600E0, 13.138E0, 13.564E0, 13.871E0, 13.994E0, 14.947E0, 15.473E0, 15.379E0, 15.455E0, 15.908E0, 16.114E0, 17.071E0, 17.135E0, 17.282E0, 17.368E0, 17.483E0, 17.764E0, 18.185E0, 18.271E0, 18.236E0, 18.237E0, 18.523E0, 18.627E0, 18.665E0, 19.086E0, 0.214E0, 0.943E0, 1.429E0, 2.241E0, 2.951E0, 3.782E0, 4.757E0, 5.602E0, 7.169E0, 8.920E0, 10.055E0, 12.035E0, 12.861E0, 13.436E0, 14.167E0, 14.755E0, 15.168E0, 15.651E0, 15.746E0, 16.216E0, 16.445E0, 16.965E0, 17.121E0, 17.206E0, 17.250E0, 17.339E0, 17.793E0, 18.123E0, 18.49E0, 18.566E0, 18.645E0, 18.706E0, 18.924E0, 19.1E0, 0.375E0, 0.471E0, 1.504E0, 2.204E0, 2.813E0, 4.765E0, 9.835E0, 10.040E0, 11.946E0, 12.596E0, 13.303E0, 13.922E0, 14.440E0, 14.951E0, 15.627E0, 15.639E0, 15.814E0, 16.315E0, 16.334E0, 16.430E0, 16.423E0, 17.024E0, 17.009E0, 17.165E0, 17.134E0, 17.349E0, 17.576E0, 17.848E0, 18.090E0, 18.276E0, 18.404E0, 18.519E0, 19.133E0, 19.074E0, 19.239E0, 19.280E0, 19.101E0, 19.398E0, 19.252E0, 19.89E0, 20.007E0, 19.929E0, 19.268E0, 19.324E0, 20.049E0, 20.107E0, 20.062E0, 20.065E0, 19.286E0, 19.972E0, 20.088E0, 20.743E0, 20.83E0, 20.935E0, 21.035E0, 20.93E0, 21.074E0, 21.085E0, 20.935E0}; // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) // called++; assert(b.size() == 7); assert(fvec.size() == 236); for (int i = 0; i < 236; i++) { double x = m_x[i], xx = x * x, xxx = xx * x; fvec[i] = (b[0] + b[1] * x + b[2] * xx + b[3] * xxx) / (1. + b[4] * x + b[5] * xx + b[6] * xxx) - m_y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 7); assert(fjac.rows() == 236); assert(fjac.cols() == 7); for (int i = 0; i < 236; i++) { double x = m_x[i], xx = x * x, xxx = xx * x; double fact = 1. / (1. + b[4] * x + b[5] * xx + b[6] * xxx); fjac(i, 0) = 1. * fact; fjac(i, 1) = x * fact; fjac(i, 2) = xx * fact; fjac(i, 3) = xxx * fact; fact = -(b[0] + b[1] * x + b[2] * xx + b[3] * xxx) * fact * fact; fjac(i, 4) = x * fact; fjac(i, 5) = xx * fact; fjac(i, 6) = xxx * fact; } return 0; } }; const double hahn1_functor::m_x[236] = { 24.41E0, 34.82E0, 44.09E0, 45.07E0, 54.98E0, 65.51E0, 70.53E0, 75.70E0, 89.57E0, 91.14E0, 96.40E0, 97.19E0, 114.26E0, 120.25E0, 127.08E0, 133.55E0, 133.61E0, 158.67E0, 172.74E0, 171.31E0, 202.14E0, 220.55E0, 221.05E0, 221.39E0, 250.99E0, 268.99E0, 271.80E0, 271.97E0, 321.31E0, 321.69E0, 330.14E0, 333.03E0, 333.47E0, 340.77E0, 345.65E0, 373.11E0, 373.79E0, 411.82E0, 419.51E0, 421.59E0, 422.02E0, 422.47E0, 422.61E0, 441.75E0, 447.41E0, 448.7E0, 472.89E0, 476.69E0, 522.47E0, 522.62E0, 524.43E0, 546.75E0, 549.53E0, 575.29E0, 576.00E0, 625.55E0, 20.15E0, 28.78E0, 29.57E0, 37.41E0, 39.12E0, 50.24E0, 61.38E0, 66.25E0, 73.42E0, 95.52E0, 107.32E0, 122.04E0, 134.03E0, 163.19E0, 163.48E0, 175.70E0, 179.86E0, 211.27E0, 217.78E0, 219.14E0, 262.52E0, 268.01E0, 268.62E0, 336.25E0, 337.23E0, 339.33E0, 427.38E0, 428.58E0, 432.68E0, 528.99E0, 531.08E0, 628.34E0, 253.24E0, 273.13E0, 273.66E0, 282.10E0, 346.62E0, 347.19E0, 348.78E0, 351.18E0, 450.10E0, 450.35E0, 451.92E0, 455.56E0, 552.22E0, 553.56E0, 555.74E0, 652.59E0, 656.20E0, 14.13E0, 20.41E0, 31.30E0, 33.84E0, 39.70E0, 48.83E0, 54.50E0, 60.41E0, 72.77E0, 75.25E0, 86.84E0, 94.88E0, 96.40E0, 117.37E0, 139.08E0, 147.73E0, 158.63E0, 161.84E0, 192.11E0, 206.76E0, 209.07E0, 213.32E0, 226.44E0, 237.12E0, 330.90E0, 358.72E0, 370.77E0, 372.72E0, 396.24E0, 416.59E0, 484.02E0, 495.47E0, 514.78E0, 515.65E0, 519.47E0, 544.47E0, 560.11E0, 620.77E0, 18.97E0, 28.93E0, 33.91E0, 40.03E0, 44.66E0, 49.87E0, 55.16E0, 60.90E0, 72.08E0, 85.15E0, 97.06E0, 119.63E0, 133.27E0, 143.84E0, 161.91E0, 180.67E0, 198.44E0, 226.86E0, 229.65E0, 258.27E0, 273.77E0, 339.15E0, 350.13E0, 362.75E0, 371.03E0, 393.32E0, 448.53E0, 473.78E0, 511.12E0, 524.70E0, 548.75E0, 551.64E0, 574.02E0, 623.86E0, 21.46E0, 24.33E0, 33.43E0, 39.22E0, 44.18E0, 55.02E0, 94.33E0, 96.44E0, 118.82E0, 128.48E0, 141.94E0, 156.92E0, 171.65E0, 190.00E0, 223.26E0, 223.88E0, 231.50E0, 265.05E0, 269.44E0, 271.78E0, 