Shamrock 2025.10.0
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sphkernels.hpp
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1// -------------------------------------------------------//
2//
3// SHAMROCK code for hydrodynamics
4// Copyright (c) 2021-2026 Timothée David--Cléris <tim.shamrock@proton.me>
5// SPDX-License-Identifier: CeCILL Free Software License Agreement v2.1
6// Shamrock is licensed under the CeCILL 2.1 License, see LICENSE for more information
7//
8// -------------------------------------------------------//
9
10#pragma once
11
19//%Impl status : Good
20
21#include "shambase/constants.hpp"
22#include "shambase/type_name_info.hpp"
23#include "shambackends/math.hpp"
24#include "shammath/integrator.hpp"
25
26namespace shammath::details {
27
28 template<class Tscal>
29 class KernelDefM4 {
30 public:
31 inline static constexpr Tscal Rkern = 2;
33 inline static constexpr Tscal hfactd = 1.2;
34
36 inline static constexpr Tscal norm_1d = 2. / 3.;
38 inline static constexpr Tscal norm_2d = 10. / (7. * shambase::constants::pi<Tscal>);
40 inline static constexpr Tscal norm_3d = 1 / shambase::constants::pi<Tscal>;
41
42 inline static Tscal f(Tscal q) {
43
44 Tscal t1 = 2 - q;
45 Tscal t2 = 1 - q;
46
47 t1 = t1 * t1 * t1;
48 t2 = t2 * t2 * t2;
49
50 constexpr Tscal div1_4 = (1. / 4.);
51 t1 *= div1_4;
52 t2 *= -1;
53
54 if (q < 1) {
55 return t1 + t2;
56 } else if (q < 2) {
57 return t1;
58 } else
59 return 0;
60 }
61
62 inline static Tscal df(Tscal q) {
63
64 constexpr Tscal div9_4 = (9. / 4.);
65 constexpr Tscal div3_4 = (3. / 4.);
66
67 if (q < 1) {
68 return -3 * q + div9_4 * q * q;
69 } else if (q < 2) {
70 return -3 + 3 * q - div3_4 * q * q;
71 } else
72 return 0;
73 }
74
75 inline static Tscal ddf(Tscal q) {
76 if (q < 1) {
77 return (9.0 / 2.0) * q - 3;
78 } else if (q < 2) {
79 return 3 - (3.0 / 2.0) * q;
80 } else
81 return 0;
82 }
83
84 inline static Tscal phi_tilde_3d(Tscal q) {
85 Tscal t1 = sham::pow_constexpr<2>(q);
86 Tscal t2 = sham::pow_constexpr<3>(q);
87 Tscal t3 = sham::pow_constexpr<4>(q);
88 Tscal t4 = sham::pow_constexpr<5>(q);
89 Tscal t5 = sham::pow_constexpr<6>(q);
90 if (q < 1) {
91 return (1.0 / 30.0) * shambase::constants::pi<Tscal>
92 * (t1 * (3 * t2 - 9 * t1 + 20) - 42);
93 } else if (q < 2) {
94 return (1.0 / 30.0) * shambase::constants::pi<Tscal>
95 * (-t5 + 9 * t4 - 30 * t3 + 40 * t2 - 48 * q + 2) / q;
96 } else
97 return -shambase::constants::pi<Tscal> / q;
98 }
99
100 inline static Tscal phi_tilde_3d_prime(Tscal q) {
101 Tscal t1 = sham::pow_constexpr<2>(q);
102 Tscal t2 = sham::pow_constexpr<3>(q);
103 Tscal t3 = sham::pow_constexpr<4>(q);
104 Tscal t4 = sham::pow_constexpr<5>(q);
105 Tscal t5 = sham::pow_constexpr<6>(q);
106 if (q < 1) {
107 return (1.0 / 30.0) * shambase::constants::pi<Tscal>
108 * (t1 * (9 * t1 - 18 * q) + 2 * q * (3 * t2 - 9 * t1 + 20));
109 } else if (q < 2) {
110 return (1.0 / 30.0) * shambase::constants::pi<Tscal>
111 * (-6 * t4 + 45 * t3 - 120 * t2 + 120 * t1 - 48) / q
112 - (1.0 / 30.0) * shambase::constants::pi<Tscal>
113 * (-t5 + 9 * t4 - 30 * t3 + 40 * t2 - 48 * q + 2) / t1;
114 } else
115 return shambase::constants::pi<Tscal> / t1;
116 }
117 };
118
119 template<class Tscal>
120 class KernelDefM5 {
121 public:
122 inline static constexpr Tscal Rkern = 5. / 2.;
124 inline static constexpr Tscal hfactd = 1.2;
125
127 inline static constexpr Tscal norm_1d = 1. / 24.;
129 inline static constexpr Tscal norm_2d = 96. / (1199 * shambase::constants::pi<Tscal>);
131 inline static constexpr Tscal norm_3d = 1 / (20 * shambase::constants::pi<Tscal>);
132
133 inline static Tscal f(Tscal q) {
134
135 constexpr Tscal div5_2 = (5. / 2.);
136 constexpr Tscal div3_2 = (3. / 2.);
137 constexpr Tscal div1_2 = (1. / 2.);
138
139 Tscal t1 = div5_2 - q;
140 Tscal t2 = div3_2 - q;
141 Tscal t3 = div1_2 - q;
142
143 Tscal t1_2 = t1 * t1;
144 Tscal t2_2 = t2 * t2;
145 Tscal t3_2 = t3 * t3;
146
147 t1 = t1_2 * t1_2;
148 t2 = t2_2 * t2_2;
149 t3 = t3_2 * t3_2;
150
151 t1 *= 1;
152 t2 *= -5;
153 t3 *= 10;
154
155 if (q < div1_2) {
156 return t1 + t2 + t3;
157 } else if (q < div3_2) {
158 return t1 + t2;
159 } else if (q < div5_2) {
160 return t1;
161 } else
162 return 0;
163 }
164
165 inline static Tscal df(Tscal q) {
166
167 constexpr Tscal div5_2 = (5. / 2.);
168 constexpr Tscal div3_2 = (3. / 2.);
169 constexpr Tscal div1_2 = (1. / 2.);
170
171 Tscal t1 = div5_2 - q;
172 Tscal t2 = div3_2 - q;
173 Tscal t3 = div1_2 - q;
174
175 Tscal t1_2 = t1 * t1;
176 Tscal t2_2 = t2 * t2;
177 Tscal t3_2 = t3 * t3;
178
179 t1 = t1 * t1_2;
180 t2 = t2 * t2_2;
181 t3 = t3 * t3_2;
182
183 t1 *= (1) * (-4);
184 t2 *= (-5) * (-4);
185 t3 *= (10) * (-4);
186
187 if (q < div1_2) {
188 return t1 + t2 + t3;
189 } else if (q < div3_2) {
190 return t1 + t2;
191 } else if (q < div5_2) {
192 return t1;
193 } else
194 return 0;
195 }
196
197 inline static Tscal ddf(Tscal q) {
198 Tscal t1 = sham::pow_constexpr<2>(1.0 / 2.0 - q);
199 Tscal t2 = sham::pow_constexpr<2>(3.0 / 2.0 - q);
200 Tscal t3 = sham::pow_constexpr<2>(5.0 / 2.0 - q);
201 if (q < 1.0 / 2.0) {
202 return 120 * t1 - 60 * t2 + 12 * t3;
203 } else if (q < 3.0 / 2.0) {
204 return -60 * t2 + 12 * t3;
205 } else if (q < 5.0 / 2.0) {
206 return 12 * t3;
207 } else
208 return 0;
209 }
210
211 inline static Tscal phi_tilde_3d(Tscal q) {
212 Tscal t1 = sham::pow_constexpr<2>(q);
213 Tscal t2 = sham::pow_constexpr<3>(q);
214 Tscal t3 = sham::pow_constexpr<4>(q);
215 Tscal t4 = sham::pow_constexpr<5>(q);
216 Tscal t5 = sham::pow_constexpr<6>(q);
217 Tscal t6 = sham::pow_constexpr<7>(q);
218 if (q < 1.0 / 2.0) {
219 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
220 * (192 * t5 - 1008 * t3 + 3220 * t1 - 8393);
221 } else if (q < 3.0 / 2.0) {
222 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
223 * (-128 * t6 + 896 * t5 - 2016 * t4 + 560 * t3 + 3080 * t2 - 8386 * q - 1)
224 / q;
225 } else if (q < 5.0 / 2.0) {
226 return (1.0 / 672.0) * shambase::constants::pi<Tscal>
227 * (64 * t6 - 896 * t5 + 5040 * t4 - 14000 * t3 + 17500 * t2 - 21875 * q
228 + 2185)
229 / q;
230 } else
231 return -20 * shambase::constants::pi<Tscal> / q;
232 }
233
234 inline static Tscal phi_tilde_3d_prime(Tscal q) {
235 Tscal t1 = sham::pow_constexpr<2>(q);
236 Tscal t2 = sham::pow_constexpr<3>(q);
237 Tscal t3 = sham::pow_constexpr<4>(q);
238 Tscal t4 = sham::pow_constexpr<5>(q);
239 Tscal t5 = sham::pow_constexpr<6>(q);
240 Tscal t6 = sham::pow_constexpr<7>(q);
241 if (q < 1.0 / 2.0) {
242 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
243 * (1152 * t4 - 4032 * t2 + 6440 * q);
244 } else if (q < 3.0 / 2.0) {
245 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
246 * (-896 * t5 + 5376 * t4 - 10080 * t3 + 2240 * t2 + 9240 * t1 - 8386) / q
247 - (1.0 / 336.0) * shambase::constants::pi<Tscal>
248 * (-128 * t6 + 896 * t5 - 2016 * t4 + 560 * t3 + 3080 * t2 - 8386 * q
249 - 1)
250 / t1;
251 } else if (q < 5.0 / 2.0) {
252 return (1.0 / 672.0) * shambase::constants::pi<Tscal>
253 * (448 * t5 - 5376 * t4 + 25200 * t3 - 56000 * t2 + 52500 * t1 - 21875)
254 / q
255 - (1.0 / 672.0) * shambase::constants::pi<Tscal>
256 * (64 * t6 - 896 * t5 + 5040 * t4 - 14000 * t3 + 17500 * t2 - 21875 * q
257 + 2185)
258 / t1;
259 } else
260 return 20 * shambase::constants::pi<Tscal> / t1;
261 }
262 };
263
264 template<class Tscal>
265 class KernelDefM6 {
266 public:
267 inline static constexpr Tscal Rkern = 3;
269 inline static constexpr Tscal hfactd = 1.0;
270
272 inline static constexpr Tscal norm_1d = 1. / 120.;
274 inline static constexpr Tscal norm_2d = 7. / (478 * shambase::constants::pi<Tscal>);
276 inline static constexpr Tscal norm_3d = 1 / (120 * shambase::constants::pi<Tscal>);
277
278 inline static Tscal f(Tscal q) {
279
280 Tscal t1 = 3 - q;
281 Tscal t2 = 2 - q;
282 Tscal t3 = 1 - q;
283
284 Tscal t1_2 = t1 * t1;
285 Tscal t2_2 = t2 * t2;
286 Tscal t3_2 = t3 * t3;
287
288 t1 = t1 * t1_2 * t1_2;
289 t2 = t2 * t2_2 * t2_2;
290 t3 = t3 * t3_2 * t3_2;
291
292 t1 *= 1;
293 t2 *= -6;
294 t3 *= 15;
295
296 if (q < 1.) {
297 return t1 + t2 + t3;
298 } else if (q < 2.) {
299 return t1 + t2;
300 } else if (q < 3.) {
301 return t1;
302 } else
303 return 0;
304 }
305
306 inline static Tscal df(Tscal q) {
307
308 Tscal t1 = 3 - q;
309 Tscal t2 = 2 - q;
310 Tscal t3 = 1 - q;
311
312 Tscal t1_2 = t1 * t1;
313 Tscal t2_2 = t2 * t2;
314 Tscal t3_2 = t3 * t3;
315
316 t1 = t1_2 * t1_2;
317 t2 = t2_2 * t2_2;
318 t3 = t3_2 * t3_2;
319
320 t1 *= (1) * (-5);
321 t2 *= (-6) * (-5);
322 t3 *= (15) * (-5);
323
324 if (q < 1.) {
325 return t1 + t2 + t3;
326 } else if (q < 2.) {
327 return t1 + t2;
328 } else if (q < 3.) {
329 return t1;
330 } else
331 return 0;
332 }
333
334 inline static Tscal ddf(Tscal q) {
335 Tscal t1 = sham::pow_constexpr<3>(1 - q);
336 Tscal t2 = sham::pow_constexpr<3>(2 - q);
337 Tscal t3 = sham::pow_constexpr<3>(3 - q);
338 if (q < 1) {
339 return 300 * t1 - 120 * t2 + 20 * t3;
340 } else if (q < 2) {
341 return -120 * t2 + 20 * t3;
342 } else if (q < 3) {
343 return 20 * t3;
344 } else
345 return 0;
346 }
347
348 inline static Tscal phi_tilde_3d(Tscal q) {
349 Tscal t1 = sham::pow_constexpr<2>(q);
350 Tscal t2 = sham::pow_constexpr<3>(q);
351 Tscal t3 = sham::pow_constexpr<4>(q);
352 Tscal t4 = sham::pow_constexpr<5>(q);
353 Tscal t5 = sham::pow_constexpr<6>(q);
354 Tscal t6 = sham::pow_constexpr<7>(q);
355 Tscal t7 = sham::pow_constexpr<8>(q);
356 if (q < 1) {
357 return (1.0 / 7.0) * shambase::constants::pi<Tscal>
358 * (-5 * t6 + 20 * t5 - 84 * t3 + 308 * t1 - 956);
359 } else if (q < 2) {
360 return (1.0 / 14.0) * shambase::constants::pi<Tscal>
361 * (5 * t7 - 60 * t6 + 280 * t5 - 588 * t4 + 350 * t3 + 476 * t2 - 1892 * q
362 - 5)
363 / q;
364 } else if (q < 3) {
365 return (1.0 / 14.0) * shambase::constants::pi<Tscal>
366 * (-t7 + 20 * t6 - 168 * t5 + 756 * t4 - 1890 * t3 + 2268 * t2 - 2916 * q
367 + 507)
368 / q;
369 } else
370 return -120 * shambase::constants::pi<Tscal> / q;
371 }
372
373 inline static Tscal phi_tilde_3d_prime(Tscal q) {
374 Tscal t1 = sham::pow_constexpr<2>(q);
375 Tscal t2 = sham::pow_constexpr<3>(q);
376 Tscal t3 = sham::pow_constexpr<4>(q);
377 Tscal t4 = sham::pow_constexpr<5>(q);
378 Tscal t5 = sham::pow_constexpr<6>(q);
379 Tscal t6 = sham::pow_constexpr<7>(q);
380 Tscal t7 = sham::pow_constexpr<8>(q);
381 if (q < 1) {
382 return (1.0 / 7.0) * shambase::constants::pi<Tscal>
383 * (-35 * t5 + 120 * t4 - 336 * t2 + 616 * q);
384 } else if (q < 2) {
385 return (1.0 / 14.0) * shambase::constants::pi<Tscal>
386 * (40 * t6 - 420 * t5 + 1680 * t4 - 2940 * t3 + 1400 * t2 + 1428 * t1
387 - 1892)
388 / q
389 - (1.0 / 14.0) * shambase::constants::pi<Tscal>
390 * (5 * t7 - 60 * t6 + 280 * t5 - 588 * t4 + 350 * t3 + 476 * t2
391 - 1892 * q - 5)
392 / t1;
393 } else if (q < 3) {
394 return (1.0 / 14.0) * shambase::constants::pi<Tscal>
395 * (-8 * t6 + 140 * t5 - 1008 * t4 + 3780 * t3 - 7560 * t2 + 6804 * t1
396 - 2916)
397 / q
398 - (1.0 / 14.0) * shambase::constants::pi<Tscal>
399 * (-t7 + 20 * t6 - 168 * t5 + 756 * t4 - 1890 * t3 + 2268 * t2
400 - 2916 * q + 507)
401 / t1;
402 } else
403 return 120 * shambase::constants::pi<Tscal> / t1;
404 }
405 };
406
407 template<class Tscal>
408 class KernelDefM7 {
409 public:
410 inline static constexpr Tscal Rkern = 3.5;
412 inline static constexpr Tscal hfactd = 1.0;
413
415 inline static constexpr Tscal norm_1d = 1. / 720;
417 inline static constexpr Tscal norm_2d = 256. / (113149 * shambase::constants::pi<Tscal>);
419 inline static constexpr Tscal norm_3d = 6. / (5040. * shambase::constants::pi<Tscal>);
