GADGET-4
ewald_test.cc
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1 /*******************************************************************************
2  * \copyright This file is part of the GADGET4 N-body/SPH code developed
3  * \copyright by Volker Springel. Copyright (C) 2014-2020 by Volker Springel
4  * \copyright (vspringel@mpa-garching.mpg.de) and all contributing authors.
5  *******************************************************************************/
6 
12 #include "gadgetconfig.h"
13 
14 #include <math.h>
15 #include <mpi.h>
16 #include <stdio.h>
17 #include <stdlib.h>
18 #include <string.h>
19 
20 #include "../data/allvars.h"
21 #include "../data/dtypes.h"
22 #include "../data/mymalloc.h"
23 #include "../gravity/ewald.h"
24 #include "../gravity/ewaldtensors.h"
25 #include "../gravtree/gravtree.h"
26 #include "../io/io.h"
27 #include "../main/simulation.h"
28 #include "../sort/cxxsort.h"
29 #include "../system/system.h"
30 
31 #ifdef EWALD_TEST
32 
45 void ewald::ewald_corr(double dx, double dy, double dz, enum interpolate_options flag, ewald_data &fper)
46 {
47  if(!ewald_is_initialized)
48  Terminate("How come that Ewald tables are not initialized?");
49 
50  int signx, signy, signz;
51 
52  if(dx < 0)
53  {
54  dx = -dx;
55  signx = -1;
56  }
57  else
58  signx = +1;
59 
60  if(dy < 0)
61  {
62  dy = -dy;
63  signy = -1;
64  }
65  else
66  signy = +1;
67 
68  if(dz < 0)
69  {
70  dz = -dz;
71  signz = -1;
72  }
73  else
74  signz = +1;
75 
76  ewald_interpolate(dx, dy, dz, flag, fper);
77 
78  /* change signs as needed */
79 
80  fper.D1phi[0] *= signx;
81  fper.D1phi[1] *= signy;
82  fper.D1phi[2] *= signz;
83 
84  if(flag == POINTMASS)
85  return;
86 
87  fper.D2phi[qXY] *= signx * signy;
88  fper.D2phi[qXZ] *= signx * signz;
89  fper.D2phi[qYZ] *= signy * signz;
90 
91  fper.D3phi[dXXX] *= signx;
92  fper.D3phi[dXXY] *= signy;
93  fper.D3phi[dXXZ] *= signz;
94  fper.D3phi[dXYY] *= signx;
95  fper.D3phi[dXYZ] *= signx * signy * signz;
96  fper.D3phi[dXZZ] *= signx;
97  fper.D3phi[dYYY] *= signy;
98  fper.D3phi[dYYZ] *= signz;
99  fper.D3phi[dYZZ] *= signy;
100  fper.D3phi[dZZZ] *= signz;
101 
102  fper.D4phi[sXXXY] *= signx * signy;
103  fper.D4phi[sXYYY] *= signx * signy;
104  fper.D4phi[sXXXZ] *= signx * signz;
105  fper.D4phi[sXZZZ] *= signx * signz;
106  fper.D4phi[sYYYZ] *= signy * signz;
107  fper.D4phi[sYZZZ] *= signy * signz;
108  fper.D4phi[sXXYZ] *= signy * signz;
109  fper.D4phi[sXYYZ] *= signx * signz;
110  fper.D4phi[sXYZZ] *= signx * signy;
111 
112  fper.D5phi[rXXXXX] *= signx;
113  fper.D5phi[rYYYYY] *= signy;
114  fper.D5phi[rZZZZZ] *= signz;
115 
116  fper.D5phi[rXXXXY] *= signy;
117  fper.D5phi[rXXXXZ] *= signz;
118  fper.D5phi[rXYYYY] *= signx;
119  fper.D5phi[rXZZZZ] *= signx;
120  fper.D5phi[rYYYYZ] *= signz;
121  fper.D5phi[rYZZZZ] *= signy;
122 
123  fper.D5phi[rXXXYY] *= signx;
124  fper.D5phi[rXXXZZ] *= signx;
125  fper.D5phi[rXXYYY] *= signy;
126  fper.D5phi[rXXZZZ] *= signz;
127  fper.D5phi[rYYYZZ] *= signy;
128  fper.D5phi[rYYZZZ] *= signz;
129 
130  fper.D5phi[rXXYZZ] *= signy;
131  fper.D5phi[rXXYYZ] *= signz;
132  fper.D5phi[rXYYZZ] *= signx;
133 
134  fper.D5phi[rXXXYZ] *= signx * signy * signz;
135  fper.D5phi[rXYYYZ] *= signx * signy * signz;
136  fper.D5phi[rXYZZZ] *= signx * signy * signz;
137 }
138 
139 void ewald::ewald_corr_exact(double dx, double dy, double dz, enum interpolate_options flag, ewald_data &fper)
140 {
141  double fac = 1.0 / All.BoxSize;
142  double x = dx * fac;
143  double y = dy * fac;
144  double z = dz * fac;
145 
146  fper.D0phi = pow(fac, 1) * ewald_D0(x, y, z);
147  fper.D1phi = pow(fac, 2) * ewald_D1(x, y, z);
148 
149  if(flag == POINTMASS)
150  return;
151 
152  fper.D2phi = pow(fac, 3) * ewald_D2(x, y, z);
153  fper.D3phi = pow(fac, 4) * ewald_D3(x, y, z);
154  fper.D4phi = pow(fac, 5) * ewald_D4(x, y, z);
155  fper.D5phi = pow(fac, 6) * ewald_D5(x, y, z);
156 }
157 
158 void ewald::ewald_interpolate(double dx, double dy, double dz, enum interpolate_options flag, ewald_data &fper)
159 {
160  double u = dx * Ewd_fac_intp[0];
161  int i = (int)u;
162  if(i >= ENX)
163  i = ENX - 1;
164  u -= i;
165 
166  double v = dy * Ewd_fac_intp[1];
167  int j = (int)v;
168  if(j >= ENY)
169  j = ENY - 1;
170  v -= j;
171 
172  double w = dz * Ewd_fac_intp[2];
173  int k = (int)w;
174  if(k >= ENZ)
175  k = ENZ - 1;
176  w -= k;
177 
178  double f1 = (1 - u) * (1 - v) * (1 - w);
179  double f2 = (1 - u) * (1 - v) * (w);
180  double f3 = (1 - u) * (v) * (1 - w);
181  double f4 = (1 - u) * (v) * (w);
182  double f5 = (u) * (1 - v) * (1 - w);
183  double f6 = (u) * (1 - v) * (w);
184  double f7 = (u) * (v) * (1 - w);
185  double f8 = (u) * (v) * (w);
186 
187  ewald_data &C1 = Ewd[ewd_offset(i, j, k)];
188  ewald_data &C2 = Ewd[ewd_offset(i, j, k + 1)];
189  ewald_data &C3 = Ewd[ewd_offset(i, j + 1, k)];
190  ewald_data &C4 = Ewd[ewd_offset(i, j + 1, k + 1)];
191  ewald_data &C5 = Ewd[ewd_offset(i + 1, j, k)];
192  ewald_data &C6 = Ewd[ewd_offset(i + 1, j, k + 1)];
193  ewald_data &C7 = Ewd[ewd_offset(i + 1, j + 1, k)];
194  ewald_data &C8 = Ewd[ewd_offset(i + 1, j + 1, k + 1)];
195 
196 #ifdef EVALPOTENTIAL
197  fper.D0phi =
198  f1 * C1.D0phi + f2 * C2.D0phi + f3 * C3.D0phi + f4 * C4.D0phi + f5 * C5.D0phi + f6 * C6.D0phi + f7 * C7.D0phi + f8 * C8.D0phi;
199 #endif
200  fper.D1phi =
201  f1 * C1.D1phi + f2 * C2.D1phi + f3 * C3.D1phi + f4 * C4.D1phi + f5 * C5.D1phi + f6 * C6.D1phi + f7 * C7.D1phi + f8 * C8.D1phi;
202 
203  if(flag == POINTMASS)
204  return;
205 
206  fper.D2phi =
207  f1 * C1.D2phi + f2 * C2.D2phi + f3 * C3.D2phi + f4 * C4.D2phi + f5 * C5.D2phi + f6 * C6.D2phi + f7 * C7.D2phi + f8 * C8.D2phi;
208 
209  fper.D3phi =
210  f1 * C1.D3phi + f2 * C2.D3phi + f3 * C3.D3phi + f4 * C4.D3phi + f5 * C5.D3phi + f6 * C6.D3phi + f7 * C7.D3phi + f8 * C8.D3phi;
211 
212  fper.D4phi =
213  f1 * C1.D4phi + f2 * C2.D4phi + f3 * C3.D4phi + f4 * C4.D4phi + f5 * C5.D4phi + f6 * C6.D4phi + f7 * C7.D4phi + f8 * C8.D4phi;
214 
215  fper.D5phi =
216  f1 * C1.D5phi + f2 * C2.D5phi + f3 * C3.D5phi + f4 * C4.D5phi + f5 * C5.D5phi + f6 * C6.D5phi + f7 * C7.D5phi + f8 * C8.D5phi;
217 }
218 
219 void ewald::test_interpolation_accuracy(void)
220 {
221  init_rng(42);
222 
223  printf("\n\n");
224 
225  double errsum0 = 0;
226  double errmax0 = 0;
227  double count0 = 0;
228  for(int i = 0; i < 1000; i++)
229  {
230  double x = get_random_number() - 0.5;
231  double y = get_random_number() - 0.5;
232  double z = get_random_number() - 0.5;
233 
234  double r = sqrt(x * x + y * y + z * z);
235 
236  double D0phi_exact = (1.0 / All.BoxSize) * ewald_D0(x, y, z);
237 
238  ewald_data ew;
239  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
240 
241  double err = fabs((D0phi_exact - ew.D0phi) / D0phi_exact);
242 
243  errsum0 += err;
244  if(err > errmax0)
245  errmax0 = err;
246  count0++;
247 
248  if(err > 0.1)
249  printf("%4d r=%g D0_exact=%g D0_interpol=%g rel_error=%g\n", i, r, D0phi_exact, ew.D0phi, err);
250  }
251 
