/* nag_opt_lsq_deriv (e04gbc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 *
 */

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

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

#define MMAX 15
#define TMAX 3

/* Define a user structure template to store data in lsqfun. */
struct user
{
  double y[MMAX];
  double t[MMAX][TMAX];
};

int main(void)
{
  const char *optionsfile = "e04gbce.opt";
  Integer exit_status = 0;
  Nag_Boolean print;
  Integer i, j, m, n, nt, tdfjac;
  Nag_Comm comm;
  Nag_E04_Opt options;
  double *fjac = 0, fsumsq, *fvec = 0, *x = 0;
  struct user s;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_opt_lsq_deriv (e04gbc) Example Program Results\n");
  fflush(stdout);
  scanf(" %*[^\n]"); /* Skip heading in data file */
  n = 3;
  m = 15;
  if (m >= 1 && n <= m) {
    if (!(fjac = NAG_ALLOC(m * n, double)) ||
        !(fvec = NAG_ALLOC(m, double)) || !(x = NAG_ALLOC(n, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdfjac = n;
  }
  else {
    printf("Invalid m or n.\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)
   */
  nt = 3;
  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;

  /* Initialize options structure and read option values from file */
  print = Nag_TRUE;
  /* nag_opt_init (e04xxc).
   * Initialization function for option setting
   */
  nag_opt_init(&options);
  /* nag_opt_read (e04xyc).
   * Read options from a text file
   */
  nag_opt_read("e04gbc", optionsfile, &options, print, "stdout", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_read (e04xyc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

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

  /* Call the optimization routine */
  /* nag_opt_lsq_deriv (e04gbc), see above. */
  nag_opt_lsq_deriv(m, n, lsqfun, x, &fsumsq, fvec, fjac, tdfjac,
                    &options, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error/Warning from nag_opt_lsq_deriv (e04gbc).\n%s\n",
           fail.message);
    if (fail.code != NW_COND_MIN)
      exit_status = 1;
  }

  /* Free memory allocated by nag_opt_lsq_deriv (e04gbc) 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 = 2;
  }
END:
  NAG_FREE(fjac);
  NAG_FREE(fvec);
  NAG_FREE(x);

  return exit_status;
}

static void NAG_CALL lsqfun(Integer m, Integer n, const double x[],
                            double fvec[], double fjac[], Integer tdfjac,
                            Nag_Comm *comm)
{
  /* Function to evaluate the residuals and their 1st derivatives.
   *
   * This function is also suitable for use when Nag_Lin_NoDeriv is specified
   * for linear minimization instead of the default of Nag_Lin_Deriv,
   * since it can deal with comm->flag = 0 or 1 as well as comm->flag = 2.
   *
   * To avoid the use of a global varibale this example assigns the address
   * of a user defined structure to comm.p in the main program (where the
   * data was also read in).
   * The address of this structure is recovered in each call to lsqfun()
   * from comm->p and the structure used in the calculation of the residuals.
   */

#define FJAC(I, J) fjac[(I) *tdfjac + (J)]

  Integer i;
  double denom, dummy;
  struct user *s = (struct user *) comm->p;

  for (i = 0; i < m; ++i) {
    denom = x[1] * s->t[i][1] + x[2] * s->t[i][2];
    if (comm->flag != 1)
      fvec[i] = x[0] + s->t[i][0] / denom - s->y[i];
    if (comm->flag != 0) {
      FJAC(i, 0) = 1.0;
      dummy = -1.0 / (denom * denom);
      FJAC(i, 1) = s->t[i][0] * s->t[i][1] * dummy;
      FJAC(i, 2) = s->t[i][0] * s->t[i][2] * dummy;
    }
  }
} /* lsqfun */