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#include <math.h>
#include "fudgit.h"
/* returns the legendre nomial of degree n */
/* Uses the recurrence relation
* P(i+1) = [(2i + 1) x P(i) - i P(i-1)] / (i + 1)
* P(i) = [(2i - 1) x P(i-1) - (i-1) P(i-2) / i
* { oddx } prev_di di
*/
double leg(expr , expr );
/* for a whole vector */
void vleg(VEC x, VEC y, expr data, expr order)
{
int n = (int) *data;
int i;
for (i=1;i<=n;i++) {
y[i] = leg(x+i, order);
}
}
/* for one element */
double leg(expr x, expr order)
{
int inl = (int)*order;
if (inl < 0) {
Ft_matherror("%s: Order cannot be negative (%d).", "leg", inl);
}
else if (inl == 0) {
return(1.0);
}
else if (inl == 1) {
return(*x);
}
else {
double p0 = 1.0;
double p1 = *x;
double di = 1.0;
double twox = 2.0 * *x;
double oddx = *x;
double prev_di, pnow;
int j;
for (j=2;j<=inl;j++) {
prev_di = di;
di += 1.0;
oddx += twox;
/* recurrence relation */
pnow = (oddx * p1 - prev_di * p0) / di;
p0 = p1;
p1 = pnow;
}
return (pnow);
}
}
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