| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2023 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // 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 |
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| // 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 |
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| // 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) |
| // |
| // 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 4. |
| |
| #include <cmath> |
| #include <iostream> // NOLINT |
| #include <sstream> // NOLINT |
| #include <string> |
| |
| #include "ceres/ceres.h" |
| #include "gflags/gflags.h" |
| #include "glog/logging.h" |
| |
| DEFINE_string(problem, "all", "Which problem to solve"); |
| DEFINE_bool(use_numeric_diff, |
| false, |
| "Use numeric differentiation instead of automatic" |
| " differentiation."); |
| DEFINE_string(numeric_diff_method, |
| "ridders", |
| "When using numeric differentiation, selects algorithm. Options " |
| "are: central, forward, ridders."); |
| DEFINE_int32(ridders_extrapolations, |
| 3, |
| "Maximal number of extrapolations in Ridders' method."); |
| |
| namespace ceres::examples { |
| |
| const double kDoubleMax = std::numeric_limits<double>::max(); |
| |
| static void SetNumericDiffOptions(ceres::NumericDiffOptions* options) { |
| options->max_num_ridders_extrapolations = |
| CERES_GET_FLAG(FLAGS_ridders_extrapolations); |
| } |
| |
| #define BEGIN_MGH_PROBLEM(name, num_parameters, num_residuals) \ |
| struct name { \ |
| static constexpr 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() { \ |
| if (CERES_GET_FLAG(FLAGS_use_numeric_diff)) { \ |
| ceres::NumericDiffOptions options; \ |
| SetNumericDiffOptions(&options); \ |
| if (CERES_GET_FLAG(FLAGS_numeric_diff_method) == "central") { \ |
| return new NumericDiffCostFunction<name, \ |
| ceres::CENTRAL, \ |
| num_residuals, \ |
| num_parameters>( \ |
| new name, ceres::TAKE_OWNERSHIP, num_residuals, options); \ |
| } else if (CERES_GET_FLAG(FLAGS_numeric_diff_method) == "forward") { \ |
| return new NumericDiffCostFunction<name, \ |
| ceres::FORWARD, \ |
| num_residuals, \ |
| num_parameters>( \ |
| new name, ceres::TAKE_OWNERSHIP, num_residuals, options); \ |
| } else if (CERES_GET_FLAG(FLAGS_numeric_diff_method) == "ridders") { \ |
| return new NumericDiffCostFunction<name, \ |
| ceres::RIDDERS, \ |
| num_residuals, \ |
| num_parameters>( \ |
| new name, ceres::TAKE_OWNERSHIP, num_residuals, options); \ |
| } else { \ |
| LOG(ERROR) << "Invalid numeric diff method specified"; \ |
| return nullptr; \ |
| } \ |
| } else { \ |
| return new AutoDiffCostFunction<name, num_residuals, num_parameters>( \ |
| new name); \ |
| } \ |
| } \ |
| template <typename T> \ |
| bool operator()(const T* const x, T* residual) const { |
| // clang-format off |
| |
| #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] = 10.0 * (x2 - x1 * x1); |
| residual[1] = 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] = -13.0 + x1 + ((5.0 - x2) * x2 - 2.0) * x2; |
| residual[1] = -29.0 + x1 + ((x2 + 1.0) * x2 - 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] = 10000.0 * x1 * x2 - 1.0; |
| residual[1] = exp(-x1) + exp(-x2) - 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 - 1000000.0; |