420
421 inline static Tscal f(Tscal q) {
422
423 constexpr Tscal div7_2 = (7. / 2.);
424 constexpr Tscal div5_2 = (5. / 2.);
425 constexpr Tscal div3_2 = (3. / 2.);
426 constexpr Tscal div1_2 = (1. / 2.);
427
428 Tscal t1 = div7_2 - q;
429 Tscal t2 = div5_2 - q;
430 Tscal t3 = div3_2 - q;
431 Tscal t4 = div1_2 - q;
432
433 // up to order 6
434 t1 = sham::pow_constexpr<6>(t1);
435 t2 = sham::pow_constexpr<6>(t2);
436 t3 = sham::pow_constexpr<6>(t3);
437 t4 = sham::pow_constexpr<6>(t4);
438
439 t1 *= 1.;
440 t2 *= -7.;
441 t3 *= 21.;
442 t4 *= -35.;
443
444 if (q < div1_2) {
445 return t1 + t2 + t3 + t4;
446 } else if (q < div3_2) {
447 return t1 + t2 + t3;
448 } else if (q < div5_2) {
449 return t1 + t2;
450 } else if (q < div7_2) {
451 return t1;
452 } else
453 return 0;
454 }
455
456 inline static Tscal df(Tscal q) {
457
458 constexpr Tscal div7_2 = (7. / 2.);
459 constexpr Tscal div5_2 = (5. / 2.);
460 constexpr Tscal div3_2 = (3. / 2.);
461 constexpr Tscal div1_2 = (1. / 2.);
462
463 Tscal t1 = div7_2 - q;
464 Tscal t2 = div5_2 - q;
465 Tscal t3 = div3_2 - q;
466 Tscal t4 = div1_2 - q;
467
468 // up to order 6
469 t1 = sham::pow_constexpr<5>(t1);
470 t2 = sham::pow_constexpr<5>(t2);
471 t3 = sham::pow_constexpr<5>(t3);
472 t4 = sham::pow_constexpr<5>(t4);
473
474 t1 *= (-6.) * (1.);
475 t2 *= (-6.) * (-7.);
476 t3 *= (-6.) * (21.);
477 t4 *= (-6.) * (-35.);
478
479 if (q < div1_2) {
480 return t1 + t2 + t3 + t4;
481 } else if (q < div3_2) {
482 return t1 + t2 + t3;
483 } else if (q < div5_2) {
484 return t1 + t2;
485 } else if (q < div7_2) {
486 return t1;
487 } else
488 return 0;
489 }
490
491 inline static Tscal ddf(Tscal q) {
492 Tscal t1 = sham::pow_constexpr<4>(1.0 / 2.0 - q);
493 Tscal t2 = sham::pow_constexpr<4>(3.0 / 2.0 - q);
494 Tscal t3 = sham::pow_constexpr<4>(5.0 / 2.0 - q);
495 Tscal t4 = sham::pow_constexpr<4>(7.0 / 2.0 - q);
496 if (q < 1.0 / 2.0) {
497 return -1050 * t1 + 630 * t2 - 210 * t3 + 30 * t4;
498 } else if (q < 3.0 / 2.0) {
499 return 630 * t2 - 210 * t3 + 30 * t4;
500 } else if (q < 5.0 / 2.0) {
501 return -210 * t3 + 30 * t4;
502 } else if (q < 7.0 / 2.0) {
503 return 30 * t4;
504 } else
505 return 0;
506 }
507
508 inline static Tscal phi_tilde_3d(Tscal q) {
509 Tscal t1 = sham::pow_constexpr<2>(q);
510 Tscal t2 = sham::pow_constexpr<3>(q);
511 Tscal t3 = sham::pow_constexpr<4>(q);
512 Tscal t4 = sham::pow_constexpr<5>(q);
513 Tscal t5 = sham::pow_constexpr<6>(q);
514 Tscal t6 = sham::pow_constexpr<7>(q);
515 Tscal t7 = sham::pow_constexpr<8>(q);
516 Tscal t8 = sham::pow_constexpr<9>(q);
517 if (q < 1.0 / 2.0) {
518 return (1.0 / 1152.0) * shambase::constants::pi<Tscal>
519 * (-1280 * t7 + 11520 * t5 - 66528 * t3 + 282576 * t1 - 1018341);
520 } else if (q < 3.0 / 2.0) {
521 return (1.0 / 4608.0) * shambase::constants::pi<Tscal>
522 * (3840 * t8 - 34560 * t7 + 103680 * t6 - 53760 * t5 - 235872 * t4
523 - 10080 * t3 + 1131984 * t2 - 4073409 * q + 5)
524 / q;
525 } else if (q < 5.0 / 2.0) {
526 return (1.0 / 2304.0) * shambase::constants::pi<Tscal>
527 * (-768 * t8 + 13824 * t7 - 103680 * t6 + 408576 * t5 - 852768 * t4
528 + 729792 * t3 + 198576 * t2 - 1948131 * q - 29522)
529 / q;
530 } else if (q < 7.0 / 2.0) {
531 return (1.0 / 4608.0) * shambase::constants::pi<Tscal>
532 * (256 * t8 - 6912 * t7 + 80640 * t6 - 526848 * t5 + 2074464 * t4
533 - 4840416 * t3 + 5647152 * t2 - 7411887 * q + 1894081)
534 / q;
535 } else
536 return -840 * shambase::constants::pi<Tscal> / q;
537 }
538
539 inline static Tscal phi_tilde_3d_prime(Tscal q) {
540 Tscal t1 = sham::pow_constexpr<2>(q);
541 Tscal t2 = sham::pow_constexpr<3>(q);
542 Tscal t3 = sham::pow_constexpr<4>(q);
543 Tscal t4 = sham::pow_constexpr<5>(q);
544 Tscal t5 = sham::pow_constexpr<6>(q);
545 Tscal t6 = sham::pow_constexpr<7>(q);
546 Tscal t7 = sham::pow_constexpr<8>(q);
547 Tscal t8 = sham::pow_constexpr<9>(q);
548 if (q < 1.0 / 2.0) {
549 return (1.0 / 1152.0) * shambase::constants::pi<Tscal>
550 * (-10240 * t6 + 69120 * t4 - 266112 * t2 + 565152 * q);
551 } else if (q < 3.0 / 2.0) {
552 return (1.0 / 4608.0) * shambase::constants::pi<Tscal>
553 * (34560 * t7 - 276480 * t6 + 725760 * t5 - 322560 * t4 - 1179360 * t3
554 - 40320 * t2 + 3395952 * t1 - 4073409)
555 / q
556 - (1.0 / 4608.0) * shambase::constants::pi<Tscal>
557 * (3840 * t8 - 34560 * t7 + 103680 * t6 - 53760 * t5 - 235872 * t4
558 - 10080 * t3 + 1131984 * t2 - 4073409 * q + 5)
559 / t1;
560 } else if (q < 5.0 / 2.0) {
561 return (1.0 / 2304.0) * shambase::constants::pi<Tscal>
562 * (-6912 * t7 + 110592 * t6 - 725760 * t5 + 2451456 * t4 - 4263840 * t3
563 + 2919168 * t2 + 595728 * t1 - 1948131)
564 / q
565 - (1.0 / 2304.0) * shambase::constants::pi<Tscal>
566 * (-768 * t8 + 13824 * t7 - 103680 * t6 + 408576 * t5 - 852768 * t4
567 + 729792 * t3 + 198576 * t2 - 1948131 * q - 29522)
568 / t1;
569 } else if (q < 7.0 / 2.0) {
570 return (1.0 / 4608.0) * shambase::constants::pi<Tscal>
571 * (2304 * t7 - 55296 * t6 + 564480 * t5 - 3161088 * t4 + 10372320 * t3
572 - 19361664 * t2 + 16941456 * t1 - 7411887)
573 / q
574 - (1.0 / 4608.0) * shambase::constants::pi<Tscal>
575 * (256 * t8 - 6912 * t7 + 80640 * t6 - 526848 * t5 + 2074464 * t4
576 - 4840416 * t3 + 5647152 * t2 - 7411887 * q + 1894081)
577 / t1;
578 } else
579 return 840 * shambase::constants::pi<Tscal> / t1;
580 }
581 };
582
583 template<class Tscal>
584 class KernelDefM8 {
585 public:
586 inline static constexpr Tscal Rkern = 4.0;
588 inline static constexpr Tscal hfactd = 1.0;
589
591 inline static constexpr Tscal norm_1d = 1.0 / 5040.0;
593 inline static constexpr Tscal norm_2d = (9.0 / 29740.0) / shambase::constants::pi<Tscal>;
595 inline static constexpr Tscal norm_3d = (1.0 / 6720.0) / shambase::constants::pi<Tscal>;
596
597 inline static Tscal f(Tscal q) {
598
599 Tscal t1 = 4 - q;
600 Tscal t2 = 3 - q;
601 Tscal t3 = 2 - q;
602 Tscal t4 = 1 - q;
603
604 t1 = sham::pow_constexpr<7>(t1);
605 t2 = sham::pow_constexpr<7>(t2);
606 t3 = sham::pow_constexpr<7>(t3);
607 t4 = sham::pow_constexpr<7>(t4);
608
609 t1 *= 1.;
610 t2 *= -8.;
611 t3 *= 28.;
612 t4 *= -56.;
613
614 if (q < 1) {
615 return t1 + t2 + t3 + t4;
616 } else if (q < 2) {
617 return t1 + t2 + t3;
618 } else if (q < 3) {
619 return t1 + t2;
620 } else if (q < 4) {
621 return t1;
622 } else
623 return 0;
624 }
625
626 inline static Tscal df(Tscal q) {
627
628 Tscal t1 = 4 - q;
629 Tscal t2 = 3 - q;
630 Tscal t3 = 2 - q;
631 Tscal t4 = 1 - q;
632
633 t1 = sham::pow_constexpr<6>(t1);
634 t2 = sham::pow_constexpr<6>(t2);
635 t3 = sham::pow_constexpr<6>(t3);
636 t4 = sham::pow_constexpr<6>(t4);
637
638 t1 *= (-7.) * (1.);
639 t2 *= (-7.) * (-8.);
640 t3 *= (-7.) * (28.);
641 t4 *= (-7.) * (-56.);
642
643 if (q < 1) {
644 return t1 + t2 + t3 + t4;
645 } else if (q < 2) {
646 return t1 + t2 + t3;
647 } else if (q < 3) {
648 return t1 + t2;
649 } else if (q < 4) {
650 return t1;
651 } else
652 return 0;
653 }
654
655 inline static Tscal ddf(Tscal q) {
656 Tscal t1 = sham::pow_constexpr<5>(1 - q);
657 Tscal t2 = sham::pow_constexpr<5>(2 - q);
658 Tscal t3 = sham::pow_constexpr<5>(3 - q);
659 Tscal t4 = sham::pow_constexpr<5>(4 - q);
660 if (q < 1) {
661 return -2352 * t1 + 1176 * t2 - 336 * t3 + 42 * t4;
662 } else if (q < 2) {
663 return 1176 * t2 - 336 * t3 + 42 * t4;
664 } else if (q < 3) {
665 return -336 * t3 + 42 * t4;
666 } else if (q < 4) {
667 return 42 * t4;
668 } else
669 return 0;
670 }
671
672 inline static Tscal phi_tilde_3d(Tscal q) {
673 Tscal t1 = sham::pow_constexpr<10>(q);
674 Tscal t2 = sham::pow_constexpr<2>(q);
675 Tscal t3 = sham::pow_constexpr<3>(q);
676 Tscal t4 = sham::pow_constexpr<4>(q);
677 Tscal t5 = sham::pow_constexpr<5>(q);
678 Tscal t6 = sham::pow_constexpr<6>(q);
679 Tscal t7 = sham::pow_constexpr<7>(q);
680 Tscal t8 = sham::pow_constexpr<8>(q);
681 Tscal t9 = sham::pow_constexpr<9>(q);
682 if (q < 1) {
683 return (2.0 / 9.0) * shambase::constants::pi<Tscal>
684 * (t2 * (7 * t7 - 35 * t6 + 240 * t4 - 1512 * t2 + 7248) - 29740);
685 } else if (q < 2) {
686 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
687 * (-21 * t1 + 315 * t9 - 1890 * t8 + 5400 * t7 - 5880 * t6 - 2268 * t5
688 - 2940 * t4 + 37080 * t3 - 148770 * q + 14)
689 / q;
690 } else if (q < 3) {
691 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
692 * (7 * t1 - 175 * t9 + 1890 * t8 - 11400 * t7 + 41160 * t6 - 86940 * t5
693 + 91140 * t4 - 16680 * t3 - 130850 * q - 7154)
694 / q;
695 } else if (q < 4) {
696 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
697 * (-t1 + 35 * t9 - 540 * t8 + 4800 * t7 - 26880 * t6 + 96768 * t5
698 - 215040 * t4 + 245760 * t3 - 327680 * q + 110944)
699 / q;
700 } else
701 return -6720 * shambase::constants::pi<Tscal> / q;
702 }
703
704 inline static Tscal phi_tilde_3d_prime(Tscal q) {
705 Tscal t1 = sham::pow_constexpr<10>(q);
706 Tscal t2 = sham::pow_constexpr<2>(q);
707 Tscal t3 = sham::pow_constexpr<3>(q);
708 Tscal t4 = sham::pow_constexpr<4>(q);
709 Tscal t5 = sham::pow_constexpr<5>(q);
710 Tscal t6 = sham::pow_constexpr<6>(q);
711 Tscal t7 = sham::pow_constexpr<7>(q);
712 Tscal t8 = sham::pow_constexpr<8>(q);
713 Tscal t9 = sham::pow_constexpr<9>(q);
714 if (q < 1) {
715 return (2.0 / 9.0) * shambase::constants::pi<Tscal>
716 * (t2 * (49 * t6 - 210 * t5 + 960 * t3 - 3024 * q)
717 + 2 * q * (7 * t7 - 35 * t6 + 240 * t4 - 1512 * t2 + 7248));
718 } else if (q < 2) {
719 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
720 * (-210 * t9 + 2835 * t8 - 15120 * t7 + 37800 * t6 - 35280 * t5
721 - 11340 * t4 - 11760 * t3 + 111240 * t2 - 148770)
722 / q
723 - (2.0 / 45.0) * shambase::constants::pi<Tscal>
724 * (-21 * t1 + 315 * t9 - 1890 * t8 + 5400 * t7 - 5880 * t6 - 2268 * t5
725 - 2940 * t4 + 37080 * t3 - 148770 * q + 14)
726 / t2;
727 } else if (q < 3) {
728 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
729 * (70 * t9 - 1575 * t8 + 15120 * t7 - 79800 * t6 + 246960 * t5
730 - 434700 * t4 + 364560 * t3 - 50040 * t2 - 130850)
731 / q
732 - (2.0 / 45.0) * shambase::constants::pi<Tscal>
733 * (7 * t1 - 175 * t9 + 1890 * t8 - 11400 * t7 + 41160 * t6 - 86940 * t5
734 + 91140 * t4 - 16680 * t3 - 130850 * q - 7154)
735 / t2;
736 } else if (q < 4) {
737 return (2.0 / 45.0) * shambase::constants::pi<Tscal>
738 * (-10 * t9 + 315 * t8 - 4320 * t7 + 33600 * t6 - 161280 * t5
739 + 483840 * t4 - 860160 * t3 + 737280 * t2 - 327680)
740 / q
741 - (2.0 / 45.0) * shambase::constants::pi<Tscal>
742 * (-t1 + 35 * t9 - 540 * t8 + 4800 * t7 - 26880 * t6 + 96768 * t5
743 - 215040 * t4 + 245760 * t3 - 327680 * q + 110944)
744 / t2;
745 } else
746 return 6720 * shambase::constants::pi<Tscal> / t2;
747 }
748 };
749
750 template<class Tscal>
751 class KernelDefM9 {
752 public:
753 inline static constexpr Tscal Rkern = 4.5;
755 inline static constexpr Tscal hfactd = 1.0;
756
758 inline static constexpr Tscal norm_1d = 1. / 40320;
760 inline static constexpr Tscal norm_2d = 512. / (14345663 * shambase::constants::pi<Tscal>);
762 inline static constexpr Tscal norm_3d = 6. / (362880. * shambase::constants::pi<Tscal>);
763
764 inline static Tscal f(Tscal q) {
765
766 constexpr Tscal div9_2 = (9. / 2.);
767 constexpr Tscal div7_2 = (7. / 2.);
768 constexpr Tscal div5_2 = (5. / 2.);
769 constexpr Tscal div3_2 = (3. / 2.);
770 constexpr Tscal div1_2 = (1. / 2.);
771
772 Tscal t1 = div9_2 - q;
773 Tscal t2 = div7_2 - q;
774 Tscal t3 = div5_2 - q;
775 Tscal t4 = div3_2 - q;
776 Tscal t5 = div1_2 - q;
777
778 t1 = sham::pow_constexpr<8>(t1);
779 t2 = sham::pow_constexpr<8>(t2);
