1// Ceres Solver - A fast non-linear least squares minimizer 2// Copyright 2012 Google Inc. All rights reserved. 3// http://code.google.com/p/ceres-solver/ 4// 5// Redistribution and use in source and binary forms, with or without 6// modification, are permitted provided that the following conditions are met: 7// 8// * Redistributions of source code must retain the above copyright notice, 9// this list of conditions and the following disclaimer. 10// * Redistributions in binary form must reproduce the above copyright notice, 11// this list of conditions and the following disclaimer in the documentation 12// and/or other materials provided with the distribution. 13// * Neither the name of Google Inc. nor the names of its contributors may be 14// used to endorse or promote products derived from this software without 15// specific prior written permission. 16// 17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27// POSSIBILITY OF SUCH DAMAGE. 28// 29// Author: sameeragarwal@google.com (Sameer Agarwal) 30// 31// The National Institute of Standards and Technology has released a 32// set of problems to test non-linear least squares solvers. 33// 34// More information about the background on these problems and 35// suggested evaluation methodology can be found at: 36// 37// http://www.itl.nist.gov/div898/strd/nls/nls_info.shtml 38// 39// The problem data themselves can be found at 40// 41// http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml 42// 43// The problems are divided into three levels of difficulty, Easy, 44// Medium and Hard. For each problem there are two starting guesses, 45// the first one far away from the global minimum and the second 46// closer to it. 47// 48// A problem is considered successfully solved, if every components of 49// the solution matches the globally optimal solution in at least 4 50// digits or more. 51// 52// This dataset was used for an evaluation of Non-linear least squares 53// solvers: 54// 55// P. F. Mondragon & B. Borchers, A Comparison of Nonlinear Regression 56// Codes, Journal of Modern Applied Statistical Methods, 4(1):343-351, 57// 2005. 58// 59// The results from Mondragon & Borchers can be summarized as 60// Excel Gnuplot GaussFit HBN MinPack 61// Average LRE 2.3 4.3 4.0 6.8 4.4 62// Winner 1 5 12 29 12 63// 64// Where the row Winner counts, the number of problems for which the 65// solver had the highest LRE. 66 67// In this file, we implement the same evaluation methodology using 68// Ceres. Currently using Levenberg-Marquard with DENSE_QR, we get 69// 70// Excel Gnuplot GaussFit HBN MinPack Ceres 71// Average LRE 2.3 4.3 4.0 6.8 4.4 9.4 72// Winner 0 0 5 11 2 41 73 74#include <iostream> 75#include <iterator> 76#include <fstream> 77#include "ceres/ceres.h" 78#include "gflags/gflags.h" 79#include "glog/logging.h" 80#include "Eigen/Core" 81 82DEFINE_string(nist_data_dir, "", "Directory containing the NIST non-linear" 83 "regression examples"); 84DEFINE_string(minimizer, "trust_region", 85 "Minimizer type to use, choices are: line_search & trust_region"); 86DEFINE_string(trust_region_strategy, "levenberg_marquardt", 87 "Options are: levenberg_marquardt, dogleg"); 88DEFINE_string(dogleg, "traditional_dogleg", 89 "Options are: traditional_dogleg, subspace_dogleg"); 90DEFINE_string(linear_solver, "dense_qr", "Options are: " 91 "sparse_cholesky, dense_qr, dense_normal_cholesky and" 92 "cgnr"); 93DEFINE_string(preconditioner, "jacobi", "Options are: " 94 "identity, jacobi"); 