1102 lines
37 KiB
C
1102 lines
37 KiB
C
#include <math.h>
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#include "qpms_types.h"
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#include "gaunt.h"
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#include "translations.h"
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#include "indexing.h" // TODO replace size_t and int with own index types here
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#include <stdbool.h>
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#include <gsl/gsl_sf_legendre.h>
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#include <gsl/gsl_sf_bessel.h>
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#include "assert_cython_workaround.h"
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#include <stdlib.h> //abort()
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/*
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* References:
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* [1] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996)
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*/
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/*
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* GENERAL TODO: use normalised Legendre functions for Kristensson and Taylor conventions directly
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* instead of normalising them here (the same applies for csphase).
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*/
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static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223871;
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//static const double ln2 = 0.693147180559945309417232121458176568075500134360255254120;
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// Associated Legendre polynomial at zero argument (DLMF 14.5.1)
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double qpms_legendre0(int m, int n) {
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return pow(2,m) * sqrtpi / tgamma(.5*n - .5*m + .5) / tgamma(.5*n-.5*m);
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}
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static inline int min1pow(int x) {
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return (x % 2) ? -1 : 1;
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}
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static inline complex double ipow(int x) {
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return cpow(I, x);
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}
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// Derivative of associated Legendre polynomial at zero argument (DLMF 14.5.2)
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double qpms_legendreD0(int m, int n) {
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return -2 * qpms_legendre0(m, n);
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}
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int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *result_array) {
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int retval;
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double tmparr[lmax+1];
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switch(typ) {
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case QPMS_BESSEL_REGULAR:
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retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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return retval;
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break;
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case QPMS_BESSEL_SINGULAR: //FIXME: is this precise enough? Would it be better to do it one-by-one?
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retval = gsl_sf_bessel_yl_array(lmax,x,tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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return retval;
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break;
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case QPMS_HANKEL_PLUS:
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case QPMS_HANKEL_MINUS:
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retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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if(retval) return retval;
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retval = gsl_sf_bessel_yl_array(lmax, x, tmparr);
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if (typ==QPMS_HANKEL_PLUS)
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for (int l = 0; l <= lmax; ++l) result_array[l] += I * tmparr[l];
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else
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for (int l = 0; l <= lmax; ++l) result_array[l] +=-I * tmparr[l];
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return retval;
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break;
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default:
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abort();
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//return GSL_EDOM;
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}
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assert(0);
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}
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static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
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int m, int n, int mu, int nu) {
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//int csphase = qpms_normalisation_t csphase(norm); // probably not needed here
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norm = qpms_normalisation_t_normonly(norm);
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switch(norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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case QPMS_NORMALISATION_TAYLOR:
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return -0.5*(lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
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break;
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case QPMS_NORMALISATION_XU:
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return 0;
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break;
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default:
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abort();
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}
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}
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static inline double qpms_trans_normfac(qpms_normalisation_t norm,
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int m, int n, int mu, int nu) {
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int csphase = qpms_normalisation_t_csphase(norm); // FIXME USEME TODO
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norm = qpms_normalisation_t_normonly(norm);
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double normfac = 1.;
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switch(norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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normfac *= sqrt((nu*(nu+1.))/(n*(n+1.)));
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case QPMS_NORMALISATION_TAYLOR:
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normfac *= sqrt((2.*n+1)/(2.*nu+1));
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break;
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case QPMS_NORMALISATION_XU:
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break;
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default:
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abort();
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}
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return normfac;
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}
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complex double qpms_trans_single_A(qpms_normalisation_t norm,
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int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
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// N.B. -m !!!!!!
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double a1q[qmax+1];
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int err;
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gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
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double a1q0 = a1q[0];
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if (err) abort();
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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int Pp_order = mu-m;
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//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
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assert(p >= abs(Pp_order));
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double a1q_n = a1q[q] / a1q0;
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double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
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if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
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complex double zp = bes[p];
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complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
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sum += summandq;
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}
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double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
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double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
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double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
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// int csphase = qpms_normalisation_t_csphase(norm); FIXME EITHER TO NORMFAC OR USE HERE
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presum *= ipow(n-nu) * (normfac * exp(normlogfac));
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return presum * sum;
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}
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complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
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// N.B. -m !!!!!!
