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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 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)
//
// An example program that minimizes Powell's singular function.
//
// F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2)
//
// f1 = x1 + 10*x2;
// f2 = sqrt(5) * (x3 - x4)
// f3 = (x2 - 2*x3)^2
// f4 = sqrt(10) * (x1 - x4)^2
//
// The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1.
// The minimum is 0 at (x1, x2, x3, x4) = 0.
//
// From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S.
// Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software,
// Vol 7(1), March 1981.
#include <vector>
#include "ceres/ceres.h"
#include "gflags/gflags.h"
#include "glog/logging.h"
using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;
class F1 {
public:
template <typename T> bool operator()(const T* const x1,
const T* const x2,
T* residual) const {
// f1 = x1 + 10 * x2;
residual[0] = x1[0] + T(10.0) * x2[0];
return true;
}
};
class F2 {
public:
template <typename T> bool operator()(const T* const x3,
const T* const x4,
T* residual) const {
// f2 = sqrt(5) (x3 - x4)
residual[0] = T(sqrt(5.0)) * (x3[0] - x4[0]);
return true;
}
};
class F3 {
public:
template <typename T> bool operator()(const T* const x2,
const T* const x4,
T* residual) const {
// f3 = (x2 - 2 x3)^2
residual[0] = (x2[0] - T(2.0) * x4[0]) * (x2[0] - T(2.0) * x4[0]);
return true;
}
};
class F4 {
public:
template <typename T> bool operator()(const T* const x1,
const T* const x4,
T* residual) const {
// f4 = sqrt(10) (x1 - x4)^2
residual[0] = T(sqrt(10.0)) * (x1[0] - x4[0]) * (x1[0] - x4[0]);
return true;
}
};
int main(int argc, char** argv) {
google::ParseCommandLineFlags(&argc, &argv, true);
google::InitGoogleLogging(argv[0]);
double x1 = 3.0;
double x2 = -1.0;
double x3 = 0.0;
double x4 = 1.0;
Problem problem;
// Add residual terms to the problem using the using the autodiff
// wrapper to get the derivatives automatically. The parameters, x1 through
// x4, are modified in place.
problem.AddResidualBlock(new AutoDiffCostFunction<F1, 1, 1, 1>(new F1),
NULL,
&x1, &x2);
problem.AddResidualBlock(new AutoDiffCostFunction<F2, 1, 1, 1>(new F2),
NULL,
&x3, &x4);
problem.AddResidualBlock(new AutoDiffCostFunction<F3, 1, 1, 1>(new F3),
NULL,
&x2, &x3);
problem.AddResidualBlock(new AutoDiffCostFunction<F4, 1, 1, 1>(new F4),
NULL,
&x1, &x4);
// Run the solver!
Solver::Options options;
options.max_num_iterations = 30;
options.linear_solver_type = ceres::DENSE_QR;
options.minimizer_progress_to_stdout = true;
Solver::Summary summary;
std::cout << "Initial x1 = " << x1
<< ", x2 = " << x2
<< ", x3 = " << x3
<< ", x4 = " << x4
<< "\n";
Solve(options, &problem, &summary);
std::cout << summary.BriefReport() << "\n";
std::cout << "Final x1 = " << x1
<< ", x2 = " << x2
<< ", x3 = " << x3
<< ", x4 = " << x4
<< "\n";
return 0;
}
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