```/* nag_2d_spline_fit_grid (e02dcc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.2, 2017.
*
*/

#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);

/* Initialize 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("%" NAG_IFMT "%" NAG_IFMT "", &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 = %2" NAG_IFMT ", spline.ny = %2" NAG_IFMT ".\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("%" NAG_IFMT "%lf%lf", &npx, &xlo, &xhi);
scanf("%" NAG_IFMT "%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;
}
```