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double a1q[qmax+1];
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int err;
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gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
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double a1q0 = a1q[0];
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if (err) abort();
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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int Pp_order = mu-m;
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//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
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assert(p >= abs(Pp_order));
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double a1q_n = a1q[q] / a1q0;
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double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
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if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
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complex double zp = bes[p];
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complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
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sum += summandq;
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}
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double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
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complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
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lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
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return (presum / prenormratio) * sum;
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}
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// [1], eq. (83)
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complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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int err;
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if (mu == nu) {
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for (int q = 0; q <= q2max; ++q)
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a2q[q] = 0;
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a2q0 = 1;
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}
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else {
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gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
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a2q0 = a2q[0];
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}
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gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
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a3q0 = a3q[0];
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double leg[gsl_sf_legendre_array_n(n+nu+1)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
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complex double bes[n+nu+2];
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
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complex double sum = 0;
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for (int q = 0; q <= Qmax; ++q) {
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int p = n+nu-2*q;
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double a2q_n = a2q[q]/a2q0;
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double a3q_n = a3q[q]/a3q0;
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complex double zp_ = bes[p+1];
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int Pp_order_ = mu-m;
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//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
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assert(p+1 >= abs(Pp_order_));
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double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
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if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
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complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
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-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
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*min1pow(q) * zp_ * Pp_);
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sum += summandq;
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}
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double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
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(4*n)*(n+1)*(n+m+1));
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// Taylor normalisation v2, proven to be equivalent
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complex double prenormratio = ipow(nu-n);
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return (presum / prenormratio) * sum;
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}
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complex double qpms_trans_single_B(qpms_normalisation_t norm,
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int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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int err;
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if (mu == nu) {
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for (int q = 0; q <= q2max; ++q)
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a2q[q] = 0;
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a2q0 = 1;
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}
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else {
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gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
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a2q0 = a2q[0];
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}
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gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
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a3q0 = a3q[0];
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double leg[gsl_sf_legendre_array_n(n+nu+1)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
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complex double bes[n+nu+2];
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
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complex double sum = 0;
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for (int q = 0; q <= Qmax; ++q) {
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int p = n+nu-2*q;
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double a2q_n = a2q[q]/a2q0;
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double a3q_n = a3q[q]/a3q0;
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complex double zp_ = bes[p+1];
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int Pp_order_ = mu-m;
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//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
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assert(p+1 >= abs(Pp_order_));
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double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
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if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
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complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
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-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
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*min1pow(q) * zp_ * Pp_);
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sum += summandq;
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}
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double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
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+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
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complex double presum = exp(exponent);
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presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
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(4*n)*(n+1)*(n+m+1));
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double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
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double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
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// int csphase = qpms_normalisation_t_csphase(norm); FIXME EITHER TO NORMFAC OR USE HERE
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presum *= ipow(n-nu) * (exp(normlogfac) * normfac);
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return presum * sum;
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}
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complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J) {
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if(r_ge_d) J = QPMS_BESSEL_REGULAR;
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double costheta = cos(kdlj.theta);
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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int err;
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if (mu == nu) {
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for (int q = 0; q <= q2max; ++q)
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a2q[q] = 0;
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a2q0 = 1;
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}
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else {
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gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
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a2q0 = a2q[0];
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}
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gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
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a3q0 = a3q[0];
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double leg[gsl_sf_legendre_array_n(n+nu+1)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
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complex double bes[n+nu+2];
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
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complex double sum = 0;
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for (int q = 0; q <= Qmax; ++q) {
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int p = n+nu-2*q;
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double a2q_n = a2q[q]/a2q0;
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double a3q_n = a3q[q]/a3q0;
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complex double zp_ = bes[p+1];
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int Pp_order_ = mu-m;
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//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
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assert(p+1 >= abs(Pp_order_));
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double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
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if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
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complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
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-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
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*min1pow(q) * zp_ * Pp_);
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sum += summandq;
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}
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double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
|
||
complex double presum = exp(exponent);
|
||
presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
|
||
(4*n)*(n+1)*(n+m+1));
|
||
|
||
// Taylor normalisation v2, proven to be equivalent
|
||
complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
|
||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
|
||
|
||
return (presum / prenormratio) * sum;
|
||
}
|
||
|
||
complex double qpms_trans_single_A_Taylor_ext(int m, int n, int mu, int nu,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi, int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_single_A_Taylor(m,n,mu,nu,kdlj,r_ge_d,J);
|
||
}
|
||
|
||
complex double qpms_trans_single_B_Taylor_ext(int m, int n, int mu, int nu,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi, int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_single_B_Taylor(m,n,mu,nu,kdlj,r_ge_d,J);
|
||
}
|
||
|
||
void qpms_trans_calculator_free(qpms_trans_calculator *c) {
|
||
free(c->A_multipliers[0]);
|
||
free(c->A_multipliers);
|
||
free(c->B_multipliers[0]);
|
||
free(c->B_multipliers);
|
||
free(c);
|
||
}
|
||
|
||
static inline size_t qpms_trans_calculator_index_mnmunu(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu){
|
||
return c->nelem * qpms_mn2y(m,n) + qpms_mn2y(mu,nu);
|
||
}
|
||
|
||
static inline size_t qpms_trans_calculator_index_yyu(const qpms_trans_calculator *c,
|
||
size_t y, size_t yu) {
|
||
return c->nelem * y + yu;
|
||
}
|
||
|
||
|
||
#define SQ(x) ((x)*(x))
|
||
|
||
|
||
static void qpms_trans_calculator_multipliers_A_general(
|
||
qpms_normalisation_t norm,
|
||
complex double *dest, int m, int n, int mu, int nu, int qmax) {
|
||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||
double a1q[qmax+1];
|
||
int err;
|
||
gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
|
||
if (err) abort();
|
||
double a1q0 = a1q[0];
|
||
|
||
int csphase = qpms_normalisation_t_csphase(norm); //TODO FIXME use this
|
||
norm = qpms_normalisation_t_normonly(norm);
|
||
double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
|
||
double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
|
||
|
||
// TODO use csphase to modify normfac here!!!!
