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Ewald 1D in 3D: jdu spát
[qpms.git] / qpms / translations.c
blob118bc280f6e2be70fbef4d7318f4dedb26ef9104
1 #include <math.h>
2 #include "qpms_types.h"
3 #include "qpms_specfunc.h"
4 #include "gaunt.h"
5 #include "translations.h"
6 #include "indexing.h" // TODO replace size_t and int with own index types here
7 #include <stdbool.h>
8 #include <gsl/gsl_sf_legendre.h>
9 #include <gsl/gsl_sf_bessel.h>
10 #include "tiny_inlines.h"
11 #include "assert_cython_workaround.h"
12 #include "kahansum.h"
13 #include <gsl/gsl_sf_coupling.h>
14 #include "qpms_error.h"
15 #include "normalisation.h"
16 #include "translations_inlines.h"
17
18 /*
19 * Define macros with additional factors that "should not be there" according
20 * to the "original" formulae but are needed to work with my vswfs.
21 * (actually, I don't know whether the error is in using "wrong" implementation
22 * of vswfs, "wrong" implementation of Xu's translation coefficient formulae,
23 * error/inconsintency in Xu's paper or something else)
24 * Anyway, the zeroes give the correct _numerical_ values according to Xu's
25 * paper tables (without Xu's typos, of course), while
26 * the predefined macros give the correct translations of the VSWFs for the
27 * QPMS_NORMALIZATION_TAYLOR_CS norm.
28 */
29 #if !(defined AN0 || defined AN1 || defined AN2 || defined AN3)
30 #pragma message "using AN1 macro as default"
31 #define AN1
32 #endif
33 //#if !(defined AM0 || defined AM2)
34 //#define AM1
35 //#endif
36 #if !(defined BN0 || defined BN1 || defined BN2 || defined BN3)
37 #pragma message "using BN1 macro as default"
38 #define BN1
39 #endif
40 //#if !(defined BM0 || defined BM2)
41 //#define BM1
42 //#endif
43 //#if !(defined BF0 || defined BF1 || defined BF2 || defined BF3)
44 //#define BF1
45 //#endif
46
47 // if defined, the pointer B_multipliers[y] corresponds to the q = 1 element;
48 // otherwise, it corresponds to the q = 0 element, which should be identically zero
49 #ifdef QPMS_PACKED_B_MULTIPLIERS
50 #define BQ_OFFSET 1
51 #else
52 #define BQ_OFFSET 0
53 #endif
54
55
56 // Translation operators for real sph. harm. based waves are not yet implemented...
57 static inline void TROPS_ONLY_EIMF_IMPLEMENTED(qpms_normalisation_t norm) {
58 if (norm & (QPMS_NORMALISATION_SPHARM_REAL | QPMS_NORMALISATION_REVERSE_AZIMUTHAL_PHASE))
59 QPMS_NOT_IMPLEMENTED("Translation operators for real or inverse complex spherical harmonics based waves are not implemented.");
60 }
61
62 // Use if only the symmetric form [[A, B], [B, A]] (without additional factors) of translation operator is allowed.
63 static inline void TROPS_ONLY_AB_SYMMETRIC_NORMS_IMPLEMENTED(qpms_normalisation_t norm) {
64 switch (norm & QPMS_NORMALISATION_NORM_BITS) {
65 case QPMS_NORMALISATION_NORM_SPHARM:
66 case QPMS_NORMALISATION_NORM_POWER:
67 break; // OK
68 default:
69 QPMS_NOT_IMPLEMENTED("Only spherical harmonic and power normalisation supported.");
70 }
71 if (
72 ( !(norm & QPMS_NORMALISATION_N_I) != !(norm & QPMS_NORMALISATION_M_I) )
73 ||
74 ( !(norm & QPMS_NORMALISATION_N_MINUS) != !(norm & QPMS_NORMALISATION_M_MINUS) )
75 )
76 QPMS_NOT_IMPLEMENTED("Only normalisations without a phase factors between M and N waves are supported.");
77 }
78
79
80 /*
81 * References:
82 * [Xu_old] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996)
83 * [Xu] Yu-Lin Xu, Journal of Computational Physics 139, 137–165 (1998)
84 */
85
86 /*
87 * GENERAL TODO: use normalised Legendre functions for Kristensson and Taylor conventions directly
88 * instead of normalising them here (the same applies for csphase).
89 */
90
91 static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223871;
92 //static const double ln2 = 0.693147180559945309417232121458176568075500134360255254120;
93
94 // Associated Legendre polynomial at zero argument (DLMF 14.5.1)
95 double qpms_legendre0(int m, int n) {
96 return pow(2,m) * sqrtpi / tgamma(.5*n - .5*m + .5) / tgamma(.5*n-.5*m);
97 }
98
99 // Derivative of associated Legendre polynomial at zero argument (DLMF 14.5.2)
100 double qpms_legendreD0(int m, int n) {
101 return -2 * qpms_legendre0(m, n);
102 }
103
104
105 static inline int imin(int x, int y) {
106 return x > y ? y : x;
107 }
108
109 // The uppermost value of q index for the B coefficient terms from [Xu](60).
110 // N.B. this is different from [Xu_old](79) due to the n vs. n+1 difference.
111 // However, the trailing terms in [Xu_old] are analytically zero (although
112 // the numerical values will carry some non-zero rounding error).
113 static inline int gauntB_Q_max(int M, int n, int mu, int nu) {
114 return imin(n, imin(nu, (n+nu+1-abs(M+mu))/2));
115 }
116
117 static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
118 int m, int n, int mu, int nu) {
119 return -0.5*(lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
120 }
121
122 static inline double qpms_trans_normfac(qpms_normalisation_t norm,
123 int m, int n, int mu, int nu) {
124 int csphase = qpms_normalisation_t_csphase(norm);
125 /* Account for csphase here. Alternatively, this could be done by
126 * using appropriate csphase in the legendre polynomials when calculating
127 * the translation operator.
128 */
129 double normfac = (1 == csphase) ? min1pow(m-mu) : 1.;
130 normfac *= sqrt((n*(n+1.))/(nu*(nu+1.)));
131 normfac *= sqrt((2.*n+1)/(2.*nu+1));
132 return normfac;
133 }
134
135 complex double qpms_trans_single_A(qpms_normalisation_t norm,
136 int m, int n, int mu, int nu, csph_t kdlj,
137 bool r_ge_d, qpms_bessel_t J) {
138 TROPS_ONLY_EIMF_IMPLEMENTED(norm);
139 if(r_ge_d) J = QPMS_BESSEL_REGULAR;
140
141 double costheta = cos(kdlj.theta);
142
143 int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
144 // N.B. -m !!!!!!
