/* nag_opt_lsq_no_deriv (e04fcc) 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>
#include <nagf16.h>
#include <nagx02.h>

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL lsqfun(Integer m, Integer n, const double x[],
                              double fvec[], Nag_Comm *comm);
  static void NAG_CALL lsqgrd(Integer m, Integer n, double *fvec, double *fjac,
                              Integer ldfjac, double *g);
#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 = "e04fcce.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, *g = 0;
  struct user s;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_opt_lsq_no_deriv (e04fcc) 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)) ||
        !(g = 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;

  /* nag_opt_init (e04xxc).
   * Initialization function for option setting
   */
  nag_opt_init(&options); /* Initialize options structure */
  /* Set one option directly. */
  /* nag_machine_precision (x02ajc).
   * The machine precision
   */
  options.optim_tol = 10.0 * sqrt(nag_machine_precision);

  /* Read remaining option values from file */
  print = Nag_FALSE;
  /* nag_opt_read (e04xyc).
   * Read options from a text file
   */
  nag_opt_read("e04fcc", 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;

  /* nag_opt_lsq_no_deriv (e04fcc), see above. */
  nag_opt_lsq_no_deriv(m, n, lsqfun, x, &fsumsq, fvec, fjac, tdfjac,
                       &options, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error/Warning from nag_opt_lsq_no_deriv (e04fcc).\n%s\n",
           fail.message);
    if (fail.code != NW_COND_MIN)
      exit_status = 1;
  }

  if (fail.code == NE_NOERROR || fail.code == NW_COND_MIN)
    {
      printf("On exit, the sum of squares is %12.4f\n", fsumsq);
      printf("at the point");
      for (i=0; i<n; i++)
        printf("%12.4f", x[i]);
      printf("\n");

      lsqgrd(m,n,fvec,fjac,tdfjac,g);
      printf("The estimated gradient is");
      for (i=0; i<n; i++)
        printf("%13.4e", g[i]);
      printf("\n");
      printf("                           (machine dependent)\n");
      printf("and the residuals are\n");
      for (i=0; i<m; i++)
        printf("%9.1e\n", fvec[i]);
    }

  /* 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 = 2;
    goto END;
  }
END:
  NAG_FREE(fjac);
  NAG_FREE(fvec);
  NAG_FREE(x);
  NAG_FREE(g);

  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.
   *
   * 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.
   */

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

  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 */

static void NAG_CALL lsqgrd(Integer m, Integer n, double *fvec, double *fjac,
                            Integer ldfjac, double *g)
{
  /* Function to evaluate gradient of the sum of squares */
  NagError fail;
  Integer i;
  INIT_FAIL(fail);
  nag_dgemv(Nag_RowMajor,Nag_Trans,m,n,1.0,fjac,ldfjac,fvec,1,0.0,g,1,&fail);
  for (i=0; i<n; i++)
    g[i] = 2.0*g[i];
  return;
}