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;
+}
