Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 1 | // Ceres Solver - A fast non-linear least squares minimizer |
| 2 | // Copyright 2014 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 | // Bounds constrained test problems from the paper |
| 32 | // |
| 33 | // Testing Unconstrained Optimization Software |
| 34 | // Jorge J. More, Burton S. Garbow and Kenneth E. Hillstrom |
| 35 | // ACM Transactions on Mathematical Software, 7(1), pp. 17-41, 1981 |
| 36 | // |
| 37 | // A subset of these problems were augmented with bounds and used for |
| 38 | // testing bounds constrained optimization algorithms by |
| 39 | // |
| 40 | // A Trust Region Approach to Linearly Constrained Optimization |
| 41 | // David M. Gay |
| 42 | // Numerical Analysis (Griffiths, D.F., ed.), pp. 72-105 |
| 43 | // Lecture Notes in Mathematics 1066, Springer Verlag, 1984. |
| 44 | // |
| 45 | // The latter paper is behind a paywall. We obtained the bounds on the |
| 46 | // variables and the function values at the global minimums from |
| 47 | // |
| 48 | // http://www.mat.univie.ac.at/~neum/glopt/bounds.html |
| 49 | // |
| 50 | // A problem is considered solved if of the log relative error of its |
| 51 | // objective function is at least 5. |
| 52 | |
| 53 | |
| 54 | #include <cmath> |
| 55 | #include <iostream> // NOLINT |
| 56 | #include "ceres/ceres.h" |
| 57 | #include "gflags/gflags.h" |
| 58 | #include "glog/logging.h" |
| 59 | |
| 60 | namespace ceres { |
| 61 | namespace examples { |
| 62 | |
| 63 | const double kDoubleMax = std::numeric_limits<double>::max(); |
| 64 | |
| 65 | #define BEGIN_MGH_PROBLEM(name, num_parameters, num_residuals) \ |
| 66 | struct name { \ |
| 67 | static const int kNumParameters = num_parameters; \ |
| 68 | static const double initial_x[kNumParameters]; \ |
| 69 | static const double lower_bounds[kNumParameters]; \ |
| 70 | static const double upper_bounds[kNumParameters]; \ |
| 71 | static const double constrained_optimal_cost; \ |
| 72 | static const double unconstrained_optimal_cost; \ |
| 73 | static CostFunction* Create() { \ |
| 74 | return new AutoDiffCostFunction<name, \ |
| 75 | num_residuals, \ |
| 76 | num_parameters>(new name); \ |
| 77 | } \ |
| 78 | template <typename T> \ |
| 79 | bool operator()(const T* const x, T* residual) const { |
| 80 | |
| 81 | #define END_MGH_PROBLEM return true; } }; // NOLINT |
| 82 | |
| 83 | // Rosenbrock function. |
| 84 | BEGIN_MGH_PROBLEM(TestProblem1, 2, 2) |
| 85 | const T x1 = x[0]; |
| 86 | const T x2 = x[1]; |
| 87 | residual[0] = T(10.0) * (x2 - x1 * x1); |
| 88 | residual[1] = T(1.0) - x1; |
| 89 | END_MGH_PROBLEM; |
| 90 | |
| 91 | const double TestProblem1::initial_x[] = {-1.2, 1.0}; |
| 92 | const double TestProblem1::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; |
| 93 | const double TestProblem1::upper_bounds[] = {kDoubleMax, kDoubleMax}; |
| 94 | const double TestProblem1::constrained_optimal_cost = |
