```/* nag_2d_spline_fit_grid (e02dcc) Example Program.
*
* Copyright 2014 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;
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;
NagError     fail;

INIT_FAIL(fail);

/* Initialise spline */
spline.lamda = 0;
spline.mu = 0;
spline.c = 0;

warmstartinf.nag_w = 0;
warmstartinf.nag_iw = 0;

printf("nag_2d_spline_fit_grid (e02dcc) Example Program Results\n");
scanf("%*[^\n]"); /* Skip heading in data file */
/* Input the number of x, y co-ordinates mx, my. */
scanf("%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)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else
{
printf("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++)
scanf("%lf", &x[i]);
for (i = 0; i < my; i++)
scanf("%lf", &y[i]);
/* Input the mx*my function values f at the grid points. */
for (i = 0; i < mx*my; i++)
scanf("%lf", &f[i]);
start = Nag_Cold;
scanf("%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)
{
printf("Error from nag_2d_spline_fit_grid (e02dcc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

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

printf("\nCalling with smoothing factor s = %13.4e:"
" spline.nx = %2ld, spline.ny = %2ld.\n\n",
s, nx, ny);
/* Print the knot sets, lamda and mu. */
printf("Distinct knots in x direction located  at\n");
for (j = 3; j < spline.nx-3; j++)
printf("%12.4f%s", spline.lamda[j],
((j-3)%5 == 4 || j == spline.nx-4)?"\n":" ");
printf("\nDistinct knots in y direction located  at\n");
for (j = 3; j < spline.ny-3; j++)
printf("%12.4f%s", spline.mu[j], ((j-3)%5 == 4 || j == spline.ny-4)
?"\n":" ");
printf("\nThe B-spline coefficients:\n\n");
for (i = 0; i < ny-4; i++)
{
for (j = 0; j < nx-4; j++)
printf("%9.4f", spline.c[i+j*(ny-4)]);
printf("\n");
}
printf("\nSum of squared residuals fp = %13.4e\n", fp);
if (fp == 0.0)
printf("\nThe spline is an interpolating spline\n");
else if (nx == 8 && ny == 8)
printf("\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).
*/
scanf("%ld%lf%lf", &npx, &xlo, &xhi);
scanf("%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)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else
{
printf("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)
{
printf("Error from nag_2d_spline_eval_rect (e02dfc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

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