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diff --git a/examples/more_garbow_hillstrom.cc b/examples/more_garbow_hillstrom.cc new file mode 100644 index 0000000..d98e57c --- /dev/null +++ b/examples/more_garbow_hillstrom.cc @@ -0,0 +1,374 @@ +// Ceres Solver - A fast non-linear least squares minimizer +// Copyright 2014 Google Inc. All rights reserved. +// http://code.google.com/p/ceres-solver/ +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are met: +// +// * Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// * Neither the name of Google Inc. nor the names of its contributors may be +// used to endorse or promote products derived from this software without +// specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +// POSSIBILITY OF SUCH DAMAGE. +// +// Author: sameeragarwal@google.com (Sameer Agarwal) +// +// Bounds constrained test problems from the paper +// +// Testing Unconstrained Optimization Software +// Jorge J. More, Burton S. Garbow and Kenneth E. Hillstrom +// ACM Transactions on Mathematical Software, 7(1), pp. 17-41, 1981 +// +// A subset of these problems were augmented with bounds and used for +// testing bounds constrained optimization algorithms by +// +// A Trust Region Approach to Linearly Constrained Optimization +// David M. Gay +// Numerical Analysis (Griffiths, D.F., ed.), pp. 72-105 +// Lecture Notes in Mathematics 1066, Springer Verlag, 1984. +// +// The latter paper is behind a paywall. We obtained the bounds on the +// variables and the function values at the global minimums from +// +// http://www.mat.univie.ac.at/~neum/glopt/bounds.html +// +// A problem is considered solved if of the log relative error of its +// objective function is at least 5. + + +#include <cmath> +#include <iostream> // NOLINT +#include "ceres/ceres.h" +#include "gflags/gflags.h" +#include "glog/logging.h" + +namespace ceres { +namespace examples { + +const double kDoubleMax = std::numeric_limits<double>::max(); + +#define BEGIN_MGH_PROBLEM(name, num_parameters, num_residuals) \ + struct name { \ + static const int kNumParameters = num_parameters; \ + static const double initial_x[kNumParameters]; \ + static const double lower_bounds[kNumParameters]; \ + static const double upper_bounds[kNumParameters]; \ + static const double constrained_optimal_cost; \ + static const double unconstrained_optimal_cost; \ + static CostFunction* Create() { \ + return new AutoDiffCostFunction<name, \ + num_residuals, \ + num_parameters>(new name); \ + } \ + template <typename T> \ + bool operator()(const T* const x, T* residual) const { + +#define END_MGH_PROBLEM return true; } }; // NOLINT + +// Rosenbrock function. +BEGIN_MGH_PROBLEM(TestProblem1, 2, 2) + const T x1 = x[0]; + const T x2 = x[1]; + residual[0] = T(10.0) * (x2 - x1 * x1); + residual[1] = T(1.0) - x1; +END_MGH_PROBLEM; + +const double TestProblem1::initial_x[] = {-1.2, 1.0}; +const double TestProblem1::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; +const double TestProblem1::upper_bounds[] = {kDoubleMax, kDoubleMax}; +const double TestProblem1::constrained_optimal_cost = + std::numeric_limits<double>::quiet_NaN(); +const double TestProblem1::unconstrained_optimal_cost = 0.0; + +// Freudenstein and Roth function. +BEGIN_MGH_PROBLEM(TestProblem2, 2, 2) + const T x1 = x[0]; + const T x2 = x[1]; + residual[0] = T(-13.0) + x1 + ((T(5.0) - x2) * x2 - T(2.0)) * x2; + residual[1] = T(-29.0) + x1 + ((x2 + T(1.0)) * x2 - T(14.0)) * x2; +END_MGH_PROBLEM; + +const double TestProblem2::initial_x[] = {0.5, -2.0}; +const double TestProblem2::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; +const double TestProblem2::upper_bounds[] = {kDoubleMax, kDoubleMax}; +const double TestProblem2::constrained_optimal_cost = + std::numeric_limits<double>::quiet_NaN(); +const double TestProblem2::unconstrained_optimal_cost = 0.0; + +// Powell badly scaled function. +BEGIN_MGH_PROBLEM(TestProblem3, 2, 2) + const T x1 = x[0]; + const T x2 = x[1]; + residual[0] = T(10000.0) * x1 * x2 - T(1.0); + residual[1] = exp(-x1) + exp(-x2) - T(1.0001); +END_MGH_PROBLEM; + +const double TestProblem3::initial_x[] = {0.0, 1.0}; +const double