252  double errsum1 = 0;
253  double errmax1 = 0;
254  double count1 = 0;
255  for(int i = 0; i < 1000; i++)
256  {
257  double x = get_random_number() - 0.5;
258  double y = get_random_number() - 0.5;
259  double z = get_random_number() - 0.5;
260 
261  double r = sqrt(x * x + y * y + z * z);
262 
263  vector<double> D1phi_exact = pow(All.BoxSize, -2) * ewald_D1(x, y, z);
264 
265  ewald_data ew;
266  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
267 
268  double norm = D1phi_exact.norm();
269 
270  for(int j = 0; j < 3; j++)
271  {
272  double err = fabs(D1phi_exact[j] - ew.D1phi[j]) / norm;
273  errsum1 += err;
274  if(err > errmax1)
275  errmax1 = err;
276  count1++;
277 
278  if(err > 0.1)
279  {
280  printf("%4d r=%g bin=%d D1_exact[%d]=%g D1_interpol[%d]=%g rel_error=%g\n", i, r,
281  (int)(r * All.BoxSize * Ewd_fac_intp[0]), j, D1phi_exact[j], j, ew.D1phi[j], err);
282  }
283  }
284  }
285 
286  double errsum2 = 0;
287  double errmax2 = 0;
288  double count2 = 0;
289  for(int i = 0; i < 1000; i++)
290  {
291  double x = get_random_number() - 0.5;
292  double y = get_random_number() - 0.5;
293  double z = get_random_number() - 0.5;
294 
295  double r = sqrt(x * x + y * y + z * z);
296 
297  symtensor2<double> D2phi_exact = pow(All.BoxSize, -3) * ewald_D2(x, y, z);
298 
299  ewald_data ew;
300  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
301 
302  double norm = D2phi_exact.norm();
303 
304  for(int j = 0; j < 6; j++)
305  {
306  double err = fabs((D2phi_exact[j] - ew.D2phi[j]) / norm);
307  errsum2 += err;
308  if(err > errmax2)
309  errmax2 = err;
310  count2++;
311 
312  if(err > 0.1)
313  printf("%4d r=%g D2_exact[%d]=%g D2_interpol[%d]=%g rel_error=%g\n", i, r, j, D2phi_exact[j], j, ew.D2phi[j], err);
314  }
315  }
316 
317  double errsum3 = 0;
318  double errmax3 = 0;
319  double count3 = 0;
320  for(int i = 0; i < 1000; i++)
321  {
322  double x = get_random_number() - 0.5;
323  double y = get_random_number() - 0.5;
324  double z = get_random_number() - 0.5;
325 
326  double r = sqrt(x * x + y * y + z * z);
327 
328  symtensor3<double> D3phi_exact = pow(All.BoxSize, -4) * ewald_D3(x, y, z);
329 
330  ewald_data ew;
331  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
332 
333  double norm = D3phi_exact.norm();
334 
335  for(int j = 0; j < 10; j++)
336  {
337  double err = fabs((D3phi_exact[j] - ew.D3phi[j]) / norm);
338  errsum3 += err;
339  if(err > errmax3)
340  errmax3 = err;
341  count3++;
342 
343  if(err > 0.1)
344  printf("%4d r=%g D3_exact[%d]=%g D3_interpol[%d]=%g rel_error=%g\n", i, r, j, D3phi_exact[j], j, ew.D3phi[j], err);
345  }
346  }
347 
348  double errsum4 = 0;
349  double errmax4 = 0;
350  double count4 = 0;
351  for(int i = 0; i < 1000; i++)
352  {
353  double x = get_random_number() - 0.5;
354  double y = get_random_number() - 0.5;
355  double z = get_random_number() - 0.5;
356 
357  double r = sqrt(x * x + y * y + z * z);
358 
359  symtensor4<double> D4phi_exact = pow(All.BoxSize, -5) * ewald_D4(x, y, z);
360 
361  ewald_data ew;
362  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
363 
364  double norm = D4phi_exact.norm();
365 
366  for(int j = 0; j < 15; j++)
367  {
368  double err = fabs((D4phi_exact[j] - ew.D4phi[j]) / norm);
369  errsum4 += err;
370  if(err > errmax4)
371  errmax4 = err;
372  count4++;
373 
374  if(err > 0.1)
375  printf("%4d r=%g D4_exact[%d]=%g D4_interpol[%d]=%g rel_error=%g\n", i, r, j, D4phi_exact[j], j, ew.D4phi[j], err);
376  }
377  }
378 
379  double errsum5 = 0;
380  double errmax5 = 0;
381  double count5 = 0;
382  for(int i = 0; i < 1000; i++)
383  {
384  double x = get_random_number() - 0.5;
385  double y = get_random_number() - 0.5;
386  double z = get_random_number() - 0.5;
387 
388  symtensor5<double> D5phi_exact = pow(All.BoxSize, -6) * ewald_D5(x, y, z);
389 
390  ewald_data ew;
391  ewald_corr(x * All.BoxSize, y * All.BoxSize, z * All.BoxSize, ewald::MULTIPOLES, ew);
392 
393  double norm = D5phi_exact.norm();
394 
395  for(int j = 0; j < 21; j++)
396  {
397  double err = fabs((D5phi_exact[j] - ew.D5phi[j]) / norm);
398  errsum5 += err;
399  if(err > errmax5)
400  errmax5 = err;
401  count5++;
402  }
403  }
404 
405  printf("\n\n");
406 
407  printf("D0: max error = %g mean error=%g\n", errmax0, errsum0 / count0);
408  printf("D1: max error = %g mean error=%g\n", errmax1, errsum1 / count1);
409  printf("D2: max error = %g mean error=%g\n", errmax2, errsum2 / count2);
410  printf("D3: max error = %g mean error=%g\n", errmax3, errsum3 / count3);
411  printf("D4: max error = %g mean error=%g\n", errmax4, errsum4 / count4);
412  printf("D5: max error = %g mean error=%g\n", errmax5, errsum5 / count5);
413 
414  printf("\n\n");
415 
416  {
417  double errsum0 = 0;
418  double errmax0 = 0;
419  double count0 = 0;
420  for(int i = 0; i < 1000; i++)
421  {
422  double x = get_random_number() - 0.5;
423  double y = get_random_number() - 0.5;
424  double z = get_random_number() - 0.5;
425 
426  double D0phi_exact = (1.0 / All.BoxSize) * ewald_D0(x, y, z);
427 
428  ewald_data ew;
429  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
430  MyIntPosType pos[3];
431  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
432  MyIntPosType ref[3] = {0, 0, 0};
433  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
434 
435  double err = fabs((D0phi_exact - ew.D0phi) / D0phi_exact);
436 
437  errsum0 += err;
438  if(err > errmax0)
439  errmax0 = err;
440  count0++;
441  }
442 
443  double errsum1 = 0;
444  double errmax1 = 0;
445  double count1 = 0;
446  for(int i = 0; i < 1000; i++)
447  {
448  double x = get_random_number() - 0.5;
449  double y = get_random_number() - 0.5;
450  double z = get_random_number() - 0.5;
451 
452  vector<double> D1phi_exact = pow(All.BoxSize, -2) * ewald_D1(x, y, z);
453 
454  ewald_data ew;
455  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
456  MyIntPosType pos[3];
457  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
458  MyIntPosType ref[3] = {0, 0, 0};
459  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
460 
461  double norm = D1phi_exact.norm();
462 
463  for(int j = 0; j < 3; j++)
464  {
465  double err = fabs(D1phi_exact[j] - ew.D1phi[j]) / norm;
466 
467  errsum1 += err;
468  if(err > errmax1)
469  errmax1 = err;
470  count1++;
471  }
472  }
473 
474  double errsum2 = 0;
475  double errmax2 = 0;
476  double count2 = 0;
477  for(int i = 0; i < 1000; i++)
478  {
479  double x = get_random_number() - 0.5;
480  double y = get_random_number() - 0.5;
481  double z = get_random_number() - 0.5;
482 
483  symtensor2<double> D2phi_exact = pow(All.BoxSize, -3) * ewald_D2(x, y, z);
484 
485  ewald_data ew;
486  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
487  MyIntPosType pos[3];
488  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
489  MyIntPosType ref[3] = {0, 0, 0};
490  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
491 
492  double norm = D2phi_exact.norm();
493 
494  for(int j = 0; j < 6; j++)
495  {
