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				|  |  | +// Ceres Solver - A fast non-linear least squares minimizer
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				|  |  | +// Copyright 2014 Google Inc. All rights reserved.
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				|  |  | +// http://code.google.com/p/ceres-solver/
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				|  |  | +//
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				|  |  | +// Redistribution and use in source and binary forms, with or without
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				|  |  | +// modification, are permitted provided that the following conditions are met:
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				|  |  | +//
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				|  |  | +// * Redistributions of source code must retain the above copyright notice,
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				|  |  | +//   this list of conditions and the following disclaimer.
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				|  |  | +// * Redistributions in binary form must reproduce the above copyright notice,
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				|  |  | +//   this list of conditions and the following disclaimer in the documentation
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				|  |  | +//   and/or other materials provided with the distribution.
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				|  |  | +// * Neither the name of Google Inc. nor the names of its contributors may be
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				|  |  | +//   used to endorse or promote products derived from this software without
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				|  |  | +//   specific prior written permission.
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				|  |  | +//
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				|  |  | +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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				|  |  | +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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				|  |  | +// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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				|  |  | +// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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				|  |  | +// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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				|  |  | +// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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				|  |  | +// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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				|  |  | +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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				|  |  | +// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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				|  |  | +// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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				|  |  | +// POSSIBILITY OF SUCH DAMAGE.
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				|  |  | +//
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				|  |  | +// Author: sameeragarwal@google.com (Sameer Agarwal)
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				|  |  | +//
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				|  |  | +// Bounds constrained test problems from the paper
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				|  |  | +//
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				|  |  | +// Testing Unconstrained Optimization Software
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				|  |  | +// Jorge J. More, Burton S. Garbow and Kenneth E. Hillstrom
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				|  |  | +// ACM Transactions on Mathematical Software, 7(1), pp. 17-41, 1981
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				|  |  | +//
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				|  |  | +// A subset of these problems were augmented with bounds and used for
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				|  |  | +// testing bounds constrained optimization algorithms by
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				|  |  | +//
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				|  |  | +// A Trust Region Approach to Linearly Constrained Optimization
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				|  |  | +// David M. Gay
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				|  |  | +// Numerical Analysis (Griffiths, D.F., ed.), pp. 72-105
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				|  |  | +// Lecture Notes in Mathematics 1066, Springer Verlag, 1984.
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				|  |  | +//
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				|  |  | +// The latter paper is behind a paywall. We obtained the bounds on the
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				|  |  | +// variables and the function values at the global minimums from
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				|  |  | +//
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				|  |  | +// http://www.mat.univie.ac.at/~neum/glopt/bounds.html
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				|  |  | +//
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				|  |  | +// A problem is considered solved if of the log relative error of its
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				|  |  | +// objective function is at least 5.
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				|  |  | +
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				|  |  | +
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				|  |  | +#include <cmath>
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				|  |  | +#include <iostream>
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				|  |  | +#include "ceres/ceres.h"
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				|  |  | +
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				|  |  | +namespace ceres {
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				|  |  | +namespace examples {
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				|  |  | +
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				|  |  | +#define BEGIN_BOUNDS_TEST(name, num_parameters, num_residuals)          \
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				|  |  | +  struct name {                                                         \
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				|  |  | +    static const int kNumParameters = num_parameters;                   \
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				|  |  | +    static const double initial_x[kNumParameters];                      \
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				|  |  | +    static const double lower_bounds[kNumParameters];                   \