95DEFINE_string(line_search, "armijo", 96 "Line search algorithm to use, choices are: armijo and wolfe."); 97DEFINE_string(line_search_direction, "lbfgs", 98 "Line search direction algorithm to use, choices: lbfgs, bfgs"); 99DEFINE_int32(max_line_search_iterations, 20, 100 "Maximum number of iterations for each line search."); 101DEFINE_int32(max_line_search_restarts, 10, 102 "Maximum number of restarts of line search direction algorithm."); 103DEFINE_string(line_search_interpolation, "cubic", 104 "Degree of polynomial aproximation in line search, " 105 "choices are: bisection, quadratic & cubic."); 106DEFINE_int32(lbfgs_rank, 20, 107 "Rank of L-BFGS inverse Hessian approximation in line search."); 108DEFINE_bool(approximate_eigenvalue_bfgs_scaling, false, 109 "Use approximate eigenvalue scaling in (L)BFGS line search."); 110DEFINE_double(sufficient_decrease, 1.0e-4, 111 "Line search Armijo sufficient (function) decrease factor."); 112DEFINE_double(sufficient_curvature_decrease, 0.9, 113 "Line search Wolfe sufficient curvature decrease factor."); 114DEFINE_int32(num_iterations, 10000, "Number of iterations"); 115DEFINE_bool(nonmonotonic_steps, false, "Trust region algorithm can use" 116 " nonmonotic steps"); 117DEFINE_double(initial_trust_region_radius, 1e4, "Initial trust region radius"); 118 119namespace ceres { 120namespace examples { 121 122using Eigen::Dynamic; 123using Eigen::RowMajor; 124typedef Eigen::Matrix<double, Dynamic, 1> Vector; 125typedef Eigen::Matrix<double, Dynamic, Dynamic, RowMajor> Matrix; 126 127void SplitStringUsingChar(const string& full, 128 const char delim, 129 vector<string>* result) { 130 back_insert_iterator< vector<string> > it(*result); 131 132 const char* p = full.data(); 133 const char* end = p + full.size(); 134 while (p != end) { 135 if (*p == delim) { 136 ++p; 137 } else { 138 const char* start = p; 139 while (++p != end && *p != delim) { 140 // Skip to the next occurence of the delimiter. 141 } 142 *it++ = string(start, p - start); 143 } 144 } 145} 146 147bool GetAndSplitLine(std::ifstream& ifs, std::vector<std::string>* pieces) { 148 pieces->clear(); 149 char buf[256]; 150 ifs.getline(buf, 256); 151 SplitStringUsingChar(std::string(buf), ' ', pieces); 152 return true; 153} 154 155void SkipLines(std::ifstream& ifs, int num_lines) { 156 char buf[256]; 157 for (int i = 0; i < num_lines; ++i) { 158 ifs.getline(buf, 256); 159 } 160} 161 162class NISTProblem { 163 public: 164 explicit NISTProblem(const std::string& filename) { 165 std::ifstream ifs(filename.c_str(), std::ifstream::in); 166 167 std::vector<std::string> pieces; 168 SkipLines(ifs, 24); 169 GetAndSplitLine(ifs, &pieces); 170 const int kNumResponses = std::atoi(pieces[1].c_str()); 171 172 GetAndSplitLine(ifs, &pieces); 173 const int kNumPredictors = std::atoi(pieces[0].c_str()); 174 175 GetAndSplitLine(ifs, &pieces); 176 const int kNumObservations = std::atoi(pieces[0].c_str()); 177 178 SkipLines(ifs, 4); 179 GetAndSplitLine(ifs, &pieces); 180 const int kNumParameters = std::atoi(pieces[0].c_str()); 181 SkipLines(ifs, 8); 182 183 // Get the first line of initial and final parameter values to 184 // determine the number of tries. 185 GetAndSplitLine(ifs, &pieces); 186 const int kNumTries = pieces.size() - 4; 187 188 predictor_.resize(kNumObservations, kNumPredictors); 189 response_.resize(kNumObservations, kNumResponses); 190 initial_parameters_.resize(kNumTries, kNumParameters); 191 final_parameters_.resize(1, kNumParameters); 192 193 // Parse the line for parameter b1. 