TestProblem3::lower_bounds[] = {0.0, 1.0}; +const double TestProblem3::upper_bounds[] = {1.0, 9.0}; +const double TestProblem3::constrained_optimal_cost = 0.15125900e-9; +const double TestProblem3::unconstrained_optimal_cost = 0.0; + +// Brown badly scaled function. +BEGIN_MGH_PROBLEM(TestProblem4, 2, 3) + const T x1 = x[0]; + const T x2 = x[1]; + residual[0] = x1 - T(1000000.0); + residual[1] = x2 - T(0.000002); + residual[2] = x1 * x2 - T(2.0); +END_MGH_PROBLEM; + +const double TestProblem4::initial_x[] = {1.0, 1.0}; +const double TestProblem4::lower_bounds[] = {0.0, 0.00003}; +const double TestProblem4::upper_bounds[] = {1000000.0, 100.0}; +const double TestProblem4::constrained_optimal_cost = 0.78400000e3; +const double TestProblem4::unconstrained_optimal_cost = 0.0; + +// Beale function. +BEGIN_MGH_PROBLEM(TestProblem5, 2, 3) + const T x1 = x[0]; + const T x2 = x[1]; + residual[0] = T(1.5) - x1 * (T(1.0) - x2); + residual[1] = T(2.25) - x1 * (T(1.0) - x2 * x2); + residual[2] = T(2.625) - x1 * (T(1.0) - x2 * x2 * x2); +END_MGH_PROBLEM; + +const double TestProblem5::initial_x[] = {1.0, 1.0}; +const double TestProblem5::lower_bounds[] = {0.6, 0.5}; +const double TestProblem5::upper_bounds[] = {10.0, 100.0}; +const double TestProblem5::constrained_optimal_cost = 0.0; +const double TestProblem5::unconstrained_optimal_cost = 0.0; + +// Jennrich and Sampson function. +BEGIN_MGH_PROBLEM(TestProblem6, 2, 10) + const T x1 = x[0]; + const T x2 = x[1]; + for (int i = 1; i <= 10; ++i) { + residual[i - 1] = T(2.0) + T(2.0 * i) - + exp(T(static_cast<double>(i)) * x1) - + exp(T(static_cast<double>(i) * x2)); + } +END_MGH_PROBLEM; + +const double TestProblem6::initial_x[] = {1.0, 1.0}; +const double TestProblem6::lower_bounds[] = {-kDoubleMax, -kDoubleMax}; +const double TestProblem6::upper_bounds[] = {kDoubleMax, kDoubleMax}; +const double TestProblem6::constrained_optimal_cost = + std::numeric_limits<double>::quiet_NaN(); +const double TestProblem6::unconstrained_optimal_cost = 124.362; + +// Helical valley function. +BEGIN_MGH_PROBLEM(TestProblem7, 3, 3) + const T x1 = x[0]; + const T x2 = x[1]; + const T x3 = x[2]; + const T theta = T(0.5 / M_PI) * atan(x2 / x1) + (x1 > 0.0 ? T(0.0) : T(0.5)); + + residual[0] = T(10.0) * (x3 - T(10.0) * theta); + residual[1] = T(10.0) * (sqrt(x1 * x1 + x2 * x2) - T(1.0)); + residual[2] = x3; +END_MGH_PROBLEM; + +const double TestProblem7::initial_x[] = {-1.0, 0.0, 0.0}; +const double TestProblem7::lower_bounds[] = {-100.0, -1.0, -1.0}; +const double TestProblem7::upper_bounds[] = {0.8, 1.0, 1.0}; +const double TestProblem7::constrained_optimal_cost = 0.99042212; +const double TestProblem7::unconstrained_optimal_cost = 0.0; + +// Bard function +BEGIN_MGH_PROBLEM(TestProblem8, 3, 15) + const T x1 = x[0]; + const T x2 = x[1]; + const T x3 = x[2]; + + double y[] = {0.14, 0.18, 0.22, 0.25, + 0.29, 0.32, 0.35, 0.39, 0.37, 0.58, + 0.73, 0.96, 1.34, 2.10, 4.39}; + + for (int i = 1; i <=15; ++i) { + const T u = T(static_cast<double>(i)); + const T v = T(static_cast<double>(16 - i)); + const T w = T(static_cast<double>(std::min(i, 16 - i))); + residual[i - 1] = T(y[i - 1]) - x1 + u / (v * x2 + w * x3); + } +END_MGH_PROBLEM; + +const double TestProblem8::initial_x[] = {1.0, 1.0, 1.0}; +const double TestProblem8::lower_bounds[] = { + -kDoubleMax, -kDoubleMax, -kDoubleMax}; +const double TestProblem8::upper_bounds[] = { + kDoubleMax, kDoubleMax, kDoubleMax}; +const double TestProblem8::constrained_optimal_cost = + std::numeric_limits<double>::quiet_NaN(); +const double TestProblem8::unconstrained_optimal_cost = 8.21487e-3; + +// Gaussian function. +BEGIN_MGH_PROBLEM(TestProblem9, 3, 15) + const T x1 = x[0]; + const T x2 = x[1]; + const T x3 = x[2]; + + const double y[] = {0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, + 0.3989, + 0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009}; + for (int i = 0; i < 15; ++i) { + const T t_i = T((8.0 - i - 1.0) / 2.0); + const T y_i = T(y[i]); + residual[i] = x1 * exp(-x2 * (t_i - x3) * (t_i - x3) / T(2.0)) - y_i; + } +END_MGH_PROBLEM; + +const double TestProblem9::initial_x[] = {0.4, 1.0, 0.0}; +const double TestProblem9::lower_bounds[] = {0.398, 