|
||
// normfac = xxx ? -normfac : normfac;
|
||
normfac *= min1pow(m+n);
|
||
double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+1) - lgamma(2*(n+nu)+1))
|
||
+ normlogfac;
|
||
double presum = exp(exponent);
|
||
presum *= normfac / (4.*n);
|
||
|
||
for(int q = 0; q <= qmax; q++) {
|
||
int p = n+nu-2*q;
|
||
int Pp_order = mu - m;
|
||
assert(p >= abs(Pp_order));
|
||
double a1q_n = a1q[q] / a1q0;
|
||
// Assuming non_normalized legendre polynomials!
|
||
double Ppfac = (Pp_order >= 0) ? 1 :
|
||
min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||
double summandfac = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n;
|
||
dest[q] = presum * summandfac * Ppfac;
|
||
// FIXME I might not need complex here
|
||
}
|
||
}
|
||
|
||
|
||
static void qpms_trans_calculator_multipliers_B_general(
|
||
qpms_normalisation_t norm,
|
||
complex double *dest, int m, int n, int mu, int nu, int Qmax) {
|
||
assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||
int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
|
||
assert(Qmax == q2max);
|
||
// FIXME remove the q2max variable altogether, as it is probably equal
|
||
// to Qmax
|
||
double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
|
||
int err;
|
||
if (mu == nu) {
|
||
for (int q = 0; q <= q2max; ++q)
|
||
a2q[q] = 0;
|
||
a2q0 = 1;
|
||
}
|
||
else {
|
||
gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
|
||
a2q0 = a2q[0];
|
||
}
|
||
gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
|
||
a3q0 = a3q[0];
|
||
|
||
|
||
int csphase = qpms_normalisation_t_csphase(norm); //TODO FIXME use this
|
||
norm = qpms_normalisation_t_normonly(norm);
|
||
double normlogfac= qpms_trans_normlogfac(norm,m,n,mu,nu);
|
||
double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
|
||
// TODO use csphase to modify normfac here!!!!
|
||
// normfac = xxx ? -normfac : normfac;
|
||
normfac *= min1pow(m+n);
|
||
|
||
|
||
|
||
double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3))
|
||
+normlogfac;
|
||
complex double presum = exp(exponent);
|
||
presum *= I * normfac / (
|
||
(4*n)*(n+1)*(n+m+1));
|
||
|
||
for (int q = 0; q <= Qmax; ++q) {
|
||
int p = n+nu-2*q;
|
||
double a2q_n = a2q[q]/a2q0;
|
||
double a3q_n = a3q[q]/a3q0;
|
||
int Pp_order_ = mu-m;
|
||
//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
|
||
assert(p+1 >= abs(Pp_order_));
|
||
double Ppfac = (Pp_order_ >= 0) ? 1 :
|
||
|
||
min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
|
||
double summandq = ((2*(n+1)*(nu-mu)*a2q_n
|
||
-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
|
||
*min1pow(q));
|
||
dest[q] = Ppfac * summandq * presum;
|
||
}
|
||
}
|
||
|
||
//#if 0
|
||
static void qpms_trans_calculator_multipliers_A_Taylor(
|
||
complex double *dest, int m, int n, int mu, int nu, int qmax) {
|
||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||
double a1q[qmax+1];
|
||
int err;
|
||
gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
|
||
if (err) abort();
|
||
double a1q0 = a1q[0];
|
||
|
||
double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+1) - lgamma(2*(n+nu)+1)) - 0.5*( // ex-prenormratio
|
||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
|
||
double presum = exp(exponent);
|
||
presum *= min1pow(m+n) * sqrt((2.*n+1)/(2.*nu+1)) / (4*n);
|
||
|
||
for(int q = 0; q <= qmax; q++) {
|
||
int p = n+nu-2*q;
|
||
int Pp_order = mu - m;
|
||
assert(p >= abs(Pp_order));
|
||
double a1q_n = a1q[q] / a1q0;
|
||
// Assuming non_normalized legendre polynomials!