194 int parameter_id = 0; 195 for (int i = 0; i < kNumTries; ++i) { 196 initial_parameters_(i, parameter_id) = std::atof(pieces[i + 2].c_str()); 197 } 198 final_parameters_(0, parameter_id) = std::atof(pieces[2 + kNumTries].c_str()); 199 200 // Parse the remaining parameter lines. 201 for (int parameter_id = 1; parameter_id < kNumParameters; ++parameter_id) { 202 GetAndSplitLine(ifs, &pieces); 203 // b2, b3, .... 204 for (int i = 0; i < kNumTries; ++i) { 205 initial_parameters_(i, parameter_id) = std::atof(pieces[i + 2].c_str()); 206 } 207 final_parameters_(0, parameter_id) = std::atof(pieces[2 + kNumTries].c_str()); 208 } 209 210 // Certfied cost 211 SkipLines(ifs, 1); 212 GetAndSplitLine(ifs, &pieces); 213 certified_cost_ = std::atof(pieces[4].c_str()) / 2.0; 214 215 // Read the observations. 216 SkipLines(ifs, 18 - kNumParameters); 217 for (int i = 0; i < kNumObservations; ++i) { 218 GetAndSplitLine(ifs, &pieces); 219 // Response. 220 for (int j = 0; j < kNumResponses; ++j) { 221 response_(i, j) = std::atof(pieces[j].c_str()); 222 } 223 224 // Predictor variables. 225 for (int j = 0; j < kNumPredictors; ++j) { 226 predictor_(i, j) = std::atof(pieces[j + kNumResponses].c_str()); 227 } 228 } 229 } 230 231 Matrix initial_parameters(int start) const { return initial_parameters_.row(start); } 232 Matrix final_parameters() const { return final_parameters_; } 233 Matrix predictor() const { return predictor_; } 234 Matrix response() const { return response_; } 235 int predictor_size() const { return predictor_.cols(); } 236 int num_observations() const { return predictor_.rows(); } 237 int response_size() const { return response_.cols(); } 238 int num_parameters() const { return initial_parameters_.cols(); } 239 int num_starts() const { return initial_parameters_.rows(); } 240 double certified_cost() const { return certified_cost_; } 241 242 private: 243 Matrix predictor_; 244 Matrix response_; 245 Matrix initial_parameters_; 246 Matrix final_parameters_; 247 double certified_cost_; 248}; 249 250#define NIST_BEGIN(CostFunctionName) \ 251 struct CostFunctionName { \ 252 CostFunctionName(const double* const x, \ 253 const double* const y) \ 254 : x_(*x), y_(*y) {} \ 255 double x_; \ 256 double y_; \ 257 template <typename T> \ 258 bool operator()(const T* const b, T* residual) const { \ 259 const T y(y_); \ 260 const T x(x_); \ 261 residual[0] = y - ( 262 263#define NIST_END ); return true; }}; 264 265// y = b1 * (b2+x)**(-1/b3) + e 266NIST_BEGIN(Bennet5) 267 b[0] * pow(b[1] + x, T(-1.0) / b[2]) 268NIST_END 269 270// y = b1*(1-exp[-b2*x]) + e 271NIST_BEGIN(BoxBOD) 272 b[0] * (T(1.0) - exp(-b[1] * x)) 273NIST_END 274 275// y = exp[-b1*x]/(b2+b3*x) + e 276NIST_BEGIN(Chwirut) 277 exp(-b[0] * x) / (b[1] + b[2] * x) 278NIST_END 279 280// y = b1*x**b2 + e 281NIST_BEGIN(DanWood) 282 b[0] * pow(x, b[1]) 283NIST_END 284 285// y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) 286// + b6*exp( -(x-b7)**2 / b8**2 ) + e 287NIST_BEGIN(Gauss) 288 b[0] * exp(-b[1] * x) + 289 b[2] * exp(-pow((x - b[3])/b[4], 2)) + 290 b[5] * exp(-pow((x - b[6])/b[7],2)) 291NIST_END 292 293// y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e 294NIST_BEGIN(Lanczos) 295 b[0] * exp(-b[1] * x) + b[2] * exp(-b[3] * x) + b[4] * exp(-b[5] * x) 296NIST_END 297 298// y = (b1+b2*x+b3*x**2+b4*x**3) / 299// (1+b5*x+b6*x**2+b7*x**3) + e 300NIST_BEGIN(Hahn1) 301 (b[0] + b[1] * x + b[2] * x * x + b[3] * x * x * x) / 302 (T(1.0) + b[4] * x + b[5] * x * x + b[6] * x * x * x) 303NIST_END 