| 95 | std::numeric_limits<double>::quiet_NaN(); |
| 96 | const double TestProblem1::unconstrained_optimal_cost = 0.0; |
| 97 | |
| 98 | // Freudenstein and Roth function. |
| 99 | BEGIN_MGH_PROBLEM(TestProblem2, 2, 2) |
| 100 | const T x1 = x[0]; |
| 101 | const T x2 = x[1]; |
| 102 | residual[0] = T(-13.0) + x1 + ((T(5.0) - x2) * x2 - T(2.0)) * x2; |
| 103 | residual[1] = T(-29.0) + x1 + ((x2 + T(1.0)) * x2 - T(14.0)) * x2; |
| 104 | END_MGH_PROBLEM; |
| 105 | |
| 106 | const double TestProblem2::initial_x[] = {0.5, -2.0}; |
| 107 | const double TestProblem2::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; |
| 108 | const double TestProblem2::upper_bounds[] = {kDoubleMax, kDoubleMax}; |
| 109 | const double TestProblem2::constrained_optimal_cost = |
| 110 | std::numeric_limits<double>::quiet_NaN(); |
| 111 | const double TestProblem2::unconstrained_optimal_cost = 0.0; |
| 112 | |
| 113 | // Powell badly scaled function. |
| 114 | BEGIN_MGH_PROBLEM(TestProblem3, 2, 2) |
| 115 | const T x1 = x[0]; |
| 116 | const T x2 = x[1]; |
| 117 | residual[0] = T(10000.0) * x1 * x2 - T(1.0); |
| 118 | residual[1] = exp(-x1) + exp(-x2) - T(1.0001); |
| 119 | END_MGH_PROBLEM; |
| 120 | |
| 121 | const double TestProblem3::initial_x[] = {0.0, 1.0}; |
| 122 | const double TestProblem3::lower_bounds[] = {0.0, 1.0}; |
| 123 | const double TestProblem3::upper_bounds[] = {1.0, 9.0}; |
| 124 | const double TestProblem3::constrained_optimal_cost = 0.15125900e-9; |
| 125 | const double TestProblem3::unconstrained_optimal_cost = 0.0; |
| 126 | |
| 127 | // Brown badly scaled function. |
| 128 | BEGIN_MGH_PROBLEM(TestProblem4, 2, 3) |
| 129 | const T x1 = x[0]; |
| 130 | const T x2 = x[1]; |
| 131 | residual[0] = x1 - T(1000000.0); |
| 132 | residual[1] = x2 - T(0.000002); |
| 133 | residual[2] = x1 * x2 - T(2.0); |
| 134 | END_MGH_PROBLEM; |
| 135 | |
| 136 | const double TestProblem4::initial_x[] = {1.0, 1.0}; |
| 137 | const double TestProblem4::lower_bounds[] = {0.0, 0.00003}; |
| 138 | const double TestProblem4::upper_bounds[] = {1000000.0, 100.0}; |
| 139 | const double TestProblem4::constrained_optimal_cost = 0.78400000e3; |
| 140 | const double TestProblem4::unconstrained_optimal_cost = 0.0; |
| 141 | |
| 142 | // Beale function. |
| 143 | BEGIN_MGH_PROBLEM(TestProblem5, 2, 3) |
| 144 | const T x1 = x[0]; |
| 145 | const T x2 = x[1]; |
| 146 | residual[0] = T(1.5) - x1 * (T(1.0) - x2); |
| 147 | residual[1] = T(2.25) - x1 * (T(1.0) - x2 * x2); |
| 148 | residual[2] = T(2.625) - x1 * (T(1.0) - x2 * x2 * x2); |
| 149 | END_MGH_PROBLEM; |
| 150 | |
| 151 | const double TestProblem5::initial_x[] = {1.0, 1.0}; |
| 152 | const double TestProblem5::lower_bounds[] = {0.6, 0.5}; |
| 153 | const double TestProblem5::upper_bounds[] = {10.0, 100.0}; |
| 154 | const double TestProblem5::constrained_optimal_cost = 0.0; |
| 155 | const double TestProblem5::unconstrained_optimal_cost = 0.0; |
| 156 | |