|
||
double Ppfac = (Pp_order >= 0) ? 1 :
|
||
min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||
double summandfac = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n;
|
||
dest[q] = presum * summandfac * Ppfac;
|
||
// FIXME I might not need complex here
|
||
}
|
||
}
|
||
//#endif
|
||
#if 0
|
||
static void qpms_trans_calculator_multipliers_A_Taylor(
|
||
complex double *dest, int m, int n, int mu, int nu, int qmax) {
|
||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||
double a1q[qmax+1];
|
||
int err;
|
||
gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
|
||
if (err) abort();
|
||
double a1q0 = a1q[0];
|
||
for(int q = 0; q <= qmax; ++q) {
|
||
int p = n+nu-2*q;
|
||
int Pp_order = mu-m;
|
||
//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
|
||
assert(p >= abs(Pp_order));
|
||
double a1q_n = a1q[q] / a1q0;
|
||
//double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
|
||
//complex double zp = bes[p];
|
||
dest[q] = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n /* * zp * Pp*/;
|
||
if (Pp_order < 0) dest[q] *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||
//sum += summandq;
|
||
}
|
||
|
||
double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
|
||
complex double presum = exp(exponent);
|
||
presum *=/* cexp(I*(mu-m)*kdlj.phi) * */ min1pow(m) * ipow(nu+n) / (4*n);
|
||
|
||
complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
|
||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
|
||
//return (presum / prenormratio) * sum;
|
||
for(int q=0;q<=qmax;++q) dest[q] *= presum / prenormratio;
|
||
}
|
||
#endif
|
||
|
||
|
||
|
||
static void qpms_trans_calculator_multipliers_B_Taylor(
|
||
complex double *dest, int m, int n, int mu, int nu, int Qmax) {
|
||
assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||
int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
|
||
assert(Qmax == q2max);
|
||
// FIXME remove the q2max variable altogether, as it is probably equal
|
||
// to Qmax
|
||
double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
|
||
int err;
|
||
if (mu == nu) {
|
||
for (int q = 0; q <= q2max; ++q)
|
||
a2q[q] = 0;
|
||
a2q0 = 1;
|
||
}
|
||
else {
|
||
gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
|
||
a2q0 = a2q[0];
|
||
}
|
||
gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
|
||
a3q0 = a3q[0];
|
||
|
||
double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
|
||
+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
|
||
+lgamma(n+nu+2) - lgamma(2*(n+nu)+3)) - 0.5 * (
|
||
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)
|
||
-lgamma(nu+mu+1));
|
||
complex double presum = exp(exponent);
|
||
presum *= I * (min1pow(m+n) *sqrt((2.*n+1)/(2.*nu+1)) / (
|
||
(4*n)*(n+1)*(n+m+1)));
|
||
|
||
for (int q = 0; q <= Qmax; ++q) {
|
||
int p = n+nu-2*q;
|
||
double a2q_n = a2q[q]/a2q0;
|
||
double a3q_n = a3q[q]/a3q0;
|
||
int Pp_order_ = mu-m;
|
||
//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
|
||
assert(p+1 >= abs(Pp_order_));
|
||
double Ppfac = (Pp_order_ >= 0) ? 1 :
|
||
|
||
min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
|
||
double summandq = ((2*(n+1)*(nu-mu)*a2q_n
|
||
-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
|
||
*min1pow(q));
|
||
dest[q] = Ppfac * summandq * presum;
|
||
}
|
||
}
|
||
|
||
int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
|
||
switch (norm) {
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
#ifdef USE_SEPARATE_TAYLOR
|
||
qpms_trans_calculator_multipliers_A_Taylor(dest,m,n,mu,nu,qmax);
|
||
return 0;
|
||
break;
|
||
#endif
|
||
case QPMS_NORMALISATION_XU:
|
||
case QPMS_NORMALISATION_KRISTENSSON:
|
||
qpms_trans_calculator_multipliers_A_general(norm, dest, m, n, mu, nu, qmax);
|
||
return 0;
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