304 305// y = (b1 + b2*x + b3*x**2) / 306// (1 + b4*x + b5*x**2) + e 307NIST_BEGIN(Kirby2) 308 (b[0] + b[1] * x + b[2] * x * x) / 309 (T(1.0) + b[3] * x + b[4] * x * x) 310NIST_END 311 312// y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e 313NIST_BEGIN(MGH09) 314 b[0] * (x * x + x * b[1]) / (x * x + x * b[2] + b[3]) 315NIST_END 316 317// y = b1 * exp[b2/(x+b3)] + e 318NIST_BEGIN(MGH10) 319 b[0] * exp(b[1] / (x + b[2])) 320NIST_END 321 322// y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] 323NIST_BEGIN(MGH17) 324 b[0] + b[1] * exp(-x * b[3]) + b[2] * exp(-x * b[4]) 325NIST_END 326 327// y = b1*(1-exp[-b2*x]) + e 328NIST_BEGIN(Misra1a) 329 b[0] * (T(1.0) - exp(-b[1] * x)) 330NIST_END 331 332// y = b1 * (1-(1+b2*x/2)**(-2)) + e 333NIST_BEGIN(Misra1b) 334 b[0] * (T(1.0) - T(1.0)/ ((T(1.0) + b[1] * x / 2.0) * (T(1.0) + b[1] * x / 2.0))) 335NIST_END 336 337// y = b1 * (1-(1+2*b2*x)**(-.5)) + e 338NIST_BEGIN(Misra1c) 339 b[0] * (T(1.0) - pow(T(1.0) + T(2.0) * b[1] * x, -0.5)) 340NIST_END 341 342// y = b1*b2*x*((1+b2*x)**(-1)) + e 343NIST_BEGIN(Misra1d) 344 b[0] * b[1] * x / (T(1.0) + b[1] * x) 345NIST_END 346 347const double kPi = 3.141592653589793238462643383279; 348// pi = 3.141592653589793238462643383279E0 349// y = b1 - b2*x - arctan[b3/(x-b4)]/pi + e 350NIST_BEGIN(Roszman1) 351 b[0] - b[1] * x - atan2(b[2], (x - b[3]))/T(kPi) 352NIST_END 353 354// y = b1 / (1+exp[b2-b3*x]) + e 355NIST_BEGIN(Rat42) 356 b[0] / (T(1.0) + exp(b[1] - b[2] * x)) 357NIST_END 358 359// y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e 360NIST_BEGIN(Rat43) 361 b[0] / pow(T(1.0) + exp(b[1] - b[2] * x), T(1.0) / b[3]) 362NIST_END 363 364// y = (b1 + b2*x + b3*x**2 + b4*x**3) / 365// (1 + b5*x + b6*x**2 + b7*x**3) + e 366NIST_BEGIN(Thurber) 367 (b[0] + b[1] * x + b[2] * x * x + b[3] * x * x * x) / 368 (T(1.0) + b[4] * x + b[5] * x * x + b[6] * x * x * x) 369NIST_END 370 371// y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 372// + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) 373// + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) + e 374NIST_BEGIN(ENSO) 375 b[0] + b[1] * cos(T(2.0 * kPi) * x / T(12.0)) + 376 b[2] * sin(T(2.0 * kPi) * x / T(12.0)) + 377 b[4] * cos(T(2.0 * kPi) * x / b[3]) + 378 b[5] * sin(T(2.0 * kPi) * x / b[3]) + 379 b[7] * cos(T(2.0 * kPi) * x / b[6]) + 380 b[8] * sin(T(2.0 * kPi) * x / b[6]) 381NIST_END 382 383// y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] + e 384NIST_BEGIN(Eckerle4) 385 b[0] / b[1] * exp(T(-0.5) * pow((x - b[2])/b[1], 2)) 386NIST_END 387 388struct Nelson { 389 public: 390 Nelson(const double* const x, const double* const y) 391 : x1_(x[0]), x2_(x[1]), y_(y[0]) {} 392 393 template <typename T> 394 bool operator()(const T* const b, T* residual) const { 395 // log[y] = b1 - b2*x1 * exp[-b3*x2] + e 396 residual[0] = T(log(y_)) - (b[0] - b[1] * T(x1_) * exp(-b[2] * T(x2_))); 397 return true; 398 } 399 400 private: 401 double x1_; 402 double x2_; 403 double y_; 404}; 405 406template <typename Model, int num_residuals, int num_parameters> 407int RegressionDriver(const std::string& filename, 408 const ceres::Solver::Options& options) { 409 NISTProblem nist_problem(FLAGS_nist_data_dir + filename); 410 CHECK_EQ(num_residuals, nist_problem.response_size()); 411 CHECK_EQ(num_parameters, nist_problem.num_parameters()); 412 413 Matrix predictor = nist_problem.predictor(); 414 Matrix response = nist_problem.response(); 415 Matrix final_parameters = nist_problem.final_parameters(); 416 417 