108 lines
3.8 KiB
C
108 lines
3.8 KiB
C
#include "qpms_specfunc.h"
|
|
#include "qpms_types.h"
|
|
#include <gsl/gsl_sf_legendre.h>
|
|
#include <gsl/gsl_math.h>
|
|
#include <stdlib.h>
|
|
#include "indexing.h"
|
|
#include <string.h>
|
|
#include "qpms_error.h"
|
|
|
|
// Legendre functions also for negative m, see DLMF 14.9.3
|
|
qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, double x, qpms_l_t lMax,
|
|
gsl_sf_legendre_t lnorm, double csphase)
|
|
{
|
|
const size_t n = gsl_sf_legendre_array_n(lMax);
|
|
double *legendre_tmp, *legendre_deriv_tmp;
|
|
QPMS_CRASHING_MALLOC(legendre_tmp, n * sizeof(double));
|
|
QPMS_CRASHING_MALLOC(legendre_deriv_tmp, n * sizeof(double));
|
|
int gsl_errno = gsl_sf_legendre_deriv_array_e(
|
|
lnorm, (size_t)lMax, x, csphase, legendre_tmp,legendre_deriv_tmp);
|
|
for (qpms_l_t l = 1; l <= lMax; ++l)
|
|
for (qpms_m_t m = 0; m <= l; ++m) {
|
|
qpms_y_t y = qpms_mn2y(m,l);
|
|
size_t i = gsl_sf_legendre_array_index(l,m);
|
|
target[y] = legendre_tmp[i];
|
|
target_deriv[y] = legendre_deriv_tmp[i];
|
|
}
|
|
|
|
// Fill negative m's.
|
|
for (qpms_l_t l = 1; l <= lMax; ++l)
|
|
for (qpms_m_t m = 1; m <= l; ++m) {
|
|
qpms_y_t y = qpms_mn2y(-m,l);
|
|
size_t i = gsl_sf_legendre_array_index(l,m);
|
|
// cf. DLMF 14.9.3, but we're normalised.
|
|
double factor = ((m%2)?-1:1);
|
|
target[y] = factor * legendre_tmp[i];
|
|
target_deriv[y] = factor * legendre_deriv_tmp[i];
|
|
}
|
|
|
|
free(legendre_tmp);
|
|
free(legendre_deriv_tmp);
|
|
return gsl_errno;
|
|
}
|
|
|
|
qpms_errno_t qpms_legendre_deriv_y_get(double **target, double **dtarget, double x, qpms_l_t lMax, gsl_sf_legendre_t lnorm,
|
|
double csphase)
|
|
{
|
|
|
|
const qpms_y_t nelem = qpms_lMax2nelem(lMax);
|
|
QPMS_CRASHING_MALLOC(target, nelem * sizeof(double));
|
|
QPMS_CRASHING_MALLOC(dtarget, nelem * sizeof(double));
|
|
return qpms_legendre_deriv_y_fill(*target, *dtarget, x, lMax, lnorm, csphase);
|
|
}
|
|
|
|
qpms_pitau_t qpms_pitau_get(double theta, qpms_l_t lMax, const double csphase)
|
|
{
|
|
QPMS_ENSURE(fabs(csphase) == 1, "The csphase argument must be either 1 or -1, not %g.", csphase);
|
|
qpms_pitau_t res;
|
|
const qpms_y_t nelem = qpms_lMax2nelem(lMax);
|
|
QPMS_CRASHING_MALLOC(res.leg, nelem * sizeof(double));
|
|
QPMS_CRASHING_MALLOC(res.pi, nelem * sizeof(double));
|
|
QPMS_CRASHING_MALLOC(res.tau, nelem * sizeof(double));
|
|
double ct = cos(theta), st = sin(theta);
|
|
if (1 == fabs(ct)) { // singular case, use DLMF 14.8.2
|
|
memset(res.pi, 0, nelem * sizeof(double));
|
|
memset(res.tau, 0, nelem * sizeof(double));
|
|
memset(res.leg, 0, nelem * sizeof(double));
|
|
for (qpms_l_t l = 1; l <= lMax; ++l) {
|
|
res.leg[qpms_mn2y(0, l)] = ((l%2)?ct:1.)*sqrt((2*l+1)/(4*M_PI *l*(l+1)));
|
|
double fl = 0.25 * sqrt((2*l+1)*M_1_PI);
|
|
int lpar = (l%2)?-1:1;
|
|
res.pi [qpms_mn2y(+1, l)] = -((ct>0) ? -1 : lpar) * fl * csphase;
|
|
res.pi [qpms_mn2y(-1, l)] = -((ct>0) ? -1 : lpar) * fl * csphase;
|
|
res.tau[qpms_mn2y(+1, l)] = ((ct>0) ? +1 : lpar) * fl * csphase;
|
|
res.tau[qpms_mn2y(-1, l)] = -((ct>0) ? +1 : lpar) * fl * csphase;
|
|
}
|
|
}
|
|
else { // cos(theta) in (-1,1), use normal calculation
|
|
double *legder;
|
|
QPMS_CRASHING_MALLOC(legder, nelem * sizeof(double));
|
|
QPMS_ENSURE_SUCCESS(qpms_legendre_deriv_y_fill(res.leg, legder, ct, lMax,
|
|
GSL_SF_LEGENDRE_SPHARM, csphase));
|
|
// Multiply by the "power normalisation" factor
|
|
for (qpms_l_t l = 1; l <= lMax; ++l) {
|
|
double prefac = 1./sqrt(l*(l+1));
|
|
for (qpms_m_t m = -l; m <= l; ++m) {
|
|
res.leg[qpms_mn2y(m,l)] *= prefac;
|
|
legder[qpms_mn2y(m,l)] *= prefac;
|
|
}
|
|
}
|
|
for (qpms_l_t l = 1; l <= lMax; ++l) {
|
|
for (qpms_m_t m = -l; m <= l; ++m) {
|
|
res.pi [qpms_mn2y(m,l)] = m / st * res.leg[qpms_mn2y(m,l)];
|
|
res.tau[qpms_mn2y(m,l)] = - st * legder[qpms_mn2y(m,l)];
|
|
}
|
|
}
|
|
free(legder);
|
|
}
|
|
res.lMax = lMax;
|
|
return res;
|
|
}
|
|
|
|
void qpms_pitau_free(qpms_pitau_t x) {
|
|
free(x.leg);
|
|
free(x.pi);
|
|
free(x.tau);
|
|
}
|
|
|