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      1 // Ceres Solver - A fast non-linear least squares minimizer
      2 // Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
      3 // http://code.google.com/p/ceres-solver/
      4 //
      5 // Redistribution and use in source and binary forms, with or without
      6 // modification, are permitted provided that the following conditions are met:
      7 //
      8 // * Redistributions of source code must retain the above copyright notice,
      9 //   this list of conditions and the following disclaimer.
     10 // * Redistributions in binary form must reproduce the above copyright notice,
     11 //   this list of conditions and the following disclaimer in the documentation
     12 //   and/or other materials provided with the distribution.
     13 // * Neither the name of Google Inc. nor the names of its contributors may be
     14 //   used to endorse or promote products derived from this software without
     15 //   specific prior written permission.
     16 //
     17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
     18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
     21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     27 // POSSIBILITY OF SUCH DAMAGE.
     28 //
     29 // Author: sameeragarwal (at) google.com (Sameer Agarwal)
     30 
     31 #include "ceres/ceres.h"
     32 #include "gflags/gflags.h"
     33 
     34 using ceres::AutoDiffCostFunction;
     35 using ceres::CostFunction;
     36 using ceres::Problem;
     37 using ceres::Solver;
     38 using ceres::Solve;
     39 
     40 // Data generated using the following octave code.
     41 //   randn('seed', 23497);
     42 //   m = 0.3;
     43 //   c = 0.1;
     44 //   x=[0:0.075:5];
     45 //   y = exp(m * x + c);
     46 //   noise = randn(size(x)) * 0.2;
     47 //   y_observed = y + noise;
     48 //   data = [x', y_observed'];
     49 
     50 const int kNumObservations = 67;
     51 const double data[] = {
     52   0.000000e+00, 1.133898e+00,
     53   7.500000e-02, 1.334902e+00,
     54   1.500000e-01, 1.213546e+00,
     55   2.250000e-01, 1.252016e+00,
     56   3.000000e-01, 1.392265e+00,
     57   3.750000e-01, 1.314458e+00,
     58   4.500000e-01, 1.472541e+00,
     59   5.250000e-01, 1.536218e+00,
     60   6.000000e-01, 1.355679e+00,
     61   6.750000e-01, 1.463566e+00,
     62   7.500000e-01, 1.490201e+00,
     63   8.250000e-01, 1.658699e+00,
     64   9.000000e-01, 1.067574e+00,
     65   9.750000e-01, 1.464629e+00,
     66   1.050000e+00, 1.402653e+00,
     67   1.125000e+00, 1.713141e+00,
     68   1.200000e+00, 1.527021e+00,
     69   1.275000e+00, 1.702632e+00,
     70   1.350000e+00, 1.423899e+00,
     71   1.425000e+00, 1.543078e+00,
     72   1.500000e+00, 1.664015e+00,
     73   1.575000e+00, 1.732484e+00,
     74   1.650000e+00, 1.543296e+00,
     75   1.725000e+00, 1.959523e+00,
     76   1.800000e+00, 1.685132e+00,
     77   1.875000e+00, 1.951791e+00,
     78   1.950000e+00, 2.095346e+00,
     79   2.025000e+00, 2.361460e+00,
     80   2.100000e+00, 2.169119e+00,
     81   2.175000e+00, 2.061745e+00,
     82   2.250000e+00, 2.178641e+00,
     83   2.325000e+00, 2.104346e+00,
     84   2.400000e+00, 2.584470e+00,
     85   2.475000e+00, 1.914158e+00,
     86   2.550000e+00, 2.368375e+00,
     87   2.625000e+00, 2.686125e+00,
     88   2.700000e+00, 2.712395e+00,
     89   2.775000e+00, 2.499511e+00,
     90   2.850000e+00, 2.558897e+00,
     91   2.925000e+00, 2.309154e+00,
     92   3.000000e+00, 2.869503e+00,
     93   3.075000e+00, 3.116645e+00,
     94   3.150000e+00, 3.094907e+00,
     95   3.225000e+00, 2.471759e+00,
     96   3.300000e+00, 3.017131e+00,
     97   3.375000e+00, 3.232381e+00,
     98   3.450000e+00, 2.944596e+00,
     99   3.525000e+00, 3.385343e+00,
    100   3.600000e+00, 3.199826e+00,
    101   3.675000e+00, 3.423039e+00,
    102   3.750000e+00, 3.621552e+00,
    103   3.825000e+00, 3.559255e+00,
    104   3.900000e+00, 3.530713e+00,
    105   3.975000e+00, 3.561766e+00,
    106   4.050000e+00, 3.544574e+00,
    107   4.125000e+00, 3.867945e+00,
    108   4.200000e+00, 4.049776e+00,
    109   4.275000e+00, 3.885601e+00,
    110   4.350000e+00, 4.110505e+00,
    111   4.425000e+00, 4.345320e+00,
    112   4.500000e+00, 4.161241e+00,
    113   4.575000e+00, 4.363407e+00,
    114   4.650000e+00, 4.161576e+00,
    115   4.725000e+00, 4.619728e+00,
    116   4.800000e+00, 4.737410e+00,
    117   4.875000e+00, 4.727863e+00,
    118   4.950000e+00, 4.669206e+00,
    119 };
    120 
    121 class ExponentialResidual {
    122  public:
    123   ExponentialResidual(double x, double y)
    124       : x_(x), y_(y) {}
    125 
    126   template <typename T> bool operator()(const T* const m,
    127                                         const T* const c,
    128                                         T* residual) const {
    129     residual[0] = T(y_) - exp(m[0] * T(x_) + c[0]);
    130     return true;
    131   }
    132 
    133  private:
    134   const double x_;
    135   const double y_;
    136 };
    137 
    138 int main(int argc, char** argv) {
    139   google::ParseCommandLineFlags(&argc, &argv, true);
    140   google::InitGoogleLogging(argv[0]);
    141 
    142   double m = 0.0;
    143   double c = 0.0;
    144 
    145   Problem problem;
    146   for (int i = 0; i < kNumObservations; ++i) {
    147     problem.AddResidualBlock(
    148         new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>(
    149             new ExponentialResidual(data[2 * i], data[2 * i + 1])),
    150         NULL,
    151         &m, &c);
    152   }
    153 
    154   Solver::Options options;
    155   options.max_num_iterations = 25;
    156   options.linear_solver_type = ceres::DENSE_QR;
    157   options.minimizer_progress_to_stdout = true;
    158 
    159   Solver::Summary summary;
    160   Solve(options, &problem, &summary);
    161   std::cout << summary.BriefReport() << "\n";
    162   std::cout << "Initial m: " << 0.0 << " c: " << 0.0 << "\n";
    163   std::cout << "Final   m: " << m << " c: " << c << "\n";
    164   return 0;
    165 }
    166