printf("%s\n", filename.c_str()); 418 419 // Each NIST problem comes with multiple starting points, so we 420 // construct the problem from scratch for each case and solve it. 421 int num_success = 0; 422 for (int start = 0; start < nist_problem.num_starts(); ++start) { 423 Matrix initial_parameters = nist_problem.initial_parameters(start); 424 425 ceres::Problem problem; 426 for (int i = 0; i < nist_problem.num_observations(); ++i) { 427 problem.AddResidualBlock( 428 new ceres::AutoDiffCostFunction<Model, num_residuals, num_parameters>( 429 new Model(predictor.data() + nist_problem.predictor_size() * i, 430 response.data() + nist_problem.response_size() * i)), 431 NULL, 432 initial_parameters.data()); 433 } 434 435 ceres::Solver::Summary summary; 436 Solve(options, &problem, &summary); 437 438 // Compute the LRE by comparing each component of the solution 439 // with the ground truth, and taking the minimum. 440 Matrix final_parameters = nist_problem.final_parameters(); 441 const double kMaxNumSignificantDigits = 11; 442 double log_relative_error = kMaxNumSignificantDigits + 1; 443 for (int i = 0; i < num_parameters; ++i) { 444 const double tmp_lre = 445 -std::log10(std::fabs(final_parameters(i) - initial_parameters(i)) / 446 std::fabs(final_parameters(i))); 447 // The maximum LRE is capped at 11 - the precision at which the 448 // ground truth is known. 449 // 450 // The minimum LRE is capped at 0 - no digits match between the 451 // computed solution and the ground truth. 452 log_relative_error = 453 std::min(log_relative_error, 454 std::max(0.0, std::min(kMaxNumSignificantDigits, tmp_lre))); 455 } 456 457 const int kMinNumMatchingDigits = 4; 458 if (log_relative_error >= kMinNumMatchingDigits) { 459 ++num_success; 460 } 461 462 printf("start: %d status: %s lre: %4.1f initial cost: %e final cost:%e " 463 "certified cost: %e total iterations: %d\n", 464 start + 1, 465 log_relative_error < kMinNumMatchingDigits ? "FAILURE" : "SUCCESS", 466 log_relative_error, 467 summary.initial_cost, 468 summary.final_cost, 469 nist_problem.certified_cost(), 470 (summary.num_successful_steps + summary.num_unsuccessful_steps)); 471 } 472 return num_success; 473} 474 475void SetMinimizerOptions(ceres::Solver::Options* options) { 476 CHECK(ceres::StringToMinimizerType(FLAGS_minimizer, 477 &options->minimizer_type)); 478 CHECK(ceres::StringToLinearSolverType(FLAGS_linear_solver, 479 &options->linear_solver_type)); 480 CHECK(ceres::StringToPreconditionerType(FLAGS_preconditioner, 481 &options->preconditioner_type)); 482 CHECK(ceres::StringToTrustRegionStrategyType( 483 FLAGS_trust_region_strategy, 484 &options->trust_region_strategy_type)); 485 CHECK(ceres::StringToDoglegType(FLAGS_dogleg, &options->dogleg_type)); 486 CHECK(ceres::StringToLineSearchDirectionType( 487 FLAGS_line_search_direction, 488 &options->line_search_direction_type)); 489 CHECK(ceres::StringToLineSearchType(FLAGS_line_search, 490 &options->line_search_type)); 491 CHECK(ceres::StringToLineSearchInterpolationType( 492 FLAGS_line_search_interpolation, 493 &options->line_search_interpolation_type)); 494 495 options->max_num_iterations = FLAGS_num_iterations; 496 options->use_nonmonotonic_steps = FLAGS_nonmonotonic_steps; 497 options->initial_trust_region_radius = FLAGS_initial_trust_region_radius; 498 options->max_lbfgs_rank = FLAGS_lbfgs_rank; 499 options->line_search_sufficient_function_decrease = FLAGS_sufficient_decrease; 500 options->line_search_sufficient_curvature_decrease = 501 