374 lines
14 KiB
C++
374 lines
14 KiB
C++
// 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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#include <cmath>
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#include <iostream> // NOLINT
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#include "ceres/ceres.h"
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#include "gflags/gflags.h"
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#include "glog/logging.h"
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namespace ceres {
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namespace examples {
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const double kDoubleMax = std::numeric_limits<double>::max();
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#define BEGIN_MGH_PROBLEM(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 constrained_optimal_cost; \
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static const double unconstrained_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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#define END_MGH_PROBLEM return true; } }; // NOLINT
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// Rosenbrock function.
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BEGIN_MGH_PROBLEM(TestProblem1, 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(10.0) * (x2 - x1 * x1);
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residual[1] = T(1.0) - x1;
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END_MGH_PROBLEM;
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const double TestProblem1::initial_x[] = {-1.2, 1.0};
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const double TestProblem1::lower_bounds[] = {-kDoubleMax, -kDoubleMax};
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const double TestProblem1::upper_bounds[] = {kDoubleMax, kDoubleMax};
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const double TestProblem1::constrained_optimal_cost =
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std::numeric_limits<double>::quiet_NaN();
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const double TestProblem1::unconstrained_optimal_cost = 0.0;
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// Freudenstein and Roth function.
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BEGIN_MGH_PROBLEM(TestProblem2, 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(-13.0) + x1 + ((T(5.0) - x2) * x2 - T(2.0)) * x2;
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residual[1] = T(-29.0) + x1 + ((x2 + T(1.0)) * x2 - T(14.0)) * x2;
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END_MGH_PROBLEM;
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const double TestProblem2::initial_x[] = {0.5, -2.0};
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const double TestProblem2::lower_bounds[] = {-kDoubleMax, -kDoubleMax};
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const double TestProblem2::upper_bounds[] = {kDoubleMax, kDoubleMax};
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const double TestProblem2::constrained_optimal_cost =
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std::numeric_limits<double>::quiet_NaN();
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const double TestProblem2::unconstrained_optimal_cost = 0.0;
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// Powell badly scaled function.
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BEGIN_MGH_PROBLEM(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_MGH_PROBLEM;
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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::constrained_optimal_cost = 0.15125900e-9;
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const double TestProblem3::unconstrained_optimal_cost = 0.0;
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// Brown badly scaled function.
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BEGIN_MGH_PROBLEM(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_MGH_PROBLEM;
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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::constrained_optimal_cost = 0.78400000e3;
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const double TestProblem4::unconstrained_optimal_cost = 0.0;
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// Beale function.
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BEGIN_MGH_PROBLEM(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_MGH_PROBLEM;
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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::constrained_optimal_cost = 0.0;
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const double TestProblem5::unconstrained_optimal_cost = 0.0;
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// Jennrich and Sampson function.
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BEGIN_MGH_PROBLEM(TestProblem6, 2, 10)
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const T x1 = x[0];
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const T x2 = x[1];
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for (int i = 1; i <= 10; ++i) {
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residual[i - 1] = T(2.0) + T(2.0 * i) -
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exp(T(static_cast<double>(i)) * x1) -
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exp(T(static_cast<double>(i) * x2));
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}
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END_MGH_PROBLEM;
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const double TestProblem6::initial_x[] = {1.0, 1.0};
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const double TestProblem6::lower_bounds[] = {-kDoubleMax, -kDoubleMax};
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const double TestProblem6::upper_bounds[] = {kDoubleMax, kDoubleMax};
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const double TestProblem6::constrained_optimal_cost =
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std::numeric_limits<double>::quiet_NaN();
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const double TestProblem6::unconstrained_optimal_cost = 124.362;
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// Helical valley function.
