```/* nag_1d_spline_fit_knots (e02bac) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*
*/

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nage02.h>

int main(void)
{
Integer exit_status = 0, j, m, ncap, ncap7, r, wght;
NagError fail;
Nag_Spline spline;
double fit, ss, *weights = 0, *x = 0, xarg, *y = 0;

INIT_FAIL(fail);

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

printf("nag_1d_spline_fit_knots (e02bac) Example Program Results\n");
scanf("%*[^\n]"); /* Skip heading in data file */
while (scanf("%" NAG_IFMT "", &m) != EOF)
{
if (m >= 4) {
if (!(weights = NAG_ALLOC(m, double)) ||
!(x = NAG_ALLOC(m, double)) || !(y = NAG_ALLOC(m, double))
)
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else {
printf("Invalid m.\n");
exit_status = 1;
goto END;
}
scanf("%" NAG_IFMT "%" NAG_IFMT "", &ncap, &wght);
if (ncap > 0) {
ncap7 = ncap + 7;
spline.n = ncap7;
if (!(spline.lamda = NAG_ALLOC(ncap7, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else {
printf("Invalid ncap.\n");
exit_status = 1;
goto END;
}
for (j = 4; j < ncap + 3; ++j)
scanf("%lf", &(spline.lamda[j]));
for (r = 0; r < m; ++r) {
if (wght == 1) {
scanf("%lf%lf", &x[r], &y[r]);
weights[r] = 1.0;
}
else
scanf("%lf%lf%lf", &x[r], &y[r], &weights[r]);
}
/* nag_1d_spline_fit_knots (e02bac).
* Least squares curve cubic spline fit (including
* interpolation), one variable
*/
nag_1d_spline_fit_knots(m, x, y, weights, &ss, &spline, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_1d_spline_fit_knots (e02bac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\nNumber of distinct knots = %" NAG_IFMT "\n\n", ncap + 1);
printf("Distinct knots located at \n\n");
for (j = 3; j < ncap + 4; j++)
printf("%8.4f%s", spline.lamda[j],
(j - 3) % 6 == 5 || j == ncap + 3 ? "\n" : " ");
printf("\n\n    J    B-spline coeff c\n\n");
for (j = 0; j < ncap + 3; ++j)
printf("    %" NAG_IFMT "  %13.4f\n", j + 1, spline.c[j]);
printf("\nResidual sum of squares = ");
printf("%11.2e\n\n", ss);
printf("Cubic spline approximation and residuals\n");
printf("  r        Abscissa        Weight       Ordinate"
"          Spline      Residual\n\n");
for (r = 0; r < m; ++r) {
/* nag_1d_spline_evaluate (e02bbc).
* Evaluation of fitted cubic spline, function only
*/
nag_1d_spline_evaluate(x[r], &fit, &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;
}

printf("%3" NAG_IFMT "    %11.4f    %11.4f    %11.4f     %11.4f"
"    %10.1e\n", r + 1, x[r], weights[r], y[r], fit, fit - y[r]);
if (r < m - 1) {
xarg = (x[r] + x[r + 1]) * 0.5;
/* nag_1d_spline_evaluate (e02bbc), see above. */
nag_1d_spline_evaluate(xarg, &fit, &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;
}
printf("    %14.4f             %33.4f\n", xarg, fit);
}
}
/* Free memory used by spline */
NAG_FREE(spline.lamda);
NAG_FREE(spline.c);
END:
NAG_FREE(weights);
NAG_FREE(x);
NAG_FREE(y);
}
return exit_status;
}
```