780 t3 = sham::pow_constexpr<8>(t3);
781 t4 = sham::pow_constexpr<8>(t4);
782 t5 = sham::pow_constexpr<8>(t5);
783
784 t1 *= 1.;
785 t2 *= -9.;
786 t3 *= 36.;
787 t4 *= -84.;
788 t5 *= 126.;
789
790 if (q < div1_2) {
791 return t1 + t2 + t3 + t4 + t5;
792 } else if (q < div3_2) {
793 return t1 + t2 + t3 + t4;
794 } else if (q < div5_2) {
795 return t1 + t2 + t3;
796 } else if (q < div7_2) {
797 return t1 + t2;
798 } else if (q < div9_2) {
799 return t1;
800 } else
801 return 0;
802 }
803
804 inline static Tscal df(Tscal q) {
805
806 constexpr Tscal div9_2 = (9. / 2.);
807 constexpr Tscal div7_2 = (7. / 2.);
808 constexpr Tscal div5_2 = (5. / 2.);
809 constexpr Tscal div3_2 = (3. / 2.);
810 constexpr Tscal div1_2 = (1. / 2.);
811
812 Tscal t1 = div9_2 - q;
813 Tscal t2 = div7_2 - q;
814 Tscal t3 = div5_2 - q;
815 Tscal t4 = div3_2 - q;
816 Tscal t5 = div1_2 - q;
817
818 t1 = sham::pow_constexpr<7>(t1);
819 t2 = sham::pow_constexpr<7>(t2);
820 t3 = sham::pow_constexpr<7>(t3);
821 t4 = sham::pow_constexpr<7>(t4);
822 t5 = sham::pow_constexpr<7>(t5);
823
824 t1 *= (-8.) * (1.);
825 t2 *= (-8.) * (-9.);
826 t3 *= (-8.) * (36.);
827 t4 *= (-8.) * (-84.);
828 t5 *= (-8.) * (126.);
829
830 if (q < div1_2) {
831 return t1 + t2 + t3 + t4 + t5;
832 } else if (q < div3_2) {
833 return t1 + t2 + t3 + t4;
834 } else if (q < div5_2) {
835 return t1 + t2 + t3;
836 } else if (q < div7_2) {
837 return t1 + t2;
838 } else if (q < div9_2) {
839 return t1;
840 } else
841 return 0;
842 }
843
844 inline static Tscal ddf(Tscal q) {
845 Tscal t1 = sham::pow_constexpr<6>(1.0 / 2.0 - q);
846 Tscal t2 = sham::pow_constexpr<6>(3.0 / 2.0 - q);
847 Tscal t3 = sham::pow_constexpr<6>(5.0 / 2.0 - q);
848 Tscal t4 = sham::pow_constexpr<6>(7.0 / 2.0 - q);
849 Tscal t5 = sham::pow_constexpr<6>(9.0 / 2.0 - q);
850 if (q < 1.0 / 2.0) {
851 return 7056 * t1 - 4704 * t2 + 2016 * t3 - 504 * t4 + 56 * t5;
852 } else if (q < 3.0 / 2.0) {
853 return -4704 * t2 + 2016 * t3 - 504 * t4 + 56 * t5;
854 } else if (q < 5.0 / 2.0) {
855 return 2016 * t3 - 504 * t4 + 56 * t5;
856 } else if (q < 7.0 / 2.0) {
857 return -504 * t4 + 56 * t5;
858 } else if (q < 9.0 / 2.0) {
859 return 56 * t5;
860 } else
861 return 0;
862 }
863
864 inline static Tscal phi_tilde_3d(Tscal q) {
865 Tscal t1 = sham::pow_constexpr<10>(q);
866 Tscal t2 = sham::pow_constexpr<11>(q);
867 Tscal t3 = sham::pow_constexpr<2>(q);
868 Tscal t4 = sham::pow_constexpr<3>(q);
869 Tscal t5 = sham::pow_constexpr<4>(q);
870 Tscal t6 = sham::pow_constexpr<5>(q);
871 Tscal t7 = sham::pow_constexpr<6>(q);
872 Tscal t8 = sham::pow_constexpr<7>(q);
873 Tscal t9 = sham::pow_constexpr<8>(q);
874 Tscal t10 = sham::pow_constexpr<9>(q);
875 if (q < 1.0 / 2.0) {
876 return (1.0 / 2816.0) * shambase::constants::pi<Tscal>
877 * (7168 * t1 - 98560 * t9 + 908160 * t7 - 6408864 * t5 + 34283436 * t3
878 - 157802293);
879 } else if (q < 3.0 / 2.0) {
880 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
881 * (-28672 * t2 + 315392 * t1 - 1182720 * t10 + 887040 * t9 + 3801600 * t8
882 + 413952 * t7 - 32199552 * t6 + 36960 * t5 + 171412560 * t4
883 - 789011388 * q - 7)
884 / q;
885 } else if (q < 5.0 / 2.0) {
886 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
887 * (14336 * t2 - 315392 * t1 + 2956800 * t10 - 15079680 * t9 + 43718400 * t8
888 - 66646272 * t7 + 43243200 * t6 - 53850720 * t5 + 191620440 * t4
889 - 792042570 * q + 826679)
890 / q;
891 } else if (q < 7.0 / 2.0) {
892 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
893 * (-4096 * t2 + 135168 * t1 - 1971200 * t10 + 16600320 * t9 - 88281600 * t8
894 + 302953728 * t7 - 649756800 * t6 + 771149280 * t5 - 324004560 * t4
895 - 577198820 * q - 96829571)
896 / q;
897 } else if (q < 9.0 / 2.0) {
898 return (1.0 / 28160.0) * shambase::constants::pi<Tscal>
899 * (1024 * t2 - 45056 * t1 + 887040 * t10 - 10264320 * t9 + 76982400 * t8
900 - 387991296 * t7 + 1309470624 * t6 - 2806008480 * t5 + 3156759540 * t4
901 - 4261625379 * q + 1783667601)
902 / q;
903 } else
904 return -60480 * shambase::constants::pi<Tscal> / q;
905 }
906
907 inline static Tscal phi_tilde_3d_prime(Tscal q) {
908 Tscal t1 = sham::pow_constexpr<10>(q);
909 Tscal t2 = sham::pow_constexpr<11>(q);
910 Tscal t3 = sham::pow_constexpr<2>(q);
911 Tscal t4 = sham::pow_constexpr<3>(q);
912 Tscal t5 = sham::pow_constexpr<4>(q);
913 Tscal t6 = sham::pow_constexpr<5>(q);
914 Tscal t7 = sham::pow_constexpr<6>(q);
915 Tscal t8 = sham::pow_constexpr<7>(q);
916 Tscal t9 = sham::pow_constexpr<8>(q);
917 Tscal t10 = sham::pow_constexpr<9>(q);
918 if (q < 1.0 / 2.0) {
919 return (1.0 / 2816.0) * shambase::constants::pi<Tscal>
920 * (71680 * t10 - 788480 * t8 + 5448960 * t6 - 25635456 * t4 + 68566872 * q);
921 } else if (q < 3.0 / 2.0) {
922 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
923 * (-315392 * t1 + 3153920 * t10 - 10644480 * t9 + 7096320 * t8
924 + 26611200 * t7 + 2483712 * t6 - 160997760 * t5 + 147840 * t4
925 + 514237680 * t3 - 789011388)
926 / q
927 - (1.0 / 14080.0) * shambase::constants::pi<Tscal>
928 * (-28672 * t2 + 315392 * t1 - 1182720 * t10 + 887040 * t9
929 + 3801600 * t8 + 413952 * t7 - 32199552 * t6 + 36960 * t5
930 + 171412560 * t4 - 789011388 * q - 7)
931 / t3;
932 } else if (q < 5.0 / 2.0) {
933 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
934 * (157696 * t1 - 3153920 * t10 + 26611200 * t9 - 120637440 * t8
935 + 306028800 * t7 - 399877632 * t6 + 216216000 * t5 - 215402880 * t4
936 + 574861320 * t3 - 792042570)
937 / q
938 - (1.0 / 14080.0) * shambase::constants::pi<Tscal>
939 * (14336 * t2 - 315392 * t1 + 2956800 * t10 - 15079680 * t9
940 + 43718400 * t8 - 66646272 * t7 + 43243200 * t6 - 53850720 * t5
941 + 191620440 * t4 - 792042570 * q + 826679)
942 / t3;
943 } else if (q < 7.0 / 2.0) {
944 return (1.0 / 14080.0) * shambase::constants::pi<Tscal>
945 * (-45056 * t1 + 1351680 * t10 - 17740800 * t9 + 132802560 * t8
946 - 617971200 * t7 + 1817722368 * t6 - 3248784000 * t5 + 3084597120 * t4
947 - 972013680 * t3 - 577198820)
948 / q
949 - (1.0 / 14080.0) * shambase::constants::pi<Tscal>
950 * (-4096 * t2 + 135168 * t1 - 1971200 * t10 + 16600320 * t9
951 - 88281600 * t8 + 302953728 * t7 - 649756800 * t6 + 771149280 * t5
952 - 324004560 * t4 - 577198820 * q - 96829571)
953 / t3;
954 } else if (q < 9.0 / 2.0) {
955 return (1.0 / 28160.0) * shambase::constants::pi<Tscal>
956 * (11264 * t1 - 450560 * t10 + 7983360 * t9 - 82114560 * t8
957 + 538876800 * t7 - 2327947776 * t6 + 6547353120 * t5
958 - 11224033920 * t4 + 9470278620 * t3 - 4261625379)
959 / q
960 - (1.0 / 28160.0) * shambase::constants::pi<Tscal>
961 * (1024 * t2 - 45056 * t1 + 887040 * t10 - 10264320 * t9
962 + 76982400 * t8 - 387991296 * t7 + 1309470624 * t6 - 2806008480 * t5
963 + 3156759540 * t4 - 4261625379 * q + 1783667601)
964 / t3;
965 } else
966 return 60480 * shambase::constants::pi<Tscal> / t3;
967 }
968 };
969
970 template<class Tscal>
971 class KernelDefM10 {
972 public:
973 inline static constexpr Tscal Rkern = 5;
975 inline static constexpr Tscal hfactd = 1.0;
976
978 inline static constexpr Tscal norm_1d = 1. / 362880;
980 inline static constexpr Tscal norm_2d = 11. / (2922230 * shambase::constants::pi<Tscal>);
982 inline static constexpr Tscal norm_3d = 6. / (3628800. * shambase::constants::pi<Tscal>);
983
984 inline static Tscal f(Tscal q) {
985
986 Tscal t1 = 5 - q;
987 Tscal t2 = 4 - q;
988 Tscal t3 = 3 - q;
989 Tscal t4 = 2 - q;
990 Tscal t5 = 1 - q;
991
992 t1 = sham::pow_constexpr<9>(t1);
993 t2 = sham::pow_constexpr<9>(t2);
994 t3 = sham::pow_constexpr<9>(t3);
995 t4 = sham::pow_constexpr<9>(t4);
996 t5 = sham::pow_constexpr<9>(t5);
997
998 t1 *= 1.;
999 t2 *= -10.;
1000 t3 *= 45.;
1001 t4 *= -120.;
1002 t5 *= 210.;
1003
1004 if (q < 1) {
1005 return t1 + t2 + t3 + t4 + t5;
1006 } else if (q < 2) {
1007 return t1 + t2 + t3 + t4;
1008 } else if (q < 3) {
1009 return t1 + t2 + t3;
1010 } else if (q < 4) {
1011 return t1 + t2;
1012 } else if (q < 5) {
1013 return t1;
1014 } else
1015 return 0;
1016 }
1017
1018 inline static Tscal df(Tscal q) {
1019
1020 Tscal t1 = 5 - q;
1021 Tscal t2 = 4 - q;
1022 Tscal t3 = 3 - q;
1023 Tscal t4 = 2 - q;
1024 Tscal t5 = 1 - q;
1025
1026 t1 = sham::pow_constexpr<8>(t1);
1027 t2 = sham::pow_constexpr<8>(t2);
1028 t3 = sham::pow_constexpr<8>(t3);
1029 t4 = sham::pow_constexpr<8>(t4);
1030 t5 = sham::pow_constexpr<8>(t5);
1031
1032 t1 *= (-9.) * (1.);
1033 t2 *= (-9.) * (-10.);
1034 t3 *= (-9.) * (45.);
1035 t4 *= (-9.) * (-120.);
1036 t5 *= (-9.) * (210.);
1037
1038 if (q < 1) {
1039 return t1 + t2 + t3 + t4 + t5;
1040 } else if (q < 2) {
1041 return t1 + t2 + t3 + t4;
1042 } else if (q < 3) {
1043 return t1 + t2 + t3;
1044 } else if (q < 4) {
1045 return t1 + t2;
1046 } else if (q < 5) {
1047 return t1;
1048 } else
1049 return 0;
1050 }
1051
1052 inline static Tscal ddf(Tscal q) {
1053 Tscal t1 = sham::pow_constexpr<7>(1 - q);
1054 Tscal t2 = sham::pow_constexpr<7>(2 - q);
1055 Tscal t3 = sham::pow_constexpr<7>(3 - q);
1056 Tscal t4 = sham::pow_constexpr<7>(4 - q);
1057 Tscal t5 = sham::pow_constexpr<7>(5 - q);
1058 if (q < 1) {
1059 return 15120 * t1 - 8640 * t2 + 3240 * t3 - 720 * t4 + 72 * t5;
1060 } else if (q < 2) {
1061 return -8640 * t2 + 3240 * t3 - 720 * t4 + 72 * t5;
1062 } else if (q < 3) {
1063 return 3240 * t3 - 720 * t4 + 72 * t5;
1064 } else if (q < 4) {
1065 return -720 * t4 + 72 * t5;
1066 } else if (q < 5) {
1067 return 72 * t5;
1068 } else
1069 return 0;
1070 }
1071
1072 inline static Tscal phi_tilde_3d(Tscal q) {
1073 Tscal t1 = sham::pow_constexpr<10>(q);
1074 Tscal t2 = sham::pow_constexpr<11>(q);
1075 Tscal t3 = sham::pow_constexpr<12>(q);
1076 Tscal t4 = sham::pow_constexpr<2>(q);
1077 Tscal t5 = sham::pow_constexpr<3>(q);
1078 Tscal t6 = sham::pow_constexpr<4>(q);
1079 Tscal t7 = sham::pow_constexpr<5>(q);
1080 Tscal t8 = sham::pow_constexpr<6>(q);
1081 Tscal t9 = sham::pow_constexpr<7>(q);
1082 Tscal t10 = sham::pow_constexpr<8>(q);
1083 Tscal t11 = sham::pow_constexpr<9>(q);
1084 if (q < 1) {
1085 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1086 * (-63 * t2 + 378 * t1 - 3850 * t10 + 37620 * t8 - 291060 * t6 + 1718090 * t4
1087 - 8766690);
1088 } else if (q < 2) {
1089 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1090 * (42 * t3 - 756 * t2 + 5544 * t1 - 20020 * t11 + 31185 * t10 - 3960 * t9
1091 + 38808 * t8 - 316008 * t7 + 10395 * t6 + 1715780 * t5 - 8766564 * q - 21)
1092 / q;
1093 } else if (q < 3) {
1094 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1095 * (-18 * t3 + 540 * t2 - 7128 * t1 + 53900 * t11 - 253935 * t10 + 756360 * t9
1096 - 1380456 * t8 + 1508760 * t7 - 1510245 * t6 + 2391620 * t5 - 8914020 * q
1097 + 49131)
1098 / q;
1099 } else if (q < 4) {
1100 return (1.0 / 33.0) * shambase::constants::pi<Tscal>
1101 * (9 * t3 - 378 * t2 + 7128 * t1 - 79310 * t11 + 574695 * t10 - 2817540 * t9
1102 + 9363816 * t8 - 20365884 * t7 + 26208765 * t6 - 14702930 * t5
1103 - 8262102 * q - 4684707)
1104 / q;
1105 } else if (q < 5) {
1106 return (1.0 / 33.0) * shambase::constants::pi<Tscal>
1107 * (-t3 + 54 * t2 - 1320 * t1 + 19250 * t11 - 185625 * t10 + 1237500 * t9
1108 - 5775000 * t8 + 18562500 * t7 - 38671875 * t6 + 42968750 * t5
1109 - 58593750 * q + 28869725)
1110 / q;
1111 } else
1112 return -604800 * shambase::constants::pi<Tscal> / q;
1113 }
1114
1115 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1116 Tscal t1 = sham::pow_constexpr<10>(q);
1117 Tscal t2 = sham::pow_constexpr<11>(q);
1118 Tscal t3 = sham::pow_constexpr<12>(q);
1119 Tscal t4 = sham::pow_constexpr<2>(q);
1120 Tscal t5 = sham::pow_constexpr<3>(q);