145 double a1q[qmax+1];
146 int err;
147 gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
148 QPMS_ENSURE_SUCCESS(err);
149 double a1q0 = a1q[0];
150
151 double leg[gsl_sf_legendre_array_n(n+nu)];
152 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg));
153 complex double bes[n+nu+1];
154 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes));
155 complex double sum = 0;
156 for(int q = 0; q <= qmax; ++q) {
157 int p = n+nu-2*q;
158 int Pp_order = mu-m;
159 //if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
160 assert(p >= abs(Pp_order));
161 double a1q_n = a1q[q] / a1q0;
162 double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
163 if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
164 complex double zp = bes[p];
165 complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
166 sum += summandq; // TODO KAHAN
167 }
168
169 double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
170 +lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
171 +lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
172 complex double presum = exp(exponent);
173 presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
174
175 double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
176 double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
177 /// N<-N type coefficients w.r.t. Kristensson's convention. Csphase has been already taken into acct ^^^.
178 normfac *= qpms_normalisation_factor_N_noCS(norm, nu, mu)
179 / qpms_normalisation_factor_N_noCS(norm, n, m);
180 // ipow(n-nu) is the difference from the Taylor formula!
181 presum *= /*ipow(n-nu) * */
182 (normfac * exp(normlogfac))
183 #ifdef AN1
184 * ipow(n-nu)
185 #elif defined AN2
186 * min1pow(-n+nu)
187 #elif defined AN3
188 * ipow (nu - n)
189 #endif
190 #ifdef AM1
191 * ipow(-m+mu)
192 #endif //NNU
193 #ifdef AM2
194 * min1pow(-m+mu)
195 #endif //NNU
196 #ifdef AM3
197 * ipow(m-mu)
198 #endif //NNU
199 ;
200 return presum * sum;
201 }
202
203
204 complex double qpms_trans_single_B(qpms_normalisation_t norm,
205 int m, int n, int mu, int nu, csph_t kdlj,
206 bool r_ge_d, qpms_bessel_t J) {
207 TROPS_ONLY_EIMF_IMPLEMENTED(norm);
208 if(r_ge_d) J = QPMS_BESSEL_REGULAR;
209 double costheta = cos(kdlj.theta);
210
211 int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
212 int Qmax = gaunt_q_max(-m,n+1,mu,nu);
213 int realQmax = gauntB_Q_max(-m,n,mu,nu);
214 double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
215 int err;
216 if (mu == nu) {
217 for (int q = 0; q <= q2max; ++q)
218 a2q[q] = 0;
219 a2q0 = 1;
220 }
221 else {
222 gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err);
223 QPMS_ENSURE_SUCCESS(err);
224 a2q0 = a2q[0];
225 }
226 gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err);
227 QPMS_ENSURE_SUCCESS(err);
228 a3q0 = a3q[0];
229
230 double leg[gsl_sf_legendre_array_n(n+nu+1)];
231 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg));
232 complex double bes[n+nu+2];
233 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes));
234
235 complex double sum = 0;
236 for (int q = 0; q <= realQmax; ++q) {
237 int p = n+nu-2*q;
238 double a2q_n = a2q[q]/a2q0;
239 double a3q_n = a3q[q]/a3q0;
240 complex double zp_ = bes[p+1];
241 int Pp_order_ = mu-m;
242 //if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
243 assert(p+1 >= abs(Pp_order_));
244 double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
245 if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
246 complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
247 -(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
248 *min1pow(q) * zp_ * Pp_);
249 sum += summandq; //TODO KAHAN
250 }
251
252 double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
253 +lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
254 +lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
255 complex double presum = exp(exponent);
256 presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
257 (4*n)*(n+1)*(n+m+1));
258
259 double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
260 double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
261 /// N<-M type coefficients w.r.t. Kristensson's convention. Csphase has been already taken into acct ^^^.
262 normfac *= qpms_normalisation_factor_M_noCS(norm, nu, mu)
263 / qpms_normalisation_factor_N_noCS(norm, n, m);
264
265 // ipow(n-nu) is the difference from the "old Taylor" formula
266 presum *= /*ipow(n-nu) * */(exp(normlogfac) * normfac)
267 #ifdef AN1
268 * ipow(n-nu)
269 #elif defined AN2
270 * min1pow(-n+nu)
271 #elif defined AN3
272 * ipow (nu - n)
273 #endif
274 #ifdef AM1
275 * ipow(-m+mu)
276 #endif //NNU
277 #ifdef AM2
278 * min1pow(-m+mu)
279 #endif //NNU
280 #ifdef AM3
281 * ipow(m-mu)
282 #endif //NNU
283 ;
284
285 return presum * sum;
286 }
287
288 void qpms_trans_calculator_free(qpms_trans_calculator *c) {
289 free(c->A_multipliers[0]);
290 free(c->A_multipliers);
291 free(c->B_multipliers[0]);
292 free(c->B_multipliers);
293 #ifdef LATTICESUMS32
294 qpms_ewald3_constants_free(c->e3c);
295 #endif
296 free(c->legendre0);
297 free(c);
298 }
299
300 static inline size_t qpms_trans_calculator_index_mnmunu(const qpms_trans_calculator *c,
301 int m, int n, int mu, int nu){
302 return c->nelem * qpms_mn2y(m,n) + qpms_mn2y(mu,nu);
303 }
304
305 static inline size_t qpms_trans_calculator_index_yyu(const qpms_trans_calculator *c,
306 size_t y, size_t yu) {
307 return c->nelem * y + yu;
308 }
309
310
311 static inline double fsq(double x) {return x * x; }
312
313 static void qpms_trans_calculator_multipliers_A(
314 qpms_normalisation_t norm,
315 complex double *dest, int m, int n, int mu, int nu, int qmax) {
316 assert(qmax == gaunt_q_max(-m,n,mu,nu));
317 double a1q[qmax+1];
318 int err;
319 gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
320 QPMS_ENSURE_SUCCESS(err);
321 double a1q0 = a1q[0];
322
323 double normlogfac = qpms_trans_normlogfac(norm,m,n,mu,nu);
324 double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
325 /// N<-N type coefficients w.r.t. Kristensson's convention. Csphase has been already taken into acct ^^^.