| residual[1] = x2 - 0.000002; |
| residual[2] = x1 * x2 - 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] = 1.5 - x1 * (1.0 - x2); |
| residual[1] = 2.25 - x1 * (1.0 - x2 * x2); |
| residual[2] = 2.625 - x1 * (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] = 2.0 + 2.0 * i - |
| (exp(static_cast<double>(i) * x1) + |
| exp(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 = (0.5 / constants::pi) * atan(x2 / x1) + (x1 > 0.0 ? 0.0 : 0.5); |
| residual[0] = 10.0 * (x3 - 10.0 * theta); |
| residual[1] = 10.0 * (sqrt(x1 * x1 + x2 * x2) - 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 double u = i; |
| const double v = 16 - i; |
| const double w = std::min(i, 16 - i); |
| residual[i - 1] = 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 double t_i = (8.0 - i - 1.0) / 2.0; |
| residual[i] = x1 * exp(-x2 * (t_i - x3) * (t_i - x3) / 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) { |
| const double ti = 45.0 + 5.0 * (i + 1); |
| residual[i] = x1 * exp(x2 / (ti + 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; |
| |
| // Gulf research and development function |
| BEGIN_MGH_PROBLEM(TestProblem11, 3, 100) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| for (int i = 1; i <= 100; ++i) { |
| const double ti = i / 100.0; |
| const double yi = 25.0 + pow(-50.0 * log(ti), 2.0 / 3.0); |
| residual[i - 1] = exp(-pow(abs((yi * 100.0 * i) * x2), x3) / x1) - ti; |
| } |
| END_MGH_PROBLEM |
| |
| const double TestProblem11::initial_x[] = {5.0, 2.5, 0.15}; |
| const double TestProblem11::lower_bounds[] = {1e-16, 0.0, 0.0}; |
| const double TestProblem11::upper_bounds[] = {10.0, 10.0, 10.0}; |
| const double TestProblem11::constrained_optimal_cost = 0.58281431e-4; |
| const double TestProblem11::unconstrained_optimal_cost = 0.0; |
| |
| // Box three-dimensional function. |
| BEGIN_MGH_PROBLEM(TestProblem12, 3, 3) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| |
| const double t1 = 0.1; |
| const double t2 = 0.2; |
| const double t3 = 0.3; |
| |
| residual[0] = exp(-t1 * x1) - exp(-t1 * x2) - x3 * (exp(-t1) - exp(-10.0 * t1)); |
| residual[1] = exp(-t2 * x1) - exp(-t2 * x2) - x3 * (exp(-t2) - exp(-10.0 * t2)); |
| residual[2] = exp(-t3 * x1) - exp(-t3 * x2) - x3 * (exp(-t3) - exp(-10.0 * t3)); |
| END_MGH_PROBLEM |
| |
| const double TestProblem12::initial_x[] = {0.0, 10.0, 20.0}; |
| const double TestProblem12::lower_bounds[] = {0.0, 5.0, 0.0}; |
| const double TestProblem12::upper_bounds[] = {2.0, 9.5, 20.0}; |
| const double TestProblem12::constrained_optimal_cost = 0.30998153e-5; |
| const double TestProblem12::unconstrained_optimal_cost = 0.0; |
| |
| // Powell Singular function. |
| BEGIN_MGH_PROBLEM(TestProblem13, 4, 4) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| |
| residual[0] = x1 + 10.0 * x2; |
| residual[1] = sqrt(5.0) * (x3 - x4); |
| residual[2] = (x2 - 2.0 * x3) * (x2 - 2.0 * x3); |
| residual[3] = sqrt(10.0) * (x1 - x4) * (x1 - x4); |
| END_MGH_PROBLEM |
| |
| const double TestProblem13::initial_x[] = {3.0, -1.0, 0.0, 1.0}; |
| const double TestProblem13::lower_bounds[] = { |
| -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| const double TestProblem13::upper_bounds[] = { |
| kDoubleMax, kDoubleMax, kDoubleMax}; |
| const double TestProblem13::constrained_optimal_cost = |