|
||
switch (norm) {
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
#ifdef USE_SEPARATE_TAYLOR
|
||
qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax);
|
||
return 0;
|
||
break;
|
||
#endif
|
||
case QPMS_NORMALISATION_XU:
|
||
case QPMS_NORMALISATION_KRISTENSSON:
|
||
qpms_trans_calculator_multipliers_B_general(norm, dest, m, n, mu, nu, qmax);
|
||
return 0;
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
qpms_trans_calculator
|
||
*qpms_trans_calculator_init (int lMax, qpms_normalisation_t normalisation) {
|
||
assert(lMax > 0);
|
||
qpms_trans_calculator *c = malloc(sizeof(qpms_trans_calculator));
|
||
c->lMax = lMax;
|
||
c->nelem = lMax * (lMax+2);
|
||
c->A_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
|
||
c->B_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
|
||
c->normalisation = normalisation;
|
||
size_t *qmaxes = malloc(SQ(c->nelem) * sizeof(size_t));
|
||
size_t qmaxsum = 0;
|
||
for(size_t y = 0; y < c->nelem; y++)
|
||
for(size_t yu = 0; yu < c->nelem; yu++) {
|
||
int m,n, mu, nu;
|
||
qpms_y2mn_p(y,&m,&n);
|
||
qpms_y2mn_p(yu,&mu,&nu);
|
||
qmaxsum += 1 + (
|
||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||
= gaunt_q_max(-m,n,mu,nu));
|
||
}
|
||
c->A_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
|
||
// calculate multiplier beginnings
|
||
for(size_t i = 0; i < SQ(c->nelem); ++i)
|
||
c->A_multipliers[i+1] = c->A_multipliers[i] + qmaxes[i] + 1;
|
||
// calculate the multipliers
|
||
for(size_t y = 0; y < c->nelem; ++y)
|
||
for(size_t yu = 0; yu < c->nelem; ++yu) {
|
||
size_t i = y * c->nelem + yu;
|
||
int m, n, mu, nu;
|
||
qpms_y2mn_p(y, &m, &n);
|
||
qpms_y2mn_p(yu, &mu, &nu);
|
||
qpms_trans_calculator_multipliers_A(normalisation,
|
||
c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||
}
|
||
|
||
qmaxsum = 0;
|
||
for(size_t y=0; y < c->nelem; y++)
|
||
for(size_t yu = 0; yu < c->nelem; yu++) {
|
||
int m, n, mu, nu;
|
||
qpms_y2mn_p(y,&m,&n);
|
||
qpms_y2mn_p(yu,&mu,&nu);
|
||
qmaxsum += 1 + (
|
||
qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
|
||
= gaunt_q_max(-m,n+1,mu,nu));
|
||
}
|
||
c->B_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
|
||
// calculate multiplier beginnings
|
||
for(size_t i = 0; i < SQ(c->nelem); ++i)
|
||
c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i] + 1;
|
||
// calculate the multipliers
|
||
for(size_t y = 0; y < c->nelem; ++y)
|
||
for(size_t yu = 0; yu < c->nelem; ++yu) {
|
||
size_t i = y * c->nelem + yu;
|
||
int m, n, mu, nu;
|
||
qpms_y2mn_p(y, &m, &n);
|
||
qpms_y2mn_p(yu, &mu, &nu);
|
||
qpms_trans_calculator_multipliers_B(normalisation,
|
||
c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
|
||
}
|
||
|
||
free(qmaxes);
|
||
return c;
|
||
}
|
||
|
||
static inline complex double qpms_trans_calculator_get_A_precalcbuf(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J,
|
||
const complex double *bessel_buf, const double *legendre_buf) {
|
||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||
size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
|
||
assert(qmax == gaunt_q_max(-m,n,mu,nu));
|
||
complex double sum = 0;
|
||
for(size_t q = 0; q <= qmax; ++q) {
|
||
int p = n+nu-2*q;
|
||
double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
|
||
complex double zp = bessel_buf[p];
|
||
complex double multiplier = c->A_multipliers[i][q];
|
||
sum += Pp * zp * multiplier;
|
||
}
|
||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||
return sum * eimf;
|
||
}
|
||
|
||
complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J,
|
||
complex double *bessel_buf, double *legendre_buf) {
|
||
// This functions gets preallocated memory for bessel and legendre functions, but computes them itself
|
||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
|
||
// TODO warn?