326 normfac *= qpms_normalisation_factor_N_noCS(norm, nu, mu)
327 / qpms_normalisation_factor_N_noCS(norm, n, m);
328
329 normfac *= min1pow(m); //different from old Taylor
330
331 double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
332 +lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
333 +lgamma(n+nu+1) - lgamma(2*(n+nu)+1))
334 + normlogfac;
335 complex double presum = exp(exponent);
336 presum *= normfac / (4.*n);
337 presum *= ipow(n+nu); // different from old Taylor
338
339 for(int q = 0; q <= qmax; q++) {
340 int p = n+nu-2*q;
341 int Pp_order = mu - m;
342 assert(p >= abs(Pp_order));
343 double a1q_n = a1q[q] / a1q0;
344 // Assuming non_normalized legendre polynomials (normalisation done here by hand)!
345 double Ppfac = (Pp_order >= 0) ? 1 :
346 min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
347 double summandfac = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n;
348 dest[q] = presum * summandfac * Ppfac
349 #ifdef AN1
350 * ipow(n-nu)
351 #elif defined AN2
352 * min1pow(-n+nu)
353 #elif defined AN3
354 * ipow (nu - n)
355 #endif
356 #ifdef AM1
357 * ipow(-m+mu)
358 #endif //NNU
359 #ifdef AM2
360 * min1pow(-m+mu)
361 #endif //NNU
362 #ifdef AM3
363 * ipow(m-mu)
364 #endif //NNU
365 ;
366 // FIXME I might not need complex here
367 }
368 }
369
370
371 // as in [Xu](61)
372 static double cruzan_bfactor(int M, int n, int mu, int nu, int p) {
373 double logprefac = lgamma(n+M+1) - lgamma(n-M+1) + lgamma(nu+mu+1) - lgamma(nu-mu+1)
374 + lgamma(p-M-mu+2) - lgamma(p+M+mu+2);
375 logprefac *= 0.5;
376 return min1pow(mu+M) * (2*p+3) * exp(logprefac)
377 * gsl_sf_coupling_3j(2*n, 2*nu, 2*(p+1), 2*M, 2*mu, 2*(-M-mu))
378 * gsl_sf_coupling_3j(2*n, 2*nu, 2*p, 0, 0, 0);
379 }
380
381
382 void qpms_trans_calculator_multipliers_B(
383 qpms_normalisation_t norm,
384 complex double *dest, int m, int n, int mu, int nu, int Qmax){
385 // This is according to the Cruzan-type formula [Xu](59)
386 assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
387
388 double normlogfac= qpms_trans_normlogfac(norm,m,n,mu,nu);
389 double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
390 /// N<-M type coefficients w.r.t. Kristensson's convention. Csphase has been already taken into acct ^^^.
391 normfac *= qpms_normalisation_factor_M_noCS(norm, nu, mu)
392 / qpms_normalisation_factor_N_noCS(norm, n, m);
393
394 double presum = min1pow(1-m) * (2*nu+1)/(2.*(n*(n+1)))
395 * exp(lgamma(n+m+1) - lgamma(n-m+1) + lgamma(nu-mu+1) - lgamma(nu+mu+1)
396 + normlogfac)
397 * normfac;
398
399 for(int q = BQ_OFFSET; q <= Qmax; ++q) {
400 int p = n+nu-2*q;
401 int Pp_order = mu - m;
402 // Assuming non-normalised Legendre polynomials, normalise here by hand.
403 // Ppfac_ differs from Ppfac in the A-case by the substitution p->p+1
404 double Ppfac_ = (Pp_order >= 0)? 1 :
405 min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order)-lgamma(1+1+p-Pp_order));
406 double t = sqrt(
407 (isq(p+1)-isq(n-nu))
408 * (isq(n+nu+1)-isq(p+1))
409 );
410 dest[q-BQ_OFFSET] = presum * t * Ppfac_
411 * cruzan_bfactor(-m,n,mu,nu,p) * ipow(p+1)
412 #ifdef BN1
413 * ipow(n-nu)
414 #elif defined BN2
415 * min1pow(-n+nu)
416 #elif defined BN3
417 * ipow (nu - n)
418 #endif
419 #ifdef BM1
420 * ipow(-m+mu)
421 #endif
422 #ifdef BM2
423 * min1pow(-m+mu)
424 #endif
425 #ifdef BM3
426 * ipow(m-mu)
427 #endif
428 #ifdef BF1
429 * I
430 #elif defined BF2
431 * (-1)
432 #elif defined BF3
433 * (-I)
434 #endif
435 ;// NNU
436 }
437 }
438
439 qpms_trans_calculator
440 *qpms_trans_calculator_init (const int lMax, const qpms_normalisation_t normalisation) {
441 TROPS_ONLY_EIMF_IMPLEMENTED(normalisation);
442 assert(lMax > 0);
443 qpms_trans_calculator *c = malloc(sizeof(qpms_trans_calculator));
444 c->lMax = lMax;
445 c->nelem = lMax * (lMax+2);
446 c->A_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
447 c->B_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
448 c->normalisation = normalisation;
449 size_t *qmaxes = malloc(SQ(c->nelem) * sizeof(size_t));
450 size_t qmaxsum = 0;
451 for(size_t y = 0; y < c->nelem; y++)
452 for(size_t yu = 0; yu < c->nelem; yu++) {
453 int m,n, mu, nu;
454 qpms_y2mn_p(y,&m,&n);
455 qpms_y2mn_p(yu,&mu,&nu);
456 qmaxsum += 1 + (
457 qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
458 = gaunt_q_max(-m,n,mu,nu));
459 }
460 c->A_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
461 // calculate multiplier beginnings
462 for(size_t i = 0; i < SQ(c->nelem); ++i)
463 c->A_multipliers[i+1] = c->A_multipliers[i] + qmaxes[i] + 1;
464 // calculate the multipliers
465 for(size_t y = 0; y < c->nelem; ++y)
466 for(size_t yu = 0; yu < c->nelem; ++yu) {
467 size_t i = y * c->nelem + yu;
468 int m, n, mu, nu;
469 qpms_y2mn_p(y, &m, &n);
470 qpms_y2mn_p(yu, &mu, &nu);
471 qpms_trans_calculator_multipliers_A(normalisation,
472 c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
473 }
474
475 qmaxsum = 0;
476 for(size_t y=0; y < c->nelem; y++)
477 for(size_t yu = 0; yu < c->nelem; yu++) {
478 int m, n, mu, nu;
479 qpms_y2mn_p(y,&m,&n);
480 qpms_y2mn_p(yu,&mu,&nu);
481 qmaxsum += (1 - BQ_OFFSET) + (
482 qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)]
483 = gauntB_Q_max(-m,n,mu,nu));
484 }
485 c->B_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
486 // calculate multiplier beginnings
487 for(size_t i = 0; i < SQ(c->nelem); ++i)
488 c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i] + (1 - BQ_OFFSET);
489 // calculate the multipliers
490 for(size_t y = 0; y < c->nelem; ++y)
491 for(size_t yu = 0; yu < c->nelem; ++yu) {
492 size_t i = y * c->nelem + yu;
493 int m, n, mu, nu;
494 qpms_y2mn_p(y, &m, &n);
495 qpms_y2mn_p(yu, &mu, &nu);
496 qpms_trans_calculator_multipliers_B(normalisation,
497 c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
498 }
499
500 free(qmaxes);
501 #ifdef LATTICESUMS32
502 c->e3c = qpms_ewald3_constants_init(2 * lMax + 1, /*csphase*/ qpms_normalisation_t_csphase(normalisation));
503 #endif
504 c->legendre0 = malloc(gsl_sf_legendre_array_n(2*lMax+1) * sizeof(double));
505 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,2*lMax+1,
506 0,-1,c->legendre0)); // TODO maybe use some "precise" analytical formula instead?
