/* nag_check_derivs (c05zdc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagc05.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL f(Integer m, Integer n, double x[], double fvec[],
                       double fjac[], Integer iflag);
#ifdef __cplusplus
}
#endif

int main(void)
{
  Integer  exit_status = 0, j, m, n, mode, iflag, err_detected;
  NagError fail;
  double   *fjac = 0, *fvec = 0, *x = 0, *xp = 0, *fvecp = 0, *err = 0;
  INIT_FAIL(fail);

  printf("nag_check_derivs (c05zdc) Example Program Results\n");
  n = 3;
  m = n;

  if (n > 0)
    {
      if (!(fjac = NAG_ALLOC(m*n, double)) ||
          !(fvec = NAG_ALLOC(m, double)) ||
          !(fvecp = NAG_ALLOC(m, double)) ||
          !(err = NAG_ALLOC(m, double)) ||
          !(x = NAG_ALLOC(n, double)) ||
          !(xp = NAG_ALLOC(n, double)))
        {
          printf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      printf("Invalid n.\n");
      exit_status = 1;
      goto END;
    }

  /* Set up an arbitrary point at which to check the 1st derivatives */
  x[0] = 9.2e-01;
  x[1] = 1.3e-01;
  x[2] = 5.4e-01;

  /* nag_check_derivs (c05zdc).
   * Derivative checker for user-supplied Jacobian
   */

  mode = 1;
  nag_check_derivs(mode, m, n, x, fvec, fjac, xp, fvecp, err, &fail);

  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_check_derivs (c05zdc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  /* Evaluate at the original point x and the update point xp */
  /* Get fvec, the functions at x */
  iflag = 1;
  f(m, n, x, fvec, fjac, iflag);

  /* Get fvecp, the functions at xp */
  iflag = 1;
  f(m, n, xp, fvecp, fjac, iflag);

  /* Get fjac, the Jacobian at x */
  iflag = 2;
  f(m, n, x, fvec, fjac, iflag);

  mode = 2;
  nag_check_derivs(mode, m, n, x, fvec, fjac, xp, fvecp, err, &fail);

  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_check_derivs (c05zdc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\nAt point ");
  for (j = 0; j < n; ++j)
    printf("%13.5e", x[j]);
  printf(",\n");

  err_detected = 0;

  for (j = 0; j < n; ++j)
    {

      if (err[j] <= 0.5)
        {
          printf("suspicious gradient number %"NAG_IFMT
                  " with error measure %13.5e\n", j, err[j]);
          err_detected = 1;
        }

    }

  if (!err_detected)
    {
      printf("gradients appear correct\n");
    }

 END:
  if (fjac) NAG_FREE(fjac);
  if (fvec) NAG_FREE(fvec);
  if (fvecp) NAG_FREE(fvecp);
  if (err) NAG_FREE(err);
  if (x) NAG_FREE(x);
  if (xp) NAG_FREE(xp);
  return exit_status;
}

static void NAG_CALL f(Integer m, Integer n, double x[], double fvec[],
		       double fjac[], Integer iflag)
{
  Integer j, k;

  if (iflag == 1)
    {
      /* Calculate the function values */
      for (k = 0; k < m; k++)
        {
          fvec[k] = (3.0-x[k]*2.0) * x[k] + 1.0;
          if (k > 0) fvec[k] -= x[k-1];
          if (k < m-1) fvec[k] -= x[k+1] * 2.0;
        }
    }
  else if (iflag == 2)
    {
      /* Calculate the corresponding first derivatives */
      for (k = 0; k < m; k++)
        {
          for (j = 0; j < n; j++)
            fjac[j*m + k] = 0.0;
          fjac[k*m + k] = 3.0 - x[k] * 4.0;
          if (k > 0)
            fjac[(k-1)*m + k] = -1.0;
          if (k < m-1)
            fjac[(k+1)*m + k] = -2.0;
        }
    }
}