Squashed 'third_party/ceres/' content from commit e51e9b4

Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/examples/curve_fitting.c b/examples/curve_fitting.c
new file mode 100644
index 0000000..0027aa8
--- /dev/null
+++ b/examples/curve_fitting.c
@@ -0,0 +1,187 @@
+/* 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;
+}