Add test problems from More, Garbow and Hillstrom. Change-Id: I50f1fec377ad020bd1537e65bed5ff08d2d8f4e7
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt index ac96de8..8a48717 100644 --- a/examples/CMakeLists.txt +++ b/examples/CMakeLists.txt
@@ -63,6 +63,9 @@ ADD_EXECUTABLE(nist nist.cc) TARGET_LINK_LIBRARIES(nist ceres ${GFLAGS_LIBRARIES}) + ADD_EXECUTABLE(more_garbow_hillstrom more_garbow_hillstrom.cc) + TARGET_LINK_LIBRARIES(more_garbow_hillstrom ceres ${GFLAGS_LIBRARIES}) + ADD_EXECUTABLE(circle_fit circle_fit.cc) TARGET_LINK_LIBRARIES(circle_fit ceres ${GFLAGS_LIBRARIES}) @@ -80,4 +83,3 @@ fields_of_experts.cc) TARGET_LINK_LIBRARIES(denoising ceres ${GFLAGS_LIBRARIES}) ENDIF (GFLAGS) -
diff --git a/examples/more_garbow_hillstrom.cc b/examples/more_garbow_hillstrom.cc new file mode 100644 index 0000000..505d9b3 --- /dev/null +++ b/examples/more_garbow_hillstrom.cc
@@ -0,0 +1,203 @@ +// 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> +#include "ceres/ceres.h" + +namespace ceres { +namespace examples { + +#define BEGIN_BOUNDS_TEST(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 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_BOUNDS_TEST return true; } }; + +BEGIN_BOUNDS_TEST(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_BOUNDS_TEST; + +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::optimal_cost = 0.15125900e-9; + +BEGIN_BOUNDS_TEST(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_BOUNDS_TEST; + +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::optimal_cost = 0.78400000e3; + +BEGIN_BOUNDS_TEST(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_BOUNDS_TEST; + +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::optimal_cost = 0.0; + +BEGIN_BOUNDS_TEST(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_BOUNDS_TEST; + +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::optimal_cost = 0.99042212; + +BEGIN_BOUNDS_TEST(TestProblem9, 3, 15) + const T x1 = x[0]; + const T x2 = x[1]; + const T x3 = x[2]; + + 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_BOUNDS_TEST; + +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::optimal_cost = 0.11279300e-7; + +#undef BEGIN_BOUNDS_TEST +#undef END_BOUNDS_TEST + +template<typename TestProblem> string Solve() { + 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::optimal_cost) / + (TestProblem::optimal_cost > 0.0 ? TestProblem::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::Solve; + + std::cout << "Test problem 3 : " << Solve<ceres::examples::TestProblem3>(); + std::cout << "Test problem 4 : " << Solve<ceres::examples::TestProblem4>(); + std::cout << "Test problem 5 : " << Solve<ceres::examples::TestProblem5>(); + std::cout << "Test problem 7 : " << Solve<ceres::examples::TestProblem7>(); + std::cout << "Test problem 9 : " << Solve<ceres::examples::TestProblem9>(); + + return 0; +}