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Former-commit-id: a56647c77be3363a71248e7ade21dd52b1d515a8
This commit is contained in:
Marek Nečada 2018-05-06 19:13:10 +00:00
parent f943cc0cdb
commit 5e45afad38
8 changed files with 1408 additions and 1475 deletions
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75
qpms/translations.c
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@ -20,7 +20,8 @@
* error/inconsintency in Xu's paper or something else)
* Anyway, the zeroes give the correct _numerical_ values according to Xu's
* paper tables (without Xu's typos, of course), while
* the predefined macros give the correct translations of the VSWFs.
* the predefined macros give the correct translations of the VSWFs for the
* QPMS_NORMALIZATION_TAYLOR_CS norm.
*/
#if !(defined AN0 || defined AN1 || defined AN2 || defined AN3)
#pragma message "using AN1 macro as default"
@ -65,75 +66,7 @@ static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223
// Associated Legendre polynomial at zero argument (DLMF 14.5.1)
double qpms_legendre0(int m, int n) {
return pow(2,m) * sqrtpi / tgamma(.5*n - .5*m + .5) / tgamma(.5*n-.5*m);
}
static inline int min1pow(int x) {
return (x % 2) ? -1 : 1;
}
static inline complex double ipow(int x) {
return cpow(I, x);
}
// Derivative of associated Legendre polynomial at zero argument (DLMF 14.5.2)
double qpms_legendreD0(int m, int n) {
return -2 * qpms_legendre0(m, n);
}
static inline int imin(int x, int y) {
return x > y ? y : x;
}
// The uppermost value of q index for the B coefficient terms from [Xu](60).
// N.B. this is different from [Xu_old](79) due to the n vs. n+1 difference.
// However, the trailing terms in [Xu_old] are analytically zero (although
// the numerical values will carry some non-zero rounding error).
static inline int gauntB_Q_max(int M, int n, int mu, int nu) {
return imin(n, imin(nu, (n+nu+1-abs(M+mu))/2));
}
int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *result_array) {
int retval;
double tmparr[lmax+1];
switch(typ) {
case QPMS_BESSEL_REGULAR:
retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
return retval;
break;
case QPMS_BESSEL_SINGULAR: //FIXME: is this precise enough? Would it be better to do it one-by-one?
retval = gsl_sf_bessel_yl_array(lmax,x,tmparr);
for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
return retval;
break;
case QPMS_HANKEL_PLUS:
case QPMS_HANKEL_MINUS:
retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
if(retval) return retval;
retval = gsl_sf_bessel_yl_array(lmax, x, tmparr);
if (typ==QPMS_HANKEL_PLUS)
for (int l = 0; l <= lmax; ++l) result_array[l] += I * tmparr[l];
else
for (int l = 0; l <= lmax; ++l) result_array[l] +=-I * tmparr[l];
return retval;
break;
default:
abort();
//return GSL_EDOM;
}
assert(0);
}
static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
int m, int n, int mu, int nu) {
//int csphase = qpms_normalisation_t csphase(norm); // probably not needed here
norm = qpms_normalisation_t_normonly(norm);
switch(norm) {
case QPMS_NORMALISATION_KRISTENSSON:
case QPMS_NORMALISATION_TAYLOR:
TAYLOR:
return -0.5*(lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
break;
case QPMS_NORMALISATION_XU:
@ -145,7 +78,7 @@ static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
}
static inline double qpms_trans_normfac(qpms_normalisation_t norm,
int m, int n, int mu, int nu) {
/*dest*/int m, int n, /*src*/int mu, int nu) {
int csphase = qpms_normalisation_t_csphase(norm); // FIXME USEME TODO
norm = qpms_normalisation_t_normonly(norm);
double normfac = 1.;