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generalise translations; does not give right values yety 

Former-commit-id: 89262c325c2c2b619d1b5b7b7fd70ef3d02b0c41
This commit is contained in:
Marek Nečada 2018-02-08 05:01:41 +02:00
parent e689df15fd
commit d5f47c1844
8 changed files with 3102 additions and 60 deletions
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1
qpms/test_translations.c
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@ -4,6 +4,7 @@
#include <complex.h> #include <complex.h>
typedef struct { typedef struct {
qpms_normalisation_t norm;
int m, n, mu, nu; int m, n, mu, nu;
sph_t kdlj; sph_t kdlj;
qpms_bessel_t J; qpms_bessel_t J;

8
qpms/test_translations2.c
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@ -4,6 +4,7 @@
#include <complex.h> #include <complex.h>
typedef struct { typedef struct {
qpms_normalisation_t norm;
int m, n, mu, nu; int m, n, mu, nu;
sph_t kdlj; sph_t kdlj;
qpms_bessel_t J; qpms_bessel_t J;
@ -17,14 +18,19 @@ testcase_single_trans_t testcases_Taylor[] = {
int lMax=10; int lMax=10;
int main() { int main() {
qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, QPMS_NORMALIZATION_TAYLOR); qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, QPMS_NORMALISATION_TAYLOR);
for(testcase_single_trans_t *tc = testcases_Taylor; tc->J != QPMS_BESSEL_UNDEF; tc++) { for(testcase_single_trans_t *tc = testcases_Taylor; tc->J != QPMS_BESSEL_UNDEF; tc++) {
if (!tc->n || !tc->nu || tc->n > lMax || tc->nu > lMax ) continue; if (!tc->n || !tc->nu || tc->n > lMax || tc->nu > lMax ) continue;
printf("m=%d, n=%d, mu=%d, nu=%d,\n", tc->m,tc->n,tc->mu,tc->nu); printf("m=%d, n=%d, mu=%d, nu=%d,\n", tc->m,tc->n,tc->mu,tc->nu);
#if 0
complex double A = qpms_trans_single_A_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J); complex double A = qpms_trans_single_A_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double B = qpms_trans_single_B_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J); complex double B = qpms_trans_single_B_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
#else
complex double A = qpms_trans_single_A(QPMS_NORMALISATION_TAYLOR, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double B = qpms_trans_single_B(QPMS_NORMALISATION_TAYLOR,tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
#endif
complex double A2 = qpms_trans_calculator_get_A(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J); complex double A2 = qpms_trans_calculator_get_A(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double B2 = qpms_trans_calculator_get_B(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J); complex double B2 = qpms_trans_calculator_get_B(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
printf("A = %.16f+%.16fj, relerr=%.16f, J=%d\n", printf("A = %.16f+%.16fj, relerr=%.16f, J=%d\n",

