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diff --git a/examples/powell.cc b/examples/powell.cc new file mode 100644 index 0000000..6cd3611 --- /dev/null +++ b/examples/powell.cc @@ -0,0 +1,151 @@ +// 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; +} |