|
||
return NAN+I*NAN;
|
||
switch(c->normalisation) {
|
||
// TODO use normalised legendre functions for Taylor and Kristensson
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
case QPMS_NORMALISATION_KRISTENSSON:
|
||
case QPMS_NORMALISATION_XU:
|
||
{
|
||
double costheta = cos(kdlj.theta);
|
||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
|
||
costheta,-1,legendre_buf)) abort();
|
||
if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bessel_buf)) abort();
|
||
return qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
}
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
static inline complex double qpms_trans_calculator_get_B_precalcbuf(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J,
|
||
const complex double *bessel_buf, const double *legendre_buf) {
|
||
size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
|
||
size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
|
||
assert(qmax == gaunt_q_max(-m,n+1,mu,nu));
|
||
complex double sum = 0;
|
||
for(int q = 0; q <= qmax; ++q) {
|
||
int p = n+nu-2*q;
|
||
double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
|
||
complex double zp_ = bessel_buf[p+1];
|
||
complex double multiplier = c->B_multipliers[i][q];
|
||
sum += Pp_ * zp_ * multiplier;
|
||
}
|
||
complex double eimf = cexp(I*(mu-m)*kdlj.phi);
|
||
return sum * eimf;
|
||
}
|
||
|
||
complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J,
|
||
complex double *bessel_buf, double *legendre_buf) {
|
||
// This functions gets preallocated memory for bessel and legendre functions, but computes them itself
|
||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
|
||
// TODO warn?
|
||
return NAN+I*NAN;
|
||
switch(c->normalisation) {
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
case QPMS_NORMALISATION_KRISTENSSON:
|
||
case QPMS_NORMALISATION_XU:
|
||
{
|
||
double costheta = cos(kdlj.theta);
|
||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
|
||
costheta,-1,legendre_buf)) abort();
|
||
if (qpms_sph_bessel_fill(J, n+nu+2, kdlj.r, bessel_buf)) abort();
|
||
return qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
}
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J,
|
||
complex double *bessel_buf, double *legendre_buf) {
|
||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR) {
|
||
*Adest = NAN+I*NAN;
|
||
*Bdest = NAN+I*NAN;
|
||
// TODO warn? different return value?
|
||
return 0;
|
||
}
|
||
switch(c->normalisation) {
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
case QPMS_NORMALISATION_KRISTENSSON:
|
||
case QPMS_NORMALISATION_XU:
|
||
{
|
||
double costheta = cos(kdlj.theta);
|
||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
|
||
costheta,-1,legendre_buf)) abort();
|
||
if (qpms_sph_bessel_fill(J, n+nu+2, kdlj.r, bessel_buf)) abort();
|
||
*Adest = qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
*Bdest = qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
return 0;
|
||
}
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
|
||
|
||
|
||
int qpms_trans_calculator_get_AB_arrays_buf(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
size_t deststride, size_t srcstride,
|
||
sph_t kdlj, bool r_ge_d, qpms_bessel_t J,
|
||
complex double *bessel_buf, double *legendre_buf) {
|
||
if (r_ge_d) J = QPMS_BESSEL_REGULAR;
|
||
if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR) {
|
||
for (size_t i = 0; i < c->nelem; ++i)
|
||
for (size_t j = 0; j < c->nelem; ++j) {
|
||
*(Adest + i*srcstride + j*deststride) = NAN+I*NAN;
|
||
*(Bdest + i*srcstride + j*deststride) = NAN+I*NAN;
|
||
}
|
||
// TODO warn? different return value?