273.46E0, 334.61E0, 339.79E0, 349.52E0, 358.18E0, 377.98E0, 394.77E0, 429.66E0, 468.22E0, 487.27E0, 519.54E0, 523.03E0, 612.99E0, 638.59E0, 641.36E0, 622.05E0, 631.50E0, 663.97E0, 646.9E0, 748.29E0, 749.21E0, 750.14E0, 647.04E0, 646.89E0, 746.9E0, 748.43E0, 747.35E0, 749.27E0, 647.61E0, 747.78E0, 750.51E0, 851.37E0, 845.97E0, 847.54E0, 849.93E0, 851.61E0, 849.75E0, 850.98E0, 848.23E0}; // http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml void testNistHahn1(void) { const int n = 7; int info; VectorXd x(n); /* * First try */ x << 10., -1., .05, -.00001, -.05, .001, -.000001; // do the computation hahn1_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 11); // VERIFY_IS_EQUAL(lm.njev(), 10); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00); // check x VERIFY_IS_APPROX(x[0], 1.0776351733E+00); VERIFY_IS_APPROX(x[1], -1.2269296921E-01); VERIFY_IS_APPROX(x[2], 4.0863750610E-03); VERIFY_IS_APPROX(x[3], -1.426264e-06); // shoulde be : -1.4262662514E-06 VERIFY_IS_APPROX(x[4], -5.7609940901E-03); VERIFY_IS_APPROX(x[5], 2.4053735503E-04); VERIFY_IS_APPROX(x[6], -1.2314450199E-07); /* * Second try */ x << .1, -.1, .005, -.000001, -.005, .0001, -.0000001; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 11); // VERIFY_IS_EQUAL(lm.njev(), 10); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00); // check x VERIFY_IS_APPROX(x[0], 1.077640); // should be : 1.0776351733E+00 VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01 VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03 VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06 VERIFY_IS_APPROX(x[4], -5.7609940901E-03); VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04 VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07 } struct misra1d_functor : DenseFunctor { misra1d_functor(void) : DenseFunctor(2, 14) {} static const double x[14]; static const double y[14]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 2); assert(fvec.size() == 14); for (int i = 0; i < 14; i++) { fvec[i] = b[0] * b[1] * x[i] / (1. + b[1] * x[i]) - y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 2); assert(fjac.rows() == 14); assert(fjac.cols() == 2); for (int i = 0; i < 14; i++) { double den = 1. + b[1] * x[i]; fjac(i, 0) = b[1] * x[i] / den; fjac(i, 1) = b[0] * x[i] * (den - b[1] * x[i]) / den / den; } return 0; } }; const double misra1d_functor::x[14] = {77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0}; const double misra1d_functor::y[14] = {10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0}; // http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml void testNistMisra1d(void) { const int n = 2; int info; VectorXd x(n); /* * First try */ x << 500., 0.0001; // do the computation misra1d_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 9); // VERIFY_IS_EQUAL(lm.njev(), 7); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02); // check x VERIFY_IS_APPROX(x[0], 4.3736970754E+02); VERIFY_IS_APPROX(x[1], 3.0227324449E-04); /* * Second try */ x << 450., 0.0003; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 4); // VERIFY_IS_EQUAL(lm.njev(), 3); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02); // check x VERIFY_IS_APPROX(x[0], 4.3736970754E+02); VERIFY_IS_APPROX(x[1], 3.0227324449E-04); } struct lanczos1_functor : DenseFunctor { lanczos1_functor(void) : DenseFunctor(6, 24) {} static const double x[24]; static const double y[24]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 6); assert(fvec.size() == 24); for (int i = 0; i < 24; i++) fvec[i] = b[0] * exp(-b[1] * x[i]) + b[2] * exp(-b[3] * x[i]) + b[4] * exp(-b[5] * x[i]) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 6); assert(fjac.rows() == 24); assert(fjac.cols() == 6); for (int i = 0; i < 24; i++) { fjac(i, 0) = exp(-b[1] * x[i]); fjac(i, 1) = -b[0] * x[i] * exp(-b[1] * x[i]); fjac(i, 2) = exp(-b[3] * x[i]); fjac(i, 3) = -b[2] * x[i] * exp(-b[3] * x[i]); fjac(i, 