507 return c;
508 }
509
510 static inline complex double qpms_trans_calculator_get_A_precalcbuf(const qpms_trans_calculator *c,
511 int m, int n, int mu, int nu, double kdlj_phi,
512 const complex double *bessel_buf, const double *legendre_buf) {
513 TROPS_ONLY_EIMF_IMPLEMENTED(c->normalisation);
514 size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
515 size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
516 assert(qmax == gaunt_q_max(-m,n,mu,nu));
517 complex double sum, kahanc;
518 ckahaninit(&sum, &kahanc);
519 for(size_t q = 0; q <= qmax; ++q) {
520 int p = n+nu-2*q;
521 double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
522 complex double zp = bessel_buf[p];
523 complex double multiplier = c->A_multipliers[i][q];
524 ckahanadd(&sum, &kahanc, Pp * zp * multiplier);
525 }
526 complex double eimf = cexp(I*(mu-m)*kdlj_phi);
527 return sum * eimf;
528 }
529
530 complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
531 int m, int n, int mu, int nu, csph_t kdlj,
532 bool r_ge_d, qpms_bessel_t J,
533 complex double *bessel_buf, double *legendre_buf) {
534 // This functions gets preallocated memory for bessel and legendre functions, but computes them itself
535 if (r_ge_d) J = QPMS_BESSEL_REGULAR;
536 if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
537 // TODO warn?
538 return NAN+I*NAN;
539 int csphase = qpms_normalisation_t_csphase(c->normalisation);
540
541 double costheta = cos(kdlj.theta);
542 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
543 costheta,csphase,legendre_buf));
544 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bessel_buf));
545 return qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
546 kdlj.phi,bessel_buf,legendre_buf);
547 }
548
549 static inline complex double qpms_trans_calculator_get_B_precalcbuf(const qpms_trans_calculator *c,
550 int m, int n, int mu, int nu, double kdlj_phi,
551 const complex double *bessel_buf, const double *legendre_buf) {
552 TROPS_ONLY_EIMF_IMPLEMENTED(c->normalisation);
553 size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
554 size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - (1 - BQ_OFFSET);
555 assert(qmax == gauntB_Q_max(-m,n,mu,nu));
556 complex double sum, kahanc;
557 ckahaninit(&sum, &kahanc);
558 for(int q = BQ_OFFSET; q <= qmax; ++q) {
559 int p = n+nu-2*q;
560 double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
561 complex double zp_ = bessel_buf[p+1];
562 complex double multiplier = c->B_multipliers[i][q-BQ_OFFSET];
563 ckahanadd(&sum, &kahanc, Pp_ * zp_ * multiplier);
564 }
565 complex double eimf = cexp(I*(mu-m)*kdlj_phi);
566 return sum * eimf;
567 }
568
569 complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
570 int m, int n, int mu, int nu, csph_t kdlj,
571 bool r_ge_d, qpms_bessel_t J,
572 complex double *bessel_buf, double *legendre_buf) {
573 // This functions gets preallocated memory for bessel and legendre functions, but computes them itself
574 if (r_ge_d) J = QPMS_BESSEL_REGULAR;
575 if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
576 // TODO warn?
577 return NAN+I*NAN;
578 int csphase = qpms_normalisation_t_csphase(c->normalisation);
579 double costheta = cos(kdlj.theta);
580 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
581 costheta,csphase,legendre_buf));
582 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bessel_buf));
583 return qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
584 kdlj.phi,bessel_buf,legendre_buf);
585 }
586
587 int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
588 complex double *Adest, complex double *Bdest,
589 int m, int n, int mu, int nu, csph_t kdlj,
590 bool r_ge_d, qpms_bessel_t J,
591 complex double *bessel_buf, double *legendre_buf) {
592 if (r_ge_d) J = QPMS_BESSEL_REGULAR;
593 if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR) {
594 *Adest = NAN+I*NAN;
595 *Bdest = NAN+I*NAN;
596 // TODO warn? different return value?
597 return 0;
598 }
599 double costheta = cos(kdlj.theta);
600 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
601 costheta,-1,legendre_buf));
602 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bessel_buf));
603 *Adest = qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
604 kdlj.phi,bessel_buf,legendre_buf);
605 *Bdest = qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
606 kdlj.phi,bessel_buf,legendre_buf);
607 return 0;
608 }
609
610 int qpms_trans_calculator_get_AB_arrays_precalcbuf(const qpms_trans_calculator *c,
611 complex double *Adest, complex double *Bdest,
612 size_t deststride, size_t srcstride, double kdlj_phi,
613 const complex double *bessel_buf, const double *legendre_buf) {
614 size_t desti = 0, srci = 0;
615 for (int n = 1; n <= c->lMax; ++n) for (int m = -n; m <= n; ++m) {
616 for (int nu = 1; nu <= c->lMax; ++nu) for (int mu = -nu; mu <= nu; ++mu) {
617 #ifndef NDEBUG
618 size_t assertindex = qpms_trans_calculator_index_mnmunu(c,m,n,mu,nu);
619 #endif
620 assert(assertindex == desti*c->nelem + srci);
621 *(Adest + deststride * desti + srcstride * srci) =
622 qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
623 kdlj_phi, bessel_buf, legendre_buf);
624 *(Bdest + deststride * desti + srcstride * srci) =
625 qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
626 kdlj_phi,bessel_buf,legendre_buf);
627 ++srci;
628 }
629 ++desti;
630 srci = 0;
631 }
632 return 0;
633 }
634
635 int qpms_trans_calculator_get_AB_arrays_buf(const qpms_trans_calculator *c,
636 complex double *Adest, complex double *Bdest,
637 size_t deststride, size_t srcstride,
638 csph_t kdlj, bool r_ge_d, qpms_bessel_t J,
639 complex double *bessel_buf, double *legendre_buf) {
640 if (r_ge_d) J = QPMS_BESSEL_REGULAR;
641 if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR) {
642 for (size_t i = 0; i < c->nelem; ++i)
643 for (size_t j = 0; j < c->nelem; ++j) {
644 *(Adest + i*srcstride + j*deststride) = NAN+I*NAN;
645 *(Bdest + i*srcstride + j*deststride) = NAN+I*NAN;
646 }
647 // TODO warn? different return value?