1121 Tscal t6 = sham::pow_constexpr<4>(q);
1122 Tscal t7 = sham::pow_constexpr<5>(q);
1123 Tscal t8 = sham::pow_constexpr<6>(q);
1124 Tscal t9 = sham::pow_constexpr<7>(q);
1125 Tscal t10 = sham::pow_constexpr<8>(q);
1126 Tscal t11 = sham::pow_constexpr<9>(q);
1127 if (q < 1) {
1128 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1129 * (-693 * t1 + 3780 * t11 - 30800 * t9 + 225720 * t7 - 1164240 * t5
1130 + 3436180 * q);
1131 } else if (q < 2) {
1132 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1133 * (504 * t2 - 8316 * t1 + 55440 * t11 - 180180 * t10 + 249480 * t9
1134 - 27720 * t8 + 232848 * t7 - 1580040 * t6 + 41580 * t5 + 5147340 * t4
1135 - 8766564)
1136 / q
1137 - (2.0 / 33.0) * shambase::constants::pi<Tscal>
1138 * (42 * t3 - 756 * t2 + 5544 * t1 - 20020 * t11 + 31185 * t10
1139 - 3960 * t9 + 38808 * t8 - 316008 * t7 + 10395 * t6 + 1715780 * t5
1140 - 8766564 * q - 21)
1141 / t4;
1142 } else if (q < 3) {
1143 return (2.0 / 33.0) * shambase::constants::pi<Tscal>
1144 * (-216 * t2 + 5940 * t1 - 71280 * t11 + 485100 * t10 - 2031480 * t9
1145 + 5294520 * t8 - 8282736 * t7 + 7543800 * t6 - 6040980 * t5
1146 + 7174860 * t4 - 8914020)
1147 / q
1148 - (2.0 / 33.0) * shambase::constants::pi<Tscal>
1149 * (-18 * t3 + 540 * t2 - 7128 * t1 + 53900 * t11 - 253935 * t10
1150 + 756360 * t9 - 1380456 * t8 + 1508760 * t7 - 1510245 * t6
1151 + 2391620 * t5 - 8914020 * q + 49131)
1152 / t4;
1153 } else if (q < 4) {
1154 return (1.0 / 33.0) * shambase::constants::pi<Tscal>
1155 * (108 * t2 - 4158 * t1 + 71280 * t11 - 713790 * t10 + 4597560 * t9
1156 - 19722780 * t8 + 56182896 * t7 - 101829420 * t6 + 104835060 * t5
1157 - 44108790 * t4 - 8262102)
1158 / q
1159 - (1.0 / 33.0) * shambase::constants::pi<Tscal>
1160 * (9 * t3 - 378 * t2 + 7128 * t1 - 79310 * t11 + 574695 * t10
1161 - 2817540 * t9 + 9363816 * t8 - 20365884 * t7 + 26208765 * t6
1162 - 14702930 * t5 - 8262102 * q - 4684707)
1163 / t4;
1164 } else if (q < 5) {
1165 return (1.0 / 33.0) * shambase::constants::pi<Tscal>
1166 * (-12 * t2 + 594 * t1 - 13200 * t11 + 173250 * t10 - 1485000 * t9
1167 + 8662500 * t8 - 34650000 * t7 + 92812500 * t6 - 154687500 * t5
1168 + 128906250 * t4 - 58593750)
1169 / q
1170 - (1.0 / 33.0) * shambase::constants::pi<Tscal>
1171 * (-t3 + 54 * t2 - 1320 * t1 + 19250 * t11 - 185625 * t10
1172 + 1237500 * t9 - 5775000 * t8 + 18562500 * t7 - 38671875 * t6
1173 + 42968750 * t5 - 58593750 * q + 28869725)
1174 / t4;
1175 } else
1176 return 604800 * shambase::constants::pi<Tscal> / t4;
1177 }
1178 };
1179
1180 template<class Tscal>
1181 class KernelDefC2 {
1182 public:
1183 inline static constexpr Tscal Rkern = 2;
1185 inline static constexpr Tscal hfactd = 1.4;
1186
1188 inline static constexpr Tscal norm_1d = 3. / 4.;
1190 inline static constexpr Tscal norm_2d = 7. / (4 * shambase::constants::pi<Tscal>);
1192 inline static constexpr Tscal norm_3d = 21 / (16 * shambase::constants::pi<Tscal>);
1193
1194 inline static Tscal f(Tscal q) {
1195
1196 constexpr Tscal div1_2 = (1. / 2.);
1197
1198 Tscal p1 = (1 - q * div1_2);
1199 Tscal p2 = (1 + q * 2);
1200
1201 p1 *= p1;
1202 p1 *= p1;
1203
1204 if (q < 2.) {
1205 return p1 * p2;
1206 } else
1207 return 0;
1208 }
1209
1210 inline static Tscal df(Tscal q) {
1211
1212 constexpr Tscal div1_2 = (1. / 2.);
1213 constexpr Tscal div1_8 = (1. / 8.);
1214 constexpr Tscal div1_4 = (1. / 4.);
1215
1216 Tscal p1 = (1 - q * div1_2);
1217 Tscal p2 = (1 + q * 2);
1218
1219 Tscal p3 = p1 * p1 * p1;
1220
1221 if (q < 2.) {
1222 return 2 * (p3 * p1 - p3 * p2);
1223 } else
1224 return 0;
1225 }
1226
1227 inline static Tscal ddf(Tscal q) {
1228 Tscal t1 = sham::pow_constexpr<2>(1 - (1.0 / 2.0) * q);
1229 Tscal t2 = sham::pow_constexpr<3>(1 - (1.0 / 2.0) * q);
1230 if (q < 2) {
1231 return -8 * t2 + 3 * t1 * (2 * q + 1);
1232 } else
1233 return 0;
1234 }
1235
1236 inline static Tscal phi_tilde_3d(Tscal q) {
1237 Tscal t1 = sham::pow_constexpr<2>(q);
1238 Tscal t2 = sham::pow_constexpr<3>(q);
1239 Tscal t3 = sham::pow_constexpr<4>(q);
1240 Tscal t4 = sham::pow_constexpr<5>(q);
1241 if (q < 2) {
1242 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
1243 * (t1 * (3 * t4 - 30 * t3 + 112 * t2 - 168 * t1 + 224) - 384);
1244 } else
1245 return -(16.0 / 21.0) * shambase::constants::pi<Tscal> / q;
1246 }
1247
1248 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1249 Tscal t1 = sham::pow_constexpr<2>(q);
1250 Tscal t2 = sham::pow_constexpr<3>(q);
1251 Tscal t3 = sham::pow_constexpr<4>(q);
1252 Tscal t4 = sham::pow_constexpr<5>(q);
1253 if (q < 2) {
1254 return (1.0 / 336.0) * shambase::constants::pi<Tscal>
1255 * (t1 * (15 * t3 - 120 * t2 + 336 * t1 - 336 * q)
1256 + 2 * q * (3 * t4 - 30 * t3 + 112 * t2 - 168 * t1 + 224));
1257 } else
1258 return (16.0 / 21.0) * shambase::constants::pi<Tscal> / t1;
1259 }
1260 };
1261
1262 template<class Tscal>
1263 class KernelDefC4 {
1264 public:
1265 inline static constexpr Tscal Rkern = 2;
1267 inline static constexpr Tscal hfactd = 1.6;
1268
1270 inline static constexpr Tscal norm_1d = 27. / 32.;
1272 inline static constexpr Tscal norm_2d = 9. / (4 * shambase::constants::pi<Tscal>);
1274 inline static constexpr Tscal norm_3d = 495. / (256. * shambase::constants::pi<Tscal>);
1275
1276 inline static Tscal f(Tscal q) {
1277
1278 constexpr Tscal div1_2 = (1. / 2.);
1279 constexpr Tscal div35_12 = (35. / 12.);
1280
1281 Tscal p1 = (1 - q * div1_2);
1282 Tscal p2 = (1 + q * 3 + div35_12 * q * q);
1283
1284 p1 *= p1;
1285 p1 = p1 * p1 * p1;
1286
1287 if (q < 2.) {
1288 return p1 * p2;
1289 } else
1290 return 0;
1291 }
1292
1293 inline static Tscal df(Tscal q) {
1294
1295 constexpr Tscal div7_96 = (7. / 96.);
1296
1297 Tscal p1 = (-2 + q);
1298 Tscal p2 = (2 + 5 * q);
1299
1300 Tscal p14 = p1 * p1;
1301 p14 *= p14;
1302
1303 if (q < 2.) {
1304 return div7_96 * p14 * p1 * q * p2;
1305 } else
1306 return 0;
1307 }
1308
1309 inline static Tscal ddf(Tscal q) {
1310 Tscal t1 = sham::pow_constexpr<2>(q);
1311 Tscal t2 = sham::pow_constexpr<4>(1 - (1.0 / 2.0) * q);
1312 Tscal t3 = sham::pow_constexpr<5>(1 - (1.0 / 2.0) * q);
1313 Tscal t4 = sham::pow_constexpr<6>(1 - (1.0 / 2.0) * q);
1314 if (q < 2) {
1315 return (35.0 / 6.0) * t4 - 6 * t3 * ((35.0 / 6.0) * q + 3)
1316 + (15.0 / 2.0) * t2 * ((35.0 / 12.0) * t1 + 3 * q + 1);
1317 } else
1318 return 0;
1319 }
1320
1321 inline static Tscal phi_tilde_3d(Tscal q) {
1322 Tscal t1 = sham::pow_constexpr<2>(q);
1323 Tscal t2 = sham::pow_constexpr<4>(q);
1324 Tscal t3 = sham::pow_constexpr<5>(q);
1325 Tscal t4 = sham::pow_constexpr<6>(q);
1326 Tscal t5 = sham::pow_constexpr<7>(q);
1327 Tscal t6 = sham::pow_constexpr<8>(q);
1328 if (q < 2) {
1329 return (1.0 / 63360.0) * shambase::constants::pi<Tscal>
1330 * (t1
1331 * (105 * t6 - 1408 * t5 + 7700 * t4 - 21120 * t3 + 26400 * t2
1332 - 29568 * t1 + 42240)
1333 - 56320);
1334 } else
1335 return -(256.0 / 495.0) * shambase::constants::pi<Tscal> / q;
1336 }
1337
1338 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1339 Tscal t1 = sham::pow_constexpr<2>(q);
1340 Tscal t2 = sham::pow_constexpr<3>(q);
1341 Tscal t3 = sham::pow_constexpr<4>(q);
1342 Tscal t4 = sham::pow_constexpr<5>(q);
1343 Tscal t5 = sham::pow_constexpr<6>(q);
1344 Tscal t6 = sham::pow_constexpr<7>(q);
1345 Tscal t7 = sham::pow_constexpr<8>(q);
1346 if (q < 2) {
1347 return (1.0 / 63360.0) * shambase::constants::pi<Tscal>
1348 * (t1
1349 * (840 * t6 - 9856 * t5 + 46200 * t4 - 105600 * t3 + 105600 * t2
1350 - 59136 * q)
1351 + 2 * q
1352 * (105 * t7 - 1408 * t6 + 7700 * t5 - 21120 * t4 + 26400 * t3
1353 - 29568 * t1 + 42240));
1354 } else
1355 return (256.0 / 495.0) * shambase::constants::pi<Tscal> / t1;
1356 }
1357 };
1358
1359 template<class Tscal>
1360 class KernelDefC6 {
1361 public:
1362 inline static constexpr Tscal Rkern = 2;
1364 inline static constexpr Tscal hfactd = 2.2;
1365
1367 inline static constexpr Tscal norm_1d = 15. / 16.;
1369 inline static constexpr Tscal norm_2d = 39. / (14. * shambase::constants::pi<Tscal>);
1371 inline static constexpr Tscal norm_3d = 1365. / (512. * shambase::constants::pi<Tscal>);
1372
1373 inline static Tscal f(Tscal q) {
1374
1375 constexpr Tscal div1_2 = (1. / 2.);
1376 constexpr Tscal div25_4 = (25. / 4.);
1377
1378 Tscal p1 = (1 - q * div1_2);
1379 Tscal p2 = (1 + q * 4 + div25_4 * q * q + 4 * q * q * q);
1380
1381 p1 *= p1;
1382 p1 *= p1;
1383 p1 *= p1;
1384
1385 if (q < 2.) {
1386 return p1 * p2;
1387 } else
1388 return 0;
1389 }
1390
1391 inline static Tscal df(Tscal q) {
1392
1393 constexpr Tscal div11_512 = (11. / 512.);
1394
1395 Tscal p1 = (-2 + q);
1396 Tscal p2 = 2 + 7 * q + 8 * q * q;
1397
1398 Tscal p12 = p1 * p1;
1399 Tscal p14 = p12 * p12;
1400 Tscal p17 = p12 * p14 * p1;
1401
1402 if (q < 2.) {
1403 return div11_512 * p17 * q * p2;
1404 } else
1405 return 0;
1406 }
1407
1408 inline static Tscal ddf(Tscal q) {
1409 Tscal t1 = sham::pow_constexpr<2>(q);
1410 Tscal t2 = sham::pow_constexpr<3>(q);
1411 Tscal t3 = sham::pow_constexpr<6>(1 - (1.0 / 2.0) * q);
1412 Tscal t4 = sham::pow_constexpr<7>(1 - (1.0 / 2.0) * q);
1413 Tscal t5 = sham::pow_constexpr<8>(1 - (1.0 / 2.0) * q);
1414 if (q < 2) {
1415 return t5 * (24 * q + 25.0 / 2.0) - 8 * t4 * (12 * t1 + (25.0 / 2.0) * q + 4)
1416 + 14 * t3 * (4 * t2 + (25.0 / 4.0) * t1 + 4 * q + 1);
1417 } else
1418 return 0;
1419 }
1420
1421 inline static Tscal phi_tilde_3d(Tscal q) {
1422 Tscal t1 = sham::pow_constexpr<10>(q);
1423 Tscal t2 = sham::pow_constexpr<11>(q);
1424 Tscal t3 = sham::pow_constexpr<2>(q);
1425 Tscal t4 = sham::pow_constexpr<4>(q);
1426 Tscal t5 = sham::pow_constexpr<6>(q);
1427 Tscal t6 = sham::pow_constexpr<7>(q);
1428 Tscal t7 = sham::pow_constexpr<8>(q);
1429 Tscal t8 = sham::pow_constexpr<9>(q);
1430 if (q < 2) {
1431 return (1.0 / 1397760.0) * shambase::constants::pi<Tscal>
1432 * (t3
1433 * (480 * t2 - 8085 * t1 + 58240 * t8 - 229320 * t7 + 512512 * t6
1434 - 560560 * t5 + 549120 * t4 - 768768 * t3 + 931840)
1435 - 1003520);
1436 } else
1437 return -(512.0 / 1365.0) * shambase::constants::pi<Tscal> / q;
1438 }
1439
1440 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1441 Tscal t1 = sham::pow_constexpr<10>(q);
1442 Tscal t2 = sham::pow_constexpr<11>(q);
1443 Tscal t3 = sham::pow_constexpr<2>(q);
1444 Tscal t4 = sham::pow_constexpr<3>(q);
1445 Tscal t5 = sham::pow_constexpr<4>(q);
1446 Tscal t6 = sham::pow_constexpr<5>(q);
1447 Tscal t7 = sham::pow_constexpr<6>(q);
1448 Tscal t8 = sham::pow_constexpr<7>(q);
1449 Tscal t9 = sham::pow_constexpr<8>(q);
1450 Tscal t10 = sham::pow_constexpr<9>(q);
1451 if (q < 2) {
1452 return (1.0 / 1397760.0) * shambase::constants::pi<Tscal>
1453 * (t3
1454 * (5280 * t1 - 80850 * t10 + 524160 * t9 - 1834560 * t8 + 3587584 * t7
1455 - 3363360 * t6 + 2196480 * t4 - 1537536 * q)
1456 + 2 * q
1457 * (480 * t2 - 8085 * t1 + 58240 * t10 - 229320 * t9 + 512512 * t8
1458 - 560560 * t7 + 549120 * t5 - 768768 * t3 + 931840));
1459 } else
1460 return (512.0 / 1365.0) * shambase::constants::pi<Tscal> / t3;
1461 }
1462 };
1463
1472 template<class Tscal>
1473 class KernelDefTGauss3 {
1474 public:
1475 inline static constexpr Tscal Rkern = 3;
1476 inline static constexpr Tscal hfactd = 1.5;
1477
1479 inline static constexpr Tscal norm_1d = 0.564202047051383;
1481 inline static constexpr Tscal norm_2d = 0.318349173592935;
1483 inline static constexpr Tscal norm_3d = 0.179666148218087;
1484
1485 inline static Tscal f(Tscal q) {
1486 Tscal t1 = sham::pow_constexpr<2>(q);
1487 if (q < 3) {
1488 return sycl::exp(-t1);
1489 } else
1490 return 0;
1491 }
1492