FLAGS_sufficient_curvature_decrease; 502 options->max_num_line_search_step_size_iterations = 503 FLAGS_max_line_search_iterations; 504 options->max_num_line_search_direction_restarts = 505 FLAGS_max_line_search_restarts; 506 options->use_approximate_eigenvalue_bfgs_scaling = 507 FLAGS_approximate_eigenvalue_bfgs_scaling; 508 options->function_tolerance = 1e-18; 509 options->gradient_tolerance = 1e-18; 510 options->parameter_tolerance = 1e-18; 511} 512 513void SolveNISTProblems() { 514 if (FLAGS_nist_data_dir.empty()) { 515 LOG(FATAL) << "Must specify the directory containing the NIST problems"; 516 } 517 518 ceres::Solver::Options options; 519 SetMinimizerOptions(&options); 520 521 std::cout << "Lower Difficulty\n"; 522 int easy_success = 0; 523 easy_success += RegressionDriver<Misra1a, 1, 2>("Misra1a.dat", options); 524 easy_success += RegressionDriver<Chwirut, 1, 3>("Chwirut1.dat", options); 525 easy_success += RegressionDriver<Chwirut, 1, 3>("Chwirut2.dat", options); 526 easy_success += RegressionDriver<Lanczos, 1, 6>("Lanczos3.dat", options); 527 easy_success += RegressionDriver<Gauss, 1, 8>("Gauss1.dat", options); 528 easy_success += RegressionDriver<Gauss, 1, 8>("Gauss2.dat", options); 529 easy_success += RegressionDriver<DanWood, 1, 2>("DanWood.dat", options); 530 easy_success += RegressionDriver<Misra1b, 1, 2>("Misra1b.dat", options); 531 532 std::cout << "\nMedium Difficulty\n"; 533 int medium_success = 0; 534 medium_success += RegressionDriver<Kirby2, 1, 5>("Kirby2.dat", options); 535 medium_success += RegressionDriver<Hahn1, 1, 7>("Hahn1.dat", options); 536 medium_success += RegressionDriver<Nelson, 1, 3>("Nelson.dat", options); 537 medium_success += RegressionDriver<MGH17, 1, 5>("MGH17.dat", options); 538 medium_success += RegressionDriver<Lanczos, 1, 6>("Lanczos1.dat", options); 539 medium_success += RegressionDriver<Lanczos, 1, 6>("Lanczos2.dat", options); 540 medium_success += RegressionDriver<Gauss, 1, 8>("Gauss3.dat", options); 541 medium_success += RegressionDriver<Misra1c, 1, 2>("Misra1c.dat", options); 542 medium_success += RegressionDriver<Misra1d, 1, 2>("Misra1d.dat", options); 543 medium_success += RegressionDriver<Roszman1, 1, 4>("Roszman1.dat", options); 544 medium_success += RegressionDriver<ENSO, 1, 9>("ENSO.dat", options); 545 546 std::cout << "\nHigher Difficulty\n"; 547 int hard_success = 0; 548 hard_success += RegressionDriver<MGH09, 1, 4>("MGH09.dat", options); 549 hard_success += RegressionDriver<Thurber, 1, 7>("Thurber.dat", options); 550 hard_success += RegressionDriver<BoxBOD, 1, 2>("BoxBOD.dat", options); 551 hard_success += RegressionDriver<Rat42, 1, 3>("Rat42.dat", options); 552 hard_success += RegressionDriver<MGH10, 1, 3>("MGH10.dat", options); 553 554 hard_success += RegressionDriver<Eckerle4, 1, 3>("Eckerle4.dat", options); 555 hard_success += RegressionDriver<Rat43, 1, 4>("Rat43.dat", options); 556 hard_success += RegressionDriver<Bennet5, 1, 3>("Bennett5.dat", options); 557 558 std::cout << "\n"; 559 std::cout << "Easy : " << easy_success << "/16\n"; 560 std::cout << "Medium : " << medium_success << "/22\n"; 561 std::cout << "Hard : " << hard_success << "/16\n"; 562 std::cout << "Total : " << easy_success + medium_success + hard_success << "/54\n"; 563} 564 565} // namespace examples 566} // namespace ceres 567 568int main(int argc, char** argv) { 569 google::ParseCommandLineFlags(&argc, &argv, true); 570 google::InitGoogleLogging(argv[0]); 571 ceres::examples::SolveNISTProblems(); 572 return 0; 573}; 574