4) = exp(-b[5] * x[i]); fjac(i, 5) = -b[4] * x[i] * exp(-b[5] * x[i]); } return 0; } }; const double lanczos1_functor::x[24] = {0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00}; const double lanczos1_functor::y[24] = {2.513400000000E+00, 2.044333373291E+00, 1.668404436564E+00, 1.366418021208E+00, 1.123232487372E+00, 9.268897180037E-01, 7.679338563728E-01, 6.388775523106E-01, 5.337835317402E-01, 4.479363617347E-01, 3.775847884350E-01, 3.197393199326E-01, 2.720130773746E-01, 2.324965529032E-01, 1.996589546065E-01, 1.722704126914E-01, 1.493405660168E-01, 1.300700206922E-01, 1.138119324644E-01, 1.000415587559E-01, 8.833209084540E-02, 7.833544019350E-02, 6.976693743449E-02, 6.239312536719E-02}; // http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml void testNistLanczos1(void) { const int n = 6; LevenbergMarquardtSpace::Status info; VectorXd x(n); /* * First try */ x << 1.2, 0.3, 5.6, 5.5, 6.5, 7.6; // do the computation lanczos1_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall); // VERIFY_IS_EQUAL(lm.nfev(), 79); // VERIFY_IS_EQUAL(lm.njev(), 72); // check norm^2 VERIFY(lm.fvec().squaredNorm() <= 1.4307867721E-25); // check x VERIFY_IS_APPROX(x[0], 9.5100000027E-02); VERIFY_IS_APPROX(x[1], 1.0000000001E+00); VERIFY_IS_APPROX(x[2], 8.6070000013E-01); VERIFY_IS_APPROX(x[3], 3.0000000002E+00); VERIFY_IS_APPROX(x[4], 1.5575999998E+00); VERIFY_IS_APPROX(x[5], 5.0000000001E+00); /* * Second try */ x << 0.5, 0.7, 3.6, 4.2, 4., 6.3; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall); // VERIFY_IS_EQUAL(lm.nfev(), 9); // VERIFY_IS_EQUAL(lm.njev(), 8); // check norm^2 VERIFY(lm.fvec().squaredNorm() <= 1.44E-25); // check x VERIFY_IS_APPROX(x[0], 9.5100000027E-02); VERIFY_IS_APPROX(x[1], 1.0000000001E+00); VERIFY_IS_APPROX(x[2], 8.6070000013E-01); VERIFY_IS_APPROX(x[3], 3.0000000002E+00); VERIFY_IS_APPROX(x[4], 1.5575999998E+00); VERIFY_IS_APPROX(x[5], 5.0000000001E+00); } struct rat42_functor : DenseFunctor { rat42_functor(void) : DenseFunctor(3, 9) {} static const double x[9]; static const double y[9]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 3); assert(fvec.size() == 9); for (int i = 0; i < 9; i++) { fvec[i] = b[0] / (1. + exp(b[1] - b[2] * x[i])) - y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 3); assert(fjac.rows() == 9); assert(fjac.cols() == 3); for (int i = 0; i < 9; i++) { double e = exp(b[1] - b[2] * x[i]); fjac(i, 0) = 1. / (1. + e); fjac(i, 1) = -b[0] * e / (1. + e) / (1. + e); fjac(i, 2) = +b[0] * e * x[i] / (1. + e) / (1. + e); } return 0; } }; const double rat42_functor::x[9] = {9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0}; const double rat42_functor::y[9] = {8.930E0, 10.800E0, 18.590E0, 22.330E0, 39.350E0, 56.110E0, 61.730E0, 64.620E0, 67.080E0}; // http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml void testNistRat42(void) { const int n = 3; LevenbergMarquardtSpace::Status info; VectorXd x(n); /* * First try */ x << 100., 1., 0.1; // do the computation rat42_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall); // VERIFY_IS_EQUAL(lm.nfev(), 10); // VERIFY_IS_EQUAL(lm.njev(), 8); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00); // check x VERIFY_IS_APPROX(x[0], 7.2462237576E+01); VERIFY_IS_APPROX(x[1], 2.6180768402E+00); VERIFY_IS_APPROX(x[2], 6.7359200066E-02); /* * Second try */ x << 75., 2.5, 0.07; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall); // VERIFY_IS_EQUAL(lm.nfev(), 6); // VERIFY_IS_EQUAL(lm.njev(), 5); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00); // check x VERIFY_IS_APPROX(x[0], 7.2462237576E+01); VERIFY_IS_APPROX(x[1], 2.6180768402E+00); VERIFY_IS_APPROX(x[2], 6.7359200066E-02); } struct MGH10_functor : DenseFunctor { MGH10_functor(void) : DenseFunctor(3, 16) {} static const double x[16]; static const double y[16]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 3); assert(fvec.size() == 16); for (int i = 0; i < 