NAG Library Manual, Mark 28.7
```/* nag_fit_dim1_spline_auto (e02bec) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.7, 2022.
*
*/

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

int main(void) {
Integer exit_status = 0, j, m, nest, r;
NagError fail;
Nag_Comm warmstartinf;
Nag_Spline spline;
Nag_Start start;
double fp, s, *sp = 0, txr, *weights = 0, *x = 0, *y = 0;

INIT_FAIL(fail);

/* Initialize spline */
spline.lamda = 0;
spline.c = 0;

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

printf("nag_fit_dim1_spline_auto (e02bec) Example Program Results\n");
scanf("%*[^\n]"); /* Skip heading in data file */
/* Input the number of data points, followed by the data
* points x, the function values y and the weights w.
*/
scanf("%" NAG_IFMT "", &m);
nest = m + 4;
if (m >= 4) {
if (!(weights = NAG_ALLOC(m, double)) || !(x = NAG_ALLOC(m, double)) ||
!(y = NAG_ALLOC(m, double)) || !(sp = NAG_ALLOC(2 * m - 1, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
} else {
printf("Invalid m.\n");
exit_status = 1;
return exit_status;
}
start = Nag_Cold;
for (r = 0; r < m; r++)
scanf("%lf%lf%lf", &x[r], &y[r], &weights[r]);
/* Read in successive values of s until end of data file. */
while (scanf("%lf", &s) != EOF)
{
/* Determine the spline approximation. */
/* nag_fit_dim1_spline_auto (e02bec).
* Least squares cubic spline curve fit, automatic knot
* placement, one variable
*/
nag_fit_dim1_spline_auto(start, m, x, y, weights, s, nest, &fp,
&warmstartinf, &spline, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_fit_dim1_spline_auto (e02bec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Evaluate the spline at each x point and midway
* between x points, saving the results in sp.
*/
for (r = 0; r < m; r++) {
/* nag_fit_dim1_spline_eval (e02bbc).
* Evaluation of fitted cubic spline, function only
*/
nag_fit_dim1_spline_eval(x[r], &sp[(r - 1) * 2 + 2], &spline, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_fit_dim1_spline_auto (e02bec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}

for (r = 0; r < m - 1; r++) {
txr = (x[r] + x[r + 1]) / 2;
/* nag_fit_dim1_spline_eval (e02bbc), see above. */
nag_fit_dim1_spline_eval(txr, &sp[r * 2 + 1], &spline, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_fit_dim1_spline_eval (e02bbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}
/* Output the results. */
printf("\nCalling with smoothing factor s = %12.3e\n", s);
printf("\nNumber of distinct knots = %" NAG_IFMT "\n\n", spline.n - 6);
printf("Distinct knots located at \n\n");
for (j = 3; j < spline.n - 3; j++)
printf("%8.4f%s", spline.lamda[j],
(j - 3) % 6 == 5 || j == spline.n - 4 ? "\n" : " ");
printf("\n\n    J      B-spline coeff c\n\n");
for (j = 0; j < spline.n - 4; ++j)
printf("  %3" NAG_IFMT "  %13.4f\n", j + 1, spline.c[j]);
printf("\nWeighted sum of squared residuals fp = %12.3e\n", fp);
if (fp == 0.0)
printf("The spline is an interpolating spline\n");
else if (spline.n == 8)
printf("The spline is the weighted least squares cubic"
"polynomial\n");
start = Nag_Warm;
}
/* Free memory allocated in spline and warmstartinf */
END:
NAG_FREE(spline.lamda);
NAG_FREE(spline.c);
NAG_FREE(warmstartinf.nag_w);
NAG_FREE(warmstartinf.nag_iw);
NAG_FREE(weights);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(sp);
return exit_status;
}
```