|
||
return 0;
|
||
}
|
||
switch(c->normalisation) {
|
||
case QPMS_NORMALISATION_TAYLOR:
|
||
{
|
||
double costheta = cos(kdlj.theta);
|
||
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,2*c->lMax+1,
|
||
costheta,-1,legendre_buf)) abort();
|
||
if (qpms_sph_bessel_fill(J, 2*c->lMax+2, kdlj.r, bessel_buf)) abort();
|
||
size_t desti = 0, srci = 0;
|
||
for (int n = 1; n <= c->lMax; ++n) for (int m = -n; m <= n; ++m) {
|
||
for (int nu = 1; nu <= c->lMax; ++nu) for (int mu = -nu; mu <= nu; ++mu) {
|
||
size_t assertindex = qpms_trans_calculator_index_mnmunu(c,m,n,mu,nu);
|
||
assert(assertindex == desti*c->nelem + srci);
|
||
*(Adest + deststride * desti + srcstride * srci) =
|
||
qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
*(Bdest + deststride * desti + srcstride * srci) =
|
||
qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
|
||
kdlj,r_ge_d,J,bessel_buf,legendre_buf);
|
||
++srci;
|
||
}
|
||
++desti;
|
||
srci = 0;
|
||
}
|
||
return 0;
|
||
}
|
||
break;
|
||
default:
|
||
abort();
|
||
}
|
||
assert(0);
|
||
}
|
||
|
||
complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J) {
|
||
double leg[gsl_sf_legendre_array_n(n+nu)];
|
||
complex double bes[n+nu+1];
|
||
return qpms_trans_calculator_get_A_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
|
||
bes,leg);
|
||
}
|
||
|
||
complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J) {
|
||
double leg[gsl_sf_legendre_array_n(n+nu+1)];
|
||
complex double bes[n+nu+2];
|
||
return qpms_trans_calculator_get_B_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
|
||
bes,leg);
|
||
}
|
||
|
||
int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
int m, int n, int mu, int nu, sph_t kdlj,
|
||
bool r_ge_d, qpms_bessel_t J) {
|
||
double leg[gsl_sf_legendre_array_n(2*c->lMax+1)];
|
||
complex double bes[2*c->lMax+2];
|
||
return qpms_trans_calculator_get_AB_buf_p(c,Adest, Bdest,m,n,mu,nu,kdlj,r_ge_d,J,
|
||
bes,leg);
|
||
}
|
||
|
||
int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
size_t deststride, size_t srcstride,
|
||
sph_t kdlj, bool r_ge_d, qpms_bessel_t J) {
|
||
double leg[gsl_sf_legendre_array_n(c->lMax+c->lMax+1)];
|
||
complex double bes[c->lMax+c->lMax+2];
|
||
return qpms_trans_calculator_get_AB_arrays_buf(c,
|
||
Adest, Bdest, deststride, srcstride,
|
||
kdlj, r_ge_d, J,
|
||
bes, leg);
|
||
}
|
||
|
||
|
||
|
||
complex double qpms_trans_calculator_get_A_ext(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||
int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_calculator_get_A(c,m,n,mu,nu,kdlj,r_ge_d,J);
|
||
}
|
||
|
||
complex double qpms_trans_calculator_get_B_ext(const qpms_trans_calculator *c,
|
||
int m, int n, int mu, int nu,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||
int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_calculator_get_B(c,m,n,mu,nu,kdlj,r_ge_d,J);
|
||
}
|
||
|
||
int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
int m, int n, int mu, int nu,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||
int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_calculator_get_AB_p(c,Adest,Bdest,m,n,mu,nu,kdlj,r_ge_d,J);
|
||
}
|
||
|
||
int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
|
||
complex double *Adest, complex double *Bdest,
|
||
size_t deststride, size_t srcstride,
|
||
double kdlj_r, double kdlj_theta, double kdlj_phi,
|
||
int r_ge_d, int J) {
|
||
sph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
|
||
return qpms_trans_calculator_get_AB_arrays(c,Adest,Bdest,deststride,srcstride,
|
||
kdlj, r_ge_d, J);
|
||
}
|
||
#ifdef QPMS_COMPILE_PYTHON_EXTENSIONS
|
||
#include <string.h>
|
||
|
||
#ifdef QPMS_USE_OMP
|
||
#include <omp.h>
|
||
#endif
|
||
|
||
int qpms_cython_trans_calculator_get_AB_arrays_loop(
|
||
const qpms_trans_calculator *c, const qpms_bessel_t J, const int resnd,
|
||
const int daxis, const int saxis,
|
||
char *A_data, const npy_intp *A_shape, const npy_intp *A_strides,
|
||
char *B_data, const npy_intp *B_shape, const npy_intp *B_strides,
|
||
const char *r_data, const npy_intp *r_shape, const npy_intp *r_strides,
|
||
const char *theta_data, const npy_intp *theta_shape, const npy_intp *theta_strides,
|
||
const char *phi_data, const npy_intp *phi_shape, const npy_intp *phi_strides,
|
||
const char *r_ge_d_data, const npy_intp *r_ge_d_shape, const npy_intp *r_ge_d_strides){
|
||
assert(daxis != saxis);
|
||
assert(resnd >= 2);
|
||
int longest_axis = 0;
|
||
int longestshape = 1;
|
||
const npy_intp *resultshape = A_shape, *resultstrides = A_strides;
|
||
// TODO put some restrict's everywhere?