| std::numeric_limits<double>::quiet_NaN(); |
| const double TestProblem13::unconstrained_optimal_cost = 0.0; |
| |
| // Wood function. |
| BEGIN_MGH_PROBLEM(TestProblem14, 4, 6) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| |
| residual[0] = 10.0 * (x2 - x1 * x1); |
| residual[1] = 1.0 - x1; |
| residual[2] = sqrt(90.0) * (x4 - x3 * x3); |
| residual[3] = 1.0 - x3; |
| residual[4] = sqrt(10.0) * (x2 + x4 - 2.0); |
| residual[5] = 1.0 / sqrt(10.0) * (x2 - x4); |
| END_MGH_PROBLEM; |
| |
| const double TestProblem14::initial_x[] = {-3.0, -1.0, -3.0, -1.0}; |
| const double TestProblem14::lower_bounds[] = {-100.0, -100.0, -100.0, -100.0}; |
| const double TestProblem14::upper_bounds[] = {0.0, 10.0, 100.0, 100.0}; |
| const double TestProblem14::constrained_optimal_cost = 0.15567008e1; |
| const double TestProblem14::unconstrained_optimal_cost = 0.0; |
| |
| // Kowalik and Osborne function. |
| BEGIN_MGH_PROBLEM(TestProblem15, 4, 11) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| |
| const double y[] = {0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627, |
| 0.0456, 0.0342, 0.0323, 0.0235, 0.0246}; |
| const double u[] = {4.0, 2.0, 1.0, 0.5, 0.25, 0.167, 0.125, 0.1, |
| 0.0833, 0.0714, 0.0625}; |
| |
| for (int i = 0; i < 11; ++i) { |
| residual[i] = y[i] - x1 * (u[i] * u[i] + u[i] * x2) / |
| (u[i] * u[i] + u[i] * x3 + x4); |
| } |
| END_MGH_PROBLEM; |
| |
| const double TestProblem15::initial_x[] = {0.25, 0.39, 0.415, 0.39}; |
| const double TestProblem15::lower_bounds[] = { |
| -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| const double TestProblem15::upper_bounds[] = { |
| kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax}; |
| const double TestProblem15::constrained_optimal_cost = |
| std::numeric_limits<double>::quiet_NaN(); |
| const double TestProblem15::unconstrained_optimal_cost = 3.07505e-4; |
| |
| // Brown and Dennis function. |
| BEGIN_MGH_PROBLEM(TestProblem16, 4, 20) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| |
| for (int i = 0; i < 20; ++i) { |
| const double ti = (i + 1) / 5.0; |
| residual[i] = (x1 + ti * x2 - exp(ti)) * (x1 + ti * x2 - exp(ti)) + |
| (x3 + x4 * sin(ti) - cos(ti)) * (x3 + x4 * sin(ti) - cos(ti)); |
| } |
| END_MGH_PROBLEM; |
| |
| const double TestProblem16::initial_x[] = {25.0, 5.0, -5.0, -1.0}; |
| const double TestProblem16::lower_bounds[] = {-10.0, 0.0, -100.0, -20.0}; |
| const double TestProblem16::upper_bounds[] = {100.0, 15.0, 0.0, 0.2}; |
| const double TestProblem16::constrained_optimal_cost = 0.88860479e5; |
| const double TestProblem16::unconstrained_optimal_cost = 85822.2; |
| |
| // Osborne 1 function. |
| BEGIN_MGH_PROBLEM(TestProblem17, 5, 33) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| const T x5 = x[4]; |
| |
| const double y[] = {0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881, 0.850, 0.818, |
| 0.784, 0.751, 0.718, 0.685, 0.658, 0.628, 0.603, 0.580, 0.558, |
| 0.538, 0.522, 0.506, 0.490, 0.478, 0.467, 0.457, 0.448, 0.438, |
| 0.431, 0.424, 0.420, 0.414, 0.411, 0.406}; |
| |
| for (int i = 0; i < 33; ++i) { |
| const double ti = 10.0 * i; |
| residual[i] = y[i] - (x1 + x2 * exp(-ti * x4) + x3 * exp(-ti * x5)); |
| } |
| END_MGH_PROBLEM; |
| |
| const double TestProblem17::initial_x[] = {0.5, 1.5, -1.0, 0.01, 0.02}; |