61
qpms/test_translations_xu.c Normal file
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@ -0,0 +1,61 @@
#include "translations.h"
#include <stdio.h>
//#include <math.h>
#include <complex.h>
typedef struct {
qpms_normalisation_t norm;
int m, n, mu, nu;
sph_t kdlj;
qpms_bessel_t J;
complex double result_A, result_B;
} testcase_single_trans_t;
testcase_single_trans_t testcases_xu[] = {
#include "testcases_translations_Xu"
};
int lMax=10;
int main() {
qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, QPMS_NORMALISATION_XU);
for(testcase_single_trans_t *tc = testcases_xu; tc->J != QPMS_BESSEL_UNDEF; tc++) {
if (!tc->n || !tc->nu || tc->n > lMax || tc->nu > lMax ) continue;
printf("m=%d, n=%d, mu=%d, nu=%d,\n", tc->m,tc->n,tc->mu,tc->nu);
complex double A = qpms_trans_single_A(QPMS_NORMALISATION_XU,tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double B = qpms_trans_single_B(QPMS_NORMALISATION_XU,tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double A2 = qpms_trans_calculator_get_A(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
complex double B2 = qpms_trans_calculator_get_B(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
printf("A = %.16f+%.16fj, relerr=%.16f, J=%d\n",
creal(A), cimag(A), (0 == cabs(tc->result_A - A)) ? 0 :
cabs(tc->result_A - A)/((cabs(A) < cabs(tc->result_A)) ? cabs(A) : cabs(tc->result_A)),
tc->J);
printf("A' = %.16f+%.16fj, relerr=%.16f, relerr2=%.3e\n",
creal(A2), cimag(A2), (0 == cabs(tc->result_A - A2)) ? 0 :
cabs(tc->result_A - A2)/((cabs(A2) < cabs(tc->result_A)) ? cabs(A2) : cabs(tc->result_A)),
(0 == cabs(A - A2)) ? 0 :
cabs(A - A2)/((cabs(A2) < cabs(A)) ? cabs(A2) : cabs(A))
);
printf("B = %.16f+%.16fj, relerr=%.16f, J=%d\n",
creal(B), cimag(B), (0 == cabs(tc->result_B - B)) ? 0 :
cabs(tc->result_B - B)/((cabs(B) < cabs(tc->result_B)) ? cabs(B) : cabs(tc->result_B)),
tc->J);
printf("B' = %.16f+%.16fj, relerr=%.16f, relerr2=%.3e\n",
creal(B2), cimag(B2), (0 == cabs(tc->result_B - B2)) ? 0 :
cabs(tc->result_B - B2)/((cabs(B2) < cabs(tc->result_B)) ? cabs(B2) : cabs(tc->result_B)),
(0 == cabs(B - B2)) ? 0 :
cabs(B - B2)/((cabs(B2) < cabs(B)) ? cabs(B2) : cabs(B))
);
}
complex double A,B;
// Test of zero R
sph_t kdlj = {0, 1, 2};
int m = -1, n = 1, mu = -1, nu = 1;
qpms_trans_calculator_get_AB_p(c,&A,&B,m,n,mu,nu,kdlj,false,3);
printf("A = %.6e+%.6ej, B = %.6e+%.6ej\n", creal(A),cimag(A),creal(B),cimag(B));
qpms_trans_calculator_free(c);
}

2
qpms/testcases_taylor.REMOVED.git-id
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@ -1 +1 @@
2b61a18b6426306ba80a50ee30339651313fc44f 7f001489805a48cf44317137517740bc40512657