1493 inline static Tscal df(Tscal q) {
1494 Tscal t1 = sham::pow_constexpr<2>(q);
1495 if (q < 3) {
1496 return -2 * q * sycl::exp(-t1);
1497 } else
1498 return 0;
1499 }
1500
1501 inline static Tscal ddf(Tscal q) {
1502 Tscal t1 = sham::pow_constexpr<2>(q);
1503 if (q < 3) {
1504 return (4 * t1 - 2) * sycl::exp(-t1);
1505 } else
1506 return 0;
1507 }
1508
1509 inline static Tscal phi_tilde_3d(Tscal q) {
1510 if (q == 0) {
1511 return -6.282409900511787;
1512 } else if (q < 3) {
1513 return 2 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-9})
1514 - sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(q) / q;
1515 } else
1516 return (-sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(Tscal{3})
1517 + 6 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-9}))
1518 / q;
1519 }
1520
1521 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1522 Tscal t1 = sham::pow_constexpr<2>(q);
1523 if (q == 0) {
1524 return 0;
1525 } else if (q < 3) {
1526 return -2 * shambase::constants::pi<Tscal> * sycl::exp(-t1) / q
1527 + sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(q) / t1;
1528 } else
1529 return -(-sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(Tscal{3})
1530 + 6 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-9}))
1531 / t1;
1532 }
1533 };
1534
1543 template<class Tscal>
1544 class KernelDefTGauss5 {
1545 public:
1546 inline static constexpr Tscal Rkern = 5;
1547 inline static constexpr Tscal hfactd = 1.5;
1548
1550 inline static constexpr Tscal norm_1d = 0.564189583548624;
1552 inline static constexpr Tscal norm_2d = 0.318309886188211;
1554 inline static constexpr Tscal norm_3d = 0.179587122139514;
1555
1556 inline static Tscal f(Tscal q) {
1557 Tscal t1 = sham::pow_constexpr<2>(q);
1558 if (q < 5) {
1559 return sycl::exp(-t1);
1560 } else
1561 return 0;
1562 }
1563
1564 inline static Tscal df(Tscal q) {
1565 Tscal t1 = sham::pow_constexpr<2>(q);
1566 if (q < 5) {
1567 return -2 * q * sycl::exp(-t1);
1568 } else
1569 return 0;
1570 }
1571
1572 inline static Tscal ddf(Tscal q) {
1573 Tscal t1 = sham::pow_constexpr<2>(q);
1574 if (q < 5) {
1575 return (4 * t1 - 2) * sycl::exp(-t1);
1576 } else
1577 return 0;
1578 }
1579
1580 inline static Tscal phi_tilde_3d(Tscal q) {
1581 if (q == 0) {
1582 return -6.283185307092326;
1583 } else if (q < 5) {
1584 return 2 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-25})
1585 - sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(q) / q;
1586 } else
1587 return (-sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(Tscal{5})
1588 + 10 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-25}))
1589 / q;
1590 }
1591
1592 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1593 Tscal t1 = sham::pow_constexpr<2>(q);
1594 if (q == 0) {
1595 return 0;
1596 } else if (q < 5) {
1597 return -2 * shambase::constants::pi<Tscal> * sycl::exp(-t1) / q
1598 + sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(q) / t1;
1599 } else
1600 return -(-sycl::pow(shambase::constants::pi<Tscal>, 3.0 / 2.0) * sycl::erf(Tscal{5})
1601 + 10 * shambase::constants::pi<Tscal> * sycl::exp(Tscal{-25}))
1602 / t1;
1603 }
1604 };
1605
1606 template<class Tscal>
1607 class KernelDefM4DoubleHump {
1608 public:
1609 inline static constexpr Tscal Rkern = 2;
1611 inline static constexpr Tscal hfactd = 1.2;
1612
1614 inline static constexpr Tscal norm_1d = 2.;
1616 inline static constexpr Tscal norm_2d
1617 = (49. / 31.) * 10. / (7. * shambase::constants::pi<Tscal>);
1619 inline static constexpr Tscal norm_3d = (10. / 9.) * 1 / shambase::constants::pi<Tscal>;
1620
1621 inline static Tscal f(Tscal q) { return KernelDefM4<Tscal>::f(q) * q * q; }
1622
1623 inline static Tscal df(Tscal q) {
1624 return KernelDefM4<Tscal>::df(q) * q * q + 2 * KernelDefM4<Tscal>::f(q) * q;
1625 }
1626
1627 inline static Tscal ddf(Tscal q) {
1628 Tscal t1 = sham::pow_constexpr<2>(1 - q);
1629 Tscal t2 = sham::pow_constexpr<2>(2 - q);
1630 Tscal t3 = sham::pow_constexpr<2>(q);
1631 Tscal t4 = sham::pow_constexpr<3>(1 - q);
1632 Tscal t5 = sham::pow_constexpr<3>(2 - q);
1633 if (q < 1) {
1634 return t3 * ((9.0 / 2.0) * q - 3) + 4 * q * (3 * t1 - (3.0 / 4.0) * t2) - 2 * t4
1635 + (1.0 / 2.0) * t5;
1636 } else if (q < 2) {
1637 return -(3.0 / 4.0) * t3 * (2 * q - 4) - 3 * q * t2 + (1.0 / 2.0) * t5;
1638 } else
1639 return 0;
1640 }
1641
1642 inline static Tscal phi_tilde_3d(Tscal q) {
1643 Tscal t1 = sham::pow_constexpr<2>(q);
1644 Tscal t2 = sham::pow_constexpr<3>(q);
1645 Tscal t3 = sham::pow_constexpr<4>(q);
1646 Tscal t4 = sham::pow_constexpr<5>(q);
1647 Tscal t5 = sham::pow_constexpr<6>(q);
1648 Tscal t6 = sham::pow_constexpr<7>(q);
1649 Tscal t7 = sham::pow_constexpr<8>(q);
1650 if (q < 1) {
1651 return (1.0 / 280.0) * shambase::constants::pi<Tscal>
1652 * (t3 * (15 * t2 - 40 * t1 + 56) - 248);
1653 } else if (q < 2) {
1654 return (1.0 / 280.0) * shambase::constants::pi<Tscal>
1655 * (-5 * t7 + 40 * t6 - 112 * t5 + 112 * t4 - 256 * q + 4) / q;
1656 } else
1657 return -(9.0 / 10.0) * shambase::constants::pi<Tscal> / q;
1658 }
1659
1660 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1661 Tscal t1 = sham::pow_constexpr<2>(q);
1662 Tscal t2 = sham::pow_constexpr<3>(q);
1663 Tscal t3 = sham::pow_constexpr<4>(q);
1664 Tscal t4 = sham::pow_constexpr<5>(q);
1665 Tscal t5 = sham::pow_constexpr<6>(q);
1666 Tscal t6 = sham::pow_constexpr<7>(q);
1667 Tscal t7 = sham::pow_constexpr<8>(q);
1668 if (q < 1) {
1669 return (1.0 / 280.0) * shambase::constants::pi<Tscal>
1670 * (t3 * (45 * t1 - 80 * q) + 4 * t2 * (15 * t2 - 40 * t1 + 56));
1671 } else if (q < 2) {
1672 return (1.0 / 280.0) * shambase::constants::pi<Tscal>
1673 * (-40 * t6 + 280 * t5 - 672 * t4 + 560 * t3 - 256) / q
1674 - (1.0 / 280.0) * shambase::constants::pi<Tscal>
1675 * (-5 * t7 + 40 * t6 - 112 * t5 + 112 * t4 - 256 * q + 4) / t1;
1676 } else
1677 return (9.0 / 10.0) * shambase::constants::pi<Tscal> / t1;
1678 }
1679 };
1680
1681 template<class Tscal>
1682 class KernelDefM4DoubleHump3 {
1683 public:
1684 inline static constexpr Tscal Rkern = 2;
1686 inline static constexpr Tscal hfactd = 1.2;
1687
1689 inline static constexpr Tscal norm_1d = (105. / 31.) * 2. / 3.;
1691 inline static constexpr Tscal norm_2d
1692 = (14. / 9.) * 10. / (7. * shambase::constants::pi<Tscal>);
1694 inline static constexpr Tscal norm_3d = (126. / 127.) * 1 / shambase::constants::pi<Tscal>;
1695
1696 inline static Tscal f(Tscal q) { return KernelDefM4<Tscal>::f(q) * q * q * q; }
1697
1698 inline static Tscal df(Tscal q) {
1699 return KernelDefM4<Tscal>::df(q) * q * q * q + 3 * KernelDefM4<Tscal>::f(q) * q * q;
1700 }
1701
1702 inline static Tscal ddf(Tscal q) {
1703 Tscal t1 = sham::pow_constexpr<2>(1 - q);
1704 Tscal t2 = sham::pow_constexpr<2>(2 - q);
1705 Tscal t3 = sham::pow_constexpr<2>(q);
1706 Tscal t4 = sham::pow_constexpr<3>(1 - q);
1707 Tscal t5 = sham::pow_constexpr<3>(2 - q);
1708 Tscal t6 = sham::pow_constexpr<3>(q);
1709 if (q < 1) {
1710 return t6 * ((9.0 / 2.0) * q - 3) + 6 * t3 * (3 * t1 - (3.0 / 4.0) * t2)
1711 + 6 * q * (-t4 + (1.0 / 4.0) * t5);
1712 } else if (q < 2) {
1713 return -(3.0 / 4.0) * t6 * (2 * q - 4) - (9.0 / 2.0) * t3 * t2
1714 + (3.0 / 2.0) * q * t5;
1715 } else
1716 return 0;
1717 }
1718
1719 inline static Tscal phi_tilde_3d(Tscal q) {
1720 Tscal t1 = sham::pow_constexpr<2>(q);
1721 Tscal t2 = sham::pow_constexpr<3>(q);
1722 Tscal t3 = sham::pow_constexpr<5>(q);
1723 Tscal t4 = sham::pow_constexpr<6>(q);
1724 Tscal t5 = sham::pow_constexpr<7>(q);
1725 Tscal t6 = sham::pow_constexpr<8>(q);
1726 Tscal t7 = sham::pow_constexpr<9>(q);
1727 if (q < 1) {
1728 return (1.0 / 840.0) * shambase::constants::pi<Tscal>
1729 * (t3 * (35 * t2 - 90 * t1 + 112) - 756);
1730 } else if (q < 2) {
1731 return (1.0 / 2520.0) * shambase::constants::pi<Tscal>
1732 * (-35 * t7 + 270 * t6 - 720 * t5 + 672 * t4 - 2304 * q + 20) / q;
1733 } else
1734 return -(127.0 / 126.0) * shambase::constants::pi<Tscal> / q;
1735 }
1736
1737 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1738 Tscal t1 = sham::pow_constexpr<2>(q);
1739 Tscal t2 = sham::pow_constexpr<3>(q);
1740 Tscal t3 = sham::pow_constexpr<4>(q);
1741 Tscal t4 = sham::pow_constexpr<5>(q);
1742 Tscal t5 = sham::pow_constexpr<6>(q);
1743 Tscal t6 = sham::pow_constexpr<7>(q);
1744 Tscal t7 = sham::pow_constexpr<8>(q);
1745 Tscal t8 = sham::pow_constexpr<9>(q);
1746 if (q < 1) {
1747 return (1.0 / 840.0) * shambase::constants::pi<Tscal>
1748 * (t4 * (105 * t1 - 180 * q) + 5 * t3 * (35 * t2 - 90 * t1 + 112));
1749 } else if (q < 2) {
1750 return (1.0 / 2520.0) * shambase::constants::pi<Tscal>
1751 * (-315 * t7 + 2160 * t6 - 5040 * t5 + 4032 * t4 - 2304) / q
1752 - (1.0 / 2520.0) * shambase::constants::pi<Tscal>
1753 * (-35 * t8 + 270 * t7 - 720 * t6 + 672 * t5 - 2304 * q + 20) / t1;
1754 } else
1755 return (127.0 / 126.0) * shambase::constants::pi<Tscal> / t1;
1756 }
1757 };
1758
1759 template<class Tscal>
1760 class KernelDefM4DoubleHump5 {
1761 public:
1762 inline static constexpr Tscal Rkern = 2;
1764 inline static constexpr Tscal hfactd = 1.2;
1765
1767 inline static constexpr Tscal norm_1d = 252.0 / 127.0;
1769 inline static constexpr Tscal norm_2d = (28.0 / 17.0) / shambase::constants::pi<Tscal>;
1771 inline static constexpr Tscal norm_3d = (330.0 / 511.0) / shambase::constants::pi<Tscal>;
1772
1773 inline static Tscal f(Tscal q) {
1774 return KernelDefM4<Tscal>::f(q) * sham::pow_constexpr<5>(q);
1775 }
1776
1777 inline static Tscal df(Tscal q) {
1778 return KernelDefM4<Tscal>::df(q) * sham::pow_constexpr<5>(q)
1779 + 5 * KernelDefM4<Tscal>::f(q) * sham::pow_constexpr<4>(q);
1780 }
1781
1782 inline static Tscal ddf(Tscal q) {
1783 Tscal t1 = sham::pow_constexpr<2>(1 - q);
1784 Tscal t2 = sham::pow_constexpr<2>(2 - q);
1785 Tscal t3 = sham::pow_constexpr<3>(1 - q);
1786 Tscal t4 = sham::pow_constexpr<3>(2 - q);
1787 Tscal t5 = sham::pow_constexpr<3>(q);
1788 Tscal t6 = sham::pow_constexpr<4>(q);
1789 Tscal t7 = sham::pow_constexpr<5>(q);
1790 if (q < 1) {
1791 return t7 * ((9.0 / 2.0) * q - 3) + 10 * t6 * (3 * t1 - (3.0 / 4.0) * t2)
1792 + 20 * t5 * (-t3 + (1.0 / 4.0) * t4);
1793 } else if (q < 2) {
1794 return -(3.0 / 4.0) * t7 * (2 * q - 4) - (15.0 / 2.0) * t6 * t2 + 5 * t5 * t4;
1795 } else
1796 return 0;
1797 }
1798
1799 inline static Tscal phi_tilde_3d(Tscal q) {
1800 Tscal t1 = sham::pow_constexpr<10>(q);
1801 Tscal t2 = sham::pow_constexpr<11>(q);
1802 Tscal t3 = sham::pow_constexpr<2>(q);
1803 Tscal t4 = sham::pow_constexpr<3>(q);
1804 Tscal t5 = sham::pow_constexpr<7>(q);
1805 Tscal t6 = sham::pow_constexpr<8>(q);
1806 Tscal t7 = sham::pow_constexpr<9>(q);
1807 if (q < 1) {
1808 return (1.0 / 2310.0) * shambase::constants::pi<Tscal>
1809 * (t5 * (63 * t4 - 154 * t3 + 165) - 2805);
1810 } else if (q < 2) {
1811 return (1.0 / 2310.0) * shambase::constants::pi<Tscal>
1812 * (-21 * t2 + 154 * t1 - 385 * t7 + 330 * t6 - 2816 * q + 7) / q;
1813 } else
1814 return -(511.0 / 330.0) * shambase::constants::pi<Tscal> / q;
1815 }
1816
1817 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1818 Tscal t1 = sham::pow_constexpr<10>(q);
1819 Tscal t2 = sham::pow_constexpr<11>(q);
1820 Tscal t3 = sham::pow_constexpr<2>(q);
1821 Tscal t4 = sham::pow_constexpr<3>(q);
1822 Tscal t5 = sham::pow_constexpr<6>(q);
1823 Tscal t6 = sham::pow_constexpr<7>(q);
1824 Tscal t7 = sham::pow_constexpr<8>(q);
1825 Tscal t8 = sham::pow_constexpr<9>(q);
1826 if (q < 1) {
1827 return (1.0 / 2310.0) * shambase::constants::pi<Tscal>
1828 * (t6 * (189 * t3 - 308 * q) + 7 * t5 * (63 * t4 - 154 * t3 + 165));