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				|  |  | +    static const double upper_bounds[kNumParameters];                   \
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				|  |  | +    static const double optimal_cost;                                   \
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				|  |  | +    static CostFunction* Create() {                                     \
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				|  |  | +      return new AutoDiffCostFunction<name,                             \
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				|  |  | +                                      num_residuals,                    \
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				|  |  | +                                      num_parameters>(new name);        \
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				|  |  | +    }                                                                   \
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				|  |  | +    template <typename T>                                               \
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				|  |  | +    bool operator()(const T* const x, T* residual) const {
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				|  |  | +
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				|  |  | +#define END_BOUNDS_TEST return true; } };
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				|  |  | +
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				|  |  | +BEGIN_BOUNDS_TEST(TestProblem3, 2, 2)
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				|  |  | +  const T x1 = x[0];
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				|  |  | +  const T x2 = x[1];
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				|  |  | +  residual[0] = T(10000.0) * x1 * x2 - T(1.0);
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				|  |  | +  residual[1] = exp(-x1) + exp(-x2) - T(1.0001);
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				|  |  | +END_BOUNDS_TEST;
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				|  |  | +
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				|  |  | +const double TestProblem3::initial_x[] = {0.0, 1.0};
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				|  |  | +const double TestProblem3::lower_bounds[] = {0.0, 1.0};
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				|  |  | +const double TestProblem3::upper_bounds[] = {1.0, 9.0};
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				|  |  | +const double TestProblem3::optimal_cost = 0.15125900e-9;
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				|  |  | +
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				|  |  | +BEGIN_BOUNDS_TEST(TestProblem4, 2, 3)
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				|  |  | +  const T x1 = x[0];
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				|  |  | +  const T x2 = x[1];
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				|  |  | +  residual[0] = x1  - T(1000000.0);
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				|  |  | +  residual[1] = x2 - T(0.000002);
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				|  |  | +  residual[2] = x1 * x2 - T(2.0);
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				|  |  | +END_BOUNDS_TEST;
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				|  |  | +
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				|  |  | +const double TestProblem4::initial_x[] = {1.0, 1.0};
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				|  |  | +const double TestProblem4::lower_bounds[] = {0.0, 0.00003};
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				|  |  | +const double TestProblem4::upper_bounds[] = {1000000.0, 100.0};
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				|  |  | +const double TestProblem4::optimal_cost = 0.78400000e3;
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				|  |  | +
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				|  |  | +BEGIN_BOUNDS_TEST(TestProblem5, 2, 3)
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				|  |  | +  const T x1 = x[0];
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				|  |  | +  const T x2 = x[1];
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				|  |  | +  residual[0] = T(1.5) - x1 * (T(1.0) - x2);
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				|  |  | +  residual[1] = T(2.25) - x1 * (T(1.0) - x2 * x2);
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				|  |  | +  residual[2] = T(2.625) - x1 * (T(1.0) - x2 * x2 * x2);
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				|  |  | +END_BOUNDS_TEST;
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				|  |  | +
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				|  |  | +const double TestProblem5::initial_x[] = {1.0, 1.0};
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				|  |  | +const double TestProblem5::lower_bounds[] = {0.6, 0.5};
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				|  |  | +const double TestProblem5::upper_bounds[] = {10.0, 100.0};
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				|  |  | +const double TestProblem5::optimal_cost = 0.0;
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				|  |  | +
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				|  |  | +BEGIN_BOUNDS_TEST(TestProblem7, 3, 3)
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				|  |  | +  const T x1 = x[0];
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				|  |  | +  const T x2 = x[1];
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				|  |  | +  const T x3 = x[2];
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				|  |  | +  const T theta = T(0.5 / M_PI)  * atan(x2 / x1) + (x1 > 0.0 ? T(0.0) : T(0.5));
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				|  |  | +
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				|  |  | +  residual[0] = T(10.0) * (x3 - T(10.0) * theta);
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				|  |  | +  residual[1] = T(10.0) * (sqrt(x1 * x1 + x2 * x2) - T(1.0));
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				|  |  | +  residual[2] = x3;
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				|  |  | +END_BOUNDS_TEST;
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				|  |  | +
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				|  |  | +const double TestProblem7::initial_x[] = {-1.0, 0.0, 0.0};
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				|  |  | +const double TestProblem7::lower_bounds[] = {-100.0, -1.0, -1.0};
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				|  |  | +const double TestProblem7::upper_bounds[] = {0.8, 1.0, 1.0};
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				|  |  | +const double TestProblem7::optimal_cost = 0.99042212;
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				|  |  | +
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				|  |  | +BEGIN_BOUNDS_TEST(TestProblem9, 3, 15)
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				|  |  | +  const T x1 = x[0];