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BEGIN_MGH_PROBLEM(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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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_MGH_PROBLEM;
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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::constrained_optimal_cost = 0.99042212;
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const double TestProblem7::unconstrained_optimal_cost = 0.0;
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// Bard function
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BEGIN_MGH_PROBLEM(TestProblem8, 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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double y[] = {0.14, 0.18, 0.22, 0.25,
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0.29, 0.32, 0.35, 0.39, 0.37, 0.58,
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0.73, 0.96, 1.34, 2.10, 4.39};
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for (int i = 1; i <=15; ++i) {
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const T u = T(static_cast<double>(i));
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const T v = T(static_cast<double>(16 - i));
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const T w = T(static_cast<double>(std::min(i, 16 - i)));
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residual[i - 1] = T(y[i - 1]) - x1 + u / (v * x2 + w * x3);
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}
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END_MGH_PROBLEM;
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const double TestProblem8::initial_x[] = {1.0, 1.0, 1.0};
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const double TestProblem8::lower_bounds[] = {
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-kDoubleMax, -kDoubleMax, -kDoubleMax};
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const double TestProblem8::upper_bounds[] = {
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kDoubleMax, kDoubleMax, kDoubleMax};
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const double TestProblem8::constrained_optimal_cost =
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std::numeric_limits<double>::quiet_NaN();
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const double TestProblem8::unconstrained_optimal_cost = 8.21487e-3;
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// Gaussian function.
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BEGIN_MGH_PROBLEM(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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const 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_MGH_PROBLEM;
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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::constrained_optimal_cost = 0.11279300e-7;
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const double TestProblem9::unconstrained_optimal_cost = 0.112793e-7;
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// Meyer function.
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BEGIN_MGH_PROBLEM(TestProblem10, 3, 16)
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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 double y[] = {34780, 28610, 23650, 19630, 16370, 13720, 11540, 9744,
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8261, 7030, 6005, 5147, 4427, 3820, 3307, 2872};
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for (int i = 0; i < 16; ++i) {
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T t = T(45 + 5.0 * (i + 1));
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residual[i] = x1 * exp(x2 / (t + x3)) - y[i];
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}
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END_MGH_PROBLEM
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const double TestProblem10::initial_x[] = {0.02, 4000, 250};
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const double TestProblem10::lower_bounds[] ={
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-kDoubleMax, -kDoubleMax, -kDoubleMax};
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const double TestProblem10::upper_bounds[] ={
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kDoubleMax, kDoubleMax, kDoubleMax};
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const double TestProblem10::constrained_optimal_cost =
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std::numeric_limits<double>::quiet_NaN();
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const double TestProblem10::unconstrained_optimal_cost = 87.9458;
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#undef BEGIN_MGH_PROBLEM
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#undef END_MGH_PROBLEM
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template<typename TestProblem> string ConstrainedSolve() {
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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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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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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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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 -
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TestProblem::constrained_optimal_cost) /
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(TestProblem::constrained_optimal_cost > 0.0
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? TestProblem::constrained_optimal_cost
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: 1.0));
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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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template<typename TestProblem> string UnconstrainedSolve() {
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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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Problem problem;
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problem.AddResidualBlock(TestProblem::Create(), NULL, x);
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Solver::Options options;
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options.parameter_tolerance = 1e-18;
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options.function_tolerance = 0.0;
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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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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 -
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TestProblem::unconstrained_optimal_cost) /
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(TestProblem::unconstrained_optimal_cost > 0.0
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? TestProblem::unconstrained_optimal_cost
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: 1.0));
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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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} // namespace examples
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} // namespace ceres
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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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using ceres::examples::UnconstrainedSolve;
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using ceres::examples::ConstrainedSolve;
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#define UNCONSTRAINED_SOLVE(n) \
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std::cout << "Problem " << n << " : " \
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<< UnconstrainedSolve<ceres::examples::TestProblem##n>();
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#define CONSTRAINED_SOLVE(n) \
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std::cout << "Problem " << n << " : " \
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<< ConstrainedSolve<ceres::examples::TestProblem##n>();
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std::cout << "Unconstrained problems\n";
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UNCONSTRAINED_SOLVE(1);
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UNCONSTRAINED_SOLVE(2);
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UNCONSTRAINED_SOLVE(3);
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UNCONSTRAINED_SOLVE(4);
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UNCONSTRAINED_SOLVE(5);
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UNCONSTRAINED_SOLVE(6);
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UNCONSTRAINED_SOLVE(7);
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UNCONSTRAINED_SOLVE(8);
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UNCONSTRAINED_SOLVE(9);
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UNCONSTRAINED_SOLVE(10);
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std::cout << "\nConstrained problems\n";
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CONSTRAINED_SOLVE(3);
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CONSTRAINED_SOLVE(4);
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CONSTRAINED_SOLVE(5);
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CONSTRAINED_SOLVE(7);
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CONSTRAINED_SOLVE(9);
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return 0;
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}
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