496  double err = fabs((D2phi_exact[j] - ew.D2phi[j]) / norm);
497  errsum2 += err;
498  if(err > errmax2)
499  errmax2 = err;
500  count2++;
501  }
502  }
503 
504  double errsum3 = 0;
505  double errmax3 = 0;
506  double count3 = 0;
507  for(int i = 0; i < 1000; i++)
508  {
509  double x = get_random_number() - 0.5;
510  double y = get_random_number() - 0.5;
511  double z = get_random_number() - 0.5;
512 
513  symtensor3<double> D3phi_exact = pow(All.BoxSize, -4) * ewald_D3(x, y, z);
514 
515  ewald_data ew;
516  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
517  MyIntPosType pos[3];
518  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
519  MyIntPosType ref[3] = {0, 0, 0};
520  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
521 
522  double norm = D3phi_exact.norm();
523 
524  for(int j = 0; j < 10; j++)
525  {
526  double err = fabs((D3phi_exact[j] - ew.D3phi[j]) / norm);
527  errsum3 += err;
528  if(err > errmax3)
529  errmax3 = err;
530  count3++;
531  }
532  }
533 
534  double errsum4 = 0;
535  double errmax4 = 0;
536  double count4 = 0;
537  for(int i = 0; i < 1000; i++)
538  {
539  double x = get_random_number() - 0.5;
540  double y = get_random_number() - 0.5;
541  double z = get_random_number() - 0.5;
542 
543  symtensor4<double> D4phi_exact = pow(All.BoxSize, -5) * ewald_D4(x, y, z);
544 
545  ewald_data ew;
546  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
547  MyIntPosType pos[3];
548  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
549  MyIntPosType ref[3] = {0, 0, 0};
550  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
551 
552  double norm = D4phi_exact.norm();
553 
554  for(int j = 0; j < 15; j++)
555  {
556  double err = fabs((D4phi_exact[j] - ew.D4phi[j]) / norm);
557  errsum4 += err;
558  if(err > errmax4)
559  errmax4 = err;
560  count4++;
561  }
562  }
563 
564  double errsum5 = 0;
565  double errmax5 = 0;
566  double count5 = 0;
567  for(int i = 0; i < 1000; i++)
568  {
569  double x = get_random_number() - 0.5;
570  double y = get_random_number() - 0.5;
571  double z = get_random_number() - 0.5;
572 
573  symtensor5<double> D5phi_exact = pow(All.BoxSize, -6) * ewald_D5(x, y, z);
574 
575  ewald_data ew;
576  double posd[3] = {x * All.BoxSize, y * All.BoxSize, z * All.BoxSize};
577  MyIntPosType pos[3];
578  pos_to_signedintpos(posd, (MySignedIntPosType *)pos);
579  MyIntPosType ref[3] = {0, 0, 0};
580  ewald_gridlookup(pos, ref, ewald::MULTIPOLES, ew);
581 
582  double norm = D5phi_exact.norm();
583 
584  for(int j = 0; j < 21; j++)
585  {
586  double err = fabs((D5phi_exact[j] - ew.D5phi[j]) / norm);
587  errsum5 += err;
588  if(err > errmax5)
589  errmax5 = err;
590  count5++;
591  }
592  }
593 
594  printf("Grid look-up: \n\n");
595 
596  printf("D0: max error = %g mean error=%g\n", errmax0, errsum0 / count0);
597  printf("D1: max error = %g mean error=%g\n", errmax1, errsum1 / count1);
598  printf("D2: max error = %g mean error=%g\n", errmax2, errsum2 / count2);
599  printf("D3: max error = %g mean error=%g\n", errmax3, errsum3 / count3);
600  printf("D4: max error = %g mean error=%g\n", errmax4, errsum4 / count4);
601  printf("D5: max error = %g mean error=%g\n", errmax5, errsum5 / count5);
602  }
603 
604  Terminate("stop");
605 }
606 
607 ewaldtensor6<double> ewald::ewald_P6(void)
608 {
609 #ifdef GRAVITY_TALLBOX
610  Terminate("GRAVITY_TALLBOX is not implemented");
611 #endif
612 
613  ewaldtensor6<double> P6 = 0.0;
614 
615  double leff = pow((1.0 / LONG_X) * (1.0 / LONG_Y) * (1.0 / LONG_Z), 1.0 / 3);
616  double alpha = 2.0 / leff;
617  double alpha2 = alpha * alpha;
618 
619  int qxmax = (int)(8.0 * LONG_X / alpha + 0.5);
620  int qymax = (int)(8.0 * LONG_Y / alpha + 0.5);
621  int qzmax = (int)(8.0 * LONG_Z / alpha + 0.5);
622 
623  int nxmax = (int)(2.0 * alpha / LONG_X + 0.5);
624  int nymax = (int)(2.0 * alpha / LONG_Y + 0.5);
625  int nzmax = (int)(2.0 * alpha / LONG_Z + 0.5);
626 
627  for(int nx = -qxmax; nx <= qxmax; nx++)
628  for(int ny = -qymax; ny <= qymax; ny++)
629  for(int nz = -qzmax; nz <= qzmax; nz++)
630  {
631  double dx = -nx * (1.0 / LONG_X);
632  double dy = -ny * (1.0 / LONG_Y);
633  double dz = -nz * (1.0 / LONG_Z);
634 
635  vector<double> dxyz(dx, dy, dz);
636 
637  double r2 = dx * dx + dy * dy + dz * dz;
638  double r = sqrt(r2);
639 
640  double rinv = (r > 0) ? 1.0 / r : 0.0;
641  double r2inv = rinv * rinv;
642  double r3inv = r2inv * rinv;
643  double r4inv = r2inv * r2inv;
644  double r7inv = r3inv * r4inv;
645 
646  if(nx != 0 || ny != 0 || nz != 0)
647  {
648  // derivatives of f(r) = -Erfc[alpha * r] /r
649 
650  double ar = alpha * r;
651  double ar2 = ar * ar;
652  double ar3 = ar * ar * ar;
653  double ar5 = ar3 * ar * ar;
654  double ar7 = ar5 * ar * ar;
655  double ar9 = ar7 * ar * ar;
656  double ar11 = ar9 * ar * ar;
657  double xir2 = pow(dx * rinv, 2);
658  double xir4 = pow(dx * rinv, 4);
659  double xir6 = pow(dx * rinv, 6);
660 
661  double yir2 = pow(dy * rinv, 2);
662  double zir2 = pow(dz * rinv, 2);
663 
664  P6.XXXXXX += (450.0 * ar + 300.0 * ar3 + 120.0 * ar5 - xir2 * (9450.0 * ar + 6300.0 * ar3 + 2520.0 * ar5 + 720.0 * ar7) +
665  xir4 * (28350.0 * ar + 18900.0 * ar3 + 7560.0 * ar5 + 2160.0 * ar7 + 480.0 * ar9) -
666  xir6 * (20790.0 * ar + 13860.0 * ar3 + 5544.0 * ar5 + 1584.0 * ar7 + 352.0 * ar9 + 64.0 * ar11)) /
667  sqrt(M_PI) * exp(-ar2) * r7inv +
668  erfc(ar) * (225.0 - 4725.0 * xir2 + 14175.0 * xir4 - 10395.0 * xir6) * r7inv;
669 
670  P6.XXXXYY += (90.0 * ar + 60.0 * ar3 + 24.0 * ar5 - xir2 * (1260.0 * ar + 840.0 * ar3 + 336.0 * ar5 + 96.0 * ar7) +
671  xir4 * (1890.0 * ar + 1260.0 * ar3 + 504.0 * ar5 + 144.0 * ar7 + 32.0 * ar9) -
672  yir2 * (630.0 * ar + 420.0 * ar3 + 168.0 * ar5 + 48.0 * ar7) +
673  xir2 * yir2 * (11340.0 * ar + 7560.0 * ar3 + 3024.0 * ar5 + 864.0 * ar7 + 192.0 * ar9) -
674  xir4 * yir2 * (20790.0 * ar + 13860.0 * ar3 + 5544.0 * ar5 + 1584.0 * ar7 + 352.0 * ar9 + 64.0 * ar11)) /
675  sqrt(M_PI) * exp(-ar2) * r7inv +
676  erfc(ar) *
677  (45.0 - 630.0 * xir2 + 945.0 * xir4 - 315.0 * yir2 + 5670.0 * xir2 * yir2 - 10395.0 * xir4 * yir2) *
678  r7inv;
679 
680  P6.XXYYZZ +=
681  (30.0 * ar + 20.0 * ar3 + 8.0 * ar5 - (xir2 + yir2 + zir2) * (210.0 * ar + 140.0 * ar3 + 56.0 * ar5 + 16.0 * ar7) +
682  +(xir2 * yir2 + xir2 * zir2 + yir2 * zir2) * (1890.0 * ar + 1260.0 * ar3 + 504.0 * ar5 + 144.0 * ar7 + 32.0 * ar9) -
683  xir2 * yir2 * zir2 * (20790.0 * ar + 13860.0 * ar3 + 5544.0 * ar5 + 1584.0 * ar7 + 352.0 * ar9 + 64.0 * ar11)) /
684  sqrt(M_PI) * exp(-ar2) * r7inv +
685  erfc(ar) *
686  (15.0 - 105.0 * (xir2 + yir2 + zir2) + 945.0 * (xir2 * yir2 + xir2 * zir2 + yir2 * zir2) -
687  10395.0 * xir2 * yir2 * zir2) *
688  r7inv;
689  }
690  else
691  {
692  /* we add the 1/r term here to the (0|0|0) entry, followed by differentiation, and the limit r->0 to obtain accurate
693  * results at the origin
694  */
695 
696  /* Note, for small r:
697  *
698  * [1/- erfc(a r)]/r = 2 a/sqrt(pi) * [ 1 - (a r)^2/3 + (a r)^4 / 10 - (a r)^6 / 42 + (a r)^8 / 216 - ...]
