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https://github.com/ultimatepp/ultimatepp.git
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169 lines
7.1 KiB
C++
169 lines
7.1 KiB
C++
#include <Core/Core.h>
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#include <plugin/Eigen/Eigen.h>
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using namespace Upp;
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using namespace Eigen;
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#define VerifyIsApprox(a, b) (fabs(a-(b)) < 0.0001)
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struct Eckerle4_functor : NonLinearOptimizationFunctor<double> {
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Eckerle4_functor() : NonLinearOptimizationFunctor(3, 35) {}
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static const double x[35];
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static const double y[35];
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int operator()(const VectorXd &b, VectorXd &fvec) const {
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ASSERT(b.size() == unknowns);
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ASSERT(fvec.size() == datasetLen);
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for(int i = 0; i < 35; i++)
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fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
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return 0;
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}
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};
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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};
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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 };
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struct Thurber_functor : NonLinearOptimizationFunctor<double> {
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static Vector<double> _x, _y;
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Thurber_functor() : NonLinearOptimizationFunctor() {
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_x << -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;
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_y << 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;
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unknowns = 7;
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datasetLen = _x.GetCount();
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}
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int operator()(const VectorXd &b, VectorXd &fvec) const {
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ASSERT(b.size() == unknowns);
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ASSERT(fvec.size() == datasetLen);
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for(int i = 0; i < datasetLen; i++) {
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double x = _x[i], xx = x*x, xxx = xx*x;
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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];
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}
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return 0;
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}
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};
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Vector<double> Thurber_functor::_x, Thurber_functor::_y;
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void NonLinearOptimization() {
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Cout() << "\n\nNon linear equations optimization using Levenberg Marquardt based on Minpack\n"
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"(Given a set of non linear equations and a set of data longer than the equations, "
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"the program finds the equation coefficients that better fit with the equations)";
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{
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Cout() << "\n\nEckerle4 equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml";
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VectorXd x(3);
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x << 1., 10., 500.; // Initial values
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Eckerle4_functor functor;
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NumericalDiff<Eckerle4_functor> numDiff(functor);
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LevenbergMarquardt<NumericalDiff<Eckerle4_functor> > lm(numDiff);
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int ret = lm.minimize(x);
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if (ret == LevenbergMarquardtSpace::ImproperInputParameters ||
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ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
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Cout() << "\nNo convergence!: " << ret;
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else {
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if (VerifyIsApprox(lm.fvec.squaredNorm(), 1.4635887487E-03))
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Cout() << "\nNorm^2 is right";
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if (VerifyIsApprox(x[0], 1.5543827178) &&
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VerifyIsApprox(x[1], 4.0888321754) &&
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VerifyIsApprox(x[2], 4.5154121844E+02))
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Cout() << "\nNon-linear function optimization is right!";
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}
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}
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{
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Cout() << "\n\nThurber equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml\n";
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VectorXd x(7);
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x << 1000, 1000, 400, 40, 0.7, 0.3, 0.0; // Initial values
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Thurber_functor functor; // Vars and equations known at run time
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NumericalDiff<Thurber_functor> numDiff(functor);
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LevenbergMarquardt<NumericalDiff<Thurber_functor> > lm(numDiff);
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lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
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lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
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int ret = lm.minimize(x);
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if (ret == LevenbergMarquardtSpace::ImproperInputParameters ||
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ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
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Cout() << "\nNo convergence!: " << ret;
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else {
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if (VerifyIsApprox(lm.fvec.squaredNorm(), 5.6427082397E+03))
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Cout() << "\nNorm^2 is right";
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if (VerifyIsApprox(x[0], 1.2881396800E+03) &&
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VerifyIsApprox(x[1], 1.4910792535E+03) &&
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VerifyIsApprox(x[2], 5.8323836877E+02) &&
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VerifyIsApprox(x[3], 7.5416644291E+01) &&
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VerifyIsApprox(x[4], 9.6629502864E-01) &&
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VerifyIsApprox(x[5], 3.9797285797E-01) &&
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VerifyIsApprox(x[6], 4.9727297349E-02))
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Cout() << "\nNon-linear function optimization is right!";
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}
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}
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}
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struct Hybrd_functor : NonLinearOptimizationFunctor<double>
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{
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Hybrd_functor() : NonLinearOptimizationFunctor<double>(9, 9) {}
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int operator()(const VectorXd &x, VectorXd &fvec) const {
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double temp, temp1, temp2;
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const ptrdiff_t n = x.size();
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ASSERT(fvec.size() == n);
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for (ptrdiff_t k = 0; k < n; k++) {
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temp = (3. - 2.*x[k])*x[k];
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temp1 = 0.;
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if (k)
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temp1 = x[k-1];
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temp2 = 0.;
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if (k != n-1)
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temp2 = x[k+1];
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fvec[k] = temp - temp1 - 2.*temp2 + 1.;
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}
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return 0;
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}
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};
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void NonLinearSolving() {
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Cout() << "\n\nNon linear equation solving using the Powell hybrid method (\"dogleg\") based on Minpack. "
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<< "(Finds a zero of a system of n nonlinear equations in n variables)";
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const int n = 9;
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VectorXd x;
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x.setConstant(n, -1.); // Initial values
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Hybrd_functor functor;
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HybridNonLinearSolver<Hybrd_functor> solver(functor);
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int ret = solver.solveNumericalDiff(x);
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if (ret == HybridNonLinearSolverSpace::ImproperInputParameters ||
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ret == HybridNonLinearSolverSpace::TooManyFunctionEvaluation ||
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ret == HybridNonLinearSolverSpace::NotMakingProgressJacobian ||
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ret == HybridNonLinearSolverSpace::NotMakingProgressIterations)
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Cout() << "\nNo convergence!: " << ret;
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else {
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if (solver.nfev != 14)
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Cout() << "\nError with nfev!";
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if (VerifyIsApprox(solver.fvec.blueNorm(), 1.192636e-08))
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Cout() << "\nNorm is right";
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if (VerifyIsApprox(x[0], -0.5706545) &&
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VerifyIsApprox(x[1], -0.6816283) &&
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VerifyIsApprox(x[2], -0.7017325) &&
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VerifyIsApprox(x[3], -0.7042129) &&
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VerifyIsApprox(x[4], -0.701369) &&
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VerifyIsApprox(x[5], -0.6918656) &&
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VerifyIsApprox(x[6], -0.665792) &&
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VerifyIsApprox(x[7], -0.5960342) &&
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VerifyIsApprox(x[8], -0.4164121))
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Cout() << "\nEquation solving is right!";
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}
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}
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void NonLinearTests() {
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NonLinearSolving();
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NonLinearOptimization();
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}
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