1.0, -0.5}; +const double TestProblem9::upper_bounds[] = {4.2, 2.0, 0.1}; +const double TestProblem9::constrained_optimal_cost = 0.11279300e-7; +const double TestProblem9::unconstrained_optimal_cost = 0.112793e-7; + +// Meyer function. +BEGIN_MGH_PROBLEM(TestProblem10, 3, 16) + const T x1 = x[0]; + const T x2 = x[1]; + const T x3 = x[2]; + + const double y[] = {34780, 28610, 23650, 19630, 16370, 13720, 11540, 9744, + 8261, 7030, 6005, 5147, 4427, 3820, 3307, 2872}; + + for (int i = 0; i < 16; ++i) { + T t = T(45 + 5.0 * (i + 1)); + residual[i] = x1 * exp(x2 / (t + x3)) - y[i]; + } +END_MGH_PROBLEM + + +const double TestProblem10::initial_x[] = {0.02, 4000, 250}; +const double TestProblem10::lower_bounds[] ={ + -kDoubleMax, -kDoubleMax, -kDoubleMax}; +const double TestProblem10::upper_bounds[] ={ + kDoubleMax, kDoubleMax, kDoubleMax}; +const double TestProblem10::constrained_optimal_cost = + std::numeric_limits<double>::quiet_NaN(); +const double TestProblem10::unconstrained_optimal_cost = 87.9458; + +#undef BEGIN_MGH_PROBLEM +#undef END_MGH_PROBLEM + +template<typename TestProblem> string ConstrainedSolve() { + double x[TestProblem::kNumParameters]; + std::copy(TestProblem::initial_x, + TestProblem::initial_x + TestProblem::kNumParameters, + x); + + Problem problem; + problem.AddResidualBlock(TestProblem::Create(), NULL, x); + for (int i = 0; i < TestProblem::kNumParameters; ++i) { + problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]); + problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]); + } + + Solver::Options options; + options.parameter_tolerance = 1e-18; + options.function_tolerance = 1e-18; + options.gradient_tolerance = 1e-18; + options.max_num_iterations = 1000; + options.linear_solver_type = DENSE_QR; + Solver::Summary summary; + Solve(options, &problem, &summary); + + const double kMinLogRelativeError = 5.0; + const double log_relative_error = -std::log10( + std::abs(2.0 * summary.final_cost - + TestProblem::constrained_optimal_cost) / + (TestProblem::constrained_optimal_cost > 0.0 + ? TestProblem::constrained_optimal_cost + : 1.0)); + + return (log_relative_error >= kMinLogRelativeError + ? "Success\n" + : "Failure\n"); +} + +template<typename TestProblem> string UnconstrainedSolve() { + double x[TestProblem::kNumParameters]; + std::copy(TestProblem::initial_x, + TestProblem::initial_x + TestProblem::kNumParameters, + x); + + Problem problem; + problem.AddResidualBlock(TestProblem::Create(), NULL, x); + + Solver::Options options; + options.parameter_tolerance = 1e-18; + options.function_tolerance = 0.0; + options.gradient_tolerance = 1e-18; + options.max_num_iterations = 1000; + options.linear_solver_type = DENSE_QR; + Solver::Summary summary; + Solve(options, &problem, &summary); + + const double kMinLogRelativeError = 5.0; + const double log_relative_error = -std::log10( + std::abs(2.0 * summary.final_cost - + TestProblem::unconstrained_optimal_cost) / + (TestProblem::unconstrained_optimal_cost > 0.0 + ? TestProblem::unconstrained_optimal_cost + : 1.0)); + + return (log_relative_error >= kMinLogRelativeError + ? "Success\n" + : "Failure\n"); +} + +} // namespace examples +} // namespace ceres + +int main(int argc, char** argv) { + google::ParseCommandLineFlags(&argc, &argv, true); + google::InitGoogleLogging(argv[0]); + + using ceres::examples::UnconstrainedSolve; + using ceres::examples::ConstrainedSolve; + +#define UNCONSTRAINED_SOLVE(n) \ + std::cout << "Problem " << n << " : " \ + << UnconstrainedSolve<ceres::examples::TestProblem##n>(); + +#define CONSTRAINED_SOLVE(n) \ + std::cout << "Problem " << n << " : " \ + << ConstrainedSolve<ceres::examples::TestProblem##n>(); + + std::cout << "Unconstrained problems\n"; + UNCONSTRAINED_SOLVE(1); + UNCONSTRAINED_SOLVE(2); + UNCONSTRAINED_SOLVE(3); + UNCONSTRAINED_SOLVE(4); + UNCONSTRAINED_SOLVE(5); + UNCONSTRAINED_SOLVE(6); + UNCONSTRAINED_SOLVE(7); + UNCONSTRAINED_SOLVE(8); + UNCONSTRAINED_SOLVE(9); + UNCONSTRAINED_SOLVE(10); + + std::cout << "\nConstrained problems\n"; + CONSTRAINED_SOLVE(3); + CONSTRAINED_SOLVE(4); + CONSTRAINED_SOLVE(5); + CONSTRAINED_SOLVE(7); + CONSTRAINED_SOLVE(9); + + return 0; +} |