648 return 0;
649 }
650 {
651 double costheta = cos(kdlj.theta);
652 QPMS_ENSURE_SUCCESS(gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,2*c->lMax+1,
653 costheta,-1,legendre_buf));
654 QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J, 2*c->lMax+1, kdlj.r, bessel_buf));
655 }
656 return qpms_trans_calculator_get_AB_arrays_precalcbuf(c, Adest, Bdest,
657 deststride, srcstride, kdlj.phi, bessel_buf, legendre_buf);
658 }
659
660 complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
661 int m, int n, int mu, int nu, csph_t kdlj,
662 bool r_ge_d, qpms_bessel_t J) {
663 double leg[gsl_sf_legendre_array_n(n+nu)];
664 complex double bes[n+nu+1]; // maximum order is 2n for A coeffs, plus the zeroth.
665 return qpms_trans_calculator_get_A_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
666 bes,leg);
667 }
668
669 complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
670 int m, int n, int mu, int nu, csph_t kdlj,
671 bool r_ge_d, qpms_bessel_t J) {
672 double leg[gsl_sf_legendre_array_n(n+nu+1)];
673 complex double bes[n+nu+2]; // maximum order is 2n+1 for B coeffs, plus the zeroth.
674 return qpms_trans_calculator_get_B_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
675 bes,leg);
676 }
677
678 int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
679 complex double *Adest, complex double *Bdest,
680 int m, int n, int mu, int nu, csph_t kdlj,
681 bool r_ge_d, qpms_bessel_t J) {
682 double leg[gsl_sf_legendre_array_n(2*c->lMax+1)];
683 complex double bes[2*c->lMax+2]; // maximum order is 2n+1 for B coeffs, plus the zeroth.
684 return qpms_trans_calculator_get_AB_buf_p(c,Adest, Bdest,m,n,mu,nu,kdlj,r_ge_d,J,
685 bes,leg);
686 }
687
688 int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
689 complex double *Adest, complex double *Bdest,
690 size_t deststride, size_t srcstride,
691 csph_t kdlj, bool r_ge_d, qpms_bessel_t J) {
692 double leg[gsl_sf_legendre_array_n(c->lMax+c->lMax+1)];
693 complex double bes[2*c->lMax+2]; // maximum order is 2n+1 for B coeffs, plus the zeroth.
694 return qpms_trans_calculator_get_AB_arrays_buf(c,
695 Adest, Bdest, deststride, srcstride,
696 kdlj, r_ge_d, J,
697 bes, leg);
698 }
699
700 // Convenience functions using VSWF base specs
701 qpms_errno_t qpms_trans_calculator_get_trans_array(const qpms_trans_calculator *c,
702 complex double *target,
703 /// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
704 const qpms_vswf_set_spec_t *destspec, size_t deststride,
705 /// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
706 const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
707 csph_t kdlj, bool r_ge_d, qpms_bessel_t J)
708 {
709 TROPS_ONLY_AB_SYMMETRIC_NORMS_IMPLEMENTED(c->normalisation);
710 assert(c->normalisation == destspec->norm && c->normalisation == srcspec->norm);
711 assert(c->lMax >= destspec->lMax && c->lMax >= srcspec->lMax);
712 assert(destspec->lMax_L < 0 && srcspec->lMax_L < 0);
713 // TODO don't use c->lMax etc. if both destspec->lMax and srcspec->lMax are smaller
714 complex double A[c->nelem][c->nelem];
715 complex double B[c->nelem][c->nelem];
716 qpms_errno_t retval = qpms_trans_calculator_get_AB_arrays(c,
717 A[0], B[0], c->nelem, 1,
718 kdlj, r_ge_d, J);
719 qpms_trans_array_from_AB(target, destspec, deststride, srcspec, srcstride,
720 A[0], B[0], c->lMax);
721 return retval;
722 }
723
724 qpms_errno_t qpms_trans_calculator_get_trans_array_e32_e(const qpms_trans_calculator *c,
725 complex double *target, double *err,
726 /// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
727 const qpms_vswf_set_spec_t *destspec, size_t deststride,
728 /// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
729 const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
730 const double eta, const complex double k,
731 cart2_t b1, cart2_t b2,
732 const cart2_t beta,
733 const cart3_t particle_shift,
734 double maxR, double maxK,
735 const qpms_ewald_part parts
736 )
737 {
738 TROPS_ONLY_AB_SYMMETRIC_NORMS_IMPLEMENTED(c->normalisation);
739 QPMS_ENSURE(c->normalisation == destspec->norm && c->normalisation == srcspec->norm,
740 "The normalisation conventions must be the same");
741 assert(c->lMax >= destspec->lMax && c->lMax >= srcspec->lMax);
742 assert(destspec->lMax_L < 0 && srcspec->lMax_L < 0);
743 // TODO don't use c->lMax etc. if both destspec->lMax and srcspec->lMax are smaller
744 const ptrdiff_t ldAB = c->nelem;
745 complex double *A, *B;
746 double *Aerr = NULL, *Berr = NULL;
747 QPMS_CRASHING_MALLOC(A, c->nelem*c->nelem*sizeof(complex double));
748 QPMS_CRASHING_MALLOC(B, c->nelem*c->nelem*sizeof(complex double));
749 if(err) {
750 QPMS_CRASHING_MALLOC(Aerr, c->nelem*c->nelem*sizeof(double));
751 QPMS_CRASHING_MALLOC(Berr, c->nelem*c->nelem*sizeof(double));
752 }
753 qpms_errno_t retval = qpms_trans_calculator_get_AB_arrays_e32_e(c,
754 A, Aerr, B, Berr, ldAB, 1,
755 eta, k, b1, b2, beta, particle_shift, maxR, maxK, parts);
756 for (size_t desti = 0; desti < destspec->n; ++desti) {
757 // TODO replace with (modified) qpms_trans_array_from_AB()
758 qpms_y_t desty; qpms_vswf_type_t destt;
759 if(QPMS_SUCCESS != qpms_uvswfi2ty(destspec->ilist[desti], &destt, &desty))
760 qpms_pr_error_at_flf(__FILE__,__LINE__,__func__,
761 "Invalid u. vswf index %llx.", destspec->ilist[desti]);
762 for (size_t srci = 0; srci < srcspec->n; ++srci){
763 qpms_y_t srcy; qpms_vswf_type_t srct;
764 if(QPMS_SUCCESS != qpms_uvswfi2ty(srcspec->ilist[srci], &srct, &srcy))