| const double TestProblem17::lower_bounds[] = { |
| -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| const double TestProblem17::upper_bounds[] = { |
| kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax}; |
| const double TestProblem17::constrained_optimal_cost = |
| std::numeric_limits<double>::quiet_NaN(); |
| const double TestProblem17::unconstrained_optimal_cost = 5.46489e-5; |
| |
| // Biggs EXP6 function. |
| BEGIN_MGH_PROBLEM(TestProblem18, 6, 13) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| const T x5 = x[4]; |
| const T x6 = x[5]; |
| |
| for (int i = 0; i < 13; ++i) { |
| const double ti = 0.1 * (i + 1.0); |
| const double yi = exp(-ti) - 5.0 * exp(-10.0 * ti) + 3.0 * exp(-4.0 * ti); |
| residual[i] = |
| x3 * exp(-ti * x1) - x4 * exp(-ti * x2) + x6 * exp(-ti * x5) - yi; |
| } |
| END_MGH_PROBLEM |
| |
| const double TestProblem18::initial_x[] = {1.0, 2.0, 1.0, 1.0, 1.0, 1.0}; |
| const double TestProblem18::lower_bounds[] = {0.0, 0.0, 0.0, 1.0, 0.0, 0.0}; |
| const double TestProblem18::upper_bounds[] = {2.0, 8.0, 1.0, 7.0, 5.0, 5.0}; |
| const double TestProblem18::constrained_optimal_cost = 0.53209865e-3; |
| const double TestProblem18::unconstrained_optimal_cost = 0.0; |
| |
| // Osborne 2 function. |
| BEGIN_MGH_PROBLEM(TestProblem19, 11, 65) |
| const T x1 = x[0]; |
| const T x2 = x[1]; |
| const T x3 = x[2]; |
| const T x4 = x[3]; |
| const T x5 = x[4]; |
| const T x6 = x[5]; |
| const T x7 = x[6]; |
| const T x8 = x[7]; |
| const T x9 = x[8]; |
| const T x10 = x[9]; |
| const T x11 = x[10]; |
| |
| const double y[] = {1.366, 1.191, 1.112, 1.013, 0.991, |
| 0.885, 0.831, 0.847, 0.786, 0.725, |
| 0.746, 0.679, 0.608, 0.655, 0.616, |
| 0.606, 0.602, 0.626, 0.651, 0.724, |
| 0.649, 0.649, 0.694, 0.644, 0.624, |
| 0.661, 0.612, 0.558, 0.533, 0.495, |
| 0.500, 0.423, 0.395, 0.375, 0.372, |
| 0.391, 0.396, 0.405, 0.428, 0.429, |
| 0.523, 0.562, 0.607, 0.653, 0.672, |
| 0.708, 0.633, 0.668, 0.645, 0.632, |
| 0.591, 0.559, 0.597, 0.625, 0.739, |
| 0.710, 0.729, 0.720, 0.636, 0.581, |
| 0.428, 0.292, 0.162, 0.098, 0.054}; |
| |
| for (int i = 0; i < 65; ++i) { |
| const double ti = i / 10.0; |
| residual[i] = y[i] - (x1 * exp(-(ti * x5)) + |
| x2 * exp(-(ti - x9) * (ti - x9) * x6) + |
| x3 * exp(-(ti - x10) * (ti - x10) * x7) + |
| x4 * exp(-(ti - x11) * (ti - x11) * x8)); |
| } |
| END_MGH_PROBLEM; |
| |
| const double TestProblem19::initial_x[] = {1.3, 0.65, 0.65, 0.7, 0.6, |
| 3.0, 5.0, 7.0, 2.0, 4.5, 5.5}; |
| const double TestProblem19::lower_bounds[] = { |
| -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax}; |
| const double TestProblem19::upper_bounds[] = { |
| kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax}; |
| const double TestProblem19::constrained_optimal_cost = |
| std::numeric_limits<double>::quiet_NaN(); |
| const double TestProblem19::unconstrained_optimal_cost = 4.01377e-2; |
| |
| |
| #undef BEGIN_MGH_PROBLEM |
| #undef END_MGH_PROBLEM |
| |
| // clang-format on |
| |
| template <typename TestProblem> |
| bool Solve(bool is_constrained, int trial) { |
| double x[TestProblem::kNumParameters]; |
| for (int i = 0; i < TestProblem::kNumParameters; ++i) { |
| x[i] = pow(10, trial) * TestProblem::initial_x[i]; |
| } |
| |
| Problem problem; |
