examples/curve_fitting.c

/* Ceres Solver - A fast non-linear least squares minimizer
 * Copyright 2015 Google Inc. All rights reserved.
 * http://ceres-solver.org/
 *
 * 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: mierle@gmail.com (Keir Mierle)
 *
 * This is a port of curve_fitting.cc to the minimal C API for Ceres.
 */

#include <math.h>
#include <stdio.h>
#include <string.h>  // For NULL
#include "ceres/c_api.h"

/* Data generated using the following octave code.
 *
 *   randn('seed', 23497);
 *   m = 0.3;
 *   c = 0.1;
 *   x=[0:0.075:5];
 *   y = exp(m * x + c);
 *   noise = randn(size(x)) * 0.2;
 *   y_observed = y + noise;
 *   data = [x', y_observed'];
 *
 */

int num_observations = 67;
double data[] = {
  0.000000e+00, 1.133898e+00,
  7.500000e-02, 1.334902e+00,
  1.500000e-01, 1.213546e+00,
  2.250000e-01, 1.252016e+00,
  3.000000e-01, 1.392265e+00,
  3.750000e-01, 1.314458e+00,
  4.500000e-01, 1.472541e+00,
  5.250000e-01, 1.536218e+00,
  6.000000e-01, 1.355679e+00,
  6.750000e-01, 1.463566e+00,
  7.500000e-01, 1.490201e+00,
  8.250000e-01, 1.658699e+00,
  9.000000e-01, 1.067574e+00,
  9.750000e-01, 1.464629e+00,
  1.050000e+00, 1.402653e+00,
  1.125000e+00, 1.713141e+00,
  1.200000e+00, 1.527021e+00,
  1.275000e+00, 1.702632e+00,
  1.350000e+00, 1.423899e+00,
  1.425000e+00, 1.543078e+00,
  1.500000e+00, 1.664015e+00,
  1.575000e+00, 1.732484e+00,
  1.650000e+00, 1.543296e+00,
  1.725000e+00, 1.959523e+00,
  1.800000e+00, 1.685132e+00,
  1.875000e+00, 1.951791e+00,
  1.950000e+00, 2.095346e+00,
  2.025000e+00, 2.361460e+00,
  2.100000e+00, 2.169119e+00,
  2.175000e+00, 2.061745e+00,
  2.250000e+00, 2.178641e+00,
  2.325000e+00, 2.104346e+00,
  2.400000e+00, 2.584470e+00,
  2.475000e+00, 1.914158e+00,
  2.550000e+00, 2.368375e+00,
  2.625000e+00, 2.686125e+00,
  2.700000e+00, 2.712395e+00,
  2.775000e+00, 2.499511e+00,
  2.850000e+00, 2.558897e+00,
  2.925000e+00, 2.309154e+00,
  3.000000e+00, 2.869503e+00,
  3.075000e+00, 3.116645e+00,
  3.150000e+00, 3.094907e+00,
  3.225000e+00, 2.471759e+00,
  3.300000e+00, 3.017131e+00,
  3.375000e+00, 3.232381e+00,
  3.450000e+00, 2.944596e+00,
  3.525000e+00, 3.385343e+00,
  3.600000e+00, 3.199826e+00,
  3.675000e+00, 3.423039e+00,
  3.750000e+00, 3.621552e+00,
  3.825000e+00, 3.559255e+00,
  3.900000e+00, 3.530713e+00,
  3.975000e+00, 3.561766e+00,
  4.050000e+00, 3.544574e+00,
  4.125000e+00, 3.867945e+00,
  4.200000e+00, 4.049776e+00,
  4.275000e+00, 3.885601e+00,
  4.350000e+00, 4.110505e+00,
  4.425000e+00, 4.345320e+00,
  4.500000e+00, 4.161241e+00,
  4.575000e+00, 4.363407e+00,
  4.650000e+00, 4.161576e+00,
  4.725000e+00, 4.619728e+00,
  4.800000e+00, 4.737410e+00,
  4.875000e+00, 4.727863e+00,
  4.950000e+00, 4.669206e+00,
};

/* This is the equivalent of a use-defined CostFunction in the C++ Ceres API.
 * This is passed as a callback to the Ceres C API, which internally converts
 * the callback into a CostFunction. */
static int exponential_residual(void* user_data,
                                double** parameters,
                                double* residuals,
                                double** jacobians) {
  double* measurement = (double*) user_data;
  double x = measurement[0];
  double y = measurement[1];
  double m = parameters[0][0];
  double c = parameters[1][0];

  residuals[0] = y - exp(m * x + c);
  if (jacobians == NULL) {
    return 1;
  }
  if (jacobians[0] != NULL) {
    jacobians[0][0] = - x * exp(m * x + c);  /* dr/dm */
  }
  if (jacobians[1] != NULL) {
    jacobians[1][0] =     - exp(m * x + c);  /* dr/dc */
  }
  return 1;
}

int main(int argc, char** argv) {
  /* Note: Typically it is better to compact m and c into one block,
   * but in this case use separate blocks to illustrate the use of
   * multiple parameter blocks. */
  double m = 0.0;
  double c = 0.0;

  double *parameter_pointers[] = { &m, &c };
  int parameter_sizes[] = { 1, 1 };
  int i;

  ceres_problem_t* problem;

  /* Ceres has some internal stuff that needs to get initialized. */
  ceres_init();

  problem = ceres_create_problem();

  /* Add all the residuals. */
  for (i = 0; i < num_observations; ++i) {
    ceres_problem_add_residual_block(
        problem,
        exponential_residual,  /* Cost function */
        &data[2 * i],          /* Points to the (x,y) measurement */
        NULL,                  /* No loss function */
        NULL,                  /* No loss function user data */
        1,                     /* Number of residuals */
        2,                     /* Number of parameter blocks */
        parameter_sizes,
        parameter_pointers);
  }

  ceres_solve(problem);
  ceres_free_problem(problem);

  printf("Initial m: 0.0, c: 0.0\n");
  printf("Final m: %g, c: %g\n", m, c);
  return 0;
}