699  *
700  */
701 
702  P6.XXXXXX += (-240.0) * pow(alpha, 7) / (7.0 * sqrt(M_PI));
703  P6.XXXXYY += (-48.0) * pow(alpha, 7) / (7.0 * sqrt(M_PI));
704  P6.XXYYZZ += 0;
705  }
706  }
707 
708  for(int nx = -nxmax; nx <= nxmax; nx++)
709  for(int ny = -nymax; ny <= nymax; ny++)
710  for(int nz = -nzmax; nz <= nzmax; nz++)
711  {
712  if(nx != 0 || ny != 0 || nz != 0)
713  {
714  double kx = (2.0 * M_PI * LONG_X) * nx;
715  double ky = (2.0 * M_PI * LONG_Y) * ny;
716  double kz = (2.0 * M_PI * LONG_Z) * nz;
717  double k2 = kx * kx + ky * ky + kz * kz;
718 
719  double val = 4.0 * M_PI * (LONG_X * LONG_Y * LONG_Z) / k2 * exp(-k2 / (4.0 * alpha2));
720 
721  P6.XXXXXX += val * pow(kx, 6);
722  P6.XXXXYY += val * pow(kx, 4) * pow(ky, 2);
723  P6.XXYYZZ += val * pow(kx, 2) * pow(ky, 2) * pow(kz, 2);
724  }
725  }
726 
727  return P6;
728 }
729 
730 ewaldtensor8<double> ewald::ewald_P8(void)
731 {
732 #ifdef GRAVITY_TALLBOX
733  Terminate("GRAVITY_TALLBOX is not implemented");
734 #endif
735 
736  ewaldtensor8<double> P8 = 0.0;
737 
738  double leff = pow((1.0 / LONG_X) * (1.0 / LONG_Y) * (1.0 / LONG_Z), 1.0 / 3);
739  double alpha = 2.0 / leff;
740  double alpha2 = alpha * alpha;
741 
742  int qxmax = (int)(8.0 * LONG_X / alpha + 0.5);
743  int qymax = (int)(8.0 * LONG_Y / alpha + 0.5);
744  int qzmax = (int)(8.0 * LONG_Z / alpha + 0.5);
745 
746  int nxmax = (int)(2.0 * alpha / LONG_X + 0.5);
747  int nymax = (int)(2.0 * alpha / LONG_Y + 0.5);
748  int nzmax = (int)(2.0 * alpha / LONG_Z + 0.5);
749 
750  for(int nx = -qxmax; nx <= qxmax; nx++)
751  for(int ny = -qymax; ny <= qymax; ny++)
752  for(int nz = -qzmax; nz <= qzmax; nz++)
753  {
754  double dx = -nx * (1.0 / LONG_X);
755  double dy = -ny * (1.0 / LONG_Y);
756  double dz = -nz * (1.0 / LONG_Z);
757 
758  vector<double> dxyz(dx, dy, dz);
759 
760  double r2 = dx * dx + dy * dy + dz * dz;
761  double r = sqrt(r2);
762 
763  double rinv = (r > 0) ? 1.0 / r : 0.0;
764  double r2inv = rinv * rinv;
765  double r3inv = r2inv * rinv;
766  double r4inv = r2inv * r2inv;
767  double r5inv = r2inv * r3inv;
768  double r9inv = r4inv * r5inv;
769 
770  if(nx != 0 || ny != 0 || nz != 0)
771  {
772  // derivatives of f(r) = -Erfc[alpha * r] /r
773 
774  double ar = alpha * r;
775  double ar2 = ar * ar;
776  double ar3 = ar * ar * ar;
777  double ar5 = ar3 * ar * ar;
778  double ar7 = ar5 * ar * ar;
779  double ar9 = ar7 * ar * ar;
780  double ar11 = ar9 * ar * ar;
781  double ar13 = ar11 * ar * ar;
782  double ar15 = ar13 * ar * ar;
783  double xir2 = pow(dx * rinv, 2);
784  double xir4 = pow(dx * rinv, 4);
785  double xir6 = pow(dx * rinv, 6);
786  double xir8 = pow(dx * rinv, 8);
787 
788  double yir2 = pow(dy * rinv, 2);
789  double yir4 = pow(dy * rinv, 4);
790  double zir2 = pow(dz * rinv, 2);
791 
792  P8.XXXXXXXX +=
793  (-(22050.0 * ar + 14700.0 * ar3 + 5880.0 * ar5 + 1680.0 * ar7) +
794  xir2 * (793800.0 * ar + 529200.0 * ar3 + 211680.0 * ar5 + 60480.0 * ar7 + 13440.0 * ar9) -
795  xir4 * (4365900.0 * ar + 2910600.0 * ar3 + 1164240.0 * ar5 + 332640.0 * ar7 + 73920.0 * ar9 + 13440.0 * ar11) +
796  xir6 * (7567560.0 * ar + 5045040.0 * ar3 + 2018016.0 * ar5 + 576576.0 * ar7 + 128128.0 * ar9 + 23296.0 * ar11 +
797  3584 * ar13) -
798  xir8 * (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
799  1920.0 * ar13 + 256.0 * ar15)) /
800  sqrt(M_PI) * exp(-ar2) * r9inv +
801  erfc(ar) * (-11025.0 + 396900.0 * xir2 - 2182950.0 * xir4 + 3783780.0 * xir6 - 2027025.0 * xir8) * r9inv;
802 
803  P8.XXXXXXYY =
804  (-(3150.0 * ar + 2100.0 * ar3 + 840.0 * ar5 + 240.0 * ar7) +
805  xir2 * (85050.0 * ar + 56700.0 * ar3 + 22680.0 * ar5 + 6480.0 * ar7 + 1440.0 * ar9) -
806  xir4 * (311850.0 * ar + 207900.0 * ar3 + 83160.0 * ar5 + 23760.0 * ar7 + 5280.0 * ar9 + 960.0 * ar11) +
807  xir6 *
808  (270270.0 * ar + 180180.0 * ar3 + 72072.0 * ar5 + 20592.0 * ar7 + 4576.0 * ar9 + 832.0 * ar11 + 128.0 * ar13) +
809  yir2 * (28350.0 * ar + 18900 * ar3 + 7560.0 * ar5 + 2160 * ar7 + 480 * ar9) -
810  xir2 * yir2 * (935550 * ar + 623700.0 * ar3 + 249480.0 * ar5 + 71280.0 * ar7 + 15840.0 * ar9 + 2880.0 * ar11) +
811  xir4 * yir2 *
812  (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
813  1920.0 * ar13) -
814  xir6 * yir2 *
815  (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
816  1920.0 * ar13 + 256.0 * ar15)) /
817  sqrt(M_PI) * exp(-ar2) * r9inv +
818  erfc(ar) *
819  (-1575.0 + 42525.0 * xir2 - 155925.0 * xir4 + 135135.0 * xir6 + 14175.0 * yir2 - 467775.0 * xir2 * yir2 +
820  2027025.0 * xir4 * yir2 - 2027025 * xir6 * yir2) *
821  r9inv;
822 
823  P8.XXXXYYYY =
824  (-(1890.0 * ar + 1260.0 * ar3 + 504.0 * ar5 + 144.0 * ar7) +
825  (xir2 + yir2) * (34020.0 * ar + 22680.0 * ar3 + 9072.0 * ar5 + 2592.0 * ar7 + 576.0 * ar9) -
826  (xir4 + yir4) * (62370.0 * ar + 41580.0 * ar3 + 16632.0 * ar5 + 4752.0 * ar7 + 1056.0 * ar9 + 192.0 * ar11) +
827  -xir2 * yir2 * (748440.0 * ar + 498960.0 * ar3 + 199584.0 * ar5 + 57024.0 * ar7 + 12672.0 * ar9 + 2304.0 * ar11) +
828 
829  (xir4 * yir2 + xir2 * yir4) * (1621620.0 * ar + 1081080.0 * ar3 + 432432.0 * ar5 + 123552.0 * ar7 + 27456.0 * ar9 +
