/* nag_1d_cheb_fit (e02adc) Example Program.
 *
 * Copyright 1998 Numerical Algorithms Group.
 *
 * Mark 5, 1998.
 * Mark 8 revised, 2004.
 *
 */

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

int main(void)
{
#define A(I,J) a[(I)*tda + J]

  Integer exit_status=0, i, iwght, j, k, m, r, tda;
  NagError fail;
  double *a=0, *ak=0, d1, fit, *s=0, *w=0, *x=0, x1, xarg, xcapr, xm, *y=0;

  INIT_FAIL(fail);

  Vprintf("nag_1d_cheb_fit (e02adc) Example Program Results \n");

  /* Skip heading in data file */
  Vscanf("%*[^\n]");

  while ((scanf("%ld",&m)) != EOF)
    {
      if (m >=2)
        {
          if (
              !( x = NAG_ALLOC(m, double)) ||
              !( y = NAG_ALLOC(m, double)) ||
              !( w = NAG_ALLOC(m, double)) )
            {
              Vprintf("Allocation failure\n");
              exit_status = -1;
              goto END;
            }

        }
      else
        {
          Vprintf("Invalid m.\n");
          exit_status = 1;
          return exit_status;
        }

      Vscanf("%ld",&k);
      if (k>=1)
        {
          if ( !( a = NAG_ALLOC((k+1)*(k+1), double)) ||
               !( s = NAG_ALLOC(k+1, double))     ||
               !( ak = NAG_ALLOC(k+1, double)) )
            {
              Vprintf("Allocation failure\n");
              exit_status = -1;
              goto END;
            }
          tda = k+1;
        }
      else
        {
          Vprintf("Invalid k.\n");
          exit_status = 1;
          return exit_status;
        }

      Vscanf("%ld",&iwght);
      for (r = 0; r < m; ++r)
        {
          if (iwght != 1)
            {
              Vscanf("%lf",&x[r]);
              Vscanf("%lf",&y[r]);
              Vscanf("%lf",&w[r]);
            }
          else
            {
              Vscanf("%lf",&x[r]);
              Vscanf("%lf",&y[r]);
              w[r] = 1.0;
            }
        }
      /* nag_1d_cheb_fit (e02adc).
       * Computes the coefficients of a Chebyshev series
       * polynomial for arbitrary data
       */
      nag_1d_cheb_fit(m, k+1, tda, x, y, w, a, s, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_1d_cheb_fit (e02adc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }

      for (i = 0; i <= k; ++i)
        {
          Vprintf("\n");
          Vprintf(" %s%4ld%s%12.2e\n", "Degree", i,
                  "   R.M.S. residual =", s[i]);
          Vprintf("\n   J  Chebyshev coeff A(J) \n");
          for (j = 0; j < i+1; ++j)
            Vprintf(" %3ld%15.4f\n", j+1, A(i,j));
        }
      for (j = 0; j < k+1; ++j)
        ak[j] = A(k,j);
      x1 = x[0];
      xm = x[m-1];
      Vprintf("\n %s%4ld\n\n",
              "Polynomial approximation and residuals for degree",k);
      Vprintf("   R   Abscissa     Weight   Ordinate  Polynomial  Residual \n");
      for (r = 1; r <= m; ++r)
        {
          xcapr = (x[r-1] - x1 - (xm - x[r-1])) / (xm - x1);
          /* nag_1d_cheb_eval (e02aec).
           * Evaluates the coefficients of a Chebyshev series
           * polynomial
           */
          nag_1d_cheb_eval(k+1, ak, xcapr, &fit, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_1d_cheb_eval (e02aec).\n%s\n",
                      fail.message);
              exit_status = 1;
              goto END;
            }

          d1 = fit - y[r-1];
          Vprintf(" %3ld%11.4f%11.4f%11.4f%11.4f%11.2e\n", r, x[r-1],
                  w[r-1], y[r-1], fit, d1);
          if (r < m)
            {
              xarg = (x[r-1]  + x[r]) * 0.5;
              xcapr = (xarg - x1 - (xm - xarg)) / (xm - x1);
              /* nag_1d_cheb_eval (e02aec), see above. */
              nag_1d_cheb_eval(k+1, ak, xcapr, &fit, &fail);
              if (fail.code != NE_NOERROR)
                {
                  Vprintf("Error from nag_1d_cheb_eval (e02aec).\n%s\n",
                          fail.message);
                  exit_status = 1;
                  goto END;
                }
              Vprintf("    %11.4f                      %11.4f\n",xarg,fit);
            }
        }
    END:
      if (a) NAG_FREE(a);
      if (x) NAG_FREE(x);
      if (y) NAG_FREE(y);
      if (w) NAG_FREE(w);
      if (s) NAG_FREE(s);
      if (ak) NAG_FREE(ak);
    }
  return exit_status;
}