Initial commit of Ceres Solver.
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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"
+
+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;
+}
