```/* nag_1d_spline_fit (e02bec) 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, 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);

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

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

printf("nag_1d_spline_fit (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("%ld", &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_1d_spline_fit (e02bec).
* Least-squares cubic spline curve fit, automatic knot
* placement, one variable
*/
nag_1d_spline_fit(start, m, x, y, weights, s, nest, &fp,
&warmstartinf, &spline, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_1d_spline_fit (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_1d_spline_evaluate (e02bbc).
* Evaluation of fitted cubic spline, function only
*/
nag_1d_spline_evaluate(x[r], &sp[(r-1)*2+2], &spline, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_1d_spline_fit (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_1d_spline_evaluate (e02bbc), see above. */
nag_1d_spline_evaluate(txr, &sp[r*2+1], &spline, &fail);
if (fail.code != NE_NOERROR)
{
printf(
"Error from nag_1d_spline_evaluate (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 = %ld\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("  %3ld  %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;
}
```