10ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Ceres Solver - A fast non-linear least squares minimizer 20ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Copyright 2010, 2011, 2012 Google Inc. All rights reserved. 30ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// http://code.google.com/p/ceres-solver/ 40ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 50ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Redistribution and use in source and binary forms, with or without 60ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// modification, are permitted provided that the following conditions are met: 70ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 80ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions of source code must retain the above copyright notice, 90ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// this list of conditions and the following disclaimer. 100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions in binary form must reproduce the above copyright notice, 110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// this list of conditions and the following disclaimer in the documentation 120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// and/or other materials provided with the distribution. 130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Neither the name of Google Inc. nor the names of its contributors may be 140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// used to endorse or promote products derived from this software without 150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// specific prior written permission. 160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// POSSIBILITY OF SUCH DAMAGE. 280ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 290ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Author: sameeragarwal@google.com (Sameer Agarwal) 300ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 310ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/ceres.h" 320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "gflags/gflags.h" 330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::AutoDiffCostFunction; 350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::CostFunction; 360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Problem; 370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Solver; 380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Solve; 390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Data generated using the following octave code. 410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// randn('seed', 23497); 420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// m = 0.3; 430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// c = 0.1; 440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// x=[0:0.075:5]; 450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// y = exp(m * x + c); 460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// noise = randn(size(x)) * 0.2; 470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// y_observed = y + noise; 480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// data = [x', y_observed']; 490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongconst int kNumObservations = 67; 510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongconst double data[] = { 520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 0.000000e+00, 1.133898e+00, 530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 7.500000e-02, 1.334902e+00, 540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.500000e-01, 1.213546e+00, 550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.250000e-01, 1.252016e+00, 560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.000000e-01, 1.392265e+00, 570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.750000e-01, 1.314458e+00, 580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.500000e-01, 1.472541e+00, 590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 5.250000e-01, 1.536218e+00, 600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 6.000000e-01, 1.355679e+00, 610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 6.750000e-01, 1.463566e+00, 620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 7.500000e-01, 1.490201e+00, 630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 8.250000e-01, 1.658699e+00, 640ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 9.000000e-01, 1.067574e+00, 650ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 9.750000e-01, 1.464629e+00, 660ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.050000e+00, 1.402653e+00, 670ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.125000e+00, 1.713141e+00, 680ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.200000e+00, 1.527021e+00, 690ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.275000e+00, 1.702632e+00, 700ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.350000e+00, 1.423899e+00, 710ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.425000e+00, 1.543078e+00, 720ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.500000e+00, 1.664015e+00, 730ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.575000e+00, 1.732484e+00, 740ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.650000e+00, 1.543296e+00, 750ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.725000e+00, 1.959523e+00, 760ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.800000e+00, 1.685132e+00, 770ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.875000e+00, 1.951791e+00, 780ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.950000e+00, 2.095346e+00, 790ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.025000e+00, 2.361460e+00, 800ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.100000e+00, 2.169119e+00, 810ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.175000e+00, 2.061745e+00, 820ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.250000e+00, 2.178641e+00, 830ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.325000e+00, 2.104346e+00, 840ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.400000e+00, 2.584470e+00, 850ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.475000e+00, 1.914158e+00, 860ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.550000e+00, 2.368375e+00, 870ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.625000e+00, 2.686125e+00, 880ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.700000e+00, 2.712395e+00, 890ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.775000e+00, 2.499511e+00, 900ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.850000e+00, 2.558897e+00, 910ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 2.925000e+00, 2.309154e+00, 920ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.000000e+00, 2.869503e+00, 930ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.075000e+00, 3.116645e+00, 940ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.150000e+00, 3.094907e+00, 950ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.225000e+00, 2.471759e+00, 960ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.300000e+00, 3.017131e+00, 970ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.375000e+00, 3.232381e+00, 980ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.450000e+00, 2.944596e+00, 990ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.525000e+00, 3.385343e+00, 1000ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.600000e+00, 3.199826e+00, 1010ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.675000e+00, 3.423039e+00, 1020ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.750000e+00, 3.621552e+00, 1030ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.825000e+00, 3.559255e+00, 1040ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.900000e+00, 3.530713e+00, 1050ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 3.975000e+00, 3.561766e+00, 1060ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.050000e+00, 3.544574e+00, 1070ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.125000e+00, 3.867945e+00, 1080ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.200000e+00, 4.049776e+00, 1090ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.275000e+00, 3.885601e+00, 1100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.350000e+00, 4.110505e+00, 1110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.425000e+00, 4.345320e+00, 1120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.500000e+00, 4.161241e+00, 1130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.575000e+00, 4.363407e+00, 1140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.650000e+00, 4.161576e+00, 1150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.725000e+00, 4.619728e+00, 1160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.800000e+00, 4.737410e+00, 1170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.875000e+00, 4.727863e+00, 1180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 4.950000e+00, 4.669206e+00, 1190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 1200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongclass ExponentialResidual { 1220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong public: 1230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong ExponentialResidual(double x, double y) 1240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong : x_(x), y_(y) {} 1250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong template <typename T> bool operator()(const T* const m, 1270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const T* const c, 1280ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong T* residual) const { 1290ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong residual[0] = T(y_) - exp(m[0] * T(x_) + c[0]); 1300ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return true; 1310ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 1320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong private: 1340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const double x_; 1350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const double y_; 1360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 1370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongint main(int argc, char** argv) { 1390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong google::ParseCommandLineFlags(&argc, &argv, true); 1400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong google::InitGoogleLogging(argv[0]); 1410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double m = 0.0; 1430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double c = 0.0; 1440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Problem problem; 1460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong for (int i = 0; i < kNumObservations; ++i) { 1470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong problem.AddResidualBlock( 1480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>( 1490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong new ExponentialResidual(data[2 * i], data[2 * i + 1])), 1500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong NULL, 1510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong &m, &c); 1520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 1530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Solver::Options options; 1550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong options.max_num_iterations = 25; 1560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong options.linear_solver_type = ceres::DENSE_QR; 1570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong options.minimizer_progress_to_stdout = true; 1580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Solver::Summary summary; 1600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Solve(options, &problem, &summary); 1610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong std::cout << summary.BriefReport() << "\n"; 1620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong std::cout << "Initial m: " << 0.0 << " c: " << 0.0 << "\n"; 1630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong std::cout << "Final m: " << m << " c: " << c << "\n"; 1640ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return 0; 1650ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 166