/* nag_opt_lsq_covariance (e04ycc) Example Program.
 *
 * Copyright 1991 Numerical Algorithms Group.
 *
 * Mark 2, 1991.
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

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

#ifdef __cplusplus
extern "C" {
#endif
  static void lsqfun(Integer m, Integer n, 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;
  Vprintf("nag_opt_lsq_covariance (e04ycc) Example Program Results.\n");
  Vscanf(" %*[^\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)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdj = n;
      tdt = nt;
    }
  else
    {
      Vprintf("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)
    {
      Vscanf("%lf", &s.y[i]);
      for (j = 0; j < nt; ++j) Vscanf("%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); /* Initialise options structure */

  /* 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)
   */
  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)
    {
      Vprintf("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)
    {
      Vprintf("Error from nag_opt_lsq_covariance (e04ycc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  Vprintf("\nEstimates of the variances of the sample regression");
  Vprintf(" coefficients are:\n");
  for (i = 0; i < n; ++i)
    Vprintf(" %15.5e", cj[i]);
  Vprintf("\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)
    {
      Vprintf("Error from nag_opt_free (e04xzc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
 END:
  if (fjac) NAG_FREE(fjac);
  if (fvec) NAG_FREE(fvec);
  if (x) NAG_FREE(x);
  if (cj) NAG_FREE(cj);
  if (s.y) NAG_FREE(s.y);
  if (s.t) NAG_FREE(s.t);
  return exit_status;
}
static void lsqfun(Integer m, Integer n, 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 */