| problem.AddResidualBlock(TestProblem::Create(), nullptr, x); |
| double optimal_cost = TestProblem::unconstrained_optimal_cost; |
| |
| if (is_constrained) { |
| for (int i = 0; i < TestProblem::kNumParameters; ++i) { |
| problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]); |
| problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]); |
| } |
| optimal_cost = TestProblem::constrained_optimal_cost; |
| } |
| |
| 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 = 4.0; |
| const double log_relative_error = |
| -std::log10(std::abs(2.0 * summary.final_cost - optimal_cost) / |
| (optimal_cost > 0.0 ? optimal_cost : 1.0)); |
| |
| const bool success = log_relative_error >= kMinLogRelativeError; |
| LOG(INFO) << "Expected : " << optimal_cost |
| << " actual: " << 2.0 * summary.final_cost << " " << success |
| << " in " << summary.total_time_in_seconds << " seconds"; |
| return success; |
| } |
| |
| } // namespace ceres::examples |
| |
| int main(int argc, char** argv) { |
| GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true); |
| google::InitGoogleLogging(argv[0]); |
| using ceres::examples::Solve; |
| |
| int unconstrained_problems = 0; |
| int unconstrained_successes = 0; |
| int constrained_problems = 0; |
| int constrained_successes = 0; |
| std::stringstream ss; |
| |
| #define UNCONSTRAINED_SOLVE(n) \ |
| ss << "Unconstrained Problem " << n << " : "; \ |
| if (CERES_GET_FLAG(FLAGS_problem) == #n || \ |
| CERES_GET_FLAG(FLAGS_problem) == "all") { \ |
| unconstrained_problems += 3; \ |
| if (Solve<ceres::examples::TestProblem##n>(false, 0)) { \ |
| unconstrained_successes += 1; \ |
| ss << "Yes "; \ |
| } else { \ |
| ss << "No "; \ |
| } \ |
| if (Solve<ceres::examples::TestProblem##n>(false, 1)) { \ |
| unconstrained_successes += 1; \ |
| ss << "Yes "; \ |
| } else { \ |
| ss << "No "; \ |
| } \ |
| if (Solve<ceres::examples::TestProblem##n>(false, 2)) { \ |
| unconstrained_successes += 1; \ |
| ss << "Yes "; \ |
| } else { \ |
| ss << "No "; \ |
| } \ |
| } \ |
| ss << std::endl; |
| |
| 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); |
| UNCONSTRAINED_SOLVE(11); |
| UNCONSTRAINED_SOLVE(12); |
| UNCONSTRAINED_SOLVE(13); |
| UNCONSTRAINED_SOLVE(14); |
| UNCONSTRAINED_SOLVE(15); |
| UNCONSTRAINED_SOLVE(16); |
| UNCONSTRAINED_SOLVE(17); |
| UNCONSTRAINED_SOLVE(18); |
| UNCONSTRAINED_SOLVE(19); |
| |
| ss << "Unconstrained : " << unconstrained_successes << "/" |
| << unconstrained_problems << std::endl; |
| |
| #define CONSTRAINED_SOLVE(n) \ |
| ss << "Constrained Problem " << n << " : "; \ |
| if (CERES_GET_FLAG(FLAGS_problem) == #n || \ |
| CERES_GET_FLAG(FLAGS_problem) == "all") { \ |
| constrained_problems += 1; \ |
| if (Solve<ceres::examples::TestProblem##n>(true, 0)) { \ |
| constrained_successes += 1; \ |
| ss << "Yes "; \ |
| } else { \ |
| ss << "No "; \ |
| } \ |
| } \ |
| ss << std::endl; |
| |
| CONSTRAINED_SOLVE(3); |
| CONSTRAINED_SOLVE(4); |
| CONSTRAINED_SOLVE(5); |
| CONSTRAINED_SOLVE(7); |
| CONSTRAINED_SOLVE(9); |
| CONSTRAINED_SOLVE(11); |
| CONSTRAINED_SOLVE(12); |
| CONSTRAINED_SOLVE(14); |
| CONSTRAINED_SOLVE(16); |
| CONSTRAINED_SOLVE(18); |
| ss << "Constrained : " << constrained_successes << "/" << constrained_problems |
| << std::endl; |
| |
| std::cout << ss.str(); |
| return 0; |
| } |