16; i++) fvec[i] = b[0] * exp(b[1] / (x[i] + b[2])) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 3); assert(fjac.rows() == 16); assert(fjac.cols() == 3); for (int i = 0; i < 16; i++) { double factor = 1. / (x[i] + b[2]); double e = exp(b[1] * factor); fjac(i, 0) = e; fjac(i, 1) = b[0] * factor * e; fjac(i, 2) = -b[1] * b[0] * factor * factor * e; } return 0; } }; const double MGH10_functor::x[16] = {5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02}; const double MGH10_functor::y[16] = {3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03}; // http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml void testNistMGH10(void) { const int n = 3; LevenbergMarquardtSpace::Status info; VectorXd x(n); /* * First try */ x << 2., 400000., 25000.; // do the computation MGH10_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // ++g_test_level; // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall); // --g_test_level; // was: VERIFY_IS_EQUAL(info, 1); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01); // check x VERIFY_IS_APPROX(x[0], 5.6096364710E-03); VERIFY_IS_APPROX(x[1], 6.1813463463E+03); VERIFY_IS_APPROX(x[2], 3.4522363462E+02); // check return value // ++g_test_level; // VERIFY_IS_EQUAL(lm.nfev(), 284 ); // VERIFY_IS_EQUAL(lm.njev(), 249 ); // --g_test_level; VERIFY(lm.nfev() < 284 * LM_EVAL_COUNT_TOL); VERIFY(lm.njev() < 249 * LM_EVAL_COUNT_TOL); /* * Second try */ x << 0.02, 4000., 250.; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // ++g_test_level; // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall); // // was: VERIFY_IS_EQUAL(info, 1); // --g_test_level; // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01); // check x VERIFY_IS_APPROX(x[0], 5.6096364710E-03); VERIFY_IS_APPROX(x[1], 6.1813463463E+03); VERIFY_IS_APPROX(x[2], 3.4522363462E+02); // check return value // ++g_test_level; // VERIFY_IS_EQUAL(lm.nfev(), 126); // VERIFY_IS_EQUAL(lm.njev(), 116); // --g_test_level; VERIFY(lm.nfev() < 126 * LM_EVAL_COUNT_TOL); VERIFY(lm.njev() < 116 * LM_EVAL_COUNT_TOL); } struct BoxBOD_functor : DenseFunctor { BoxBOD_functor(void) : DenseFunctor(2, 6) {} static const double x[6]; int operator()(const VectorXd &b, VectorXd &fvec) { static const double y[6] = {109., 149., 149., 191., 213., 224.}; assert(b.size() == 2); assert(fvec.size() == 6); for (int i = 0; i < 6; i++) fvec[i] = b[0] * (1. - exp(-b[1] * x[i])) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 2); assert(fjac.rows() == 6); assert(fjac.cols() == 2); for (int i = 0; i < 6; i++) { double e = exp(-b[1] * x[i]); fjac(i, 0) = 1. - e; fjac(i, 1) = b[0] * x[i] * e; } return 0; } }; const double BoxBOD_functor::x[6] = {1., 2., 3., 5., 7., 10.}; // http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml void testNistBoxBOD(void) { const int n = 2; int info; VectorXd x(n); /* * First try */ x << 1., 1.; // do the computation BoxBOD_functor functor; LevenbergMarquardt lm(functor); lm.setFtol(1.E6 * NumTraits::epsilon()); lm.setXtol(1.E6 * NumTraits::epsilon()); lm.setFactor(10); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03); // check x VERIFY_IS_APPROX(x[0], 2.1380940889E+02); VERIFY_IS_APPROX(x[1], 5.4723748542E-01); // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY(lm.nfev() < 31); // 31 // VERIFY(lm.njev() < 25); // 25 /* * Second try */ x << 100., 0.75; // do the computation lm.resetParameters(); lm.setFtol(NumTraits::epsilon()); lm.setXtol(NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // ++g_test_level; // VERIFY_IS_EQUAL(lm.nfev(), 16 ); // VERIFY_IS_EQUAL(lm.njev(), 15 ); // --g_test_level; VERIFY(lm.nfev() < 16 * LM_EVAL_COUNT_TOL); VERIFY(lm.njev() < 15 * LM_EVAL_COUNT_TOL); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03); // check x VERIFY_IS_APPROX(x[0], 2.1380940889E+02); VERIFY_IS_APPROX(x[1], 5.4723748542E-01); } struct MGH17_functor : DenseFunctor { MGH17_functor(void) : DenseFunctor(5, 