/* nag_roots_sys_deriv_expert (c05rcc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.2, 2023.
 */

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

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL fcn(Integer n, const double x[], double fvec[],
                         double fjac[], Nag_Comm *comm, Integer *iflag);
#ifdef __cplusplus
}
#endif

static Integer nprint = 0;

int main(void) {
  static double ruser[1] = {-1.0};
  Integer exit_status = 0, i, n = 9, maxfev, nfev, njev;
  double *diag = 0, *fjac = 0, *fvec = 0, *qtf = 0, *r = 0, *x = 0;
  double factor, xtol;
  /* Nag Types */
  NagError fail;
  Nag_Comm comm;
  Nag_ScaleType scale_mode;

  INIT_FAIL(fail);

  printf("nag_roots_sys_deriv_expert (c05rcc) "
         "Example Program Results\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  if (n > 0) {
    if (!(diag = NAG_ALLOC(n, double)) || !(fjac = NAG_ALLOC(n * n, double)) ||
        !(fvec = NAG_ALLOC(n, double)) || !(qtf = NAG_ALLOC(n, double)) ||
        !(r = NAG_ALLOC(n * (n + 1) / 2, double)) ||
        !(x = NAG_ALLOC(n, double))) {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
  } else {
    printf("Invalid n.\n");
    exit_status = 1;
    goto END;
  }

  /* The following starting values provide a rough solution. */
  for (i = 0; i < n; i++)
    x[i] = -1.0;

  /* nag_machine_precision (x02ajc).
   * The machine precision
   */
  xtol = sqrt(nag_machine_precision);

  for (i = 0; i < n; i++)
    diag[i] = 1.0;

  maxfev = 2000;
  scale_mode = Nag_ScaleProvided;
  factor = 100.0;

  /* nag_roots_sys_deriv_expert (c05rcc).
   * Solution of a system of nonlinear equations (function
   * values only)
   */
  nag_roots_sys_deriv_expert(fcn, n, x, fvec, fjac, xtol, maxfev, scale_mode,
                             diag, factor, nprint, &nfev, &njev, r, qtf, &comm,
                             &fail);

  if (fail.code != NE_NOERROR) {
    printf("Error from nag_roots_sys_deriv_expert (c05rcc).\n%s\n",
           fail.message);
    exit_status = 1;
    if (fail.code != NE_TOO_MANY_FEVALS && fail.code != NE_TOO_SMALL &&
        fail.code != NE_NO_IMPROVEMENT)
      goto END;
  }

  printf(fail.code == NE_NOERROR ? "Final approximate" : "Approximate");
  printf(" solution\n\n");
  for (i = 0; i < n; i++)
    printf("%12.4f%s", x[i], (i % 3 == 2 || i == n - 1) ? "\n" : " ");

  if (fail.code != NE_NOERROR)
    exit_status = 2;

END:
  NAG_FREE(diag);
  NAG_FREE(fjac);
  NAG_FREE(fvec);
  NAG_FREE(qtf);
  NAG_FREE(r);
  NAG_FREE(x);
  return exit_status;
}

static void NAG_CALL fcn(Integer n, const double x[], double fvec[],
                         double fjac[], Nag_Comm *comm, Integer *iflag) {
  Integer j, k;

  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback fcn, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  if (*iflag == 0) {
    if (nprint > 0) {
      /* Insert print statements here if desired. */
    }
  } else if (*iflag != 2) {
    for (k = 0; k < n; k++) {
      fvec[k] = (3.0 - x[k] * 2.0) * x[k] + 1.0;
      if (k > 0)
        fvec[k] -= x[k - 1];
      if (k < n - 1)
        fvec[k] -= x[k + 1] * 2.0;
    }
  } else {
    for (k = 0; k < n; k++) {
      for (j = 0; j < n; j++)
        fjac[j * n + k] = 0.0;
      fjac[k * n + k] = 3.0 - x[k] * 4.0;
      if (k > 0)
        fjac[(k - 1) * n + k] = -1.0;
      if (k < n - 1)
        fjac[(k + 1) * n + k] = -2.0;
    }
  }
  /* Set iflag negative to terminate execution for any reason. */
  *iflag = 0;
}