```/* nag_1d_cheb_fit (e02adc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 5, 1998.
* Mark 8 revised, 2004.
*
*/

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

int main(void)
{
#define A(I, J) a[(I) *tda + J]

Integer  exit_status = 0, i, iwght, j, k, m, r, tda;
NagError fail;
double   *a = 0, *ak = 0, d1, fit, *s = 0, *w = 0, *x = 0, x1, xarg, xcapr,
xm, *y = 0;

INIT_FAIL(fail);

printf("nag_1d_cheb_fit (e02adc) Example Program Results \n");

/* Skip heading in data file */
scanf("%*[^\n]");
while ((scanf("%ld", &m)) != EOF)
{
if (m >= 2)
{
if (
!(x = NAG_ALLOC(m, double)) ||
!(y = NAG_ALLOC(m, double)) ||
!(w = NAG_ALLOC(m, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else
{
printf("Invalid m.\n");
exit_status = 1;
return exit_status;
}
scanf("%ld", &k);
if (k >= 1)
{
if (!(a = NAG_ALLOC((k+1)*(k+1), double)) ||
!(s = NAG_ALLOC(k+1, double)) ||
!(ak = NAG_ALLOC(k+1, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tda = k+1;
}
else
{
printf("Invalid k.\n");
exit_status = 1;
return exit_status;
}
scanf("%ld", &iwght);
for (r = 0; r < m; ++r)
{
if (iwght != 1)
{
scanf("%lf", &x[r]);
scanf("%lf", &y[r]);
scanf("%lf", &w[r]);
}
else
{
scanf("%lf", &x[r]);
scanf("%lf", &y[r]);
w[r] = 1.0;
}
}
/* nag_1d_cheb_fit (e02adc).
* Computes the coefficients of a Chebyshev series
* polynomial for arbitrary data
*/
nag_1d_cheb_fit(m, k+1, tda, x, y, w, a, s, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_1d_cheb_fit (e02adc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

for (i = 0; i <= k; ++i)
{
printf("\n");
printf(" %s%4ld%s%12.2e\n", "Degree", i,
"   R.M.S. residual =", s[i]);
printf("\n   J  Chebyshev coeff A(J) \n");
for (j = 0; j < i+1; ++j)
printf(" %3ld%15.4f\n", j+1, A(i, j));
}
for (j = 0; j < k+1; ++j)
ak[j] = A(k, j);
x1 = x[0];
xm = x[m-1];
printf("\n %s%4ld\n\n",
"Polynomial approximation and residuals for degree", k);
printf(
"   R   Abscissa     Weight   Ordinate  Polynomial  Residual \n");
for (r = 1; r <= m; ++r)
{
xcapr = (x[r-1] - x1 - (xm - x[r-1])) / (xm - x1);
/* nag_1d_cheb_eval (e02aec).
* Evaluates the coefficients of a Chebyshev series
* polynomial
*/
nag_1d_cheb_eval(k+1, ak, xcapr, &fit, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_1d_cheb_eval (e02aec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

d1 = fit - y[r-1];
printf(" %3ld%11.4f%11.4f%11.4f%11.4f%11.2e\n", r, x[r-1],
w[r-1], y[r-1], fit, d1);
if (r < m)
{
xarg = (x[r-1]  + x[r]) * 0.5;
xcapr = (xarg - x1 - (xm - xarg)) / (xm - x1);
/* nag_1d_cheb_eval (e02aec), see above. */
nag_1d_cheb_eval(k+1, ak, xcapr, &fit, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_1d_cheb_eval (e02aec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("    %11.4f                      %11.4f\n", xarg,
fit);
}
}
END:
NAG_FREE(a);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(w);
NAG_FREE(s);
NAG_FREE(ak);
}
return exit_status;
}
```