33
qpms/testcases_translations_Xu Normal file
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@ -0,0 +1,33 @@
//{norm, m,n,mu,nu, {kd.r, kd.theta, kd.phi}, J, areal + aimag * I, breal + bimag* I},
// Yu-lin Xu, Journal of computational physics 127, 285–298 (1996), Table II
{QPMS_NORMALISATION_XU, 1,2,1,2, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .40952764e0 + -.37687246e-1 * I, -.95439506e0 + .14571311e0* I},
{QPMS_NORMALISATION_XU, 1,5,2,6, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .42246528e6 + .23079387e6 * I, .24466070e5 + -.44784830e5* I},
{QPMS_NORMALISATION_XU, -2,10,7,15, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .13425435e14 + .62258200e14 * I, .20835862e13 + -.44930709e12* I},
{QPMS_NORMALISATION_XU, 10,20,3,22, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .12643610e58 + .33753591e58 * I, .18943589e57 + -.70959965e56* I},
{QPMS_NORMALISATION_XU, -28,30,29,32, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, -.13928339e-10 + .60669708-10 * I, -.31805959e-13 + -.73019004e-14* I},
{QPMS_NORMALISATION_XU, 22,40,-39,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .34997554e216 + .45574651e216 * I, -.23949371e214 + .18391132e214* I},
{QPMS_NORMALISATION_XU, 5,50,-22,61, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .89567769e226 + -.12101307e227 * I, .50442227e224 + .37334790e224* I},
// Yu-lin Xu, Journal of computational physics 139, 137–165 (1998), Table 12
{QPMS_NORMALISATION_XU, 8,10,-9,12, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3663964990e+35 + -.2762412192e+35 * I, -.8370892023e+32 + -.1110285257e+32* I},
{QPMS_NORMALISATION_XU, 0,10,0,10, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2969682019e+00 + -.1928601440e+18 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, -2,11,3,9, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .7726121583e+12 + .1034255820e+13 * I, .1222239141e+11 + -.9130398908e+10* I},
{QPMS_NORMALISATION_XU, -12,13,10,15, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3290937356e+01 + .1456483748e-01 * I, -.1763167849e-03 + .3983892680e-01* I},
{QPMS_NORMALISATION_XU, -15,16,17,18, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3793897303e-08 + -.1261972860e-07 * I, -.3042702016e-11 + -.9147343290e-12* I},
{QPMS_NORMALISATION_XU, -5,20,5,20, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4040625669e+34 + -.1195269260e+34 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, 10,18,15,22, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, -.6206840651e+36 + -.8308775621e+36 * I, -.3610252125e+35 + .2696938836e+35* I},
{QPMS_NORMALISATION_XU, 10,30,-10,30, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .1807705110e+110 + .2788115866e+110 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, 18,33,20,38, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3343492687e+92 + .5207181338e+92 * I, .1759309957e+91 + -.1129639932e+91* I},
{QPMS_NORMALISATION_XU, -35,36,11,12, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, -.1901528547e-15 + .1197320691e-15 * I, -.1618572254e-18 + -.2570540515e-18* I},
{QPMS_NORMALISATION_XU, 36,36,-38,38, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4146334728e+191 + -.4931584782e+191 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, -35,40,35,40, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, -.6514262216e-05 + .1374854333e-04 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, 32,35,-43,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2762232925e+212 + -.1368895313e+213 * I, .8373862584e+209 + .1689724460e+209* I},
{QPMS_NORMALISATION_XU, 38,42,-39,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, -.2298689786e+235 + .2371029493e+235 * I, .1277697908e+232 + .1238711556e+232* I},
{QPMS_NORMALISATION_XU, -42,42,45,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3488835702e-28 + -.1826524477e-28 * I, .0000000000e+00 + .0000000000e+00* I},
{QPMS_NORMALISATION_XU, -43,45,41,42, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .5178100899e-22 + .1186503822e-21 * I, .3274958627e-25 + -.1429246656e-25* I},
{QPMS_NORMALISATION_XU, 48,50,-30,49, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3393827523e+267 + -.1226717423e+268 * I, -.5718637033e+265 + -.1582113973e+265* I},
{QPMS_NORMALISATION_XU, -72,72,1,3, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .6946365327e-42 + -.1782022552e-41 * I, .1833377882e-43 + .7146549596e-44* I},
{QPMS_NORMALISATION_XU, 42,52,9,81, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3656934399e+271 + .3705813223e+271 * I, -.4499925012e+269 + -.4440572037e+269* I},
{QPMS_NORMALISATION_XU, 18,100,-5,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4118769973e+293 + .7460688240e+293 * I, .5914795871e+291 + -.3265339985e+291* I},
// THE END
{QPMS_NORMALISATION_UNDEF, 0,0,0,0, {0, 0, 0}, QPMS_BESSEL_UNDEF, 0 + 0 * I, 0 + 0* I}

2759
qpms/testcases_translations_Xu.fods Normal file
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File diff suppressed because it is too large Load Diff