33) {} static const double x[33]; static const double y[33]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 5); assert(fvec.size() == 33); for (int i = 0; i < 33; i++) fvec[i] = b[0] + b[1] * exp(-b[3] * x[i]) + b[2] * exp(-b[4] * x[i]) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 5); assert(fjac.rows() == 33); assert(fjac.cols() == 5); for (int i = 0; i < 33; i++) { fjac(i, 0) = 1.; fjac(i, 1) = exp(-b[3] * x[i]); fjac(i, 2) = exp(-b[4] * x[i]); fjac(i, 3) = -x[i] * b[1] * exp(-b[3] * x[i]); fjac(i, 4) = -x[i] * b[2] * exp(-b[4] * x[i]); } return 0; } }; const double MGH17_functor::x[33] = {0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02}; const double MGH17_functor::y[33] = {8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01}; // http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml void testNistMGH17(void) { const int n = 5; int info; VectorXd x(n); /* * First try */ x << 50., 150., -100., 1., 2.; // do the computation MGH17_functor functor; LevenbergMarquardt lm(functor); lm.setFtol(NumTraits::epsilon()); lm.setXtol(NumTraits::epsilon()); lm.setMaxfev(1000); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05); // check x VERIFY_IS_APPROX(x[0], 3.7541005211E-01); VERIFY_IS_APPROX(x[1], 1.9358469127E+00); VERIFY_IS_APPROX(x[2], -1.4646871366E+00); VERIFY_IS_APPROX(x[3], 1.2867534640E-02); VERIFY_IS_APPROX(x[4], 2.2122699662E-02); // check return value // VERIFY_IS_EQUAL(info, 2); //FIXME Use (lm.info() == Success) // VERIFY(lm.nfev() < 700 ); // 602 // VERIFY(lm.njev() < 600 ); // 545 /* * Second try */ x << 0.5, 1.5, -1, 0.01, 0.02; // do the computation lm.resetParameters(); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 18); // VERIFY_IS_EQUAL(lm.njev(), 15); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05); // check x VERIFY_IS_APPROX(x[0], 3.7541005211E-01); VERIFY_IS_APPROX(x[1], 1.9358469127E+00); VERIFY_IS_APPROX(x[2], -1.4646871366E+00); VERIFY_IS_APPROX(x[3], 1.2867534640E-02); VERIFY_IS_APPROX(x[4], 2.2122699662E-02); } struct MGH09_functor : DenseFunctor { MGH09_functor(void) : DenseFunctor(4, 11) {} static const double _x[11]; static const double y[11]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 4); assert(fvec.size() == 11); for (int i = 0; i < 11; i++) { double x = _x[i], xx = x * x; fvec[i] = b[0] * (xx + x * b[1]) / (xx + x * b[2] + b[3]) - y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 4); assert(fjac.rows() == 11); assert(fjac.cols() == 4); for (int i = 0; i < 11; i++) { double x = _x[i], xx = x * x; double factor = 1. / (xx + x * b[2] + b[3]); fjac(i, 0) = (xx + x * b[1]) * factor; fjac(i, 1) = b[0] * x * factor; fjac(i, 2) = -b[0] * (xx + x * b[1]) * x * factor * factor; fjac(i, 3) = -b[0] * (xx + x * b[1]) * factor * factor; } return 0; } }; const double MGH09_functor::_x[11] = {4., 2., 1., 5.E-1, 2.5E-01, 1.670000E-01, 1.250000E-01, 1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02}; const double MGH09_functor::y[11] = {1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02}; // http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml void testNistMGH09(void) { const int n = 4; int info; VectorXd x(n); /* * First try */ x << 25., 39, 41.5, 39.; // do the computation MGH09_functor functor; LevenbergMarquardt lm(functor); lm.setMaxfev(1000); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04); // check x VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01 VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01 VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01 VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01 // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY(lm.nfev() < 510 ); // 490 // VERIFY(lm.njev() < 400 ); // 376 /* * Second try */ x << 0.25, 0.39, 0.415, 0.39; // do the computation lm.resetParameters(); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 18); // VERIFY_IS_EQUAL(lm.njev(), 16); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04); // check x VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01 VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01 VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01 VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01 } struct Bennett5_functor : DenseFunctor { Bennett5_functor(void) : DenseFunctor(3, 154) {} static const double x[154]; static const double y[154]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 3); assert(fvec.size() == 154); for (int i = 0; i < 154; i++) fvec[i] = b[0] * pow(b[1] + x[i], -1. / b[2]) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 3); assert(fjac.rows() == 154); assert(fjac.cols() == 3); for (int i = 0; i < 154; i++) { double e = pow(b[1] + x[i], -1. / b[2]); fjac(i, 0) = e; fjac(i, 1) = -b[0] * e / b[2] / (b[1] + x[i]); fjac(i, 2) = b[0] * e * log(b[1] + x[i]) / b[2] / b[2]; } return 0; } }; const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0, 11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0}; const double Bennett5_functor::y[154] = { -34.834702E0, -34.393200E0, -34.152901E0, -33.979099E0, -33.845901E0, -33.732899E0, -33.640301E0, -33.559200E0, -33.486801E0, -33.423100E0, -33.365101E0, -33.313000E0, -33.260899E0, -33.217400E0, -33.176899E0, -33.139198E0, -33.101601E0, -33.066799E0, -33.035000E0, -33.003101E0, -32.971298E0, -32.942299E0, -32.916302E0, -32.890202E0, -32.864101E0, -32.841000E0, -32.817799E0, -32.797501E0, -32.774300E0, -32.757000E0, -32.733799E0, -32.716400E0, -32.699100E0, -32.678799E0, -32.661400E0, -32.644001E0, -32.626701E0, -32.612202E0, -32.597698E0, -32.583199E0, -32.568699E0, -32.554298E0, -32.539799E0, -32.525299E0, -32.510799E0, -32.499199E0, -32.487598E0, -32.473202E0, -32.461601E0, -32.435501E0, -32.435501E0, -32.426800E0, -32.412300E0, -32.400799E0, -32.392101E0, -32.380501E0, -32.366001E0, -32.357300E0, -32.348598E0, -32.339901E0, -32.328400E0, -32.319698E0, -32.311001E0, -32.299400E0, -32.290699E0, -32.282001E0, -32.273300E0, -32.264599E0, -32.256001E0, -32.247299E0, -32.238602E0, -32.229900E0, -32.224098E0, -32.215401E0, -32.203800E0, -32.198002E0, -32.189400E0, -32.183601E0, -32.174900E0, -32.169102E0, -32.163300E0, -32.154598E0, -32.145901E0, -32.140099E0, -32.131401E0, -32.125599E0, -32.119801E0, -32.111198E0, -32.105400E0, -32.096699E0, -32.090900E0, -32.088001E0, -32.079300E0, -32.073502E0, -32.067699E0, -32.061901E0, -32.056099E0, -32.050301E0, -32.044498E0, -32.038799E0, -32.033001E0, -32.027199E0, -32.024300E0, -32.018501E0, -32.012699E0, -32.004002E0, -32.001099E0, -31.995300E0, -31.989500E0, -31.983700E0, -31.977900E0, -31.972099E0, -31.969299E0, -31.963501E0, -31.957701E0, -31.951900E0, -31.946100E0, -31.940300E0, -31.937401E0, -31.931601E0, -31.925800E0, -31.922899E0, -31.917101E0, -31.911301E0, -31.908400E0, -31.902599E0, -31.896900E0, -31.893999E0, -31.888201E0, -31.885300E0, -31.882401E0, -31.876600E0, -31.873699E0, -31.867901E0, -31.862101E0, -31.859200E0, -31.856300E0, -31.850500E0, -31.844700E0, -31.841801E0, -31.838900E0, -31.833099E0, -31.830200E0, -31.827299E0, -31.821600E0, -31.818701E0, -31.812901E0, -31.809999E0, -31.807100E0, -31.801300E0, -31.798401E0, -31.795500E0, -31.789700E0, -31.786800E0}; // http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml void testNistBennett5(void) { const int n = 3; int info; VectorXd x(n); /* * First try */ x << -2000., 50., 0.8; // do the computation Bennett5_functor functor; LevenbergMarquardt lm(functor); lm.setMaxfev(1000); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 758); // VERIFY_IS_EQUAL(lm.njev(), 744); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04); // check x VERIFY_IS_APPROX(x[0], -2.5235058043E+03); VERIFY_IS_APPROX(x[1], 4.6736564644E+01); VERIFY_IS_APPROX(x[2], 9.3218483193E-01); /* * Second try */ x << -1500., 45., 0.85; // do the computation