/* nag_opt_lsq_covariance (e04ycc) Example Program.
 *
 * NAGPRODCODE Version.
 *
 * Copyright 2016 Numerical Algorithms Group.
 *
 * Mark 26, 2016.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <nag_stdlib.h>
#include <nage04.h>

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL lsqfun(Integer m, Integer n, const double x[],
                              double fvec[], Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

/* Define a user structure template to store data in lsqfun */
struct user
{
  double *y;
  double *t;
};

#define T(I, J) t[(I) *tdt + J]

int main(void)
{
  Integer exit_status = 0, i, j, job, m, n, nt, tdj, tdt;
  NagError fail;
  Nag_Comm comm;
  Nag_E04_Opt options;
  double *cj = 0, *fjac = 0, fsumsq, *fvec = 0, *x = 0;
  struct user s;

  INIT_FAIL(fail);

  s.y = 0;
  s.t = 0;
  printf("nag_opt_lsq_covariance (e04ycc) Example Program Results\n");
  scanf(" %*[^\n]"); /* Skip heading in data file */
  n = 3;
  m = 15;
  nt = 3;
  if (n >= 1 && n <= m) {
    if (!(fjac = NAG_ALLOC(m * n, double)) ||
        !(fvec = NAG_ALLOC(m, double)) ||
        !(x = NAG_ALLOC(n, double)) ||
        !(cj = NAG_ALLOC(n, double)) ||
        !(s.y = NAG_ALLOC(m, double)) || !(s.t = NAG_ALLOC(m * nt, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdj = n;
    tdt = nt;
  }
  else {
    printf("Invalid n or m.\n");
    exit_status = 1;
    return exit_status;
  }
  /* Read data into structure.
   * Observations t (j = 0, 1, 2) are held in s->t[i][j]
   * (i = 0, 1, 2, . . .,  14)
   */
  for (i = 0; i < m; ++i) {
    scanf("%lf", &s.y[i]);
    for (j = 0; j < nt; ++j)
      scanf("%lf", &s.T(i, j));
  }

  /* Set up the starting point */
  x[0] = 0.5;
  x[1] = 1.0;
  x[2] = 1.5;

  /* nag_opt_init (e04xxc).
   * Initialization function for option setting
   */
  nag_opt_init(&options); /* Initialize options structure */

  /* Turn off most monitoring information from e04fcc */
  options.list = Nag_FALSE;
  options.print_level = Nag_Soln;

  /* Assign address of user defined structure to
   * comm.p for communication to lsqfun().
   */
  comm.p = (Pointer) &s;

  /* nag_opt_lsq_no_deriv (e04fcc).
   * Unconstrained nonlinear least squares (no derivatives
   * required)
   */
  fflush(stdout);
  nag_opt_lsq_no_deriv(m, n, lsqfun, x, &fsumsq, fvec, fjac, tdj,
                       &options, &comm, &fail);
  if (fail.code != NE_NOERROR && fail.code != NW_COND_MIN) {
    printf("Error from nag_opt_lsq_no_deriv (e04fcc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  job = 0;
  /* nag_opt_lsq_covariance (e04ycc).
   * Covariance matrix for nonlinear least squares
   */
  nag_opt_lsq_covariance(job, m, n, fsumsq, cj, &options, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_lsq_covariance (e04ycc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\nEstimates of the variances of the sample regression");
  printf(" coefficients are:\n");
  for (i = 0; i < n; ++i)
    printf(" %15.5e", cj[i]);
  printf("\n");

  /* Free memory allocated to pointers s and v */
  /* nag_opt_free (e04xzc).
   * Memory freeing function for use with option setting
   */
  nag_opt_free(&options, "all", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_free (e04xzc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(fjac);
  NAG_FREE(fvec);
  NAG_FREE(x);
  NAG_FREE(cj);
  NAG_FREE(s.y);
  NAG_FREE(s.t);

  return exit_status;
}

static void NAG_CALL lsqfun(Integer m, Integer n, const double x[],
                            double fvec[], Nag_Comm *comm)
{
  /* Function to evaluate the residuals.
   *
   * The address of the user defined structure is recovered in each call
   * to lsqfun() from comm->p and the structure used in the calculation
   * of the residuals.
   */

  Integer i, tdt;
  struct user *s = (struct user *) comm->p;
  tdt = n;

  for (i = 0; i < m; ++i)
    fvec[i] = x[0] +
           s->T(i, 0) / (x[1] * s->T(i, 1) + x[2] * s->T(i, 2)) - s->y[i];
} /* lsqfun */