Version: SMASH-3.1
clebschgordan_lookup.h
Go to the documentation of this file.
1 /*
2  * Copyright (c) 2023
3  * SMASH Team
4  *
5  * GNU General Public License (GPLv3 or later)
6  */
7 
8 #ifndef SRC_INCLUDE_SMASH_CLEBSCHGORDAN_LOOKUP_H_
9 #define SRC_INCLUDE_SMASH_CLEBSCHGORDAN_LOOKUP_H_
10 
11 #include <cassert>
12 #include <iostream>
13 #include <unordered_map>
14 
15 #include "smash/iomanipulators.h"
16 
17 namespace smash {
18 
22 class ClebschGordan {
23  public:
32  static double coefficient(const int j_a, const int j_b, const int j_c,
33  const int m_a, const int m_b, const int m_c);
34 
41  struct ThreeSpins {
42  int j1;
43  int j2;
44  int j3;
45  int m1;
46  int m2;
47  int m3;
48 
49  private:
57  auto tied() const { return std::tie(j1, j2, j3, m1, m2, m3); }
58 
59  public:
68  bool operator==(const ThreeSpins &other) const {
69  return tied() == other.tied();
70  }
71  };
72 
73  private:
88  static double calculate_coefficient(const int j_a, const int j_b,
89  const int j_c, const int m_a,
90  const int m_b, const int m_c);
91 
101  struct ThreeSpinHash {
163  std::size_t operator()(const ThreeSpins &in) const noexcept {
164  assert(in.j1 >= 0 && in.j1 < 16);
165  assert(in.j2 >= 0 && in.j2 < 16);
166  assert(in.j3 >= 0 && in.j3 < 16);
167  assert(std::abs(in.m1) < 16);
168  assert(std::abs(in.m2) < 16);
169  assert(std::abs(in.m3) < 16);
170  /*
171  * Although strictly speaking, this would only generate a very poor hash,
172  * we prefer making compilation fail if size_t has less than 32 bits.
173  * This is after all very unlikely and we'll deal with it only if needed.
174  */
175  static_assert(sizeof(std::size_t) >= 4);
176  // This is the amount to shift to obtain "5-bits numbers"
177  constexpr auto bitshift = sizeof(size_t) * 8 - 5;
178  // The different shift to the right make the 5-bit occupy different bits
179  return (static_cast<std::size_t>(in.j1) << bitshift >> (bitshift - 25)) +
180  (static_cast<std::size_t>(in.j2) << bitshift >> (bitshift - 20)) +
181  (static_cast<std::size_t>(in.j3) << bitshift >> (bitshift - 15)) +
182  (static_cast<std::size_t>(in.m1) << bitshift >> (bitshift - 10)) +
183  (static_cast<std::size_t>(in.m2) << bitshift >> (bitshift - 5)) +
184  (static_cast<std::size_t>(in.m3) << bitshift >> bitshift);
185  }
186  };
187 
192  inline static std::unordered_map<ThreeSpins, double, ThreeSpinHash>
193  lookup_table = {
194  {{0, 0, 0, +0, +0, +0}, 1.00000000000000000},
195  {{0, 1, 1, +0, -1, -1}, 1.00000000000000022},
196  {{0, 1, 1, +0, +1, +1}, 1.00000000000000022},
197  {{0, 2, 2, +0, -2, -2}, 0.99999999999999989},