| 157 | // Jennrich and Sampson function. |
| 158 | BEGIN_MGH_PROBLEM(TestProblem6, 2, 10) |
| 159 | const T x1 = x[0]; |
| 160 | const T x2 = x[1]; |
| 161 | for (int i = 1; i <= 10; ++i) { |
| 162 | residual[i - 1] = T(2.0) + T(2.0 * i) - |
| 163 | exp(T(static_cast<double>(i)) * x1) - |
| 164 | exp(T(static_cast<double>(i) * x2)); |
| 165 | } |
| 166 | END_MGH_PROBLEM; |
| 167 | |
| 168 | const double TestProblem6::initial_x[] = {1.0, 1.0}; |
| 169 | const double TestProblem6::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; |
| 170 | const double TestProblem6::upper_bounds[] = {kDoubleMax, kDoubleMax}; |
| 171 | const double TestProblem6::constrained_optimal_cost = |
| 172 | std::numeric_limits<double>::quiet_NaN(); |
| 173 | const double TestProblem6::unconstrained_optimal_cost = 124.362; |
| 174 | |
| 175 | // Helical valley function. |
| 176 | BEGIN_MGH_PROBLEM(TestProblem7, 3, 3) |
| 177 | const T x1 = x[0]; |
| 178 | const T x2 = x[1]; |
| 179 | const T x3 = x[2]; |
| 180 | const T theta = T(0.5 / M_PI) * atan(x2 / x1) + (x1 > 0.0 ? T(0.0) : T(0.5)); |
| 181 | |
| 182 | residual[0] = T(10.0) * (x3 - T(10.0) * theta); |
| 183 | residual[1] = T(10.0) * (sqrt(x1 * x1 + x2 * x2) - T(1.0)); |
| 184 | residual[2] = x3; |
| 185 | END_MGH_PROBLEM; |
| 186 | |
| 187 | const double TestProblem7::initial_x[] = {-1.0, 0.0, 0.0}; |
| 188 | const double TestProblem7::lower_bounds[] = {-100.0, -1.0, -1.0}; |
| 189 | const double TestProblem7::upper_bounds[] = {0.8, 1.0, 1.0}; |
| 190 | const double TestProblem7::constrained_optimal_cost = 0.99042212; |
| 191 | const double TestProblem7::unconstrained_optimal_cost = 0.0; |
| 192 | |
| 193 | // Bard function |
| 194 | BEGIN_MGH_PROBLEM(TestProblem8, 3, 15) |
| 195 | const T x1 = x[0]; |
| 196 | const T x2 = x[1]; |
| 197 | const T x3 = x[2]; |
| 198 | |
| 199 | double y[] = {0.14, 0.18, 0.22, 0.25, |
| 200 | 0.29, 0.32, 0.35, 0.39, 0.37, 0.58, |
| 201 | 0.73, 0.96, 1.34, 2.10, 4.39}; |
| 202 | |
| 203 | for (int i = 1; i <=15; ++i) { |
| 204 | const T u = T(static_cast<double>(i)); |
| 205 | const T v = T(static_cast<double>(16 - i)); |
| 206 | const T w = T(static_cast<double>(std::min(i, 16 - i))); |
| 207 | residual[i - 1] = T(y[i - 1]) - x1 + u / (v * x2 + w * x3); |
| 208 | } |
| 209 | END_MGH_PROBLEM; |
| 210 | |
| 211 | const double TestProblem8::initial_x[] = {1.0, 1.0, 1.0}; |
| 212 | const double TestProblem8::lower_bounds[] = { |
| 213 | -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| 214 | const double TestProblem8::upper_bounds[] = { |
| 215 | kDoubleMax, kDoubleMax, kDoubleMax}; |
| 216 | const double TestProblem8::constrained_optimal_cost = |
| 217 | std::numeric_limits<double>::quiet_NaN(); |
| 218 | const double TestProblem8::unconstrained_optimal_cost = 8.21487e-3; |
| 219 | |
| 220 | // Gaussian function. |
| 221 | BEGIN_MGH_PROBLEM(TestProblem9, 3, 15) |
| 222 | const T x1 = x[0]; |
| 223 | const T x2 = x[1]; |
