/* nag_2d_spline_fit_scat (e02ddc) Example Program.
 *
 * Copyright 1991 Numerical Algorithms Group.
 *
 * Mark 2, 1991.
 *
 * Mark 6 revised, 2000.
 * Mark 8 revised, 2004.
 */

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

int main(void)
{

  Integer exit_status=0, i, j, m, npx, npy, nx, nxest, ny, nyest, rank;
  NagError fail;
  Nag_2dSpline spline;
  Nag_Start start;
  double delta, *f=0, *fg=0, fp, *px=0, *py=0, s, warmstartinf, *weights=0;
  double *x=0, xhi, xlo, *y=0, yhi, ylo;

  INIT_FAIL(fail);

  nxest = 14;
  nyest = 14;
  Vprintf("nag_2d_spline_fit_scat (e02ddc) Example Program Results\n");
  Vscanf("%*[^\n]"); /* Skip heading in data file */
  /* Input the number of data-points m. */
  Vscanf("%ld",&m);
  if (m>=16)
    {
      if ( !( f = NAG_ALLOC(m, double)) ||
           !( weights = NAG_ALLOC(m, double)) ||
           !( x = NAG_ALLOC(m, double)) ||
           !( y = NAG_ALLOC(m, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      Vprintf("Invalid m.\n");
      exit_status = 1;
      return exit_status;
    }
  /* Input the data-points and the weights. */
  for (i=0; i<m;  i++)
    Vscanf("%lf%lf%lf%lf",&x[i],&y[i],&f[i],&weights[i]);
  start = Nag_Cold;
  if (scanf("%lf",&s) != EOF)
    {
      /* Determine the spline approximation. */

      /* nag_2d_spline_fit_scat (e02ddc).
       * Least-squares bicubic spline fit with automatic knot
       * placement, two variables (scattered data)
       */
      nag_2d_spline_fit_scat(start, m, x, y, f, weights, s, nxest, nyest, &fp,
                             &rank, &warmstartinf, &spline, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_2d_spline_fit_scat (e02ddc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      nx = spline.nx;
      ny = spline.ny;
      Vprintf("\nCalling with smoothing factor s = %11.4e, nx = %1ld,"
              " ny = %1ld\n",s,nx,ny);

      Vprintf("rank deficiency = %1ld\n\n",(nx-4)*(ny-4)-rank);

      /* Print the knot sets, lamda and mu. */
      Vprintf("Distinct knots in x direction located  at\n");
      for (j=3; j<spline.nx-3; j++)
        Vprintf("%12.4f%s",spline.lamda[j],((j-3)%5==4 || j==spline.nx-4)
                ? "\n" : " ");
      Vprintf("\nDistinct knots in y direction located  at\n");
      for (j=3; j<spline.ny-3; j++)
        Vprintf("%12.4f%s",spline.mu[j],((j-3)%5==4 || j==spline.ny-4)
                ? "\n" : " ");
      Vprintf("\nThe B-spline coefficients:\n\n");
      for (i=0; i<ny-4; i++)
        {
          for (j=0; j<nx-4; j++)
            Vprintf("%9.2f",spline.c[i+j*(ny-4)]);
          Vprintf("\n");
        }

      Vprintf("\n Sum of squared residuals fp = %11.4e\n",fp);
      if (nx==8 && ny==8)
        Vprintf("The spline is the least-squares bi-cubic polynomial\n");

      /* Evaluate the spline on a rectangular grid at npx*npy points
       * over the domain (xlo to xhi) x (ylo to yhi).
       */

      Vscanf("%ld%lf%lf",&npx,&xlo,&xhi);
      Vscanf("%ld%lf%lf",&npy,&ylo,&yhi);

      if (npx>=1 && npy>=1)
        {
          if ( !( fg = NAG_ALLOC(npx*npy, double)) ||
               !( px = NAG_ALLOC(npx, double)) ||
               !( py = NAG_ALLOC(npy, double)) )
            {
              Vprintf("Allocation failure\n");
              exit_status = -1;
              goto END;
            }
        }
      else
        {
          Vprintf("Invalid npx or npy.\n");
          exit_status = 1;
          return exit_status;
        }
      delta = (xhi-xlo)/(npx-1);
      for (i=0; i<npx;  i++)
        px[i] = MIN(xhi,xlo+i*delta);
      for (i=0; i<npy;  i++)
        py[i] = MIN(yhi,ylo+i*delta);

      /* nag_2d_spline_eval_rect (e02dfc).
       * Evaluation of bicubic spline, at a mesh of points
       */
      nag_2d_spline_eval_rect(npx, npy, px, py, fg, &spline, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_2d_spline_eval_rect (e02dfc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      Vprintf("\nValues of computed spline:\n\n");
      Vprintf("          x");
      for (i=0; i<npx; i++)
        Vprintf("%8.2f ",px[i]);
      Vprintf("\n     y\n");
      for (i=npy-1; i>=0; i--)
        {
          Vprintf("%8.2f   ",py[i]);
          for (j=0; j<npx; j++)
            Vprintf("%8.2f ", fg[npy*j+i]);
          Vprintf("\n");
        }
      /* Free memory used by spline */
      NAG_FREE(spline.lamda);
      NAG_FREE(spline.mu);
      NAG_FREE(spline.c);
      if (fg) NAG_FREE(fg);
      if (px) NAG_FREE(px);
      if (py) NAG_FREE(py);
    }
 END:
  if (f) NAG_FREE(f);
  if (weights) NAG_FREE(weights);
  if (x) NAG_FREE(x);
  if (y) NAG_FREE(y);
  return exit_status;
}