/* nag_roots_sys_deriv_rcomm (c05rdc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */

#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[], Integer irevcm);
#ifdef __cplusplus
}
#endif

int main(void) {
  Integer exit_status = 0, i, n = 9, irevcm;
  double *diag = 0, *fjac = 0, *fvec = 0, *qtf = 0, *r = 0, *x = 0, *rwsav = 0;
  Integer *iwsav = 0;
  double factor, xtol;
  /* Nag Types */
  NagError fail;
  Nag_ScaleType scale_mode;

  INIT_FAIL(fail);

  printf("nag_roots_sys_deriv_rcomm (c05rdc) Example Program Results\n");
  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)) || !(iwsav = NAG_ALLOC(17, Integer)) ||
        !(rwsav = NAG_ALLOC(4 * n + 10, 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;

  scale_mode = Nag_ScaleProvided;
  factor = 100.0;
  irevcm = 0;

  /* nag_roots_sys_deriv_rcomm (c05rdc).
   * Solution of a system of nonlinear equations (function values only,
   * reverse communication)
   */

  do {
    nag_roots_sys_deriv_rcomm(&irevcm, n, x, fvec, fjac, xtol, scale_mode, diag,
                              factor, r, qtf, iwsav, rwsav, &fail);

    switch (irevcm) {
    case 1:
      /* x and fvec are available for printing */
      break;
    case 2:
    case 3:
      fcn(n, x, fvec, fjac, irevcm);
      break;
    }

  } while (irevcm != 0);

  if (fail.code != NE_NOERROR) {
    printf("Error from nag_roots_sys_deriv_rcomm (c05rdc).\n%s\n",
           fail.message);
    exit_status = 1;
    if (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);
  NAG_FREE(iwsav);
  NAG_FREE(rwsav);
  return exit_status;
}

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

  if (irevcm == 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 if (irevcm == 3) {
    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;
    }
  }
}