/* nag_1d_pade (e02rac) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 * Mark 7b revised, 2004.
 */

#include <stdio.h>
#include <nag.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagc02.h>
#include <nage02.h>

int main(int argc, char *argv[])
{
  FILE     *fpout;
  /* Scalars */
  Integer  exit_status, i, l, m, ia, ib, ic;
  NagError fail;

  /* Arrays */
  double   *aa = 0, *bb = 0, *cc = 0, *dd = 0;
  Complex  *z = 0;

  INIT_FAIL(fail);

  /* Check for command-line IO options */
  fpout = nag_example_file_io(argc, argv, "-results", NULL);
  exit_status = 0;
  fprintf(fpout, "nag_1d_pade (e02rac) Example Program Results\n");

  l = 4;
  m = 4;
  ia = l + 1;
  ib = m + 1;
  ic = ia + ib - 1;

  /* Allocate memory */
  if (!(aa = NAG_ALLOC(ia, double)) ||
      !(bb = NAG_ALLOC(ib, double)) ||
      !(cc = NAG_ALLOC(ic, double)) ||
      !(dd = NAG_ALLOC(ia + ib, double)) ||
      !(z = NAG_ALLOC(l+m, Complex)))
    {
      fprintf(fpout, "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;

  fprintf(fpout, "\n");

  fprintf(fpout, "The given series coefficients are\n");

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

  /* nag_1d_pade (e02rac).
   * Pade-approximants
   */
  nag_1d_pade(ia, ib, cc, aa, bb, &fail);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout, "Error from nag_1d_pade (e02rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }


  fprintf(fpout, "\n");
  fprintf(fpout, "Numerator coefficients\n");

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

  fprintf(fpout, "\n");
  fprintf(fpout, "Denominator coefficients\n");

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

  /* Calculate zeros of the approximant using nag_zeros_real_poly (c02agc) */
  /* First need to reverse order of coefficients */
  for (i = 1; i <= ia; ++i)
    dd[ia-i] = aa[i-1];

  /* nag_zeros_real_poly (c02agc).
   * Zeros of a polynomial with real coefficients
   */
  nag_zeros_real_poly(l, dd, Nag_TRUE, z, &fail);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout,
              "Error from nag_zeros_real_poly (c02agc), 1st call.\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* Calculate poles of the approximant using nag_zeros_real_poly (c02agc) */
  /* Reverse order of coefficients */
  for (i = 1; i <= ib; ++i)
    dd[ib-i] = bb[i-1];

  /* nag_zeros_real_poly (c02agc), see above. */
  nag_zeros_real_poly(m, dd, Nag_TRUE, z, &fail);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout,
              "Error from nag_zeros_real_poly (c02agc), 2nd call.\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

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

 END:
  if (fpout != stdout) fclose(fpout);
  if (aa) NAG_FREE(aa);
  if (bb) NAG_FREE(bb);
  if (cc) NAG_FREE(cc);
  if (dd) NAG_FREE(dd);
  if (z) NAG_FREE(z);

  return exit_status;
}