/* nag_opt_lsq_deriv (e04gbc) Example Program.
 *
 * Copyright 1991 Numerical Algorithms Group.
 *
 * Mark 2, 1991.
 * Mark 7 revised, 2001.
 * Mark 7a revised, 2003.
 * Mark 8 revised, 2004.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <math.h>
#include <nage04.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 int ex1(void);
static int 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)
{
  Integer exit_status_ex1=0;
  Integer exit_status_ex2=0;

  /* 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("nag_opt_lsq_deriv (e04gbc) Example Program Results.\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */
  exit_status_ex1 = ex1();
  exit_status_ex2 = ex2();

  return exit_status_ex1 == 0 && exit_status_ex2 == 0 ? 0 : 1;
}

static int ex1(void)
{
  Integer exit_status=0, m, n, tdj;
  NagError fail;
  double *fjac=0, fsumsq, *fvec=0, *x=0;

  INIT_FAIL(fail);


  Vprintf("\nnag_opt_lsq_deriv (e04gbc) example 1: no option setting.\n");
  Vscanf(" %*[^\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)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      Vprintf("Invalid m or n.\n");
      exit_status = 1;
      return exit_status;
    }

  tdj = n;

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

  /* Call the optimization routine */
  /* nag_opt_lsq_deriv (e04gbc).
   * Unconstrained nonlinear least-squares (first derivatives
   * required)
   */
  nag_opt_lsq_deriv(m, n, lsqfun1, x, &fsumsq, fvec, fjac, tdj,
                    E04_DEFAULT, NAGCOMM_NULL, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error/Warning from nag_opt_lsq_deriv (e04gbc).\n%s\n",
              fail.message);
      if (fail.code != NW_COND_MIN)
        exit_status = 1;
      goto END;
    }
 END:
  if (fjac) NAG_FREE(fjac);
  if (fvec) NAG_FREE(fvec);
  if (x) NAG_FREE(x);
  return exit_status;
} /* 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 int ex2(void)
{
  Nag_Boolean print;
  Integer exit_status=0, i, j, m, n, nt, tdfjac;
  NagError fail;
  Nag_Comm comm;
  Nag_E04_Opt options;
  double *fjac=0, fsumsq, *fvec=0, *x=0;
  struct user s;

  INIT_FAIL(fail);

  Vprintf("\n\nnag_opt_lsq_deriv (e04gbc) example 2: using option setting.\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */
  n = 3;
  m = 15;
  nt = 3;
  if ( m >=1 && n<=m)
    {
      if ( !( fjac = NAG_ALLOC(m*n, double)) ||
           !( fvec = NAG_ALLOC(m, double)) ||
           !( x = NAG_ALLOC(n, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdfjac = n;
    }
  else
    {
      Vprintf("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)
    {
      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 */
  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", "stdin", &options, print, "stdout", &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("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 lsqfun2().
   */
  comm.p = (Pointer)&s;

  /* Call the optimization routine */
  /* nag_opt_lsq_deriv (e04gbc), see above. */
  nag_opt_lsq_deriv(m, n, lsqfun2, x, &fsumsq, fvec, fjac, tdfjac,
                    &options, &comm, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("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)
    {
      Vprintf("Error from nag_opt_free (e04xzc).\n%s\n", fail.message);
      exit_status = 2;
    }
 END:
  if (fjac) NAG_FREE(fjac);
  if (fvec) NAG_FREE(fvec);
  if (x) NAG_FREE(x);
  return exit_status;
} /* 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 */