830  4992.0 * ar11 + 768.0 * ar13) -
831  xir4 * yir4 *
832  (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
833  1920.0 * ar13 + 256.0 * ar15)) /
834  sqrt(M_PI) * exp(-ar2) * r9inv +
835  erfc(ar) *
836  (-945.0 + 17010.0 * (xir2 + yir2) - 31185.0 * (xir4 + yir4) - 374220.0 * xir2 * yir2 +
837  810810.0 * (xir4 * yir2 + xir2 * yir4) - 2027025.0 * xir4 * yir4) *
838  r9inv;
839 
840  P8.XXXXYYZZ = (-(630.0 * ar + 420.0 * ar3 + 168.0 * ar5 + 48.0 * ar7) +
841  (xir2) * (11340.0 * ar + 7560.0 * ar3 + 3024.0 * ar5 + 864.0 * ar7 + 192.0 * ar9) -
842  (xir4) * (20790.0 * ar + 13860.0 * ar3 + 5544.0 * ar5 + 1584.0 * ar7 + 352.0 * ar9 + 64.0 * ar11) +
843  +(yir2 + zir2) * (5670.0 * ar + 3780.0 * ar3 + 1512.0 * ar5 + 432.0 * ar7 + 96.0 * ar9) -
844  (xir2 * yir2 + xir2 * zir2) *
845  (124740 * ar + 83160.0 * ar3 + 33264.0 * ar5 + 9504 * ar7 + 2112.0 * ar9 + 384.0 * ar11) +
846  (xir4 * yir2 + xir4 * zir2) * (270270.0 * ar + 180180.0 * ar3 + 72072 * ar5 + 20592.0 * ar7 +
847  4576.0 * ar9 + 832.0 * ar11 + 128.0 * ar13) -
848  yir2 * zir2 * (62370.0 * ar + 41580 * ar3 + 16632.0 * ar5 + 4752 * ar7 + 1056.0 * ar9 + 192.0 * ar11) +
849  (xir2 * yir2 * zir2) * (1621620.0 * ar + 1081080.0 * ar3 + 432432.0 * ar5 + 123552.0 * ar7 +
850  27456.0 * ar9 + 4992.0 * ar11 + 768.0 * ar13) -
851  xir4 * yir2 * zir2 *
852  (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 +
853  12480.0 * ar11 + 1920.0 * ar13 + 256.0 * ar15)) /
854  sqrt(M_PI) * exp(-ar2) * r9inv +
855  erfc(ar) *
856  (-315.0 + 5670.0 * xir2 - 10395.0 * xir4 + 2835.0 * (yir2 + zir2) -
857  62370.0 * (xir2 * yir2 + xir2 * zir2) + 135135.0 * xir4 * (yir2 + zir2) - 31185.0 * yir2 * zir2 +
858  810810.0 * xir2 * yir2 * zir2 - 2027025 * xir4 * yir2 * zir2) *
859  r9inv;
860  }
861  else
862  {
863  /* we add the 1/r term here to the (0|0|0) entry, followed by differentiation, and the limit r->0 to obtain accurate
864  * results at the origin
865  */
866 
867  /* Note, for small r:
868  *
869  * [1/- erfc(a r)]/r = 2 a/sqrt(pi) * [ 1 - (a r)^2/3 + (a r)^4 / 10 - (a r)^6 / 42 + (a r)^8 / 216 - ...]
870  *
871  */
872 
873  P8.XXXXXXXX += 1120.0 * pow(alpha, 9) / (3.0 * sqrt(M_PI));
874  P8.XXXXXXYY += 160.0 * pow(alpha, 9) / (3.0 * sqrt(M_PI));
875  P8.XXXXYYYY += 0;
876  P8.XXXXYYZZ += 32.0 * pow(alpha, 9) / (3.0 * sqrt(M_PI));
877  }
878  }
879 
880  for(int nx = -nxmax; nx <= nxmax; nx++)
881  for(int ny = -nymax; ny <= nymax; ny++)
882  for(int nz = -nzmax; nz <= nzmax; nz++)
883  {
884  if(nx != 0 || ny != 0 || nz != 0)
885  {
886  double kx = (2.0 * M_PI * LONG_X) * nx;
887  double ky = (2.0 * M_PI * LONG_Y) * ny;
888  double kz = (2.0 * M_PI * LONG_Z) * nz;
889  double k2 = kx * kx + ky * ky + kz * kz;
890 
891  double val = -4.0 * M_PI * (LONG_X * LONG_Y * LONG_Z) / k2 * exp(-k2 / (4.0 * alpha2));
892 
893  P8.XXXXXXXX += val * pow(kx, 8);
894  P8.XXXXXXYY += val * pow(kx, 6) * pow(ky, 2);
895  P8.XXXXYYYY += val * pow(kx, 4) * pow(ky, 4);
896  P8.XXXXYYZZ += val * pow(kx, 4) * pow(ky, 2) * pow(kz, 2);
897  }
898  }
899 
900  return P8;
901 }
902 
903 ewaldtensor10<double> ewald::ewald_P10(void)
904 {
905 #ifdef GRAVITY_TALLBOX
906  Terminate("GRAVITY_TALLBOX is not implemented");
907 #endif
908 
909  ewaldtensor10<double> P10 = 0.0;
910 
911  double leff = pow((1.0 / LONG_X) * (1.0 / LONG_Y) * (1.0 / LONG_Z), 1.0 / 3);
912  double alpha = 2.0 / leff;
913  double alpha2 = alpha * alpha;
914 
915  int qxmax = (int)(8.0 * LONG_X / alpha + 0.5);
916  int qymax = (int)(8.0 * LONG_Y / alpha + 0.5);
917  int qzmax = (int)(8.0 * LONG_Z / alpha + 0.5);
918 
919  int nxmax = (int)(2.0 * alpha / LONG_X + 0.5);
920  int nymax = (int)(2.0 * alpha / LONG_Y + 0.5);
921  int nzmax = (int)(2.0 * alpha / LONG_Z + 0.5);
922 
923  for(int nx = -qxmax; nx <= qxmax; nx++)
924  for(int ny = -qymax; ny <= qymax; ny++)
925  for(int nz = -qzmax; nz <= qzmax; nz++)
926  {
927  double dx = -nx * (1.0 / LONG_X);
928  double dy = -ny * (1.0 / LONG_Y);
929  double dz = -nz * (1.0 / LONG_Z);
930 
931  vector<double> dxyz(dx, dy, dz);
932 
933  double r2 = dx * dx + dy * dy + dz * dz;
934  double r = sqrt(r2);
935 
936  double rinv = (r > 0) ? 1.0 / r : 0.0;
937  double r2inv = rinv * rinv;
938  double r3inv = r2inv * rinv;
939  double r4inv = r2inv * r2inv;
940  double r7inv = r3inv * r4inv;
941  double r11inv = r4inv * r7inv;
942 
943  if(nx != 0 || ny != 0 || nz != 0)
944  {
945  double ar = alpha * r;
946  double ar2 = ar * ar;
947  double ar3 = ar * ar * ar;
948  double ar5 = ar3 * ar * ar;
949  double ar7 = ar5 * ar * ar;
950  double ar9 = ar7 * ar * ar;
951  double ar11 = ar9 * ar * ar;
952  double ar13 = ar11 * ar * ar;
953  double ar15 = ar13 * ar * ar;
954  double ar17 = ar15 * ar * ar;
955  double ar19 = ar17 * ar * ar;
956 
957  double xir2 = pow(dx * rinv, 2);
958  double xir4 = pow(dx * rinv, 4);
959  double xir6 = pow(dx * rinv, 6);
960  double xir8 = pow(dx * rinv, 8);
961  double xir10 = pow(dx * rinv, 10);
962 
963  double yir2 = pow(dy * rinv, 2);
964  double yir4 = pow(dy * rinv, 4);
