/* nag_1d_minimax_polynomial (e02alc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 24, 2013.
*/
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nage02.h>

int main(void)
{

/* Scalars */
Integer     exit_status = 0;
double      dxx, ref, s, t, xx;
Integer     i, j, m, n, neval;
/* Local Arrays */
double      *a = 0,  *x = 0,  *y = 0;
/* NAG types */
NagError    fail;

INIT_FAIL(fail);

printf("nag_1d_minimax_polynomial (e02alc) Example Program Results\n\n");

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

/* n is number of data points to be fitted,
* m is degree of fitting polynomial
* neval is number of evaluation points of fitted polynomial
*/
scanf("%ld%ld%ld%*[^\n] ", &n, &m, &neval);

if (
!(a = NAG_ALLOC((m + 1), double))||
!(x = NAG_ALLOC((n), double))||
!(y = NAG_ALLOC((n), double))
)
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

for (i=0; i<n; i++)
scanf("%lf%lf", &x[i], &y[i]);
scanf("%*[^\n] ");

/* Fit minimax polynomial of degree m using
* nag_1d_minimax_polynomial (e02alc).
*/
nag_1d_minimax_polynomial(n, x, y, m, a, &ref, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_1d_minimax_polynomial (e02alc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("\n  Polynomial coefficients\n");
for (i=0; i<m+1; i++)
printf("     %12.4e \n", a[i]);
printf("\n\n  Reference deviation = %10.2e\n\n", ref);
printf("  x      Fit     exp(x)   Residual\n");

/* The neval evaluation points are equispaced on [0,1]. */
dxx = 1.0/(double)(neval - 1);
for (j=0; j<neval; j++) {
xx = (double)(j) * dxx;
s = a[m];
for ( i=m-1; i>=0; i--)
s = s * xx + a[i];
t = exp(xx);
printf("%5.2f%9.4f%9.4f%11.2e\n", xx, s, t, s-t);
}
END:
NAG_FREE(a);
NAG_FREE(x);
NAG_FREE(y);

return exit_status;
}