/* nag_fit_pade_app (e02rac) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.1, 2023.
 */

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

int main(void) {
  /* Scalars */
  Integer exit_status, i, k, m, ia, ib, ic, itmax, maxkm;
  Nag_Root_Polish polish;
  NagError fail;

  /* Arrays */
  double *aa = 0, *bb = 0, *berr = 0, *cc = 0, *cond = 0, *dd = 0;
  Complex *z = 0;
  Integer *conv = 0;

  INIT_FAIL(fail);

  exit_status = 0;
  printf("nag_fit_pade_app (e02rac) Example Program Results\n");

  k = 4;
  m = 4;
  ia = k + 1;
  ib = m + 1;
  ic = ia + ib - 1;
  maxkm = k > m ? k : m;

  /* Allocate memory */
  if (!(aa = NAG_ALLOC(ia, double)) || !(bb = NAG_ALLOC(ib, double)) ||
      !(cc = NAG_ALLOC(ic, double)) || !(dd = NAG_ALLOC(ia + ib, double)) ||
      !(berr = NAG_ALLOC(maxkm, double)) ||
      !(cond = NAG_ALLOC(maxkm, double)) ||
      !(conv = NAG_ALLOC(maxkm, Integer)) || !(z = NAG_ALLOC(maxkm, Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Power series coefficients in cc */
  cc[0] = 1.0;
  for (i = 1; i <= 8; ++i)
    cc[i] = cc[i - 1] / (double)i;

  printf("\n");

  printf("The given series coefficients are\n");

  for (i = 1; i <= ic; ++i) {
    printf("%13.4e", cc[i - 1]);
    printf(i % 5 == 0 || i == ic ? "\n" : " ");
  }

  /* nag_fit_pade_app (e02rac).
   * Pade-approximants
   */
  nag_fit_pade_app(ia, ib, cc, aa, bb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_fit_pade_app (e02rac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\n");
  printf("Numerator coefficients\n");

  for (i = 1; i <= ia; ++i) {
    printf("%13.4e", aa[i - 1]);
    printf(i % 5 == 0 || i == ia ? "\n" : " ");
  }

  printf("\n");
  printf("Denominator coefficients\n");

  for (i = 1; i <= ib; ++i) {
    printf("%13.4e", bb[i - 1]);
    printf(i % 5 == 0 || i == ib ? "\n" : " ");
  }

  /* Calculate zeros of the approximant using
     nag_zeros_poly_real_fpml (c02abc) */
  /* First need to reverse order of coefficients */
  for (i = 1; i <= ia; ++i)
    dd[ia - i] = aa[i - 1];

  /* nag_zeros_poly_real_fpml (c02abc).
   * Zeros of a polynomial with real coefficients
   */
  itmax = 30;
  polish = Nag_Root_Polish_Simple;
  nag_zeros_poly_real_fpml(dd, k, itmax, polish, z, berr, cond, conv, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_zeros_poly_real_fmpl (c02abc), 1st call.\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\n");
  printf("Zeros of approximant are at\n");
  printf("    Real part    Imag part\n");
  for (i = 1; i <= k; ++i)
    printf("%13.4e%13.4e\n", z[i - 1].re, z[i - 1].im);

  /* Calculate poles of the approximant using
     nag_zeros_poly_real_fpml (c02abc) */
  /* Reverse order of coefficients */
  for (i = 1; i <= ib; ++i)
    dd[ib - i] = bb[i - 1];

  /* nag_zeros_poly_real_fpml (c02abc), see above. */
  nag_zeros_poly_real_fpml(dd, m, itmax, polish, z, berr, cond, conv, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_zeros_poly_real_fpml (c02abc), 2nd call.\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\n");
  printf("Poles of approximant are at\n");
  printf("    Real part    Imag part\n");
  for (i = 1; i <= m; ++i)
    printf("%13.4e%13.4e\n", z[i - 1].re, z[i - 1].im);

END:
  NAG_FREE(aa);
  NAG_FREE(bb);
  NAG_FREE(cc);
  NAG_FREE(dd);
  NAG_FREE(berr);
  NAG_FREE(cond);
  NAG_FREE(conv);
  NAG_FREE(z);

  return exit_status;
}