965  double zir2 = pow(dz * rinv, 2);
966 
967  P10.XXXXXXXXXX +=
968  ((1786050.0 * ar + 1190700.0 * ar3 + 476280.0 * ar5 + 136080.0 * ar7 + 30240 * ar9) -
969  xir2 * (98232750.0 * ar + 65488500.0 * ar3 + 26195400.0 * ar5 + 7484400.0 * ar7 + 1663200.0 * ar9 + 302400 * ar11) +
970  xir4 * (851350500.0 * ar + 567567000.0 * ar3 + 227026800.0 * ar5 + 64864800.0 * ar7 + 14414400.0 * ar9 +
971  2620800.0 * ar11 + 403200 * ar13) -
972  xir6 * (2554051500.0 * ar + 1702701000.0 * ar3 + 681080400.0 * ar5 + 194594400.0 * ar7 + 43243200.0 * ar9 +
973  7862400.0 * ar11 + 1209600.0 * ar13 + 161280 * ar15) +
974  xir8 * (3101348250.0 * ar + 2067565500.0 * ar3 + 827026200.0 * ar5 + 236293200.0 * ar7 + 52509600.0 * ar9 +
975  9547200.0 * ar11 + 1468800.0 * ar13 + 195840.0 * ar15 + 23040 * ar17) -
976  xir10 * (1309458150 * ar + 872972100 * ar3 + 349188840 * ar5 + 99768240 * ar7 + 22170720 * ar9 + 4031040 * ar11 +
977  620160 * ar13 + 82688 * ar15 + 9728 * ar17 + 1024.0 * ar19)) /
978  sqrt(M_PI) * exp(-ar2) * r11inv +
979  erfc(ar) *
980  (893025.0 - 49116375.0 * xir2 + 425675250.0 * xir4 - 1277025750 * xir6 + 1550674125.0 * xir8 -
981  654729075.0 * xir10) *
982  r11inv;
983 
984  P10.XXXXXXXXYY +=
985  ((198450.0 * ar + 132300.0 * ar3 + 52920.0 * ar5 + 15120.0 * ar7 + 3360.0 * ar9) -
986  xir2 * (8731800.0 * ar + 5821200.0 * ar3 + 2328480.0 * ar5 + 665280.0 * ar7 + 147840.0 * ar9 + 26880.0 * ar11) +
987  xir4 * (56756700.0 * ar + 37837800.0 * ar3 + 15135120.0 * ar5 + 4324320.0 * ar7 + 960960.0 * ar9 + 174720.0 * ar11 +
988  26880.0 * ar13) -
989  xir6 * (113513400.0 * ar + 75675600.0 * ar3 + 30270240.0 * ar5 + 8648640.0 * ar7 + 1921920.0 * ar9 +
990  349440.0 * ar11 + 53760.0 * ar13 + 7168.0 * ar15) +
991  xir8 * (68918850.0 * ar + 45945900.0 * ar3 + 18378360.0 * ar5 + 5250960.0 * ar7 + 1166880.0 * ar9 +
992  212160.0 * ar11 + 32640.0 * ar13 + 4352.0 * ar15 + 512.0 * ar17) -
993  yir2 * (2182950.0 * ar + 1455300.0 * ar3 + 582120.0 * ar5 + 166320.0 * ar7 + 36960.0 * ar9 + 6720.0 * ar11) +
994  xir2 * yir2 *
995  (113513400.0 * ar + 75675600.0 * ar3 + 30270240.0 * ar5 + 8648640.0 * ar7 + 1921920.0 * ar9 + 349440.0 * ar11 +
996  53760.0 * ar13) -
997  xir4 * yir2 *
998  (851350500.0 * ar + 567567000.0 * ar3 + 227026800.0 * ar5 + 64864800.0 * ar7 + 14414400.0 * ar9 +
999  2620800.0 * ar11 + 403200.0 * ar13 + 53760.0 * ar15) +
1000  xir6 * yir2 *
1001  (1929727800.0 * ar + 1286485200.0 * ar3 + 514594080.0 * ar5 + 147026880.0 * ar7 + 32672640.0 * ar9 +
1002  5940480.0 * ar11 + 913920.0 * ar13 + 121856.0 * ar15 + 14336.0 * ar17) -
1003  xir8 * yir2 *
1004  (1309458150.0 * ar + 872972100.0 * ar3 + 349188840.0 * ar5 + 99768240 * ar7 + 22170720 * ar9 + 4031040 * ar11 +
1005  620160 * ar13 + 82688 * ar15 + 9728 * ar17 + 1024.0 * ar19)) /
1006  sqrt(M_PI) * exp(-ar2) * r11inv +
1007  erfc(ar) *
1008  (99225.0 - 4365900.0 * xir2 + 28378350.0 * xir4 - 56756700 * xir6 + 34459425.0 * xir8 - 1091475.0 * yir2 +
1009  56756700.0 * xir2 * yir2 - 425675250.0 * xir4 * yir2 + 964863900.0 * xir6 * yir2 - 654729075.0 * xir8 * yir2) *
1010  r11inv;
1011 
1012  P10.XXXXXXYYYY +=
1013  ((85050.0 * ar + 56700.0 * ar3 + 22680.0 * ar5 + 6480.0 * ar7 + 1440.0 * ar9) -
1014  xir2 * (2806650.0 * ar + 1871100.0 * ar3 + 748440.0 * ar5 + 213840.0 * ar7 + 47520.0 * ar9 + 8640.0 * ar11) +
1015  xir4 * (12162150.0 * ar + 8108100.0 * ar3 + 3243240.0 * ar5 + 926640.0 * ar7 + 205920.0 * ar9 + 37440.0 * ar11 +
1016  5760.0 * ar13) -
1017  xir6 * (12162150.0 * ar + 8108100.0 * ar3 + 3243240.0 * ar5 + 926640.0 * ar7 + 205920.0 * ar9 + 37440.0 * ar11 +
1018  5760.0 * ar13 + 768.0 * ar15) -
1019  yir2 * (1871100.0 * ar + 1247400.0 * ar3 + 498960.0 * ar5 + 142560.0 * ar7 + 31680.0 * ar9 + 5760.0 * ar11) +
1020  xir2 * yir2 *
1021  (72972900.0 * ar + 48648600 * ar3 + 19459440.0 * ar5 + 5559840.0 * ar7 + 1235520.0 * ar9 + 224640.0 * ar11 +
1022  34560.0 * ar13) -
1023  xir4 * yir2 *
1024  (364864500.0 * ar + 243243000.0 * ar3 + 97297200.0 * ar5 + 27799200.0 * ar7 + 6177600.0 * ar9 +
1025  1123200.0 * ar11 + 172800.0 * ar13 + 23040.0 * ar15) +
1026  xir6 * yir2 *
1027  (413513100.0 * ar + 275675400.0 * ar3 + 110270160.0 * ar5 + 31505760.0 * ar7 + 7001280.0 * ar9 +
1028  1272960.0 * ar11 + 195840.0 * ar13 + 26112.0 * ar15 + 3072.0 * ar17) +
1029  yir4 * (4054050.0 * ar + 2702700.0 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
1030  1920 * ar13) -
1031  xir2 * yir4 *
1032  (182432250.0 * ar + 121621500.0 * ar3 + 48648600.0 * ar5 + 13899600 * ar7 + 3088800 * ar9 + 561600 * ar11 +
1033  86400 * ar13 + 11520 * ar15) +
1034  xir4 * yir4 *
1035  (1033782750.0 * ar + 689188500.0 * ar3 + 275675400.0 * ar5 + 78764400 * ar7 + 17503200 * ar9 + 3182400 * ar11 +
1036  489600 * ar13 + 65280 * ar15 + 7680 * ar17) -
1037  xir6 * yir4 *
1038  (1309458150.0 * ar + 872972100.0 * ar3 + 349188840.0 * ar5 + 99768240.0 * ar7 + 22170720.0 * ar9 +
1039  4031040.0 * ar11 + 620160.0 * ar13 + 82688.0 * ar15 + 9728.0 * ar17 + 1024.0 * ar19)) /
1040  sqrt(M_PI) * exp(-ar2) * r11inv +
1041  erfc(ar) *
1042  (42525.0 - 1403325 * xir2 + 6081075.0 * xir4 - 6081075 * xir6 - 935550.0 * yir2 + 36486450.0 * xir2 * yir2 -