198  {{0, 2, 2, +0, +0, +0}, 0.99999999999999989},
199  {{0, 2, 2, +0, +2, +2}, 0.99999999999999989},
200  {{0, 3, 3, +0, -3, -3}, 1.00000000000000000},
201  {{0, 3, 3, +0, -1, -1}, 0.99999999999999989},
202  {{0, 3, 3, +0, +1, +1}, 0.99999999999999989},
203  {{0, 3, 3, +0, +3, +3}, 1.00000000000000000},
204  {{1, 0, 1, -1, +0, -1}, 1.00000000000000022},
205  {{1, 0, 1, +1, +0, +1}, 1.00000000000000022},
206  {{1, 1, 0, -1, +1, +0}, -0.70710678118654757},
207  {{1, 1, 0, +1, -1, +0}, 0.70710678118654757},
208  {{1, 1, 2, -1, -1, -2}, 0.99999999999999989},
209  {{1, 1, 2, -1, +1, +0}, 0.70710678118654746},
210  {{1, 1, 2, +1, -1, +0}, 0.70710678118654746},
211  {{1, 1, 2, +1, +1, +2}, 0.99999999999999989},
212  {{1, 2, 1, -1, +0, -1}, -0.57735026918962584},
213  {{1, 2, 1, -1, +2, +1}, -0.81649658092772615},
214  {{1, 2, 1, +1, -2, -1}, 0.81649658092772615},
215  {{1, 2, 1, +1, +0, +1}, 0.57735026918962584},
216  {{1, 2, 3, -1, -2, -3}, 1.00000000000000000},
217  {{1, 2, 3, -1, +0, -1}, 0.81649658092772615},
218  {{1, 2, 3, -1, +2, +1}, 0.57735026918962584},
219  {{1, 2, 3, +1, -2, -1}, 0.57735026918962584},
220  {{1, 2, 3, +1, +0, +1}, 0.81649658092772615},
221  {{1, 2, 3, +1, +2, +3}, 1.00000000000000000},
222  {{1, 3, 2, -1, -1, -2}, -0.49999999999999983},
223  {{1, 3, 2, -1, +1, +0}, -0.70710678118654724},
224  {{1, 3, 2, -1, +3, +2}, -0.86602540378443837},
225  {{1, 3, 2, +1, -3, -2}, 0.86602540378443837},
226  {{1, 3, 2, +1, -1, +0}, 0.70710678118654724},
227  {{1, 3, 2, +1, +1, +2}, 0.49999999999999983},
228  {{1, 3, 4, -1, -3, -4}, 1.00000000000000022},
229  {{1, 3, 4, -1, -1, -2}, 0.86602540378443871},
230  {{1, 3, 4, -1, +1, +0}, 0.70710678118654746},
231  {{1, 3, 4, -1, +3, +2}, 0.49999999999999994},
232  {{1, 3, 4, +1, -3, -2}, 0.49999999999999994},
233  {{1, 3, 4, +1, -1, +0}, 0.70710678118654746},
234  {{1, 3, 4, +1, +1, +2}, 0.86602540378443871},
235  {{1, 3, 4, +1, +3, +4}, 1.00000000000000022},
236  {{2, 0, 2, -2, +0, -2}, 0.99999999999999989},
237  {{2, 0, 2, +0, +0, +0}, 0.99999999999999989},
238  {{2, 0, 2, +2, +0, +2}, 0.99999999999999989},
239  {{2, 1, 1, -2, +1, -1}, -0.81649658092772615},
240  {{2, 1, 1, +0, -1, -1}, 0.57735026918962584},
241  {{2, 1, 1, +0, +1, +1}, -0.57735026918962584},
242  {{2, 1, 1, +2, -1, +1}, 0.81649658092772615},
243  {{2, 1, 3, -2, -1, -3}, 1.00000000000000000},
244  {{2, 1, 3, -2, +1, -1}, 0.57735026918962584},
245  {{2, 1, 3, +0, -1, -1}, 0.81649658092772615},
246  {{2, 1, 3, +0, +1, +1}, 0.81649658092772615},
247  {{2, 1, 3, +2, -1, +1}, 0.57735026918962584},
248  {{2, 1, 3, +2, +1, +3}, 1.00000000000000000},