lm.resetParameters(); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 203); // VERIFY_IS_EQUAL(lm.njev(), 192); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04); // check x VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03 VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01); VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01); } struct thurber_functor : DenseFunctor { thurber_functor(void) : DenseFunctor(7, 37) {} static const double _x[37]; static const double _y[37]; int operator()(const VectorXd &b, VectorXd &fvec) { // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) // called++; assert(b.size() == 7); assert(fvec.size() == 37); for (int i = 0; i < 37; i++) { double x = _x[i], xx = x * x, xxx = xx * x; fvec[i] = (b[0] + b[1] * x + b[2] * xx + b[3] * xxx) / (1. + b[4] * x + b[5] * xx + b[6] * xxx) - _y[i]; } return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 7); assert(fjac.rows() == 37); assert(fjac.cols() == 7); for (int i = 0; i < 37; i++) { double x = _x[i], xx = x * x, xxx = xx * x; double fact = 1. / (1. + b[4] * x + b[5] * xx + b[6] * xxx); fjac(i, 0) = 1. * fact; fjac(i, 1) = x * fact; fjac(i, 2) = xx * fact; fjac(i, 3) = xxx * fact; fact = -(b[0] + b[1] * x + b[2] * xx + b[3] * xxx) * fact * fact; fjac(i, 4) = x * fact; fjac(i, 5) = xx * fact; fjac(i, 6) = xxx * fact; } return 0; } }; const double thurber_functor::_x[37] = {-3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0}; const double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0}; // http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml void testNistThurber(void) { const int n = 7; int info; VectorXd x(n); /* * First try */ x << 1000, 1000, 400, 40, 0.7, 0.3, 0.0; // do the computation thurber_functor functor; LevenbergMarquardt lm(functor); lm.setFtol(1.E4 * NumTraits::epsilon()); lm.setXtol(1.E4 * NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 39); // VERIFY_IS_EQUAL(lm.njev(), 36); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03); // check x VERIFY_IS_APPROX(x[0], 1.2881396800E+03); VERIFY_IS_APPROX(x[1], 1.4910792535E+03); VERIFY_IS_APPROX(x[2], 5.8323836877E+02); VERIFY_IS_APPROX(x[3], 7.5416644291E+01); VERIFY_IS_APPROX(x[4], 9.6629502864E-01); VERIFY_IS_APPROX(x[5], 3.9797285797E-01); VERIFY_IS_APPROX(x[6], 4.9727297349E-02); /* * Second try */ x << 1300, 1500, 500, 75, 1, 0.4, 0.05; // do the computation lm.resetParameters(); lm.setFtol(1.E4 * NumTraits::epsilon()); lm.setXtol(1.E4 * NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 29); // VERIFY_IS_EQUAL(lm.njev(), 28); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03); // check x VERIFY_IS_APPROX(x[0], 1.2881396800E+03); VERIFY_IS_APPROX(x[1], 1.4910792535E+03); VERIFY_IS_APPROX(x[2], 5.8323836877E+02); VERIFY_IS_APPROX(x[3], 7.5416644291E+01); VERIFY_IS_APPROX(x[4], 9.6629502864E-01); VERIFY_IS_APPROX(x[5], 3.9797285797E-01); VERIFY_IS_APPROX(x[6], 4.9727297349E-02); } struct rat43_functor : DenseFunctor { rat43_functor(void) : DenseFunctor(4, 15) {} static const double x[15]; static const double y[15]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 4); assert(fvec.size() == 15); for (int i = 0; i < 15; i++) fvec[i] = b[0] * pow(1. + exp(b[1] - b[2] * x[i]), -1. / b[3]) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 4); assert(fjac.rows() == 15); assert(fjac.cols() == 4); for (int i = 0; i < 15; i++) { double e = exp(b[1] - b[2] * x[i]); double power = -1. / b[3]; fjac(i, 0) = pow(1. + e, power); fjac(i, 1) = power * b[0] * e * pow(1. + e, power - 1.); fjac(i, 2) = -power * b[0] * e * x[i] * pow(1. + e, power - 1.); fjac(i, 3) = b[0] * power * power * log(1. + e) * pow(1. + e, power); } return 0; } }; const double rat43_functor::x[15] = {1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15.