290
qpms/translations.c
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@ -14,6 +14,11 @@
* [1] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996) * [1] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996)
*/ */
/*
* GENERAL TODO: use normalised Legendre functions for Kristensson and Taylor conventions directly
* instead of normalising them here (the same applies for csphase).
*/
static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223871; static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223871;
//static const double ln2 = 0.693147180559945309417232121458176568075500134360255254120; //static const double ln2 = 0.693147180559945309417232121458176568075500134360255254120;
@ -68,10 +73,46 @@ int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *
assert(0); assert(0);
} }
// [1], eq. (82) static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
complex double qpms_trans_single_A_Xu(int m, int n, int mu, int nu, sph_t kdlj, int m, int n, int mu, int nu) {
//int csphase = qpms_normalisation_t csphase(norm); // probably not needed here
norm = qpms_normalisation_t_normonly(norm);
switch(norm) {
case QPMS_NORMALISATION_KRISTENSSON:
case QPMS_NORMALISATION_TAYLOR:
return -0.5*(lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
break;
case QPMS_NORMALISATION_XU:
return 0;
break;
default:
abort();
}
}
static inline double qpms_trans_normfac(qpms_normalisation_t norm,
int m, int n, int mu, int nu) {
int csphase = qpms_normalisation_t_csphase(norm); // FIXME USEME TODO
norm = qpms_normalisation_t_normonly(norm);
double normfac = 1.;
switch(norm) {
case QPMS_NORMALISATION_KRISTENSSON:
normfac *= sqrt((nu*(nu+1.))/(n*(n+1.)));
case QPMS_NORMALISATION_TAYLOR:
normfac *= sqrt((2.*n+1)/(2.*nu+1));
break;
case QPMS_NORMALISATION_XU:
break;
default:
abort();
}
return normfac;
}
complex double qpms_trans_single_A(qpms_normalisation_t norm,
int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) { bool r_ge_d, qpms_bessel_t J) {
abort(); // FIXME, THIS IS STILL TAYLOR
if(r_ge_d) J = QPMS_BESSEL_REGULAR; if(r_ge_d) J = QPMS_BESSEL_REGULAR;
double costheta = cos(kdlj.theta); double costheta = cos(kdlj.theta);
@ -108,59 +149,16 @@ complex double qpms_trans_single_A_Xu(int m, int n, int mu, int nu, sph_t kdlj,
complex double presum = exp(exponent); complex double presum = exp(exponent);
presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n); 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( double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1))); double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
return (presum / prenormratio) * sum;
// int csphase = qpms_normalisation_t_csphase(norm); FIXME EITHER TO NORMFAC OR USE HERE
presum *= ipow(n-nu) * (normfac * exp(normlogfac));
return presum * sum;
} }
complex double qpms_trans_single_A_Kristensson(int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) {
abort();// FIXME, THIS IS STILL TAYLOR
if(r_ge_d) J = QPMS_BESSEL_REGULAR;
double costheta = cos(kdlj.theta);
int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
// N.B. -m !!!!!!
double a1q[qmax+1];
int err;
gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
double a1q0 = a1q[0];
if (err) abort();
double leg[gsl_sf_legendre_array_n(n+nu)];
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
complex double bes[n+nu+1];
if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
complex double sum = 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))];
if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
complex double zp = bes[p];
complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
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;
}
complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj, complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) { bool r_ge_d, qpms_bessel_t J) {
if(r_ge_d) J = QPMS_BESSEL_REGULAR; if(r_ge_d) J = QPMS_BESSEL_REGULAR;
@ -207,7 +205,6 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
// [1], eq. (83) // [1], eq. (83)
complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj, complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) { bool r_ge_d, qpms_bessel_t J) {
abort(); // FIXME, this is still Taylor
if(r_ge_d) J = QPMS_BESSEL_REGULAR; if(r_ge_d) J = QPMS_BESSEL_REGULAR;
double costheta = cos(kdlj.theta); double costheta = cos(kdlj.theta);
@ -257,12 +254,71 @@ complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
(4*n)*(n+1)*(n+m+1)); (4*n)*(n+1)*(n+m+1));
// Taylor normalisation v2, proven to be equivalent // Taylor normalisation v2, proven to be equivalent
complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp( complex double prenormratio = ipow(nu-n);
lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
return (presum / prenormratio) * sum; return (presum / prenormratio) * sum;
} }
complex double qpms_trans_single_B(qpms_normalisation_t norm,
int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) {
if(r_ge_d) J = QPMS_BESSEL_REGULAR;
double costheta = cos(kdlj.theta);
int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
int Qmax = gaunt_q_max(-m,n+1,mu,nu);
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 leg[gsl_sf_legendre_array_n(n+nu+1)];
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
complex double bes[n+nu+2];
if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
complex double sum = 0;
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;
complex double zp_ = bes[p+1];
int Pp_order_ = mu-m;
//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
assert(p+1 >= abs(Pp_order_));
double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
complex 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) * zp_ * Pp_);
sum += summandq;
}
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));
double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
// int csphase = qpms_normalisation_t_csphase(norm); FIXME EITHER TO NORMFAC OR USE HERE
presum *= ipow(n-nu) * (exp(normlogfac) * normfac);
return presum * sum;
}
complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj, complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J) { bool r_ge_d, qpms_bessel_t J) {
@ -354,6 +410,105 @@ static inline size_t qpms_trans_calculator_index_yyu(const qpms_trans_calculator
#define SQ(x) ((x)*(x)) #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 //#if 0
static void qpms_trans_calculator_multipliers_A_Taylor( static void qpms_trans_calculator_multipliers_A_Taylor(
complex double *dest, int m, int n, int mu, int nu, int qmax) { complex double *dest, int m, int n, int mu, int nu, int qmax) {
@ -472,9 +627,16 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) { 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) { switch (norm) {
case QPMS_NORMALISATION_TAYLOR: case QPMS_NORMALISATION_TAYLOR:
#ifdef USE_SEPARATE_TAYLOR
qpms_trans_calculator_multipliers_A_Taylor(dest,m,n,mu,nu,qmax); qpms_trans_calculator_multipliers_A_Taylor(dest,m,n,mu,nu,qmax);
return 0; return 0;
break; 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: default:
abort(); abort();
} }
@ -484,9 +646,16 @@ int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex doubl
int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) { 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) { switch (norm) {
case QPMS_NORMALISATION_TAYLOR: case QPMS_NORMALISATION_TAYLOR:
#ifdef USE_SEPARATE_TAYLOR
qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax); qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax);
return 0; return 0;
break; 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: default:
abort(); abort();
} }
@ -586,7 +755,10 @@ complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
// TODO warn? // TODO warn?
return NAN+I*NAN; return NAN+I*NAN;
switch(c->normalisation) { switch(c->normalisation) {
// TODO use normalised legendre functions for Taylor and Kristensson
case QPMS_NORMALISATION_TAYLOR: case QPMS_NORMALISATION_TAYLOR:
case QPMS_NORMALISATION_KRISTENSSON:
case QPMS_NORMALISATION_XU:
{ {
double costheta = cos(kdlj.theta); double costheta = cos(kdlj.theta);
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu, if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
@ -632,6 +804,8 @@ complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
return NAN+I*NAN; return NAN+I*NAN;
switch(c->normalisation) { switch(c->normalisation) {
case QPMS_NORMALISATION_TAYLOR: case QPMS_NORMALISATION_TAYLOR:
case QPMS_NORMALISATION_KRISTENSSON:
case QPMS_NORMALISATION_XU:
{ {
double costheta = cos(kdlj.theta); double costheta = cos(kdlj.theta);
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1, if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
@ -661,6 +835,8 @@ int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
} }
switch(c->normalisation) { switch(c->normalisation) {
case QPMS_NORMALISATION_TAYLOR: case QPMS_NORMALISATION_TAYLOR:
case QPMS_NORMALISATION_KRISTENSSON:
case QPMS_NORMALISATION_XU:
{ {
double costheta = cos(kdlj.theta); double costheta = cos(kdlj.theta);
if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1, if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,