249  {{2, 2, 0, -2, +2, +0}, 0.57735026918962584},
250  {{2, 2, 0, +0, +0, +0}, -0.57735026918962573},
251  {{2, 2, 0, +2, -2, +0}, 0.57735026918962584},
252  {{2, 2, 2, -2, +0, -2}, -0.70710678118654735},
253  {{2, 2, 2, -2, +2, +0}, -0.70710678118654735},
254  {{2, 2, 2, +0, -2, -2}, 0.70710678118654735},
255  {{2, 2, 2, +0, +2, +2}, -0.70710678118654735},
256  {{2, 2, 2, +2, -2, +0}, 0.70710678118654735},
257  {{2, 2, 2, +2, +0, +2}, 0.70710678118654735},
258  {{2, 2, 4, -2, -2, -4}, 1.00000000000000022},
259  {{2, 2, 4, -2, +0, -2}, 0.70710678118654746},
260  {{2, 2, 4, -2, +2, +0}, 0.40824829046386313},
261  {{2, 2, 4, +0, -2, -2}, 0.70710678118654746},
262  {{2, 2, 4, +0, +0, +0}, 0.81649658092772615},
263  {{2, 2, 4, +0, +2, +2}, 0.70710678118654746},
264  {{2, 2, 4, +2, -2, +0}, 0.40824829046386313},
265  {{2, 2, 4, +2, +0, +2}, 0.70710678118654746},
266  {{2, 2, 4, +2, +2, +4}, 1.00000000000000022},
267  {{2, 3, 1, -2, +1, -1}, 0.40824829046386302},
268  {{2, 3, 1, -2, +3, +1}, 0.70710678118654746},
269  {{2, 3, 1, +0, -1, -1}, -0.57735026918962573},
270  {{2, 3, 1, +0, +1, +1}, -0.57735026918962573},
271  {{2, 3, 1, +2, -3, -1}, 0.70710678118654746},
272  {{2, 3, 1, +2, -1, +1}, 0.40824829046386302},
273  {{2, 3, 3, -2, -1, -3}, -0.63245553203367610},
274  {{2, 3, 3, -2, +1, -1}, -0.73029674334022165},
275  {{2, 3, 3, -2, +3, +1}, -0.63245553203367610},
276  {{2, 3, 3, +0, -3, -3}, 0.77459666924148352},
277  {{2, 3, 3, +0, -1, -1}, 0.25819888974716126},
278  {{2, 3, 3, +0, +1, +1}, -0.25819888974716126},
279  {{2, 3, 3, +0, +3, +3}, -0.77459666924148352},
280  {{2, 3, 3, +2, -3, -1}, 0.63245553203367610},
281  {{2, 3, 3, +2, -1, +1}, 0.73029674334022165},
282  {{2, 3, 3, +2, +1, +3}, 0.63245553203367610},
283  {{2, 3, 5, -2, -3, -5}, 0.99999999999999989},
284  {{2, 3, 5, -2, -1, -3}, 0.77459666924148318},
285  {{2, 3, 5, -2, +1, -1}, 0.54772255750516596},
286  {{2, 3, 5, -2, +3, +1}, 0.31622776601683794},
287  {{2, 3, 5, +0, -3, -3}, 0.63245553203367599},
288  {{2, 3, 5, +0, -1, -1}, 0.77459666924148318},
289  {{2, 3, 5, +0, +1, +1}, 0.77459666924148318},
290  {{2, 3, 5, +0, +3, +3}, 0.63245553203367599},
291  {{2, 3, 5, +2, -3, -1}, 0.31622776601683794},
292  {{2, 3, 5, +2, -1, +1}, 0.54772255750516596},
293  {{2, 3, 5, +2, +1, +3}, 0.77459666924148318},
294  {{2, 3, 5, +2, +3, +5}, 0.99999999999999989},
295  {{3, 0, 3, -3, +0, -3}, 1.00000000000000000},
296  {{3, 0, 3, -1, +0, -1}, 0.99999999999999989},
297  {{3, 0, 3, +1, +0, +1}, 0.99999999999999989},
298  {{3, 0, 3, +3, +0, +3}, 1.00000000000000000},
299  {{3, 1, 2, -3, +1, -2}, -0.86602540378443837},