1043  182432250.0 * xir4 * yir2 + 206756550.0 * xir6 * yir2 + 2027025.0 * yir4 - 91216125.0 * xir2 * yir4 +
1044  516891375.0 * xir4 * yir4 - 654729075.0 * xir6 * yir4) *
1045  r11inv;
1046 
1047  P10.XXXXXXYYZZ +=
1048  ((28350 * ar + 18900 * ar3 + 7560 * ar5 + 2160 * ar7 + 480 * ar9) -
1049  xir2 * (935550 * ar + 623700 * ar3 + 249480 * ar5 + 71280 * ar7 + 15840 * ar9 + 2880 * ar11) +
1050  xir4 * (4054050 * ar + 2702700 * ar3 + 1081080 * ar5 + 308880 * ar7 + 68640 * ar9 + 12480 * ar11 + 1920 * ar13) -
1051  xir6 * (4054050 * ar + 2702700 * ar3 + 1081080 * ar5 + 308880 * ar7 + 68640 * ar9 + 12480 * ar11 + 1920 * ar13 +
1052  256 * ar15) -
1053  (yir2 + zir2) * (311850 * ar + 207900 * ar3 + 83160 * ar5 + 23760 * ar7 + 5280 * ar9 + 960 * ar11) +
1054  (xir2 * yir2 + xir2 * zir2) *
1055  (12162150 * ar + 8108100 * ar3 + 3243240 * ar5 + 926640 * ar7 + 205920 * ar9 + 37440 * ar11 + 5760 * ar13) -
1056  (xir4 * yir2 + xir4 * zir2) * (60810750 * ar + 40540500 * ar3 + 16216200 * ar5 + 4633200 * ar7 + 1029600 * ar9 +
1057  187200 * ar11 + 28800 * ar13 + 3840 * ar15) +
1058  (xir6 * yir2 + xir6 * zir2) * (68918850 * ar + 45945900 * ar3 + 18378360 * ar5 + 5250960 * ar7 + 1166880 * ar9 +
1059  212160 * ar11 + 32640 * ar13 + 4352 * ar15 + 512 * ar17) +
1060  yir2 * zir2 *
1061  (4054050 * ar + 2702700 * ar3 + 1081080.0 * ar5 + 308880.0 * ar7 + 68640.0 * ar9 + 12480.0 * ar11 +
1062  1920 * ar13) -
1063  xir2 * yir2 * zir2 *
1064  (182432250.0 * ar + 121621500.0 * ar3 + 48648600.0 * ar5 + 13899600 * ar7 + 3088800 * ar9 + 561600 * ar11 +
1065  86400 * ar13 + 11520 * ar15) +
1066  xir4 * yir2 * zir2 *
1067  (1033782750.0 * ar + 689188500.0 * ar3 + 275675400.0 * ar5 + 78764400 * ar7 + 17503200 * ar9 + 3182400 * ar11 +
1068  489600 * ar13 + 65280 * ar15 + 7680 * ar17) -
1069  xir6 * yir2 * zir2 *
1070  (1309458150.0 * ar + 872972100.0 * ar3 + 349188840.0 * ar5 + 99768240.0 * ar7 + 22170720.0 * ar9 +
1071  4031040.0 * ar11 + 620160.0 * ar13 + 82688.0 * ar15 + 9728.0 * ar17 + 1024.0 * ar19)) /
1072  sqrt(M_PI) * exp(-ar2) * r11inv +
1073  erfc(ar) *
1074  (14175.0 - 467775 * xir2 + 2027025 * xir4 - 2027025 * xir6 - 155925.0 * (yir2 + zir2) +
1075  6081075.0 * xir2 * (yir2 + zir2) - 30405375.0 * xir4 * (yir2 + zir2) + 34459425.0 * xir6 * (yir2 + zir2) +
1076  2027025.0 * yir2 * zir2 - 91216125.0 * xir2 * yir2 * zir2 + 516891375.0 * xir4 * yir2 * zir2 -
1077  654729075.0 * xir6 * yir2 * zir2) *
1078  r11inv;
1079 
1080  P10.XXXXYYYYZZ +=
1081  ((17010 * ar + 11340 * ar3 + 4536 * ar5 + 1296 * ar7 + 288 * ar9) -
1082  (xir2 + yir2) * (374220 * ar + 249480 * ar3 + 99792 * ar5 + 28512 * ar7 + 6336 * ar9 + 1152 * ar11) +
1083  (xir4 + yir4) * (810810 * ar + 540540 * ar3 + 216216 * ar5 + 61776 * ar7 + 13728 * ar9 + 2496 * ar11 + 384 * ar13) +
1084  xir2 * yir2 *
1085  (9729720 * ar + 6486480 * ar3 + 2594592 * ar5 + 741312 * ar7 + 164736 * ar9 + 29952 * ar11 + 4608 * ar13) -
1086  (xir4 * yir2 + xir2 * yir4) * (24324300 * ar + 16216200 * ar3 + 6486480 * ar5 + 1853280 * ar7 + 411840 * ar9 +
1087  74880 * ar11 + 11520 * ar13 + 1536 * ar15) +
1088  xir4 * yir4 *
1089  (68918850 * ar + 45945900 * ar3 + 18378360 * ar5 + 5250960 * ar7 + 1166880 * ar9 + 212160 * ar11 +
1090  32640 * ar13 + 4352 * ar15 + 512.0 * ar17) -
1091  zir2 * (187110 * ar + 124740 * ar3 + 49896 * ar5 + 14256 * ar7 + 3168 * ar9 + 576 * ar11) +
1092  (xir2 + yir2) * zir2 *
1093  (4864860 * ar + 3243240 * ar3 + 1297296 * ar5 + 370656 * ar7 + 82368 * ar9 + 14976 * ar11 + 2304 * ar13) -
1094  (xir4 + yir4) * zir2 *
1095  (12162150 * ar + 8108100 * ar3 + 3243240 * ar5 + 926640 * ar7 + 205920 * ar9 + 37440 * ar11 + 5760 * ar13 +
1096  768 * ar15) -
1097  xir2 * yir2 * zir2 *
1098  (145945800 * ar + 97297200 * ar3 + 38918880 * ar5 + 11119680 * ar7 + 2471040 * ar9 + 449280 * ar11 +
1099  69120 * ar13 + 9216 * ar15) +
1100  (xir4 * yir2 + xir2 * yir4) * zir2 *
1101  (413513100 * ar + 275675400 * ar3 + 110270160 * ar5 + 31505760 * ar7 + 7001280 * ar9 + 1272960 * ar11 +
1102  195840 * ar13 + 26112 * ar15 + 3072 * ar17) -
1103  xir4 * yir4 * zir2 *
1104  (1309458150.0 * ar + 872972100.0 * ar3 + 349188840.0 * ar5 + 99768240.0 * ar7 + 22170720.0 * ar9 +
1105  4031040.0 * ar11 + 620160.0 * ar13 + 82688.0 * ar15 + 9728.0 * ar17 + 1024.0 * ar19)) /
1106  sqrt(M_PI) * exp(-ar2) * r11inv +
1107  erfc(ar) *
1108  (8505.0 - 187110 * (xir2 + yir2) + 405405 * (xir4 + yir4) + 4864860 * xir2 * yir2 -
1109  12162150 * (xir4 * yir2 + xir2 * yir4) + 34459425 * xir4 * yir4 - 93555 * zir2 +
1110  2432430 * (xir2 + yir2) * zir2 - 6081075 * (xir4 + yir4) * zir2 - 72972900 * xir2 * yir2 * zir2 +
1111  206756550 * (xir4 * yir2 + xir2 * yir4) * zir2 - 654729075.0 * xir4 * yir4 * zir2) *
1112  r11inv;
1113  }
1114  else
1115  {
1116  /* we add the 1/r term here to the (0|0|0) entry, followed by differentiation, and the limit r->0 to obtain accurate
1117  * results at the origin
1118  */
1119 
1120  /* Note, for small r:
1121  *
1122  * [1/- erfc(a r)]/r = 2 a/sqrt(pi) * [ 1 - (a r)^2/3 + (a r)^4 / 10 - (a r)^6 / 42 + (a r)^8 / 216 - ...]
