/* nag_opt_lsq_check_deriv (e04yac) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 *
 */

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

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL lsqfun(Integer m, Integer n, const 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);

  printf("nag_opt_lsq_check_deriv (e04yac) Example Program Results\n");
  scanf(" %*[^\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))
           )
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdfjac = n;
  }
  else {
    printf("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) {
    scanf("%lf", &Y(i));
    for (j = 0; j < n; ++j)
      scanf("%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;
  printf("\nThe test point is ");
  for (j = 0; j < n; ++j)
    printf(" %12.3e", x[j]);
  printf("\n");

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

  printf("\nDerivatives are consistent with residual values.\n");
  printf("\nAt the test point, lsqfun() gives\n\n");
  printf("      Residuals                   1st derivatives\n");
  for (i = 0; i < m; ++i) {
    printf("     %12.3e  ", fvec[i]);
    for (j = 0; j < n; ++j)
      printf("     %12.3e", FJAC(i, j));
    printf("\n");
  }
END:
  NAG_FREE(fjac);
  NAG_FREE(fvec);
  NAG_FREE(x);
  NAG_FREE(work);
  return exit_status;
}

static void NAG_CALL lsqfun(Integer m, Integer n, const 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 */