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