300  {{3, 1, 2, -1, -1, -2}, 0.49999999999999983},
301  {{3, 1, 2, -1, +1, +0}, -0.70710678118654724},
302  {{3, 1, 2, +1, -1, +0}, 0.70710678118654724},
303  {{3, 1, 2, +1, +1, +2}, -0.49999999999999983},
304  {{3, 1, 2, +3, -1, +2}, 0.86602540378443837},
305  {{3, 1, 4, -3, -1, -4}, 1.00000000000000022},
306  {{3, 1, 4, -3, +1, -2}, 0.49999999999999994},
307  {{3, 1, 4, -1, -1, -2}, 0.86602540378443871},
308  {{3, 1, 4, -1, +1, +0}, 0.70710678118654746},
309  {{3, 1, 4, +1, -1, +0}, 0.70710678118654746},
310  {{3, 1, 4, +1, +1, +2}, 0.86602540378443871},
311  {{3, 1, 4, +3, -1, +2}, 0.49999999999999994},
312  {{3, 1, 4, +3, +1, +4}, 1.00000000000000022},
313  {{3, 2, 1, -3, +2, -1}, 0.70710678118654746},
314  {{3, 2, 1, -1, +0, -1}, -0.57735026918962573},
315  {{3, 2, 1, -1, +2, +1}, 0.40824829046386302},
316  {{3, 2, 1, +1, -2, -1}, 0.40824829046386302},
317  {{3, 2, 1, +1, +0, +1}, -0.57735026918962573},
318  {{3, 2, 1, +3, -2, +1}, 0.70710678118654746},
319  {{3, 2, 3, -3, +0, -3}, -0.77459666924148352},
320  {{3, 2, 3, -3, +2, -1}, -0.63245553203367610},
321  {{3, 2, 3, -1, -2, -3}, 0.63245553203367610},
322  {{3, 2, 3, -1, +0, -1}, -0.25819888974716126},
323  {{3, 2, 3, -1, +2, +1}, -0.73029674334022165},
324  {{3, 2, 3, +1, -2, -1}, 0.73029674334022165},
325  {{3, 2, 3, +1, +0, +1}, 0.25819888974716126},
326  {{3, 2, 3, +1, +2, +3}, -0.63245553203367610},
327  {{3, 2, 3, +3, -2, +1}, 0.63245553203367610},
328  {{3, 2, 3, +3, +0, +3}, 0.77459666924148352},
329  {{3, 2, 5, -3, -2, -5}, 0.99999999999999989},
330  {{3, 2, 5, -3, +0, -3}, 0.63245553203367599},
331  {{3, 2, 5, -3, +2, -1}, 0.31622776601683794},
332  {{3, 2, 5, -1, -2, -3}, 0.77459666924148318},
333  {{3, 2, 5, -1, +0, -1}, 0.77459666924148318},
334  {{3, 2, 5, -1, +2, +1}, 0.54772255750516596},
335  {{3, 2, 5, +1, -2, -1}, 0.54772255750516596},
336  {{3, 2, 5, +1, +0, +1}, 0.77459666924148318},
337  {{3, 2, 5, +1, +2, +3}, 0.77459666924148318},
338  {{3, 2, 5, +3, -2, +1}, 0.31622776601683794},
339  {{3, 2, 5, +3, +0, +3}, 0.63245553203367599},
340  {{3, 2, 5, +3, +2, +5}, 0.99999999999999989},
341  {{3, 3, 0, -3, +3, +0}, -0.49999999999999994},
342  {{3, 3, 0, -1, +1, +0}, 0.49999999999999994},
343  {{3, 3, 0, +1, -1, +0}, -0.49999999999999994},
344  {{3, 3, 0, +3, -3, +0}, 0.49999999999999994},
345  {{3, 3, 2, -3, +1, -2}, 0.54772255750516596},
346  {{3, 3, 2, -3, +3, +0}, 0.67082039324993692},
347  {{3, 3, 2, -1, -1, -2}, -0.63245553203367599},
348  {{3, 3, 2, -1, +1, +0}, -0.22360679774997907},
349  {{3, 3, 2, -1, +3, +2}, 0.54772255750516596},
350  {{3, 3, 2, +1, -3, -2}, 0.54772255750516596},