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				|  |  | +  const T x2 = x[1];
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				|  |  | +  const T x3 = x[2];
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				|  |  | +
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				|  |  | +  double y[] = {0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521,
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				|  |  | +                0.3989,
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				|  |  | +                0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009};
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				|  |  | +  for (int i = 0; i < 15; ++i) {
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				|  |  | +    const T t_i = T((8.0 - i - 1.0) / 2.0);
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				|  |  | +    const T y_i = T(y[i]);
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				|  |  | +    residual[i] = x1 * exp( -x2 * (t_i - x3) * (t_i - x3) / T(2.0)) - y_i;
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				|  |  | +  }
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				|  |  | +END_BOUNDS_TEST;
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				|  |  | +
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				|  |  | +const double TestProblem9::initial_x[] = {0.4, 1.0, 0.0};
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				|  |  | +const double TestProblem9::lower_bounds[] = {0.398, 1.0 ,-0.5};
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				|  |  | +const double TestProblem9::upper_bounds[] = {4.2, 2.0, 0.1};
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				|  |  | +const double TestProblem9::optimal_cost = 0.11279300e-7;
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				|  |  | +
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				|  |  | +#undef BEGIN_BOUNDS_TEST
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				|  |  | +#undef END_BOUNDS_TEST
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				|  |  | +
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				|  |  | +template<typename TestProblem> string Solve() {
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				|  |  | +  double x[TestProblem::kNumParameters];
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				|  |  | +  std::copy(TestProblem::initial_x,
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				|  |  | +            TestProblem::initial_x + TestProblem::kNumParameters,
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				|  |  | +            x);
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				|  |  | +
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				|  |  | +  Problem problem;
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				|  |  | +  problem.AddResidualBlock(TestProblem::Create(), NULL, x);
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				|  |  | +  for (int i = 0; i < TestProblem::kNumParameters; ++i) {
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				|  |  | +    problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]);
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				|  |  | +    problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]);
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				|  |  | +  }
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				|  |  | +
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				|  |  | +  Solver::Options options;
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				|  |  | +  options.parameter_tolerance = 1e-18;
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				|  |  | +  options.function_tolerance = 1e-18;
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				|  |  | +  options.gradient_tolerance = 1e-18;
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				|  |  | +  options.max_num_iterations = 1000;
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				|  |  | +  options.linear_solver_type = DENSE_QR;
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				|  |  | +  Solver::Summary summary;
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				|  |  | +  Solve(options, &problem, &summary);
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				|  |  | +
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				|  |  | +  const double kMinLogRelativeError = 5.0;
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				|  |  | +  const double log_relative_error = -std::log10(
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				|  |  | +      std::abs(2.0 * summary.final_cost - TestProblem::optimal_cost) /
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				|  |  | +      (TestProblem::optimal_cost > 0.0 ? TestProblem::optimal_cost : 1.0));
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				|  |  | +
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				|  |  | +  return (log_relative_error >= kMinLogRelativeError
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				|  |  | +          ? "Success\n"
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				|  |  | +          : "Failure\n");
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				|  |  | +}
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				|  |  | +
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				|  |  | +}  // namespace examples
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				|  |  | +}  // namespace ceres
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				|  |  | +
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				|  |  | +int main(int argc, char** argv) {
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				|  |  | +  google::ParseCommandLineFlags(&argc, &argv, true);
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				|  |  | +  google::InitGoogleLogging(argv[0]);
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				|  |  | +
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				|  |  | +  using ceres::examples::Solve;
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				|  |  | +
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				|  |  | +  std::cout << "Test problem 3 : " << Solve<ceres::examples::TestProblem3>();
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				|  |  | +  std::cout << "Test problem 4 : " << Solve<ceres::examples::TestProblem4>();
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				|  |  | +  std::cout << "Test problem 5 : " << Solve<ceres::examples::TestProblem5>();
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				|  |  | +  std::cout << "Test problem 7 : " << Solve<ceres::examples::TestProblem7>();
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				|  |  | +  std::cout << "Test problem 9 : " << Solve<ceres::examples::TestProblem9>();
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				|  |  | +
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				|  |  | +  return 0;
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				|  |  | +}
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