1829 } else if (q < 2) {
1830 return (1.0 / 2310.0) * shambase::constants::pi<Tscal>
1831 * (-231 * t1 + 1540 * t8 - 3465 * t7 + 2640 * t6 - 2816) / q
1832 - (1.0 / 2310.0) * shambase::constants::pi<Tscal>
1833 * (-21 * t2 + 154 * t1 - 385 * t8 + 330 * t7 - 2816 * q + 7) / t3;
1834 } else
1835 return (511.0 / 330.0) * shambase::constants::pi<Tscal> / t3;
1836 }
1837 };
1838
1839 template<class Tscal>
1840 class KernelDefM4DoubleHump7 {
1841 public:
1842 inline static constexpr Tscal Rkern = 2;
1844 inline static constexpr Tscal hfactd = 1.2;
1845
1847 inline static constexpr Tscal norm_1d = 660.0 / 511.0;
1849 inline static constexpr Tscal norm_2d = (30.0 / 31.0) / shambase::constants::pi<Tscal>;
1851 inline static constexpr Tscal norm_3d = (715.0 / 2047.0) / shambase::constants::pi<Tscal>;
1852
1853 inline static Tscal f(Tscal q) {
1854 return KernelDefM4<Tscal>::f(q) * sham::pow_constexpr<7>(q);
1855 }
1856
1857 inline static Tscal df(Tscal q) {
1858 return KernelDefM4<Tscal>::df(q) * sham::pow_constexpr<7>(q)
1859 + 7 * KernelDefM4<Tscal>::f(q) * sham::pow_constexpr<6>(q);
1860 }
1861
1862 inline static Tscal ddf(Tscal q) {
1863 Tscal t1 = sham::pow_constexpr<2>(1 - q);
1864 Tscal t2 = sham::pow_constexpr<2>(2 - q);
1865 Tscal t3 = sham::pow_constexpr<3>(1 - q);
1866 Tscal t4 = sham::pow_constexpr<3>(2 - q);
1867 Tscal t5 = sham::pow_constexpr<5>(q);
1868 Tscal t6 = sham::pow_constexpr<6>(q);
1869 Tscal t7 = sham::pow_constexpr<7>(q);
1870 if (q < 1) {
1871 return t7 * ((9.0 / 2.0) * q - 3) + 14 * t6 * (3 * t1 - (3.0 / 4.0) * t2)
1872 + 42 * t5 * (-t3 + (1.0 / 4.0) * t4);
1873 } else if (q < 2) {
1874 return -(3.0 / 4.0) * t7 * (2 * q - 4) - (21.0 / 2.0) * t6 * t2
1875 + (21.0 / 2.0) * t5 * t4;
1876 } else
1877 return 0;
1878 }
1879
1880 inline static Tscal phi_tilde_3d(Tscal q) {
1881 Tscal t1 = sham::pow_constexpr<10>(q);
1882 Tscal t2 = sham::pow_constexpr<11>(q);
1883 Tscal t3 = sham::pow_constexpr<12>(q);
1884 Tscal t4 = sham::pow_constexpr<13>(q);
1885 Tscal t5 = sham::pow_constexpr<2>(q);
1886 Tscal t6 = sham::pow_constexpr<3>(q);
1887 Tscal t7 = sham::pow_constexpr<9>(q);
1888 if (q < 1) {
1889 return (1.0 / 25740.0) * shambase::constants::pi<Tscal>
1890 * (t7 * (495 * t6 - 1170 * t5 + 1144) - 53196);
1891 } else if (q < 2) {
1892 return (1.0 / 25740.0) * shambase::constants::pi<Tscal>
1893 * (-165 * t4 + 1170 * t3 - 2808 * t2 + 2288 * t1 - 53248 * q + 36) / q;
1894 } else
1895 return -(2047.0 / 715.0) * shambase::constants::pi<Tscal> / q;
1896 }
1897
1898 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1899 Tscal t1 = sham::pow_constexpr<10>(q);
1900 Tscal t2 = sham::pow_constexpr<11>(q);
1901 Tscal t3 = sham::pow_constexpr<12>(q);
1902 Tscal t4 = sham::pow_constexpr<13>(q);
1903 Tscal t5 = sham::pow_constexpr<2>(q);
1904 Tscal t6 = sham::pow_constexpr<3>(q);
1905 Tscal t7 = sham::pow_constexpr<8>(q);
1906 Tscal t8 = sham::pow_constexpr<9>(q);
1907 if (q < 1) {
1908 return (1.0 / 25740.0) * shambase::constants::pi<Tscal>
1909 * (t8 * (1485 * t5 - 2340 * q) + 9 * t7 * (495 * t6 - 1170 * t5 + 1144));
1910 } else if (q < 2) {
1911 return (1.0 / 25740.0) * shambase::constants::pi<Tscal>
1912 * (-2145 * t3 + 14040 * t2 - 30888 * t1 + 22880 * t8 - 53248) / q
1913 - (1.0 / 25740.0) * shambase::constants::pi<Tscal>
1914 * (-165 * t4 + 1170 * t3 - 2808 * t2 + 2288 * t1 - 53248 * q + 36)
1915 / t5;
1916 } else
1917 return (2047.0 / 715.0) * shambase::constants::pi<Tscal> / t5;
1918 }
1919 };
1920
1921 template<class Tscal>
1922 class KernelDefM4Shift2 {
1923 public:
1924 inline static constexpr Tscal Rkern = 2;
1926 inline static constexpr Tscal hfactd = 1.2;
1927
1929 inline static constexpr Tscal norm_1d = 4.0 / 11.0;
1931 inline static constexpr Tscal norm_2d = (40.0 / 77.0) / shambase::constants::pi<Tscal>;
1933 inline static constexpr Tscal norm_3d = (120.0 / 439.0) / shambase::constants::pi<Tscal>;
1934
1935 inline static Tscal f(Tscal q) {
1936 if (q < 1.) {
1937 return 1.;
1938 } else {
1939 return KernelDefM4<Tscal>::f((q - 1) * 2);
1940 }
1941 }
1942
1943 inline static Tscal df(Tscal q) {
1944 if (q < 1.) {
1945 return 0.;
1946 } else {
1947 return 2 * KernelDefM4<Tscal>::df((q - 1) * 2);
1948 }
1949 }
1950
1951 inline static Tscal ddf(Tscal q) {
1952 if (q < 1.) {
1953 return 0.;
1954 } else {
1955 return 4 * KernelDefM4<Tscal>::ddf((q - 1) * 2);
1956 }
1957 }
1958
1959 inline static Tscal phi_tilde_3d(Tscal q) {
1960 Tscal t1 = sham::pow_constexpr<2>(q);
1961 Tscal t2 = sham::pow_constexpr<3>(q);
1962 Tscal t3 = sham::pow_constexpr<4>(q);
1963 Tscal t4 = sham::pow_constexpr<5>(q);
1964 Tscal t5 = sham::pow_constexpr<6>(q);
1965 if (q < 1) {
1966 return (1.0 / 60.0) * shambase::constants::pi<Tscal> * (40 * t1 - 231);
1967 } else if (q < 3.0 / 2.0) {
1968 return (1.0 / 60.0) * shambase::constants::pi<Tscal>
1969 * (48 * t5 - 288 * t4 + 600 * t3 - 440 * t2 - 39 * q - 72) / q;
1970 } else if (q < 2) {
1971 return (1.0 / 120.0) * shambase::constants::pi<Tscal>
1972 * (-32 * t5 + 288 * t4 - 960 * t3 + 1280 * t2 - 1536 * q + 585) / q;
1973 } else
1974 return -(439.0 / 120.0) * shambase::constants::pi<Tscal> / q;
1975 }
1976
1977 inline static Tscal phi_tilde_3d_prime(Tscal q) {
1978 Tscal t1 = sham::pow_constexpr<2>(q);
1979 Tscal t2 = sham::pow_constexpr<3>(q);
1980 Tscal t3 = sham::pow_constexpr<4>(q);
1981 Tscal t4 = sham::pow_constexpr<5>(q);
1982 Tscal t5 = sham::pow_constexpr<6>(q);
1983 if (q < 1) {
1984 return (4.0 / 3.0) * shambase::constants::pi<Tscal> * q;
1985 } else if (q < 3.0 / 2.0) {
1986 return (1.0 / 60.0) * shambase::constants::pi<Tscal>
1987 * (288 * t4 - 1440 * t3 + 2400 * t2 - 1320 * t1 - 39) / q
1988 - (1.0 / 60.0) * shambase::constants::pi<Tscal>
1989 * (48 * t5 - 288 * t4 + 600 * t3 - 440 * t2 - 39 * q - 72) / t1;
1990 } else if (q < 2) {
1991 return (1.0 / 120.0) * shambase::constants::pi<Tscal>
1992 * (-192 * t4 + 1440 * t3 - 3840 * t2 + 3840 * t1 - 1536) / q
1993 - (1.0 / 120.0) * shambase::constants::pi<Tscal>
1994 * (-32 * t5 + 288 * t4 - 960 * t3 + 1280 * t2 - 1536 * q + 585) / t1;
1995 } else
1996 return (439.0 / 120.0) * shambase::constants::pi<Tscal> / t1;
1997 }
1998 };
1999
2000 template<class Tscal>
2001 class KernelDefM4Shift4 {
2002 public:
2003 inline static constexpr Tscal Rkern = 2;
2005 inline static constexpr Tscal hfactd = 1.2;
2006
2008 inline static constexpr Tscal norm_1d = 8.0 / 27.0;
2010 inline static constexpr Tscal norm_2d = (160.0 / 457.0) / shambase::constants::pi<Tscal>;
2012 inline static constexpr Tscal norm_3d = (320.0 / 2069.0) / shambase::constants::pi<Tscal>;
2013
2014 inline static Tscal f(Tscal q) {
2015 if (q < 1.5) {
2016 return 1.;
2017 } else {
2018 return KernelDefM4<Tscal>::f((q - 1.5) * 4);
2019 }
2020 }
2021
2022 inline static Tscal df(Tscal q) {
2023 if (q < 1.5) {
2024 return 0.;
2025 } else {
2026 return 4 * KernelDefM4<Tscal>::df((q - 1.5) * 4);
2027 }
2028 }
2029
2030 inline static Tscal ddf(Tscal q) {
2031 if (q < 1.5) {
2032 return 0.;
2033 } else {
2034 return 16 * KernelDefM4<Tscal>::ddf((q - 1.5) * 4);
2035 }
2036 }
2037
2038 inline static Tscal phi_tilde_3d(Tscal q) {
2039 Tscal t1 = sham::pow_constexpr<2>(q);
2040 Tscal t2 = sham::pow_constexpr<3>(q);
2041 Tscal t3 = sham::pow_constexpr<4>(q);
2042 Tscal t4 = sham::pow_constexpr<5>(q);
2043 Tscal t5 = sham::pow_constexpr<6>(q);
2044 if (q < 3.0 / 2.0) {
2045 return (1.0 / 240.0) * shambase::constants::pi<Tscal> * (160 * t1 - 1371);
2046 } else if (q < 7.0 / 4.0) {
2047 return (1.0 / 240.0) * shambase::constants::pi<Tscal>
2048 * (1536 * t5 - 11520 * t4 + 31680 * t3 - 34400 * t2 + 25845 * q - 14580) / q;
2049 } else if (q < 2) {
2050 return (1.0 / 960.0) * shambase::constants::pi<Tscal>
2051 * (-2048 * t5 + 18432 * t4 - 61440 * t3 + 81920 * t2 - 98304 * q + 59329)
2052 / q;
2053 } else
2054 return -(2069.0 / 320.0) * shambase::constants::pi<Tscal> / q;
2055 }
2056
2057 inline static Tscal phi_tilde_3d_prime(Tscal q) {
2058 Tscal t1 = sham::pow_constexpr<2>(q);
2059 Tscal t2 = sham::pow_constexpr<3>(q);
2060 Tscal t3 = sham::pow_constexpr<4>(q);
2061 Tscal t4 = sham::pow_constexpr<5>(q);
2062 Tscal t5 = sham::pow_constexpr<6>(q);
2063 if (q < 3.0 / 2.0) {
2064 return (4.0 / 3.0) * shambase::constants::pi<Tscal> * q;
2065 } else if (q < 7.0 / 4.0) {
2066 return (1.0 / 240.0) * shambase::constants::pi<Tscal>
2067 * (9216 * t4 - 57600 * t3 + 126720 * t2 - 103200 * t1 + 25845) / q
2068 - (1.0 / 240.0) * shambase::constants::pi<Tscal>
2069 * (1536 * t5 - 11520 * t4 + 31680 * t3 - 34400 * t2 + 25845 * q
2070 - 14580)
2071 / t1;
2072 } else if (q < 2) {
2073 return (1.0 / 960.0) * shambase::constants::pi<Tscal>
2074 * (-12288 * t4 + 92160 * t3 - 245760 * t2 + 245760 * t1 - 98304) / q
2075 - (1.0 / 960.0) * shambase::constants::pi<Tscal>
2076 * (-2048 * t5 + 18432 * t4 - 61440 * t3 + 81920 * t2 - 98304 * q
2077 + 59329)
2078 / t1;
2079 } else
2080 return (2069.0 / 320.0) * shambase::constants::pi<Tscal> / t1;
2081 }
2082 };
2083
2084 template<class Tscal>
2085 class KernelDefM4Shift8 {
2086 public:
2087 inline static constexpr Tscal Rkern = 2;
2089 inline static constexpr Tscal hfactd = 1.2;
2090
2092 inline static constexpr Tscal norm_1d = 16.0 / 59.0;
2094 inline static constexpr Tscal norm_2d = (640.0 / 2177.0) / shambase::constants::pi<Tscal>;
2096 inline static constexpr Tscal norm_3d = (7680.0 / 64303.0) / shambase::constants::pi<Tscal>;
2097
2098 inline static Tscal f(Tscal q) {
2099 if (q < 1.75) {
2100 return 1.;
2101 } else {
2102 return KernelDefM4<Tscal>::f((q - 1.75) * 8);
2103 }
2104 }
2105
2106 inline static Tscal df(Tscal q) {
2107 if (q < 1.75) {
2108 return 0.;
2109 } else {
2110 return 8 * KernelDefM4<Tscal>::df((q - 1.75) * 8);
2111 }
2112 }
2113
2114 inline static Tscal ddf(Tscal q) {
2115 if (q < 1.75) {
2116 return 0.;
2117 } else {
2118 return 64 * KernelDefM4<Tscal>::ddf((q - 1.75) * 8);
2119 }
2120 }
2121
2122 inline static Tscal phi_tilde_3d(Tscal q) {
2123 Tscal t1 = sham::pow_constexpr<2>(q);
2124 Tscal t2 = sham::pow_constexpr<3>(q);
2125 Tscal t3 = sham::pow_constexpr<4>(q);
2126 Tscal t4 = sham::pow_constexpr<5>(q);
2127 Tscal t5 = sham::pow_constexpr<6>(q);
2128 if (q < 7.0 / 4.0) {
2129 return (1.0 / 960.0) * shambase::constants::pi<Tscal> * (640 * t1 - 6531);
2130 } else if (q < 15.0 / 8.0) {
2131 return (1.0 / 960.0) * shambase::constants::pi<Tscal>
2132 * (49152 * t5 - 405504 * t4 + 1236480 * t3 - 1504640 * t2 + 1491693 * q
2133 - 907578)
2134 / q;
2135 } else if (q < 2) {
2136 return (1.0 / 7680.0) * shambase::constants::pi<Tscal>
2137 * (-131072 * t5 + 1179648 * t4 - 3932160 * t3 + 5242880 * t2 - 6291456 * q
2138 + 4130001)
2139 / q;
2140 } else
2141 return -(64303.0 / 7680.0) * shambase::constants::pi<Tscal> / q;
2142 }
2143
2144 inline static Tscal phi_tilde_3d_prime(Tscal q) {
2145 Tscal t1 = sham::pow_constexpr<2>(q);
2146 Tscal t2 = sham::pow_constexpr<3>(q);
2147 Tscal t3 = sham::pow_constexpr<4>(q);
2148 Tscal t4 = sham::pow_constexpr<5>(q);
2149 Tscal t5 = sham::pow_constexpr<6>(q);
2150 if (q < 7.0 / 4.0) {
2151 return (4.0 / 3.0) * shambase::constants::pi<Tscal> * q;
2152 } else if (q < 15.0 / 8.0) {
2153 return (1.0 / 960.0) * shambase::constants::pi<Tscal>
2154 * (294912 * t4 - 2027520 * t3 + 4945920 * t2 - 4513920 * t1 + 1491693)
2155 / q
2156 - (1.0 / 960.0) * shambase::constants::pi<Tscal>
2157 * (49152 * t5 - 405504 * t4 + 1236480 * t3 - 1504640 * t2 + 1491693 * q
2158 - 907578)
2159 / t1;
2160 } else if (q < 2) {
2161 return (1.0 / 7680.0) * shambase::constants::pi<Tscal>