1123  *
1124  */
1125 
1126  P10.XXXXXXXXXX += (-60480.0) * pow(alpha, 11) / (11.0 * sqrt(M_PI));
1127  P10.XXXXXXXXYY += (-6720.0) * pow(alpha, 11) / (11.0 * sqrt(M_PI));
1128  P10.XXXXXXYYYY += (-2880.0) * pow(alpha, 11) / (11.0 * sqrt(M_PI));
1129  P10.XXXXXXYYZZ += (-960.0) * pow(alpha, 11) / (11.0 * sqrt(M_PI));
1130  P10.XXXXYYYYZZ += (-576.0) * pow(alpha, 11) / (11.0 * sqrt(M_PI));
1131  }
1132  }
1133 
1134  for(int nx = -nxmax; nx <= nxmax; nx++)
1135  for(int ny = -nymax; ny <= nymax; ny++)
1136  for(int nz = -nzmax; nz <= nzmax; nz++)
1137  {
1138  if(nx != 0 || ny != 0 || nz != 0)
1139  {
1140  double kx = (2.0 * M_PI * LONG_X) * nx;
1141  double ky = (2.0 * M_PI * LONG_Y) * ny;
1142  double kz = (2.0 * M_PI * LONG_Z) * nz;
1143  double k2 = kx * kx + ky * ky + kz * kz;
1144 
1145  double val = 4.0 * M_PI * (LONG_X * LONG_Y * LONG_Z) / k2 * exp(-k2 / (4.0 * alpha2));
1146 
1147  P10.XXXXXXXXXX += val * pow(kx, 10);
1148  P10.XXXXXXXXYY += val * pow(kx, 8) * pow(ky, 2);
1149  P10.XXXXXXYYYY += val * pow(kx, 6) * pow(ky, 4);
1150  P10.XXXXXXYYZZ += val * pow(kx, 6) * pow(ky, 2) * pow(kz, 2);
1151  P10.XXXXYYYYZZ += val * pow(kx, 4) * pow(ky, 4) * pow(kz, 2);
1152  }
1153  }
1154 
1155  return P10;
1156 }
1157 
1158 #endif
All
global_data_all_processes All
Definition: main.cc:40
ewald::ewald_D3
symtensor3< double > ewald_D3(double x, double y, double z)
Definition: ewald.cc:1114
ewald::ewald_D0
double ewald_D0(double x, double y, double z)
This function computes the potential correction term by means of Ewald summation.
Definition: ewald.cc:623
ewald::ewald_D4
symtensor4< double > ewald_D4(double x, double y, double z)
Definition: ewald.cc:1241
ewald::ewald_corr
void ewald_corr(double dx, double dy, double dz, enum interpolate_options, ewald_data &fper)
ewald::ewald_P6
ewaldtensor6< double > ewald_P6(void)
ewald::POINTMASS
@ POINTMASS
Definition: ewald.h:67
ewald::MULTIPOLES
@ MULTIPOLES
Definition: ewald.h:68
ewald::ewald_D5
symtensor5< double > ewald_D5(double x, double y, double z)
Definition: ewald.cc:1385
ewald::ewald_D1
vector< double > ewald_D1(double x, double y, double z)
This function computes the force correction term (difference between full force of infinite lattice a...
Definition: ewald.cc:807
ewald::ewald_corr_exact
void ewald_corr_exact(double dx, double dy, double dz, enum interpolate_options flag, ewald_data &fper)
ewald::ewald_P8
ewaldtensor8< double > ewald_P8(void)
ewald::ewald_P10
ewaldtensor10< double > ewald_P10(void)
ewald::ewald_D2
symtensor2< double > ewald_D2(double x, double y, double z)
Definition: ewald.cc:996
ewald::ewald_gridlookup
void ewald_gridlookup(const MyIntPosType *p_intpos, const MyIntPosType *target_intpos, enum interpolate_options flag, ewald_data &fper)
Definition: ewald.cc:304
intposconvert::pos_to_signedintpos
MySignedIntPosType pos_to_signedintpos(T posdiff)
Definition: intposconvert.h:325
symtensor2::norm
double norm(void)
Definition: symtensors.h:287
symtensor3::norm
double norm(void)
Definition: symtensors.h:417
symtensor4::norm
double norm(void)
Definition: symtensors.h:504
symtensor5::norm
double norm(void)
Definition: symtensors.h:597
vector::norm
double norm(void)
Definition: symtensors.h:189
M_PI
#define M_PI
Definition: constants.h:56
LONG_Y
#define LONG_Y
Definition: dtypes.h:369
MyIntPosType
uint32_t MyIntPosType
Definition: dtypes.h:35
MySignedIntPosType
int32_t MySignedIntPosType
Definition: dtypes.h:36
LONG_X
#define LONG_X
Definition: dtypes.h:361
LONG_Z
#define LONG_Z
Definition: dtypes.h:377
ENX
#define ENX
Definition: ewald.h:45
ENZ
#define ENZ
Definition: ewald.h:47
ENY
#define ENY
Definition: ewald.h:46
Terminate
#define Terminate(...)
Definition: macros.h:19
half_float::detail::exp
expr exp(half arg)
Definition: half.hpp:2724
half_float::detail::fabs
half fabs(half arg)
Definition: half.hpp:2627
half_float::detail::pow
expr pow(half base, half exp)
Definition: half.hpp:2803
half_float::detail::erfc
expr erfc(half arg)
Definition: half.hpp:2925
half_float::detail::sqrt
expr sqrt(half arg)
Definition: half.hpp:2777
ewald_data
Definition: gravtree.h:184
ewald_data::D1phi
vector< MyReal > D1phi
Definition: gravtree.h:186
ewald_data::D3phi
symtensor3< MyReal > D3phi
Definition: gravtree.h:188
ewald_data::D0phi
MyReal D0phi
Definition: gravtree.h:185
ewald_data::D2phi
symtensor2< MyReal > D2phi
Definition: gravtree.h:187
global_data_all_processes::BoxSize
double BoxSize
Definition: allvars.h:144
rYZZZZ
#define rYZZZZ
Definition: symtensor_indices.h:334
rXXYZZ
#define rXXYZZ
Definition: symtensor_indices.h:190
dYZZ
#define dYZZ
Definition: symtensor_indices.h:49
rYYZZZ
#define rYYZZZ
Definition: symtensor_indices.h:307
sXXXY
#define sXXXY
Definition: symtensor_indices.h:65
rXXZZZ
#define rXXZZZ
Definition: symtensor_indices.h:199
dXYY
#define dXYY
Definition: symtensor_indices.h:32
rXXXYY
#define rXXXYY
Definition: symtensor_indices.h:177
sXXYZ
#define sXXYZ
Definition: symtensor_indices.h:70
sXYYZ
#define sXYYZ
Definition: symtensor_indices.h:82
dZZZ
#define dZZZ
Definition: symtensor_indices.h:61
rXXXYZ
#define rXXXYZ
Definition: symtensor_indices.h:178
dYYY
#define dYYY
Definition: symtensor_indices.h:44
dXYZ
#define dXYZ
Definition: symtensor_indices.h:33
sYYYZ
#define sYYYZ
Definition: symtensor_indices.h:118
rXXYYY
#define rXXYYY
Definition: symtensor_indices.h:186
rXXXXZ
#define rXXXXZ
Definition: symtensor_indices.h:175
sXZZZ
#define sXZZZ
Definition: symtensor_indices.h:98
rXXXXY
#define rXXXXY
Definition: symtensor_indices.h:174
rYYYYZ
#define rYYYYZ
Definition: symtensor_indices.h:295
rXYYYZ
#define rXYYYZ
Definition: symtensor_indices.h:214
qYZ
#define qYZ
Definition: symtensor_indices.h:21
rXYYYY
#define rXYYYY
Definition: symtensor_indices.h:213
sXYYY
#define sXYYY
Definition: symtensor_indices.h:81
dXXY
#define dXXY
Definition: symtensor_indices.h:28
dXXX
#define dXXX
Definition: symtensor_indices.h:27
dXXZ
#define dXXZ
Definition: symtensor_indices.h:29
rYYYZZ
#define rYYYZZ
Definition: symtensor_indices.h:298
dYYZ
#define dYYZ
Definition: symtensor_indices.h:45
rXXXXX
#define rXXXXX
Definition: symtensor_indices.h:173
rXXYYZ
#define rXXYYZ
Definition: symtensor_indices.h:187
sXYZZ
#define sXYZZ
Definition: symtensor_indices.h:86
rZZZZZ
#define rZZZZZ
Definition: symtensor_indices.h:415
rXXXZZ
#define rXXXZZ
Definition: symtensor_indices.h:181
rXYYZZ
#define rXYYZZ
Definition: symtensor_indices.h:217
sXXXZ
#define sXXXZ
Definition: symtensor_indices.h:66
sYZZZ
#define sYZZZ
Definition: symtensor_indices.h:134
qXY
#define qXY
Definition: symtensor_indices.h:17
rXYZZZ
#define rXYZZZ
Definition: symtensor_indices.h:226
rYYYYY
#define rYYYYY
Definition: symtensor_indices.h:294
dXZZ
#define dXZZ
Definition: symtensor_indices.h:37
rXZZZZ
#define rXZZZZ
Definition: symtensor_indices.h:253
qXZ
#define qXZ
Definition: symtensor_indices.h:18
init_rng
void init_rng(int thistask)
Definition: system.cc:42
get_random_number
double get_random_number(void)
Definition: system.cc:49