"fix" the q ranges for the B coefficients in translations.c
Former-commit-id: 17084dd0b57cb4271c67d5d95b7e033c3968276f
This commit is contained in:
Marek Nečada
parent
e231e095c3
commit
4b7797edaf
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@ -4,6 +4,11 @@
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//#include <math.h>
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#include <complex.h>
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#ifdef QPMS_PACKED_B_MULTIPLIERS
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#define BQ_OFFSET 1
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#else
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#define BQ_OFFSET 0
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#endif
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void qpms_trans_calculator_multipliers_B_general(
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qpms_normalisation_t norm,
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@ -13,6 +18,7 @@ int lMax=13;
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#define MIN(x,y) ((x)<(y)?(x):(y))
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// Python test: Qmax(M, n, mu, nu) = floor(min(n,nu,(n+nu+1-abs(M+mu))/2))
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// q in IntegerRange(1, Qmax(-m,n,mu,nu))
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@ -24,15 +30,14 @@ int main() {
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for(int nu = 1; nu <= lMax; ++nu)
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for(int m = -n; m <= n; ++m)
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for(int mu = -nu; mu <= nu; ++mu){
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int Qmax = gaunt_q_max(-m, n+1, mu, nu);
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int Qmax_alt = MIN(n,MIN(nu,(n+nu+1-abs(mu-m))));
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int Qmax_alt = MIN(n,MIN(nu,(n+nu+1-abs(mu-m))/2));
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qpms_trans_calculator_multipliers_B_general(QPMS_NORMALISATION_XU_CS,
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dest, m, n, mu, nu, Qmax);
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for(int q = 0; q <= Qmax; ++q) {
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dest, m, n, mu, nu, Qmax_alt);
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for(int q = BQ_OFFSET; q <= Qmax_alt; ++q) {
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// int p = n + nu - 2*q;
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int tubig = cabs(dest[q]) > 1e-8;
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int tubig = cabs(dest[q-BQ_OFFSET]) > 1e-8;
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printf("%.16g + %.16g*I, // %d, %d, %d, %d, %d,%s\n",
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creal(dest[q]), cimag(dest[q]), m, n, mu, nu, q,
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creal(dest[q-BQ_OFFSET]), cimag(dest[q-BQ_OFFSET]), m, n, mu, nu, q,
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q > Qmax_alt ? (tubig?" //tubig":" //tu") : "");
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}
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fflush(stdout);
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@ -9,9 +9,19 @@
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#include "assert_cython_workaround.h"
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#include <stdlib.h> //abort()
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// if defined, the pointer B_multipliers[y] corresponds to the q = 1 element;
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// otherwise, it corresponds to the q = 0 element, which should be identically zero
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#ifdef QPMS_PACKED_B_MULTIPLIERS
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#define BQ_OFFSET 1
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#else
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#define BQ_OFFSET 0
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#endif
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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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* [Xu_old] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996)
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* [Xu] Yu-Lin Xu, Journal of Computational Physics 139, 137–165 (1998)
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*/
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/*
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@ -40,6 +50,19 @@ 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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static inline int imin(int x, int y) {
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return x > y ? y : x;
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}
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// The uppermost value of q index for the B coefficient terms from [Xu](60).
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// N.B. this is different from [Xu_old](79) due to the n vs. n+1 difference.
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// However, the trailing terms in [Xu_old] are analytically zero (although
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// the numerical values will carry some non-zero rounding error).
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static inline int gauntB_Q_max(int M, int n, int mu, int nu) {
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return imin(n, imin(nu, (n+nu+1-abs(M+mu))/2));
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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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@ -202,14 +225,16 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
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return (presum / prenormratio) * sum;
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}
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// [1], eq. (83)
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// [Xu_old], 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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// TODO Qmax cleanup: can I replace Qmax with realQmax???
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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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int realQmax = gauntB_Q_max(-m, n, 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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@ -230,7 +255,7 @@ complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
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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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for (int q = 0; q <= realQmax; ++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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@ -267,6 +292,7 @@ complex double qpms_trans_single_B(qpms_normalisation_t norm,
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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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int realQmax = gauntB_Q_max(-m,n,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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@ -288,7 +314,7 @@ complex double qpms_trans_single_B(qpms_normalisation_t norm,
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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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for (int q = 0; q <= realQmax; ++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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@ -327,6 +353,7 @@ complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kd
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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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int realQmax = gauntB_Q_max(-m,n,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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@ -347,7 +374,7 @@ complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kd
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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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for (int q = 0; q <= realQmax; ++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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@ -453,14 +480,13 @@ static void qpms_trans_calculator_multipliers_A_general(
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}
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static void qpms_trans_calculator_multipliers_B_general(
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/*static*/ void qpms_trans_calculator_multipliers_B_general(
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qpms_normalisation_t norm,
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complex double *dest, int m, int n, int mu, int nu, int Qmax) {
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assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
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assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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assert(Qmax == q2max);
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// FIXME remove the q2max variable altogether, as it is probably equal
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// to Qmax
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// assert(Qmax == q2max);
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// FIXME is it safe to replace q2max with Qmax in gaunt_xu??
