qpms/qpms/bessels.c

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#include "bessels.h"
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
static const double ln2 = 0.693147180559945309417;
// general; gives an array of size xxx with TODODESC
complex double * hankelcoefftable_init(size_t maxn) {
complex double *hct = malloc((maxn+1)*(maxn+2)/2 * sizeof(complex double));
for(size_t n = 0; n <= maxn; ++n) {
complex double *hcs = hankelcoeffs_get(hct,n);
for (size_t k = 0; k <= n; ++k) {
double lcoeff = lgamma(n+k+1) - lgamma(n-k+1) - lgamma(k+1) - k*ln2;
// for some reason, casting k-n to double does not work,so
// cpow (I, k-n-1) cannot be used...
complex double ifactor;
switch ((n+1-k) % 4) {
case 0:
ifactor = 1;
break;
case 1:
ifactor = -I;
break;
case 2:
ifactor = -1;
break;
case 3:
ifactor = I;
break;
default:
abort();
}
// the result should be integer, so round to remove inaccuracies
hcs[k] = round(exp(lcoeff)) * ifactor;
}
}
return hct;
}
void hankelparts_fill(complex double *lrt, complex double *srt, size_t maxn,
size_t lrk_cutoff, complex double const * const hct,
unsigned kappa, double c, double x) {
if (lrt) memset(lrt, 0, (maxn+1)*sizeof(complex double));
memset(srt, 0, (maxn+1)*sizeof(complex double));
double regularisator = pow(1. - exp(-c * x), (double) kappa);
double antiregularisator = 1. - regularisator;
double xfrac = 1.; // x ** (-1-k)
for (size_t k = 0; k <= maxn; ++k) {
xfrac /= x;
for(size_t n = k; n <= maxn; ++n) // TODO Kahan sums here
srt[n] += ((k<lrk_cutoff) ? antiregularisator : 1)
* xfrac * hankelcoeffs_get(hct,n)[k];
if (lrt && k < lrk_cutoff) for (size_t n = k; n <= maxn; ++n)
lrt[n] += regularisator * xfrac * hankelcoeffs_get(hct,n)[k];
}
complex double expix = cexp(I * x);
for(size_t n = 0; n <= maxn; ++n)
srt[n] *= expix;
if (lrt) for(size_t n = 0; n <= maxn; ++n)
srt[n] *= expix;
}