2162 * (-786432 * t4 + 5898240 * t3 - 15728640 * t2 + 15728640 * t1 - 6291456)
2163 / q
2164 - (1.0 / 7680.0) * shambase::constants::pi<Tscal>
2165 * (-131072 * t5 + 1179648 * t4 - 3932160 * t3 + 5242880 * t2
2166 - 6291456 * q + 4130001)
2167 / t1;
2168 } else
2169 return (64303.0 / 7680.0) * shambase::constants::pi<Tscal> / t1;
2170 }
2171 };
2172
2173 template<class Tscal>
2174 class KernelDefM4Shift16 {
2175 public:
2176 inline static constexpr Tscal Rkern = 2;
2178 inline static constexpr Tscal hfactd = 1.2;
2179
2181 inline static constexpr Tscal norm_1d = 32.0 / 123.0;
2183 inline static constexpr Tscal norm_2d = (2560.0 / 9457.0) / shambase::constants::pi<Tscal>;
2185 inline static constexpr Tscal norm_3d = (4096.0 / 38785.0) / shambase::constants::pi<Tscal>;
2186
2187 inline static Tscal f(Tscal q) {
2188 if (q < 1.875) {
2189 return 1.;
2190 } else {
2191 return KernelDefM4<Tscal>::f((q - 1.875) * 16);
2192 }
2193 }
2194
2195 inline static Tscal df(Tscal q) {
2196 if (q < 1.875) {
2197 return 0.;
2198 } else {
2199 return 16 * KernelDefM4<Tscal>::df((q - 1.875) * 16);
2200 }
2201 }
2202
2203 inline static Tscal ddf(Tscal q) {
2204 if (q < 1.875) {
2205 return 0.;
2206 } else {
2207 return 256 * KernelDefM4<Tscal>::ddf((q - 1.875) * 16);
2208 }
2209 }
2210
2211 inline static Tscal phi_tilde_3d(Tscal q) {
2212 Tscal t1 = sham::pow_constexpr<2>(q);
2213 Tscal t2 = sham::pow_constexpr<3>(q);
2214 Tscal t3 = sham::pow_constexpr<4>(q);
2215 Tscal t4 = sham::pow_constexpr<5>(q);
2216 Tscal t5 = sham::pow_constexpr<6>(q);
2217 if (q < 15.0 / 8.0) {
2218 return (1.0 / 3840.0) * shambase::constants::pi<Tscal> * (2560 * t1 - 28371);
2219 } else if (q < 31.0 / 16.0) {
2220 return (1.0 / 3840.0) * shambase::constants::pi<Tscal>
2221 * (1572864 * t5 - 13565952 * t4 + 43315200 * t3 - 55293440 * t2
2222 + 60721629 * q - 38728125)
2223 / q;
2224 } else if (q < 2) {
2225 return (1.0 / 61440.0) * shambase::constants::pi<Tscal>
2226 * (-8388608 * t5 + 75497472 * t4 - 251658240 * t3 + 335544320 * t2
2227 - 402653184 * q + 267853681)
2228 / q;
2229 } else
2230 return -(38785.0 / 4096.0) * shambase::constants::pi<Tscal> / q;
2231 }
2232
2233 inline static Tscal phi_tilde_3d_prime(Tscal q) {
2234 Tscal t1 = sham::pow_constexpr<2>(q);
2235 Tscal t2 = sham::pow_constexpr<3>(q);
2236 Tscal t3 = sham::pow_constexpr<4>(q);
2237 Tscal t4 = sham::pow_constexpr<5>(q);
2238 Tscal t5 = sham::pow_constexpr<6>(q);
2239 if (q < 15.0 / 8.0) {
2240 return (4.0 / 3.0) * shambase::constants::pi<Tscal> * q;
2241 } else if (q < 31.0 / 16.0) {
2242 return (1.0 / 3840.0) * shambase::constants::pi<Tscal>
2243 * (9437184 * t4 - 67829760 * t3 + 173260800 * t2 - 165880320 * t1
2244 + 60721629)
2245 / q
2246 - (1.0 / 3840.0) * shambase::constants::pi<Tscal>
2247 * (1572864 * t5 - 13565952 * t4 + 43315200 * t3 - 55293440 * t2
2248 + 60721629 * q - 38728125)
2249 / t1;
2250 } else if (q < 2) {
2251 return (1.0 / 61440.0) * shambase::constants::pi<Tscal>
2252 * (-50331648 * t4 + 377487360 * t3 - 1006632960 * t2 + 1006632960 * t1
2253 - 402653184)
2254 / q
2255 - (1.0 / 61440.0) * shambase::constants::pi<Tscal>
2256 * (-8388608 * t5 + 75497472 * t4 - 251658240 * t3 + 335544320 * t2
2257 - 402653184 * q + 267853681)
2258 / t1;
2259 } else
2260 return (38785.0 / 4096.0) * shambase::constants::pi<Tscal> / t1;
2261 }
2262 };
2263} // namespace shammath::details
2264
2265namespace shammath {
2266
2267 // Type trait to detect if BaseKernel has phi_tilde_3d method
2268 template<typename T, typename Tscal, typename = void>
2269 struct has_phi_tilde_3d : std::false_type {};
2270
2271 template<typename T, typename Tscal>
2272 struct has_phi_tilde_3d<T, Tscal, std::void_t<decltype(T::phi_tilde_3d(std::declval<Tscal>()))>>
2273 : std::true_type {};
2274
2275 // Type trait to detect if BaseKernel has phi_tilde_3d_prime method
2276 template<typename T, typename Tscal, typename = void>
2277 struct has_phi_tilde_3d_prime : std::false_type {};
2278
2279 template<typename T, typename Tscal>
2280 struct has_phi_tilde_3d_prime<
2281 T,
2282 Tscal,
2283 std::void_t<decltype(T::phi_tilde_3d_prime(std::declval<Tscal>()))>> : std::true_type {};
2284
2285 template<class Tscal_, class BaseKernel>
2286 class SPHKernelGen {
2287 public:
2288 using Generator = BaseKernel;
2289 using Tscal = Tscal_;
2290 inline static constexpr Tscal Rkern = BaseKernel::Rkern;
2291 inline static constexpr Tscal hfactd
2292 = BaseKernel::hfactd;
2302 inline static Tscal f(Tscal q) { return BaseKernel::f(q); }
2303
2310 inline static Tscal df(Tscal q) { return BaseKernel::df(q); }
2311
2312 inline static Tscal ddf(Tscal q) { return BaseKernel::ddf(q); }
2313
2314 inline static Tscal W_1d(Tscal r, Tscal h) { return BaseKernel::norm_1d * f(r / h) / (h); }
2315
2316 inline static Tscal W_2d(Tscal r, Tscal h) {
2317 return BaseKernel::norm_2d * f(r / h) / (h * h);
2318 }
2319
2329 inline static Tscal W_3d(Tscal r, Tscal h) {
2330 return BaseKernel::norm_3d * f(r / h) / (h * h * h);
2331 }
2332
2333 inline static Tscal dW_3d(Tscal r, Tscal h) {
2334 return BaseKernel::norm_3d * df(r / h) / (h * h * h * h);
2335 }
2336
2337 inline static Tscal ddW_3d(Tscal r, Tscal h) {
2338 return BaseKernel::norm_3d * ddf(r / h) / (h * h * h * h * h);
2339 }
2340
2341 inline static Tscal dhW_3d(Tscal r, Tscal h) {
2342 return -(BaseKernel::norm_3d) * (3 * f(r / h) + (r / h) * df(r / h)) / (h * h * h * h);
2343 }
2344
2345 inline static Tscal f3d_integ_z(Tscal x, int np = 32) {
2346 return integ_riemann_sum<Tscal>(-Rkern, Rkern, Rkern / np, [&](Tscal z) {
2347 return f(sqrt(x * x + z * z));
2348 });
2349 }
2350
2351 inline static Tscal Y_3d(Tscal r, Tscal h, int np = 32) {
2352 return BaseKernel::norm_3d * f3d_integ_z(r / h, np) / (h * h);
2353 }
2354
2355 static constexpr bool has_3d_phi_soft
2356 = ::shammath::has_phi_tilde_3d<BaseKernel, Tscal>::value;
2357
2358 inline static Tscal phi_tilde_3d(Tscal q) {
2359 if constexpr (has_3d_phi_soft) {
2360 return BaseKernel::phi_tilde_3d(q);
2361 } else {
2362 return std::numeric_limits<Tscal>::quiet_NaN();
2363 }
2364 }
2365
2366 static constexpr bool has_3d_phi_soft_prime
2367 = ::shammath::has_phi_tilde_3d_prime<BaseKernel, Tscal>::value;
2368
2369 inline static Tscal phi_tilde_3d_prime(Tscal q) {
2370 if constexpr (has_3d_phi_soft_prime) {
2371 return BaseKernel::phi_tilde_3d_prime(q);
2372 } else {
2373 return std::numeric_limits<Tscal>::quiet_NaN();
2374 }
2375 }
2376
2377 inline static Tscal phi_3D(Tscal r, Tscal h) {
2378 return BaseKernel::norm_3d * phi_tilde_3d(r / h) / h;
2379 }
2380
2381 inline static Tscal phi_3D_prime(Tscal r, Tscal h) {
2382 return BaseKernel::norm_3d * phi_tilde_3d_prime(r / h) / (h * h);
2383 }
2384 };
2385
2392 template<class flt_type>
2393 using M4 = SPHKernelGen<flt_type, details::KernelDefM4<flt_type>>;
2394
2401 template<class flt_type>
2402 using M5 = SPHKernelGen<flt_type, details::KernelDefM5<flt_type>>;
2403
2410 template<class flt_type>
2411 using M6 = SPHKernelGen<flt_type, details::KernelDefM6<flt_type>>;
2412
2419 template<class flt_type>
2420 using M7 = SPHKernelGen<flt_type, details::KernelDefM7<flt_type>>;
2421
2428 template<class flt_type>
2429 using M8 = SPHKernelGen<flt_type, details::KernelDefM8<flt_type>>;
2430
2437 template<class flt_type>
2438 using M9 = SPHKernelGen<flt_type, details::KernelDefM9<flt_type>>;
2439
2446 template<class flt_type>
2447 using M10 = SPHKernelGen<flt_type, details::KernelDefM10<flt_type>>;
2448
2455 template<class flt_type>
2456 using C2 = SPHKernelGen<flt_type, details::KernelDefC2<flt_type>>;
2457
2464 template<class flt_type>
2465 using C4 = SPHKernelGen<flt_type, details::KernelDefC4<flt_type>>;
2466
2473 template<class flt_type>
2474 using C6 = SPHKernelGen<flt_type, details::KernelDefC6<flt_type>>;
2475
2481 template<class flt_type>
2482 using TGauss3 = SPHKernelGen<flt_type, details::KernelDefTGauss3<flt_type>>;
2483
2489 template<class flt_type>
2490 using TGauss5 = SPHKernelGen<flt_type, details::KernelDefTGauss5<flt_type>>;
2491
2498 template<class flt_type>
2499 using M4DH = SPHKernelGen<flt_type, details::KernelDefM4DoubleHump<flt_type>>;
2500
2507 template<class flt_type>
2508 using M4DH3 = SPHKernelGen<flt_type, details::KernelDefM4DoubleHump3<flt_type>>;
2509
2516 template<class flt_type>
2517 using M4DH5 = SPHKernelGen<flt_type, details::KernelDefM4DoubleHump5<flt_type>>;
2518
2525 template<class flt_type>
2526 using M4DH7 = SPHKernelGen<flt_type, details::KernelDefM4DoubleHump7<flt_type>>;
2527
2534 template<class flt_type>
2535 using M4Shift2 = SPHKernelGen<flt_type, details::KernelDefM4Shift2<flt_type>>;
2536
2543 template<class flt_type>
2544 using M4Shift4 = SPHKernelGen<flt_type, details::KernelDefM4Shift4<flt_type>>;
2545
2552 template<class flt_type>
2553 using M4Shift8 = SPHKernelGen<flt_type, details::KernelDefM4Shift8<flt_type>>;
2554
2561 template<class flt_type>
2562 using M4Shift16 = SPHKernelGen<flt_type, details::KernelDefM4Shift16<flt_type>>;
2563
2564} // namespace shammath
2565
2566namespace shambase {
2567
2568 template<class flt_type>
2569 struct TypeNameInfo<shammath::M4<flt_type>> {
2570 inline static const std::string name = "M4<" + get_type_name<flt_type>() + ">";
2571 };
2572 template<class flt_type>
2573 struct TypeNameInfo<shammath::M5<flt_type>> {
2574 inline static const std::string name = "M5<" + get_type_name<flt_type>() + ">";
2575 };
2576 template<class flt_type>
2577 struct TypeNameInfo<shammath::M6<flt_type>> {
2578 inline static const std::string name = "M6<" + get_type_name<flt_type>() + ">";
2579 };
2580 template<class flt_type>
2581 struct TypeNameInfo<shammath::M7<flt_type>> {
2582 inline static const std::string name = "M7<" + get_type_name<flt_type>() + ">";
2583 };
2584 template<class flt_type>
2585 struct TypeNameInfo<shammath::M8<flt_type>> {
2586 inline static const std::string name = "M8<" + get_type_name<flt_type>() + ">";
2587 };
2588 template<class flt_type>
2589 struct TypeNameInfo<shammath::M9<flt_type>> {
2590 inline static const std::string name = "M9<" + get_type_name<flt_type>() + ">";
2591 };
2592 template<class flt_type>
2593 struct TypeNameInfo<shammath::M10<flt_type>> {
2594 inline static const std::string name = "M10<" + get_type_name<flt_type>() + ">";
2595 };
2596
2597 template<class flt_type>
2598 struct TypeNameInfo<shammath::C2<flt_type>> {
2599 inline static const std::string name = "C2<" + get_type_name<flt_type>() + ">";
2600 };
2601 template<class flt_type>
2602 struct TypeNameInfo<shammath::C4<flt_type>> {
2603 inline static const std::string name = "C4<" + get_type_name<flt_type>() + ">";
2604 };
2605 template<class flt_type>
2606 struct TypeNameInfo<shammath::C6<flt_type>> {
2607 inline static const std::string name = "C6<" + get_type_name<flt_type>() + ">";
2608 };
2609
2610 template<class flt_type>
2611 struct TypeNameInfo<shammath::TGauss3<flt_type>> {
2612 inline static const std::string name = "TGauss3<" + get_type_name<flt_type>() + ">";
2613 };
2614
2615 template<class flt_type>
2616 struct TypeNameInfo<shammath::TGauss5<flt_type>> {
2617 inline static const std::string name = "TGauss5<" + get_type_name<flt_type>() + ">";
2618 };
2619
2620 template<class flt_type>
2621 struct TypeNameInfo<shammath::M4DH<flt_type>> {
2622 inline static const std::string name = "M4DH<" + get_type_name<flt_type>() + ">";
2623 };
2624
2625 template<class flt_type>
2626 struct TypeNameInfo<shammath::M4DH3<flt_type>> {
2627 inline static const std::string name = "M4DH3<" + get_type_name<flt_type>() + ">";
2628 };
2629
