add c simple example

libRALFit/example/C/nlls_example_box.c

@@ -0,0 +1,106 @@
+// examples/Fortran/nlls_example2.f90
+// 
+// Attempts to fit the model y_i = x_1 e^(x_2 t_i)
+// For parameters x_1 and x_2, and input data (t_i, y_i)
+#include "ral_nlls.h"
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+struct params_type {
+   double *t; // The m data points t_i
+   double *y; // The m data points y_i
+};
+
+// Calculate r_i(x; t_i, y_i) = x_1 e^(x_2 * t_i) - y_i
+int eval_r(int n, int m, void * params, double const* x, double* r) {
+   double x1 = x[0];
+   double x2 = x[1];
+   double const* t = ((struct params_type*) params)->t;
+   double const* y = ((struct params_type*) params)->y;
+
+   for(int i=0; i<m; i++)
+      r[i] = x1 * exp(x2*t[i]) - y[i];
+
+   return 0; // Success
+}
+
+// Calculate:
+// J_i1 = e^(x_2 * t_i)
+// J_i2 = t_i x_1 e^(x_2 * t_i)
+int eval_J(int n, int m, void * params, double const* x, double* J) {
+   double x1 = x[0];
+   double x2 = x[1];
+   double const* t = ((struct params_type*) params)->t;
+
+   for(int i=0; i<m; i++) {
+      J[0*m+i] = exp(x2*t[i]);               // J_i1
+      J[1*m+i] = t[i] * x1 * exp(x2*t[i]);   // J_i2
+   }
+
+   return 0; // Success
+}
+
+// Calculate:
+// HF = sum_i r_i H_i
+// Where H_i = [ 1                t_i e^(x_2 t_i)    ]
+//             [ t_i e^(x_2 t_i)  t_i^2 e^(x_2 t_i)  ]
+int eval_HF(int n, int m, void * params, double const* x, double const* r, double* HF) {
+   double x1 = x[0];
+   double x2 = x[1];
+   double const* t = ((struct params_type*) params)->t;
+
+   for(int i=0; i<n*n; i++) HF[i] = 0.0;
+   for(int i=0; i<m; i++) {
+      HF[    0] += 0;                                      // H_11
+      HF[    1] += r[i] * t[i] * exp(x2*t[i]);             // H_21
+      HF[1*n+1] += r[i] * t[i]*t[i] * x1 * exp(x2*t[i]);   // H_22
+   }
+   HF[1*n+0] = HF[1]; // H_12 by symmetry of Hessian
+
+   return 0; // Success
+}
+
+int main(void) {
+   // Data to be fitted
+   int m = 5;
+   struct params_type params = {
+      .t = (double []) { 1.0, 2.0, 4.0,  5.0,  8.0 },
+      .y = (double []) { 3.0, 4.0, 6.0, 11.0, 20.0 }
+   };
+
+   // Initialize options values
+   struct ral_nlls_options options;
+   ral_nlls_default_options(&options);
+   // options.model = 4;
+   // options.exact_second_derivatives = true;
+
+   // initialize the workspace
+   void * workspace;
+   void * inner_workspace;
+
+   // init workspace allocates and links together workspace with inner_workspace
+   ral_nlls_init_workspace(&workspace, &inner_workspace);
+
+   // Call fitting routine
+   double x[2] = { 1.0, 1.0 }; // Initial guess
+
+   double lower_bounds[2] = { 0.0, 1.0};
+   double upper_bounds[2] = { 1.0, 10.0};
+
+   struct ral_nlls_inform inform;
+
+   nlls_solve(2, m, x, eval_r, eval_J, eval_HF, &params,
+	      &options, &inform, NULL, NULL, lower_bounds, upper_bounds);
+
+   ral_nlls_free_workspace(&workspace);
+   ral_nlls_free_workspace(&inner_workspace);
+
+   // Print result
+   printf ("Found a local optimum at x = %e %e\n", x[0], x[1]);
+   printf ("Took %d iterations\n", inform.iter);
+   printf ("     %d function evaluations\n", inform.f_eval);
+   printf ("     %d gradient evaluations\n", inform.g_eval);
+   printf ("     %d hessian evaluations\n", inform.h_eval);
+}