765 qpms_pr_error_at_flf(__FILE__,__LINE__,__func__,
766 "Invalid u. vswf index %llx.", srcspec->ilist[srci]);
767 target[srci * srcstride + desti * deststride]
768 = (srct == destt) ? A[ldAB*desty + srcy] : B[ldAB*desty + srcy];
769 if(err) err[srci * srcstride + desti * deststride]
770 = (srct == destt) ? Aerr[ldAB*desty + srcy] : Berr[ldAB*desty + srcy];
771 }
772 }
773 free(A); free(B);
774 if (err) { free(Aerr); free(Berr); }
775 return retval;
776 }
777
778 qpms_errno_t qpms_trans_calculator_get_trans_array_e32(const qpms_trans_calculator *c,
779 complex double *target, double *err,
780 /// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
781 const qpms_vswf_set_spec_t *destspec, size_t deststride,
782 /// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
783 const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
784 const double eta, const complex double k,
785 cart2_t b1, cart2_t b2,
786 const cart2_t beta,
787 const cart3_t particle_shift,
788 double maxR, double maxK
789 )
790 {
791 return qpms_trans_calculator_get_trans_array_e32_e(c, target, err, destspec, deststride,
792 srcspec, srcstride, eta, k, b1, b2, beta, particle_shift, maxR, maxK, QPMS_EWALD_FULL);
793 }
794
795
796 qpms_errno_t qpms_trans_calculator_get_trans_array_lc3p(
797 const qpms_trans_calculator *c,
798 complex double *target,
799 /// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
800 const qpms_vswf_set_spec_t *destspec, size_t deststride,
801 /// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
802 const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
803 complex double k, cart3_t destpos, cart3_t srcpos, qpms_bessel_t J
804 /// Workspace has to be at least 2 * c->neleme**2 long
805 )
806 {
807 csph_t kdlj = cart2csph(cart3_substract(destpos, srcpos));
808 kdlj.r *= k;
809 return qpms_trans_calculator_get_trans_array(c, target,
810 destspec, deststride, srcspec, srcstride, kdlj,
811 false, J);
812 }
813
814 #ifdef LATTICESUMS31
815 int qpms_trans_calculator_get_AB_arrays_e31z_both_points_and_shift(const qpms_trans_calculator *c,
816 complex double * const Adest, double * const Aerr,
817 complex double * const Bdest, double * const Berr,
818 const ptrdiff_t deststride, const ptrdiff_t srcstride,
819 /* qpms_bessel_t J*/ // assume QPMS_HANKEL_PLUS
820 const double eta, const double k, const double unitcell_area,
821 const size_t nRpoints, const cart2_t *Rpoints, // n.b. can't contain 0; TODO automatic recognition and skip
822 const size_t nKpoints, const cart2_t *Kpoints,
823 const double beta,//DIFF21
824 const double particle_shift//DIFF21
825 )
826 {
827
828 const qpms_y_t nelem2_sc = qpms_lMax2nelem_sc(c->e3c->lMax);
829 //const qpms_y_t nelem = qpms_lMax2nelem(c->lMax);
830 const bool doerr = Aerr || Berr;
831 const bool do_sigma0 = (particle_shift == 0)//DIFF21((particle_shift.x == 0) && (particle_shift.y == 0)); // FIXME ignoring the case where particle_shift equals to lattice vector
832
833 complex double *sigmas_short = malloc(sizeof(complex double)*nelem2_sc);
834 complex double *sigmas_long = malloc(sizeof(complex double)*nelem2_sc);
835 complex double *sigmas_total = malloc(sizeof(complex double)*nelem2_sc);
836 double *serr_short, *serr_long, *serr_total;
837 if(doerr) {
838 serr_short = malloc(sizeof(double)*nelem2_sc);
839 serr_long = malloc(sizeof(double)*nelem2_sc);
840 serr_total = malloc(sizeof(double)*nelem2_sc);
841 } else serr_short = serr_long = serr_total = NULL;
842
843 QPMS_ENSURE_SUCCESS(ewald31z_sigma_long_points_and_shift(sigmas_long, serr_long, //DIFF21
844 c->e3c, eta, k, unitcell_area, nKpoints, Kpoints, beta, particle_shift));
845
846 QPMS_ENSURE_SUCCESS(ewald31z_sigma_short_points_and_shift(sigmas_short, serr_short, //DIFF21
847 c->e3c, eta, k, nRpoints, Rpoints, beta, particle_shift));
848
849 for(qpms_y_t y = 0; y < nelem2_sc; ++y)
850 sigmas_total[y] = sigmas_short[y] + sigmas_long[y];
851 if (doerr) for(qpms_y_t y = 0; y < nelem2_sc; ++y)
852 serr_total[y] = serr_short[y] + serr_long[y];
853
854 complex double sigma0 = 0; double sigma0_err = 0;
855 if (do_sigma0) {
856 QPMS_ENSURE_SUCCESS(ewald31z_sigma0(&sigma0, &sigma0_err, c->e3c, eta, k));
857 const qpms_l_t y = qpms_mn2y_sc(0,0);
858 sigmas_total[y] += sigma0;
859 if(doerr) serr_total[y] += sigma0_err;
860 }
861
862 {
863 ptrdiff_t desti = 0, srci = 0;
864 for (qpms_l_t n = 1; n <= c->lMax; ++n) for (qpms_m_t m = -n; m <= n; ++m) {
865 for (qpms_l_t nu = 1; nu <= c->lMax; ++nu) for (qpms_m_t mu = -nu; mu <= nu; ++mu){
866 const size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
867 const size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
868 complex double Asum, Asumc; ckahaninit(&Asum, &Asumc);
869 double Asumerr, Asumerrc; if(Aerr) kahaninit(&Asumerr, &Asumerrc);
870
871 const qpms_m_t mu_m = mu - m;
872 // TODO skip if ... (N.B. skip will be different for 31z and 32)
873 for(qpms_l_t q = 0; q <= qmax; ++q) {
874 const qpms_l_t p = n + nu - 2*q;
875 const qpms_y_t y_sc = qpms_mn2y_sc(mu_m, p);
876 const complex double multiplier = c->A_multipliers[i][q];
877 complex double sigma = sigmas_total[y_sc];
878 ckahanadd(&Asum, &Asumc, multiplier * sigma);
879 if (Aerr) kahanadd(&Asumerr, &Asumerrc, multiplier * serr_total[y_sc]);
880 }
881
882 *(Adest + deststride * desti + srcstride * srci) = Asum;
883 if (Aerr) *(Aerr + deststride * desti + srcstride * srci) = Asumerr;
884
885 // TODO skip if ...