| 224 | const T x3 = x[2]; |
| 225 | |
| 226 | const double y[] = {0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, |
| 227 | 0.3989, |
| 228 | 0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009}; |
| 229 | for (int i = 0; i < 15; ++i) { |
| 230 | const T t_i = T((8.0 - i - 1.0) / 2.0); |
| 231 | const T y_i = T(y[i]); |
| 232 | residual[i] = x1 * exp(-x2 * (t_i - x3) * (t_i - x3) / T(2.0)) - y_i; |
| 233 | } |
| 234 | END_MGH_PROBLEM; |
| 235 | |
| 236 | const double TestProblem9::initial_x[] = {0.4, 1.0, 0.0}; |
| 237 | const double TestProblem9::lower_bounds[] = {0.398, 1.0, -0.5}; |
| 238 | const double TestProblem9::upper_bounds[] = {4.2, 2.0, 0.1}; |
| 239 | const double TestProblem9::constrained_optimal_cost = 0.11279300e-7; |
| 240 | const double TestProblem9::unconstrained_optimal_cost = 0.112793e-7; |
| 241 | |
| 242 | // Meyer function. |
| 243 | BEGIN_MGH_PROBLEM(TestProblem10, 3, 16) |
| 244 | const T x1 = x[0]; |
| 245 | const T x2 = x[1]; |
| 246 | const T x3 = x[2]; |
| 247 | |
| 248 | const double y[] = {34780, 28610, 23650, 19630, 16370, 13720, 11540, 9744, |
| 249 | 8261, 7030, 6005, 5147, 4427, 3820, 3307, 2872}; |
| 250 | |
| 251 | for (int i = 0; i < 16; ++i) { |
| 252 | T t = T(45 + 5.0 * (i + 1)); |
| 253 | residual[i] = x1 * exp(x2 / (t + x3)) - y[i]; |
| 254 | } |
| 255 | END_MGH_PROBLEM |
| 256 | |
| 257 | |
| 258 | const double TestProblem10::initial_x[] = {0.02, 4000, 250}; |
| 259 | const double TestProblem10::lower_bounds[] ={ |
| 260 | -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| 261 | const double TestProblem10::upper_bounds[] ={ |
| 262 | kDoubleMax, kDoubleMax, kDoubleMax}; |
| 263 | const double TestProblem10::constrained_optimal_cost = |
| 264 | std::numeric_limits<double>::quiet_NaN(); |
| 265 | const double TestProblem10::unconstrained_optimal_cost = 87.9458; |
| 266 | |
| 267 | #undef BEGIN_MGH_PROBLEM |
| 268 | #undef END_MGH_PROBLEM |
| 269 | |
| 270 | template<typename TestProblem> string ConstrainedSolve() { |
| 271 | double x[TestProblem::kNumParameters]; |
| 272 | std::copy(TestProblem::initial_x, |
| 273 | TestProblem::initial_x + TestProblem::kNumParameters, |
| 274 | x); |
| 275 | |
| 276 | Problem problem; |
| 277 | problem.AddResidualBlock(TestProblem::Create(), NULL, x); |
| 278 | for (int i = 0; i < TestProblem::kNumParameters; ++i) { |
| 279 | problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]); |
| 280 | problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]); |
| 281 | } |
| 282 | |
| 283 | Solver::Options options; |
| 284 | options.parameter_tolerance = 1e-18; |
| 285 | options.function_tolerance = 1e-18; |
| 286 | options.gradient_tolerance = 1e-18; |
| 287 | options.max_num_iterations = 1000; |
| 288 | options.linear_solver_type = DENSE_QR; |
| 289 | Solver::Summary summary; |
| 290 | Solve(options, &problem, &summary); |
| 291 | |
| 292 | const double kMinLogRelativeError = 5.0; |
