/* 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. */
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;
}