/* nag_opt_lsq_check_deriv (e04yac) 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 <nag_stdlib.h>
#include <nage04.h>

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

#define Y(I) comm.user[I]
#define T(I,J) comm.user[(I)*n + (J) + m]
#define YC(I) comm->user[(I)]
#define TC(I,J) comm->user[(I)*n + (J) + m]
#define FJAC(I,J) fjac[(I)*tdfjac + (J)]
int main(void)
{

  Integer exit_status=0, i, j, m, n, tdfjac;
  NagError fail;
  Nag_Comm comm;
  double *fjac=0, *fvec=0, *work=0, *x=0;

  INIT_FAIL(fail);

  Vprintf("nag_opt_lsq_check_deriv (e04yac) Example Program Results\n");
  Vscanf(" %*[^\n]"); /* Skip heading in data file */

  n = 3;
  m = 15;
  if (n>=1 && m>=1 && n<=m)
    {
      if ( !( fjac = NAG_ALLOC(m*n, double)) ||
           !( fvec = NAG_ALLOC(m, double)) ||
           !( x = NAG_ALLOC(n, double)) ||
           !( work = NAG_ALLOC(m + m*n, double))
           )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdfjac = n;
    }
  else
    {
      Vprintf("Invalid n or m.\n");
      exit_status = 1;
      return exit_status;
    }

  /* Allocate memory to communication array */
  comm.user = work;

  /* Observations t (j = 0, 1, 2) are held in T(i, j)
   * (i = 0, 1, 2, . . .,  14) */
  for (i = 0; i < m; ++i)
    {
      Vscanf("%lf", &Y(i));
      for (j = 0; j < n; ++j) Vscanf("%lf", &T(i,j));
    }

  /* Set up an arbitrary point at which to check the 1st derivatives */
  x[0] = 0.19;
  x[1] = -1.34;
  x[2] = 0.88;
  Vprintf("\nThe test point is ");
  for (j = 0; j < n; ++j)
    Vprintf(" %9.3e", x[j]);
  Vprintf("\n");

  /* nag_opt_lsq_check_deriv (e04yac).
   * Least-squares derivative checker for use with
   * nag_opt_lsq_deriv (e04gbc)
   */
  nag_opt_lsq_check_deriv(m, n, lsqfun, x, fvec, fjac, tdfjac, &comm, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_opt_lsq_check_deriv (e04yac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  Vprintf("\nDerivatives are consistent with residual values.\n");
  Vprintf("\nAt the test point, lsqfun() gives\n\n");
  Vprintf("      Residuals                   1st derivatives\n");
  for (i = 0; i < m; ++i)
    {
      Vprintf("     %9.3e  ", fvec[i]);
      for (j = 0; j < n; ++j)
        Vprintf("     %9.3e", FJAC(i,j));
      Vprintf("\n");
    }
 END:
  if (fjac) NAG_FREE(fjac);
  if (fvec) NAG_FREE(fvec);
  if (x) NAG_FREE(x);
  if (work) NAG_FREE(work);
  return exit_status;
}
static void lsqfun(Integer m, Integer n, double x[], double fvec[],
                   double fjac[], Integer tdfjac, Nag_Comm *comm)
{
  /* Function to evaluate the residuals and their 1st derivatives. */


  Integer i;
  double denom, dummy;

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