|
||
for (int ax = 0; ax < resnd; ++ax){
|
||
assert(A_shape[ax] == B_shape[ax]);
|
||
assert(A_strides[ax] == B_strides[ax]);
|
||
if (daxis == ax || saxis == ax) continue;
|
||
if (A_shape[ax] > longestshape) {
|
||
longest_axis = ax;
|
||
longestshape = 1;
|
||
}
|
||
}
|
||
const npy_intp longlen = resultshape[longest_axis];
|
||
|
||
npy_intp innerloop_shape[resnd];
|
||
for (int ax = 0; ax < resnd; ++ax) {
|
||
innerloop_shape[ax] = resultshape[ax];
|
||
}
|
||
/* longest axis will be iterated in the outer (parallelized) loop.
|
||
* Therefore, longest axis, together with saxis and daxis,
|
||
* will not be iterated in the inner loop:
|
||
*/
|
||
innerloop_shape[longest_axis] = 1;
|
||
innerloop_shape[daxis] = 1;
|
||
innerloop_shape[saxis] = 1;
|
||
|
||
// these are the 'strides' passed to the qpms_trans_calculator_get_AB_arrays_ext
|
||
// function, which expects 'const double *' strides, not 'char *' ones.
|
||
const npy_intp dstride = resultstrides[daxis] / sizeof(complex double);
|
||
const npy_intp sstride = resultstrides[saxis] / sizeof(complex double);
|
||
|
||
int errval = 0;
|
||
// TODO here start parallelisation
|
||
//#pragma omp parallel
|
||
{
|
||
npy_intp local_indices[resnd];
|
||
memset(local_indices, 0, sizeof(local_indices));
|
||
int errval_local = 0;
|
||
size_t longi;
|
||
//#pragma omp for
|
||
for(longi = 0; longi < longlen; ++longi) {
|
||
// this might be done also in the inverse order, but this is more
|
||
// 'c-contiguous' way of incrementing the indices
|
||
int ax = resnd - 1;
|
||
while(ax >= 0) {
|
||
/* calculate the correct index/pointer for each array used.
|
||
* This can be further optimized from O(resnd * total size of
|
||
* the result array) to O(total size of the result array), but
|
||
* fick that now
|
||
*/
|
||
const char *r_p = r_data + r_strides[longest_axis] * longi;
|
||
const char *theta_p = theta_data + theta_strides[longest_axis] * longi;
|
||
const char *phi_p = phi_data + phi_strides[longest_axis] * longi;
|
||
const char *r_ge_d_p = r_ge_d_data + r_ge_d_strides[longest_axis] * longi;
|
||
char *A_p = A_data + A_strides[longest_axis] * longi;
|
||
char *B_p = B_data + B_strides[longest_axis] * longi;
|
||
for(int i = 0; i < resnd; ++i) {
|
||
// following two lines are probably not needed, as innerloop_shape is there 1 anyway
|
||
// so if i == daxis, saxis, or longest_axis, local_indices[i] is zero.
|
||
if (i == longest_axis) continue;
|
||
if (daxis == i || saxis == i) continue;
|
||
r_p += r_strides[i] * local_indices[i];
|
||
theta_p += theta_strides[i] * local_indices[i];
|
||
phi_p += phi_strides[i] * local_indices[i];
|
||
A_p += A_strides[i] * local_indices[i];
|
||
B_p += B_strides[i] * local_indices[i];
|
||
}
|
||
|
||
// perform the actual task here
|
||
errval_local |= qpms_trans_calculator_get_AB_arrays_ext(c, (complex double *)A_p,
|
||
(complex double *)B_p,
|
||
dstride, sstride,
|
||
// FIXME change all the _ext function types to npy_... so that
|
||
// these casts are not needed
|
||
*((double *) r_p), *((double *) theta_p), *((double *)phi_p),
|
||
(int)(*((npy_bool *) r_ge_d_p)), J);
|
||
if (errval_local) abort();
|
||
|
||
// increment the last index 'digit' (ax is now resnd-1; we don't have do-while loop in python)
|
||
++local_indices[ax];
|
||
while(local_indices[ax] == innerloop_shape[ax] && ax >= 0) {
|
||
// overflow to the next digit but stop when reached below the last one
|
||
local_indices[ax] = 0;
|
||
local_indices[--ax]++;
|
||
}
|
||
if (ax >= 0) // did not overflow, get back to the lowest index
|
||
ax = resnd - 1;
|
||
}
|
||
}
|
||
errval |= errval_local;
|
||
}
|
||
// FIXME when parallelizing
|
||
// TODO Here end parallelisation
|
||
return errval;
|
||
}
|
||
|
||
|
||
#endif // QPMS_COMPILE_PYTHON_EXTENSIONS
|
||
|