/* nag_2d_spline_fit_grid (e02dcc) 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, mx, my, npx, npy, nx, ny;
  NagError fail;
  Nag_2dSpline spline;
  Nag_Comm warmstartinf;
  Nag_Start start;
  double delta, *f=0, *fg=0, fp, *px=0, *py=0, s, *x=0, xhi, xlo, *y=0, yhi;
  double ylo;

  INIT_FAIL(fail);

  Vprintf("nag_2d_spline_fit_grid (e02dcc) Example Program Results\n");
  Vscanf("%*[^\n]"); /* Skip heading in data file */
  /* Input the number of x, y co-ordinates mx, my. */
  Vscanf("%ld%ld",&mx,&my);

  if (mx>=4 && my>=4)
    {
      if ( !( f = NAG_ALLOC(mx*my, double)) ||
           !( x = NAG_ALLOC(mx, double)) ||
           !( y = NAG_ALLOC(my, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      Vprintf("Invalid mx or my.\n");
      exit_status = 1;
      return exit_status;
    }
  /* Input the x co-ordinates followed by the y co-ordinates. */
  for (i=0; i<mx;  i++)
    Vscanf("%lf",&x[i]);
  for (i=0; i<my; i++)
    Vscanf("%lf",&y[i]);
  /* Input the mx*my function values f at the grid points. */
  for (i=0; i<mx*my; i++)
    Vscanf("%lf",&f[i]);
  start = Nag_Cold;
  Vscanf("%lf",&s);
  /* Determine the spline approximation. */

  /* nag_2d_spline_fit_grid (e02dcc).
   * Least-squares bicubic spline fit with automatic knot
   * placement, two variables (rectangular grid)
   */
  nag_2d_spline_fit_grid(start, mx, x, my, y, f, s, mx+4, my+4,
                         &fp, &warmstartinf, &spline, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_2d_spline_fit_grid (e02dcc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  nx = spline.nx;
  ny = spline.ny;

  Vprintf("\nCalling with smoothing factor s = %11.4e:"
          " spline.nx = %2ld, spline.ny = %2ld.\n\n",s,nx,ny);
  /* 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("%9.4f",spline.c[i+j*(ny-4)]);
      Vprintf("\n");
    }
  Vprintf("\nSum of squared residuals fp = %11.4e\n",fp);
  if (fp==0.0)
    Vprintf("\nThe spline is an interpolating spline\n");
  else if (nx==8 && ny==8)
    Vprintf("\nThe 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(xlo+i*delta,xhi);
  for (i=0; i<npy; i++)
    py[i] = MIN(ylo+i*delta,yhi);

  /* 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");
  Vprintf("\n          x");
  for (i=0; i<npx; i++)
    Vprintf("%7.2f  ",px[i]);
  Vprintf("\n     y\n");
  for (i=npy-1; i>=0; i--)
    {
      Vprintf("%7.2f   ",py[i]);
      for (j=0; j<npx; ++j)
        Vprintf("%8.2f ",fg[npy*j+i]);
      Vprintf("\n");
    }
 END:
  NAG_FREE(spline.lamda);
  NAG_FREE(spline.mu);
  NAG_FREE(spline.c);
  NAG_FREE(warmstartinf.nag_w);
  NAG_FREE(warmstartinf.nag_iw);
  if (f) NAG_FREE(f);
  if (x) NAG_FREE(x);
  if (y) NAG_FREE(y);
  if (fg) NAG_FREE(fg);
  if (px) NAG_FREE(px);
  if (py) NAG_FREE(py);
  return exit_status;
}