886 complex double Bsum, Bsumc; ckahaninit(&Bsum, &Bsumc);
887 double Bsumerr, Bsumerrc; if(Berr) kahaninit(&Bsumerr, &Bsumerrc);
888 for(qpms_l_t q = 0; q <= qmax; ++q) {
889 const qpms_l_t p_ = n + nu - 2*q + 1;
890 const qpms_y_t y_sc = qpms_mn2y_sc(mu_m, p_);
891 const complex double multiplier = c->B_multipliers[i][q-BQ_OFFSET];
892 complex double sigma = sigmas_total[y_sc];
893 ckahanadd(&Bsum, &Bsumc, multiplier * sigma);
894 if (Berr) kahanadd(&Bsumerr, &Bsumerrc, multiplier * serr_total[y_sc]);
895 }
896
897 *(Bdest + deststride * desti + srcstride * srci) = Bsum;
898 if (Berr) *(Berr + deststride * desti + srcstride * srci) = Bsumerr;
899
900 ++srci;
901 }
902 ++desti;
903 srci = 0;
904 }
905 }
906
907 free(sigmas_short);
908 free(sigmas_long);
909 free(sigmas_total);
910 if(doerr) {
911 free(serr_short);
912 free(serr_long);
913 free(serr_total);
914 }
915 return 0;
916 }
917 #endif // LATTICESUMS_31
918
919
920 #ifdef LATTICESUMS32
921
922 // N.B. alternative point generation strategy toggled by macro GEN_RSHIFTEDPOINTS
923 // and GEN_KSHIFTEDPOINTS.
924 // The results should be the same. The performance can slightly differ (especially
925 // if some optimizations in the point generators are implemented.)
926 int qpms_trans_calculator_get_AB_arrays_e32_e(const qpms_trans_calculator *c,
927 complex double * const Adest, double * const Aerr,
928 complex double * const Bdest, double * const Berr,
929 const ptrdiff_t deststride, const ptrdiff_t srcstride,
930 /* qpms_bessel_t J*/ // assume QPMS_HANKEL_PLUS
931 const double eta, const complex double k,
932 const cart2_t b1, const cart2_t b2,
933 const cart2_t beta,
934 const cart3_t particle_shift,
935 double maxR, double maxK,
936 const qpms_ewald_part parts
937 )
938 {
939
940 const qpms_y_t nelem2_sc = qpms_lMax2nelem_sc(c->e3c->lMax);
941 //const qpms_y_t nelem = qpms_lMax2nelem(c->lMax);
942 const bool doerr = Aerr || Berr;
943 const bool do_sigma0 = ((particle_shift.x == 0) && (particle_shift.y == 0) && (particle_shift.z == 0)); // FIXME ignoring the case where particle_shift equals to lattice vector
944
945 complex double *sigmas_short = malloc(sizeof(complex double)*nelem2_sc);
946 complex double *sigmas_long = malloc(sizeof(complex double)*nelem2_sc);
947 complex double *sigmas_total = malloc(sizeof(complex double)*nelem2_sc);
948 double *serr_short, *serr_long, *serr_total;
949 if(doerr) {
950 serr_short = malloc(sizeof(double)*nelem2_sc);
951 serr_long = malloc(sizeof(double)*nelem2_sc);
952 serr_total = malloc(sizeof(double)*nelem2_sc);
953 } else serr_short = serr_long = serr_total = NULL;
954
955 const double unitcell_area = l2d_unitcell_area(b1, b2);
956 cart2_t rb1, rb2; // reciprocal basis
957 QPMS_ENSURE_SUCCESS(l2d_reciprocalBasis2pi(b1, b2, &rb1, &rb2));
958
959 if (parts & QPMS_EWALD_LONG_RANGE) {
960 PGen Kgen = PGen_xyWeb_new(rb1, rb2, BASIS_RTOL,
961 #ifdef GEN_KSHIFTEDPOINTS
962 beta,
963 #else
964 CART2_ZERO,
965 #endif
966 0, true, maxK, false);
967
968 QPMS_ENSURE_SUCCESS(ewald3_sigma_long(sigmas_long, serr_long, c->e3c, eta, k,
969 unitcell_area, LAT_2D_IN_3D_XYONLY, &Kgen,
970 #ifdef GEN_KSHIFTEDPOINTS
971 true,
972 #else
973 false,
974 #endif
975 cart22cart3xy(beta), particle_shift));
976 if(Kgen.stateData) // PGen not consumed entirely (converged earlier)
977 PGen_destroy(&Kgen);
978 }
979
980 if (parts & QPMS_EWALD_SHORT_RANGE) {
981 PGen Rgen = PGen_xyWeb_new(b1, b2, BASIS_RTOL,
982 #ifdef GEN_RSHIFTEDPOINTS
983 cart2_scale(-1 /*CHECKSIGN*/, cart3xy2cart2(particle_shift)),
984 #else
985 CART2_ZERO,
986 #endif
987 0, !do_sigma0, maxR, false);
988 #ifdef GEN_RSHIFTEDPOINTS // rather ugly hacks, LPTODO cleanup
989 if (particle_shift.z != 0) {
990 const cart3_t zshift = {0, 0, -particle_shift.z /*CHECKSIGN*/};
991 Rgen = Pgen_shifted_new(Rgen, zshift);
992 }
993 #endif
994
995
996 QPMS_ENSURE_SUCCESS(ewald3_sigma_short(sigmas_short, serr_short, c->e3c, eta, k,
997 particle_shift.z ? LAT_2D_IN_3D : LAT_2D_IN_3D_XYONLY, &Rgen,
998 #ifdef GEN_RSHIFTEDPOINTS
999 true,
1000 #else
1001 false,
1002 #endif
1003 cart22cart3xy(beta), particle_shift));
1004
1005 if(Rgen.stateData) // PGen not consumed entirely (converged earlier)
1006 PGen_destroy(&Rgen);
1007 }
1008
1009 for(qpms_y_t y = 0; y < nelem2_sc; ++y)
1010 sigmas_total[y] = ((parts & QPMS_EWALD_SHORT_RANGE) ? sigmas_short[y] : 0)
1011 + ((parts & QPMS_EWALD_LONG_RANGE) ? sigmas_long[y] : 0);
1012 if (doerr) for(qpms_y_t y = 0; y < nelem2_sc; ++y)
1013 serr_total[y] = ((parts & QPMS_EWALD_SHORT_RANGE) ? serr_short[y] : 0)
1014 + ((parts & QPMS_EWALD_LONG_RANGE) ? serr_long[y] : 0);
1015
1016 complex double sigma0 = 0; double sigma0_err = 0;
1017 if (do_sigma0 && (parts & QPMS_EWALD_0TERM)) {
1018 QPMS_ENSURE_SUCCESS(ewald3_sigma0(&sigma0, &sigma0_err, c->e3c, eta, k));
1019 const qpms_l_t y = qpms_mn2y_sc(0,0);
1020 sigmas_total[y] += sigma0;
1021 if(doerr) serr_total[y] += sigma0_err;
1022 }
1023
1024 {
1025 ptrdiff_t desti = 0, srci = 0;
1026 for (qpms_l_t n = 1; n <= c->lMax; ++n) for (qpms_m_t m = -n; m <= n; ++m) {
1027 for (qpms_l_t nu = 1; nu <= c->lMax; ++nu) for (qpms_m_t mu = -nu; mu <= nu; ++mu){
1028 const size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
1029 const size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
1030 complex double Asum, Asumc; ckahaninit(&Asum, &Asumc);
1031 double Asumerr, Asumerrc; if(Aerr) kahaninit(&Asumerr, &Asumerrc);
1032
1033 const qpms_m_t mu_m = mu - m;
1034 // TODO skip if ...