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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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@ -472,7 +498,7 @@ static void qpms_trans_calculator_multipliers_B_general(
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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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gaunt_xu(-m,n+1,mu,nu,q2max,a3q,&err); if (err) abort(); // FIXME this should probably go away
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a3q0 = a3q[0];
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@ -494,7 +520,7 @@ static void qpms_trans_calculator_multipliers_B_general(
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presum *= I * ipow(nu+n) /*different from old Taylor */ * normfac / (
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(4*n)*(n+1)*(n+m+1));
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for (int q = 0; q <= Qmax; ++q) {
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for (int q = BQ_OFFSET; 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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@ -507,7 +533,7 @@ static void qpms_trans_calculator_multipliers_B_general(
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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));
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dest[q] = Ppfac * summandq * presum;
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dest[q-BQ_OFFSET] = Ppfac * summandq * presum;
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}
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}
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@ -581,12 +607,12 @@ static void qpms_trans_calculator_multipliers_A_Taylor(
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static void qpms_trans_calculator_multipliers_B_Taylor(
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complex double *dest, int m, int n, int mu, int nu, int Qmax) {
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assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
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assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
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int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
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assert(Qmax == q2max);
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//assert(Qmax == q2max);
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// FIXME remove the q2max variable altogether, as it is probably equal
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// to Qmax
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double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
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double a2q[q2max+1], a3q[q2max+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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@ -597,7 +623,7 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
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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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gaunt_xu(-m,n+1,mu,nu,q2max,a3q,&err); if (err) abort();
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a3q0 = a3q[0];
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double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
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@ -609,7 +635,7 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
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presum *= I * (min1pow(m+n) *sqrt((2.*n+1)/(2.*nu+1)) / (
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(4*n)*(n+1)*(n+m+1)));
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for (int q = 0; q <= Qmax; ++q) {
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for (int q = BQ_OFFSET; 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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@ -622,7 +648,7 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
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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));
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dest[q] = Ppfac * summandq * presum;
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dest[q-BQ_OFFSET] = Ppfac * summandq * presum;
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}
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}
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@ -645,17 +671,17 @@ int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex doubl
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assert(0);
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}
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int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
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int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int Qmax) {
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switch (qpms_normalisation_t_normonly(norm)) {
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case QPMS_NORMALISATION_TAYLOR:
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#ifdef USE_SEPARATE_TAYLOR
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qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax);
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qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,Qmax);
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return 0;
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break;
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#endif
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case QPMS_NORMALISATION_XU:
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case QPMS_NORMALISATION_KRISTENSSON:
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qpms_trans_calculator_multipliers_B_general(norm, dest, m, n, mu, nu, qmax);
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qpms_trans_calculator_multipliers_B_general(norm, dest, m, n, mu, nu, Qmax);
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return 0;
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break;
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default:
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@ -705,14 +731,14 @@ qpms_trans_calculator
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int m, n, mu, nu;
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qpms_y2mn_p(y,&m,&n);
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qpms_y2mn_p(yu,&mu,&nu);
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qmaxsum += 1 + (
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qmaxsum += (1 - BQ_OFFSET) + (
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qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
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= gaunt_q_max(-m,n+1,mu,nu));
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= gauntB_Q_max(-m,n,mu,nu));
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}
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c->B_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
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// calculate multiplier beginnings
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for(size_t i = 0; i < SQ(c->nelem); ++i)
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c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i] + 1;
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c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i] + (1 - BQ_OFFSET);
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// calculate the multipliers
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for(size_t y = 0; y < c->nelem; ++y)
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for(size_t yu = 0; yu < c->nelem; ++yu) {
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@ -782,14 +808,14 @@ static inline complex double qpms_trans_calculator_get_B_precalcbuf(const qpms_t
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bool r_ge_d, qpms_bessel_t J,
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const complex double *bessel_buf, const double *legendre_buf) {
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size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
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size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
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assert(qmax == gaunt_q_max(-m,n+1,mu,nu));
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size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - (1 - BQ_OFFSET);
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assert(qmax == gauntB_Q_max(-m,n,mu,nu));
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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for(int q = BQ_OFFSET; q <= qmax; ++q) {
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int p = n+nu-2*q;
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double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
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complex double zp_ = bessel_buf[p+1];
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complex double multiplier = c->B_multipliers[i][q];
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complex double multiplier = c->B_multipliers[i][q-BQ_OFFSET];
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sum += Pp_ * zp_ * multiplier;
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}
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complex double eimf = cexp(I*(mu-m)*kdlj.phi);
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