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