/* nag_opt_lsq_deriv (e04gbc) Example Program
 *
 * Copyright 1991 Numerical Algorithms Group.
 *
 * Mark 2, 1991.
 * Mark 7 revised, 2001.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <math.h>
#include <nage04.h>
#include <nagx02.h>

#ifdef __cplusplus
extern "C" {
#endif
static void lsqfun1(Integer m, Integer n, double x[], double fvec[],
                    double fjac[], Integer tdj, Nag_Comm *comm);
static void lsqfun2(Integer m, Integer n, double x[], double fvec[],
                    double fjac[], Integer tdj, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif
static void ex1(void);
static void ex2(void);

#define MMAX 15
#define NMAX 3
#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)
{
  /* Two examples are called, ex1() which uses the
   * default settings to solve the problem and
   * ex2() which solves the same problem with
   * some optional parameters set by the user.
   */


  Vprintf("e04gbc Example Program Results.\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */
  ex1();
  ex2();
  return EXIT_SUCCESS;
}

static void ex1(void)
{
  double fjac[MMAX][NMAX], fvec[MMAX], x[NMAX];
  Integer m, n, tdj;
  double fsumsq;
  static NagError fail;

  Vprintf("\ne04gbc example 1: no option setting.\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */
  n = 3;
  m = 15;
  tdj = NMAX;

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

  /* Call the optimization routine */
  fail.print = TRUE;
  e04gbc(m, n, lsqfun1, x, &fsumsq, fvec, &fjac[0][0], tdj,
         E04_DEFAULT, NAGCOMM_NULL, &fail);
  if (fail.code != NE_NOERROR && fail.code != NW_COND_MIN) exit(EXIT_FAILURE);
} /* ex1 */

static void lsqfun1(Integer m, Integer n, double x[], double fvec[],
                    double fjac[], Integer tdj, Nag_Comm *comm)
{
  /* Function to evaluate the residuals and their 1st derivatives
   * in example 1.
   *
   * 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 comm->flag = 2.
   *
   * In this example a static variable is used to hold the
   * initial observations. The data is read into the structure
   * gs on the first call to lsqfun1(), it could alternatively
   * be read in from within int main(void).
   */

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

  Integer i, j, nt;
  double denom, dummy;

  static struct user gs;

  if (comm->first)
    {
      /* First call to lsqfun(), read data into structure.
       * Observations t (j = 0, 1, 2) are held in gs.t[i][j]
       * (i = 0, 1, 2, . . . , 14)
       */
      nt = 3;
      for (i = 0; i < m; ++i)
        {
          Vscanf("%lf", &gs.y[i]);
          for (j = 0; j < nt; ++j) Vscanf("%lf", &gs.t[i][j]);
        }
    }

  for (i = 0; i < m; ++i)
    {
      denom = x[1]*gs.t[i][1] + x[2]*gs.t[i][2];
      if (comm->flag != 1)
        fvec[i] = x[0] + gs.t[i][0]/denom - gs.y[i];
      if (comm->flag != 0)
        {
          FJAC(i,0) = 1.0;
          dummy = -1.0 / (denom * denom);
          FJAC(i,1) = gs.t[i][0]*gs.t[i][1]*dummy;
          FJAC(i,2) = gs.t[i][0]*gs.t[i][2]*dummy;
        }
    }
}                               /* lsqfun1 */


static void ex2(void)
{
  double fjac[MMAX][NMAX], fvec[MMAX], x[NMAX];
  Integer i, j, m, n, nt, tdj;
  double fsumsq;
  Boolean print;
  Nag_E04_Opt options;
  Nag_Comm comm;
  static NagError fail, fail2;
  struct user s;

  Vprintf("\n\ne04gbc example 2: using option setting.\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */
  n = 3;
  m = 15;
  tdj = NMAX;
  nt = 3;

  /* 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)
    {
      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;

  /* Initialise options structure and read option values from file */
  fail.print = TRUE;
  print = TRUE;
  e04xxc(&options);
  e04xyc("e04gbc", "stdin", &options, print, "stdout", &fail);
  if (fail.code != NE_NOERROR) exit(EXIT_FAILURE);

  /* Assign address of user defined structure to
   * comm.p for communication to lsqfun2().
   */
  comm.p = (Pointer)&s;

  /* Call the optimization routine */
  e04gbc(m, n, lsqfun2, x, &fsumsq, fvec, &fjac[0][0], tdj,
         &options, &comm, &fail);

  /* Free memory allocated by e04gbc to pointers s and v */
  fail2.print = TRUE;
  e04xzc(&options, "all", &fail2);
  if ((fail.code != NE_NOERROR && fail.code != NW_COND_MIN)
      || fail2.code != NE_NOERROR) exit(EXIT_FAILURE);
} /* ex2 */

static void lsqfun2(Integer m, Integer n, double x[], double fvec[],
                    double fjac[], Integer tdj, Nag_Comm *comm)
{
  /* Function to evaluate the residuals and their 1st derivatives
   * in example 2.
   *
   * 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 lsqfun2()
   * from comm->p and the structure used in the calculation of the residuals.
   */

#define FJAC(I,J) fjac[(I)*tdj + (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;
        }
    }
}                               /* lsqfun2 */