NAG Library Manual, Mark 27.3
```/* nag_fit_dim2_cheb_lines (e02cac) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

int main(void) {
/* Scalars */
double ymax;
Integer exit_status, i, j, k, l, mi, mj, n, r, t, na, one;
NagError fail;

/* Arrays */
double *a = 0, *f = 0, *ff = 0, *w = 0, *x = 0, *xmax = 0, *xmin = 0, *y = 0;
Integer *m = 0;

INIT_FAIL(fail);

exit_status = 0;
printf("nag_fit_dim2_cheb_lines (e02cac) Example Program Results\n");

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

/* Input the number of lines Y = Y(I) on which data is given, */
/* and the required degree of fit in the X and Y directions */
while (scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &k, &l) !=
EOF)
{
printf("\n");
if (n > 0) {
/* Allocate arrays m, y, xmin and xmax */
if (!(m = NAG_ALLOC(n, Integer)) || !(y = NAG_ALLOC(n, double)) ||
!(xmin = NAG_ALLOC(n, double)) || !(xmax = NAG_ALLOC(n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

mj = 0;
/* Input Y(I), the number of data points on Y = Y(I) and the */
/* range of X-values on this line, for I = 1,2,...N */
for (i = 0; i < n; ++i) {
scanf("%lf%" NAG_IFMT "%lf%lf%*[^\n] ", &y[i], &mi, &xmin[i], &xmax[i]);
m[i] = mi;
mj += mi;
}

/* Allocate arrays x, f, ff, w and a */
na = (k + 1) * (l + 1);
if (!(x = NAG_ALLOC(mj, double)) || !(f = NAG_ALLOC(mj, double)) ||
!(ff = NAG_ALLOC(mj, double)) || !(w = NAG_ALLOC(mj, double)) ||
!(a = NAG_ALLOC(na, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Input the X-values and function values, F, together with */
/* their weights, W. */
for (i = 0; i < mj; ++i)
scanf("%lf%lf%lf", &x[i], &f[i], &w[i]);
scanf("%*[^\n] ");

/* Evaluate the coefficients, A, of the fit to this set of data */
one = 1;
/* nag_fit_dim2_cheb_lines (e02cac).
* Least squares surface fit by polynomials, data on lines
*/
nag_fit_dim2_cheb_lines(m, n, k, l, x, y, f, w, a, xmin, xmax, y, one, y,
one, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_fit_dim2_cheb_lines (e02cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("     Data Y     Data X     Data F   Fitted F   Residual\n");
printf("\n");

mi = 0;
for (r = 1; r <= n; ++r) {
t = mi + 1;
mi += m[r - 1];
ymax = y[n - 1];
if (n == 1)
ymax += 1.0;

/* Evaluate the fitted polynomial at each of the data points */
/* on the line Y = Y(R) */
/* nag_fit_dim2_cheb_eval (e02cbc).
* Evaluation of fitted polynomial in two variables
*/
nag_fit_dim2_cheb_eval(t, mi, k, l, x, xmin[r - 1], xmax[r - 1],
y[r - 1], y, ymax, ff, a, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_fit_dim2_cheb_eval (e02cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Output the data and fitted values on the line Y = Y(R) */
for (i = t - 1; i < mi; ++i) {
printf("%11.4f%11.4f%11.4f%11.4f", y[r - 1], x[i], f[i], ff[i]);
printf("%11.2e\n", ff[i] - f[i]);
}
printf("\n");
}

/* Output the Chebyshev coefficients of the fit */
printf("Chebyshev coefficients of the fit\n");
printf("\n");

for (j = 1; j <= k + 1; ++j) {
for (i = (j - 1) * (l + 1); i < j * (l + 1); ++i)
printf("%11.4f ", a[i]);
printf("\n");
}
}
}

END:
NAG_FREE(a);
NAG_FREE(f);
NAG_FREE(ff);
NAG_FREE(w);
NAG_FREE(x);
NAG_FREE(xmax);
NAG_FREE(xmin);
NAG_FREE(y);
NAG_FREE(m);

return exit_status;
}
```