2630 template<class flt_type>
2631 struct TypeNameInfo<shammath::M4DH5<flt_type>> {
2632 inline static const std::string name = "M4DH5<" + get_type_name<flt_type>() + ">";
2633 };
2634
2635 template<class flt_type>
2636 struct TypeNameInfo<shammath::M4DH7<flt_type>> {
2637 inline static const std::string name = "M4DH7<" + get_type_name<flt_type>() + ">";
2638 };
2639
2640 template<class flt_type>
2641 struct TypeNameInfo<shammath::M4Shift2<flt_type>> {
2642 inline static const std::string name = "M4Shift2<" + get_type_name<flt_type>() + ">";
2643 };
2644
2645 template<class flt_type>
2646 struct TypeNameInfo<shammath::M4Shift4<flt_type>> {
2647 inline static const std::string name = "M4Shift4<" + get_type_name<flt_type>() + ">";
2648 };
2649
2650 template<class flt_type>
2651 struct TypeNameInfo<shammath::M4Shift8<flt_type>> {
2652 inline static const std::string name = "M4Shift8<" + get_type_name<flt_type>() + ">";
2653 };
2654
2655 template<class flt_type>
2656 struct TypeNameInfo<shammath::M4Shift16<flt_type>> {
2657 inline static const std::string name = "M4Shift16<" + get_type_name<flt_type>() + ">";
2658 };
2659
2660} // namespace shambase
shammath::SPHKernelGen::W_3d
static Tscal W_3d(Tscal r, Tscal h)
compute the normed & resized version of the kernel :
Definition sphkernels.hpp:2329
shammath::SPHKernelGen::hfactd
static constexpr Tscal hfactd
Definition sphkernels.hpp:2292
shammath::SPHKernelGen::f
static Tscal f(Tscal q)
the base function for this SPH kernel
Definition sphkernels.hpp:2302
shammath::SPHKernelGen::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:2290
shammath::SPHKernelGen::df
static Tscal df(Tscal q)
derivative of M4::f
Definition sphkernels.hpp:2310
shammath::details::KernelDefC2::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1188
shammath::details::KernelDefC2::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1185
shammath::details::KernelDefC2::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1192
shammath::details::KernelDefC2::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:1183
shammath::details::KernelDefC2::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1190
shammath::details::KernelDefC4::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1272
shammath::details::KernelDefC4::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1274
shammath::details::KernelDefC4::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:1265
shammath::details::KernelDefC4::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1270
shammath::details::KernelDefC4::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1267
shammath::details::KernelDefC6::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1371
shammath::details::KernelDefC6::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1367
shammath::details::KernelDefC6::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1364
shammath::details::KernelDefC6::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:1362
shammath::details::KernelDefC6::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1369
shammath::details::KernelDefM10::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:978
shammath::details::KernelDefM10::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:975
shammath::details::KernelDefM10::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:982
shammath::details::KernelDefM10::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:973
shammath::details::KernelDefM10::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:980
shammath::details::KernelDefM4DoubleHump3::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1686
shammath::details::KernelDefM4DoubleHump3::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1692
shammath::details::KernelDefM4DoubleHump3::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1689
shammath::details::KernelDefM4DoubleHump3::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1694
shammath::details::KernelDefM4DoubleHump5::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1771
shammath::details::KernelDefM4DoubleHump5::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1769
shammath::details::KernelDefM4DoubleHump5::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1767
shammath::details::KernelDefM4DoubleHump5::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1764
shammath::details::KernelDefM4DoubleHump7::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1847
shammath::details::KernelDefM4DoubleHump7::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1844
shammath::details::KernelDefM4DoubleHump7::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1851
shammath::details::KernelDefM4DoubleHump7::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1849
shammath::details::KernelDefM4DoubleHump::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1611
shammath::details::KernelDefM4DoubleHump::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1614
shammath::details::KernelDefM4DoubleHump::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1617
shammath::details::KernelDefM4DoubleHump::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1619
shammath::details::KernelDefM4Shift16::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:2181
shammath::details::KernelDefM4Shift16::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:2183
shammath::details::KernelDefM4Shift16::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:2178
shammath::details::KernelDefM4Shift16::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:2185
shammath::details::KernelDefM4Shift2::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1931
shammath::details::KernelDefM4Shift2::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1933
shammath::details::KernelDefM4Shift2::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1929
shammath::details::KernelDefM4Shift2::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1926
shammath::details::KernelDefM4Shift4::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:2008
shammath::details::KernelDefM4Shift4::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:2012
shammath::details::KernelDefM4Shift4::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:2010
shammath::details::KernelDefM4Shift4::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:2005
shammath::details::KernelDefM4Shift8::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:2094
shammath::details::KernelDefM4Shift8::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:2092
shammath::details::KernelDefM4Shift8::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:2096
shammath::details::KernelDefM4Shift8::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:2089
shammath::details::KernelDefM4::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:38
shammath::details::KernelDefM4::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:40
shammath::details::KernelDefM4::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:33
shammath::details::KernelDefM4::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:36
shammath::details::KernelDefM4::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:31
shammath::details::KernelDefM5::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:129
shammath::details::KernelDefM5::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:122
shammath::details::KernelDefM5::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:127
shammath::details::KernelDefM5::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:131
shammath::details::KernelDefM5::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:124
shammath::details::KernelDefM6::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:272
shammath::details::KernelDefM6::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:269
shammath::details::KernelDefM6::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:267
shammath::details::KernelDefM6::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:274
shammath::details::KernelDefM6::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:276
shammath::details::KernelDefM7::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:410
shammath::details::KernelDefM7::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:415
shammath::details::KernelDefM7::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:412
shammath::details::KernelDefM7::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:417
shammath::details::KernelDefM7::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:419
shammath::details::KernelDefM8::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:591
shammath::details::KernelDefM8::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:588
shammath::details::KernelDefM8::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:586
shammath::details::KernelDefM8::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:595
shammath::details::KernelDefM8::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:593
shammath::details::KernelDefM9::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:762
shammath::details::KernelDefM9::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:760
shammath::details::KernelDefM9::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:758
shammath::details::KernelDefM9::Rkern
static constexpr Tscal Rkern
Definition sphkernels.hpp:753
shammath::details::KernelDefM9::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:755
shammath::details::KernelDefTGauss3
Truncated Gaussian kernel with compact support R=3h.
Definition sphkernels.hpp:1473
shammath::details::KernelDefTGauss3::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1479
shammath::details::KernelDefTGauss3::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1483
shammath::details::KernelDefTGauss3::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel (accounts for truncation at q=3)
Definition sphkernels.hpp:1481
shammath::details::KernelDefTGauss3::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1476
shammath::details::KernelDefTGauss3::Rkern
static constexpr Tscal Rkern
Compact support radius of the kernel.
Definition sphkernels.hpp:1475
shammath::details::KernelDefTGauss5
Truncated Gaussian kernel with compact support R=5h.
Definition sphkernels.hpp:1544
shammath::details::KernelDefTGauss5::norm_2d
static constexpr Tscal norm_2d
2D norm of the kernel
Definition sphkernels.hpp:1552
shammath::details::KernelDefTGauss5::norm_1d
static constexpr Tscal norm_1d
1D norm of the kernel
Definition sphkernels.hpp:1550
shammath::details::KernelDefTGauss5::Rkern
static constexpr Tscal Rkern
Compact support radius of the kernel.
Definition sphkernels.hpp:1546
shammath::details::KernelDefTGauss5::norm_3d
static constexpr Tscal norm_3d
3D norm of the kernel
Definition sphkernels.hpp:1554
shammath::details::KernelDefTGauss5::hfactd
static constexpr Tscal hfactd
default hfact to be used for this kernel
Definition sphkernels.hpp:1547
constants.hpp
Class holding the value of numerous constants generated from the following source.
shambase
namespace for basic c++ utilities
Definition sycl_builtins.hpp:25
shambase::throw_with_loc
void throw_with_loc(std::string message, SourceLocation loc=SourceLocation{})
Throw an exception and append the source location to it.
Definition exception.hpp:132
shammath
namespace for math utility
Definition AABB.hpp:26
std
STL namespace.
shammath::has_phi_tilde_3d_prime
Definition sphkernels.hpp:2277
shammath::has_phi_tilde_3d
Definition sphkernels.hpp:2269
type_name_info.hpp
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