1035 for(qpms_l_t q = 0; q <= qmax; ++q) {
1036 const qpms_l_t p = n + nu - 2*q;
1037 const qpms_y_t y_sc = qpms_mn2y_sc(mu_m, p);
1038 const complex double multiplier = c->A_multipliers[i][q];
1039 complex double sigma = sigmas_total[y_sc];
1040 ckahanadd(&Asum, &Asumc, multiplier * sigma);
1041 if (Aerr) kahanadd(&Asumerr, &Asumerrc, multiplier * serr_total[y_sc]);
1042 }
1043
1044 *(Adest + deststride * desti + srcstride * srci) = Asum;
1045 if (Aerr) *(Aerr + deststride * desti + srcstride * srci) = Asumerr;
1046
1047 // TODO skip if ...
1048 complex double Bsum, Bsumc; ckahaninit(&Bsum, &Bsumc);
1049 double Bsumerr, Bsumerrc; if(Berr) kahaninit(&Bsumerr, &Bsumerrc);
1050 for(qpms_l_t q = 0; q <= qmax; ++q) {
1051 const qpms_l_t p_ = n + nu - 2*q + 1;
1052 const qpms_y_t y_sc = qpms_mn2y_sc(mu_m, p_);
1053 const complex double multiplier = c->B_multipliers[i][q-BQ_OFFSET];
1054 complex double sigma = sigmas_total[y_sc];
1055 ckahanadd(&Bsum, &Bsumc, multiplier * sigma);
1056 if (Berr) kahanadd(&Bsumerr, &Bsumerrc, multiplier * serr_total[y_sc]);
1057 }
1058
1059 *(Bdest + deststride * desti + srcstride * srci) = Bsum;
1060 if (Berr) *(Berr + deststride * desti + srcstride * srci) = Bsumerr;
1061
1062 ++srci;
1063 }
1064 ++desti;
1065 srci = 0;
1066 }
1067 }
1068
1069 free(sigmas_short);
1070 free(sigmas_long);
1071 free(sigmas_total);
1072 if(doerr) {
1073 free(serr_short);
1074 free(serr_long);
1075 free(serr_total);
1076 }
1077 return 0;
1078 }
1079
1080 int qpms_trans_calculator_get_AB_arrays_e32(const qpms_trans_calculator *c,
1081 complex double * const Adest, double * const Aerr,
1082 complex double * const Bdest, double * const Berr,
1083 const ptrdiff_t deststride, const ptrdiff_t srcstride,
1084 /* qpms_bessel_t J*/ // assume QPMS_HANKEL_PLUS
1085 const double eta, const complex double k,
1086 const cart2_t b1, const cart2_t b2,
1087 const cart2_t beta,
1088 const cart3_t particle_shift,
1089 double maxR, double maxK)
1090 {
1091 return qpms_trans_calculator_get_AB_arrays_e32_e(
1092 c, Adest, Aerr, Bdest, Berr, deststride, srcstride,
1093 eta, k, b1, b2, beta, particle_shift, maxR, maxK, QPMS_EWALD_FULL);
1094 }
1095
1096 #endif // LATTICESUMS32
1097
1098
1099 complex double qpms_trans_calculator_get_A_ext(const qpms_trans_calculator *c,
1100 int m, int n, int mu, int nu,
1101 complex double kdlj_r, double kdlj_theta, double kdlj_phi,
1102 int r_ge_d, int J) {
1103 csph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
1104 return qpms_trans_calculator_get_A(c,m,n,mu,nu,kdlj,r_ge_d,J);
1105 }
1106
1107 complex double qpms_trans_calculator_get_B_ext(const qpms_trans_calculator *c,
1108 int m, int n, int mu, int nu,
1109 complex double kdlj_r, double kdlj_theta, double kdlj_phi,
1110 int r_ge_d, int J) {
1111 csph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
1112 return qpms_trans_calculator_get_B(c,m,n,mu,nu,kdlj,r_ge_d,J);
1113 }
1114
1115 int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
1116 complex double *Adest, complex double *Bdest,
1117 int m, int n, int mu, int nu,
1118 complex double kdlj_r, double kdlj_theta, double kdlj_phi,
1119 int r_ge_d, int J) {
1120 csph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
1121 return qpms_trans_calculator_get_AB_p(c,Adest,Bdest,m,n,mu,nu,kdlj,r_ge_d,J);
1122 }
1123
1124 int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
1125 complex double *Adest, complex double *Bdest,
1126 size_t deststride, size_t srcstride,
1127 complex double kdlj_r, double kdlj_theta, double kdlj_phi,
1128 int r_ge_d, int J) {
1129 csph_t kdlj = {kdlj_r, kdlj_theta, kdlj_phi};
1130 return qpms_trans_calculator_get_AB_arrays(c,Adest,Bdest,deststride,srcstride,
1131 kdlj, r_ge_d, J);
1132 }
1133
QPMS photonic multiple scattering suite