| 293 | const double log_relative_error = -std::log10( |
| 294 | std::abs(2.0 * summary.final_cost - |
| 295 | TestProblem::constrained_optimal_cost) / |
| 296 | (TestProblem::constrained_optimal_cost > 0.0 |
| 297 | ? TestProblem::constrained_optimal_cost |
| 298 | : 1.0)); |
| 299 | |
| 300 | return (log_relative_error >= kMinLogRelativeError |
| 301 | ? "Success\n" |
| 302 | : "Failure\n"); |
| 303 | } |
| 304 | |
| 305 | template<typename TestProblem> string UnconstrainedSolve() { |
| 306 | double x[TestProblem::kNumParameters]; |
| 307 | std::copy(TestProblem::initial_x, |
| 308 | TestProblem::initial_x + TestProblem::kNumParameters, |
| 309 | x); |
| 310 | |
| 311 | Problem problem; |
| 312 | problem.AddResidualBlock(TestProblem::Create(), NULL, x); |
| 313 | |
| 314 | Solver::Options options; |
| 315 | options.parameter_tolerance = 1e-18; |
| 316 | options.function_tolerance = 0.0; |
| 317 | options.gradient_tolerance = 1e-18; |
| 318 | options.max_num_iterations = 1000; |
| 319 | options.linear_solver_type = DENSE_QR; |
| 320 | Solver::Summary summary; |
| 321 | Solve(options, &problem, &summary); |
| 322 | |
| 323 | const double kMinLogRelativeError = 5.0; |
| 324 | const double log_relative_error = -std::log10( |
| 325 | std::abs(2.0 * summary.final_cost - |
| 326 | TestProblem::unconstrained_optimal_cost) / |
| 327 | (TestProblem::unconstrained_optimal_cost > 0.0 |
| 328 | ? TestProblem::unconstrained_optimal_cost |
| 329 | : 1.0)); |
| 330 | |
| 331 | return (log_relative_error >= kMinLogRelativeError |
| 332 | ? "Success\n" |
| 333 | : "Failure\n"); |
| 334 | } |
| 335 | |
| 336 | } // namespace examples |
| 337 | } // namespace ceres |
| 338 | |
| 339 | int main(int argc, char** argv) { |
| 340 | google::ParseCommandLineFlags(&argc, &argv, true); |
| 341 | google::InitGoogleLogging(argv[0]); |
| 342 | |
| 343 | using ceres::examples::UnconstrainedSolve; |
| 344 | using ceres::examples::ConstrainedSolve; |
| 345 | |
| 346 | #define UNCONSTRAINED_SOLVE(n) \ |
| 347 | std::cout << "Problem " << n << " : " \ |
| 348 | << UnconstrainedSolve<ceres::examples::TestProblem##n>(); |
| 349 | |
| 350 | #define CONSTRAINED_SOLVE(n) \ |
| 351 | std::cout << "Problem " << n << " : " \ |
| 352 | << ConstrainedSolve<ceres::examples::TestProblem##n>(); |
| 353 | |
| 354 | std::cout << "Unconstrained problems\n"; |
| 355 | UNCONSTRAINED_SOLVE(1); |
| 356 | UNCONSTRAINED_SOLVE(2); |
| 357 | UNCONSTRAINED_SOLVE(3); |
| 358 | UNCONSTRAINED_SOLVE(4); |
| 359 | UNCONSTRAINED_SOLVE(5); |
| 360 | UNCONSTRAINED_SOLVE(6); |
| 361 | UNCONSTRAINED_SOLVE(7); |
| 362 | UNCONSTRAINED_SOLVE(8); |
| 363 | UNCONSTRAINED_SOLVE(9); |
| 364 | UNCONSTRAINED_SOLVE(10); |
| 365 | |
| 366 | std::cout << "\nConstrained problems\n"; |
| 367 | CONSTRAINED_SOLVE(3); |
| 368 | CONSTRAINED_SOLVE(4); |
| 369 | CONSTRAINED_SOLVE(5); |
| 370 | CONSTRAINED_SOLVE(7); |
| 371 | CONSTRAINED_SOLVE(9); |
| 372 | |
| 373 | return 0; |
| 374 | } |