8
qpms/translations.h
View File

@ -7,7 +7,7 @@
#include <stddef.h> #include <stddef.h>
// TODO replace the xplicit "Taylor" functions with general, // TODO replace the xplicit "Taylor" functions with general,
// taking qpms_bessel_t argument. // taking qpms_normalisation_t argument.
complex double qpms_trans_single_A_Taylor(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj, complex double qpms_trans_single_A_Taylor(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J); bool r_ge_d, qpms_bessel_t J);
@ -20,6 +20,12 @@ complex double qpms_trans_single_A_Taylor_ext(qpms_m_t m, qpms_l_t n, qpms_m_t m
complex double qpms_trans_single_B_Taylor_ext(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, double kdlj_r, complex double qpms_trans_single_B_Taylor_ext(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, double kdlj_r,
double kdlj_th, double kdlj_phi, int r_ge_d, int J); double kdlj_th, double kdlj_phi, int r_ge_d, int J);
complex double qpms_trans_single_A(qpms_normalisation_t norm, qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
complex double qpms_trans_single_B(qpms_normalisation_t norm, qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
typedef struct qpms_trans_calculator { typedef struct qpms_trans_calculator {
qpms_normalisation_t normalisation; qpms_normalisation_t normalisation;
qpms_l_t lMax; qpms_l_t lMax;