}; const double rat43_functor::y[15] = {16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41}; // http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml void testNistRat43(void) { const int n = 4; int info; VectorXd x(n); /* * First try */ x << 100., 10., 1., 1.; // do the computation rat43_functor functor; LevenbergMarquardt lm(functor); lm.setFtol(1.E6 * NumTraits::epsilon()); lm.setXtol(1.E6 * NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 27); // VERIFY_IS_EQUAL(lm.njev(), 20); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03); // check x VERIFY_IS_APPROX(x[0], 6.9964151270E+02); VERIFY_IS_APPROX(x[1], 5.2771253025E+00); VERIFY_IS_APPROX(x[2], 7.5962938329E-01); VERIFY_IS_APPROX(x[3], 1.2792483859E+00); /* * Second try */ x << 700., 5., 0.75, 1.3; // do the computation lm.resetParameters(); lm.setFtol(1.E5 * NumTraits::epsilon()); lm.setXtol(1.E5 * NumTraits::epsilon()); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 9); // VERIFY_IS_EQUAL(lm.njev(), 8); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03); // check x VERIFY_IS_APPROX(x[0], 6.9964151270E+02); VERIFY_IS_APPROX(x[1], 5.2771253025E+00); VERIFY_IS_APPROX(x[2], 7.5962938329E-01); VERIFY_IS_APPROX(x[3], 1.2792483859E+00); } struct eckerle4_functor : DenseFunctor { eckerle4_functor(void) : DenseFunctor(3, 35) {} static const double x[35]; static const double y[35]; int operator()(const VectorXd &b, VectorXd &fvec) { assert(b.size() == 3); assert(fvec.size() == 35); for (int i = 0; i < 35; i++) fvec[i] = b[0] / b[1] * exp(-0.5 * (x[i] - b[2]) * (x[i] - b[2]) / (b[1] * b[1])) - y[i]; return 0; } int df(const VectorXd &b, MatrixXd &fjac) { assert(b.size() == 3); assert(fjac.rows() == 35); assert(fjac.cols() == 3); for (int i = 0; i < 35; i++) { double b12 = b[1] * b[1]; double e = exp(-0.5 * (x[i] - b[2]) * (x[i] - b[2]) / b12); fjac(i, 0) = e / b[1]; fjac(i, 1) = ((x[i] - b[2]) * (x[i] - b[2]) / b12 - 1.) * b[0] * e / b12; fjac(i, 2) = (x[i] - b[2]) * e * b[0] / b[1] / b12; } return 0; } }; const double eckerle4_functor::x[35] = {400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0}; const double eckerle4_functor::y[35] = {0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710}; // http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml void testNistEckerle4(void) { const int n = 3; int info; VectorXd x(n); /* * First try */ x << 1., 10., 500.; // do the computation eckerle4_functor functor; LevenbergMarquardt lm(functor); info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 18); // VERIFY_IS_EQUAL(lm.njev(), 15); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03); // check x VERIFY_IS_APPROX(x[0], 1.5543827178); VERIFY_IS_APPROX(x[1], 4.0888321754); VERIFY_IS_APPROX(x[2], 4.5154121844E+02); /* * Second try */ x << 1.5, 5., 450.; // do the computation info = lm.minimize(x); EIGEN_UNUSED_VARIABLE(info) // check return value // VERIFY_IS_EQUAL(info, 1); // VERIFY_IS_EQUAL(lm.nfev(), 7); // VERIFY_IS_EQUAL(lm.njev(), 6); // check norm^2 VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03); // check x VERIFY_IS_APPROX(x[0], 1.5543827178); VERIFY_IS_APPROX(x[1], 4.0888321754); VERIFY_IS_APPROX(x[2], 4.5154121844E+02); } EIGEN_DECLARE_TEST(levenberg_marquardt) { // Tests using the examples provided by (c)minpack CALL_SUBTEST(testLmder1()); CALL_SUBTEST(testLmder()); CALL_SUBTEST(testLmdif1()); // CALL_SUBTEST(testLmstr1()); // CALL_SUBTEST(testLmstr()); CALL_SUBTEST(testLmdif()); // NIST tests, level of difficulty = "Lower" CALL_SUBTEST(testNistMisra1a()); CALL_SUBTEST(testNistChwirut2()); // NIST tests, level of difficulty = "Average" CALL_SUBTEST(testNistHahn1()); CALL_SUBTEST(testNistMisra1d()); CALL_SUBTEST(testNistMGH17()); CALL_SUBTEST(testNistLanczos1()); // // NIST tests, level of difficulty = "Higher" CALL_SUBTEST(testNistRat42()); CALL_SUBTEST(testNistMGH10()); CALL_SUBTEST(testNistBoxBOD()); // CALL_SUBTEST(testNistMGH09()); CALL_SUBTEST(testNistBennett5()); CALL_SUBTEST(testNistThurber()); CALL_SUBTEST(testNistRat43()); CALL_SUBTEST(testNistEckerle4()); }