351  {{3, 3, 2, +1, -1, +0}, -0.22360679774997907},
352  {{3, 3, 2, +1, +1, +2}, -0.63245553203367599},
353  {{3, 3, 2, +3, -3, +0}, 0.67082039324993692},
354  {{3, 3, 2, +3, -1, +2}, 0.54772255750516596},
355  {{3, 3, 4, -3, -1, -4}, -0.70710678118654746},
356  {{3, 3, 4, -3, +1, -2}, -0.70710678118654746},
357  {{3, 3, 4, -3, +3, +0}, -0.49999999999999994},
358  {{3, 3, 4, -1, -3, -4}, 0.70710678118654746},
359  {{3, 3, 4, -1, +1, +0}, -0.49999999999999994},
360  {{3, 3, 4, -1, +3, +2}, -0.70710678118654746},
361  {{3, 3, 4, +1, -3, -2}, 0.70710678118654746},
362  {{3, 3, 4, +1, -1, +0}, 0.49999999999999994},
363  {{3, 3, 4, +1, +3, +4}, -0.70710678118654746},
364  {{3, 3, 4, +3, -3, +0}, 0.49999999999999994},
365  {{3, 3, 4, +3, -1, +2}, 0.70710678118654746},
366  {{3, 3, 4, +3, +1, +4}, 0.70710678118654746},
367  {{3, 3, 6, -3, -3, -6}, 1.00000000000000022},
368  {{3, 3, 6, -3, -1, -4}, 0.70710678118654746},
369  {{3, 3, 6, -3, +1, -2}, 0.44721359549995793},
370  {{3, 3, 6, -3, +3, +0}, 0.22360679774997894},
371  {{3, 3, 6, -1, -3, -4}, 0.70710678118654746},
372  {{3, 3, 6, -1, -1, -2}, 0.77459666924148352},
373  {{3, 3, 6, -1, +1, +0}, 0.67082039324993670},
374  {{3, 3, 6, -1, +3, +2}, 0.44721359549995793},
375  {{3, 3, 6, +1, -3, -2}, 0.44721359549995793},
376  {{3, 3, 6, +1, -1, +0}, 0.67082039324993670},
377  {{3, 3, 6, +1, +1, +2}, 0.77459666924148352},
378  {{3, 3, 6, +1, +3, +4}, 0.70710678118654746},
379  {{3, 3, 6, +3, -3, +0}, 0.22360679774997894},
380  {{3, 3, 6, +3, -1, +2}, 0.44721359549995793},
381  {{3, 3, 6, +3, +1, +4}, 0.70710678118654746},
382  {{3, 3, 6, +3, +3, +6}, 1.00000000000000022},
383  };
384 };
385 
386 } // namespace smash
387 
388 #endif // SRC_INCLUDE_SMASH_CLEBSCHGORDAN_LOOKUP_H_
smash::ClebschGordan
Class to store and retrieve/calculate Clebsch-Gordan coefficients.
Definition: clebschgordan_lookup.h:22
smash::ClebschGordan::lookup_table
static std::unordered_map< ThreeSpins, double, ThreeSpinHash > lookup_table
Tabulation of Clebsch-Gordan coefficients.
Definition: clebschgordan_lookup.h:193
smash::ClebschGordan::coefficient
static double coefficient(const int j_a, const int j_b, const int j_c, const int m_a, const int m_b, const int m_c)
Check in the Clebsch-Gordan lookup table if the requested coefficient is available.
Definition: clebschgordan_lookup.cc:41
smash::ClebschGordan::calculate_coefficient
static double calculate_coefficient(const int j_a, const int j_b, const int j_c, const int m_a, const int m_b, const int m_c)
Calculate Clebsch-Gordan coefficient .
Definition: clebschgordan_lookup.cc:22
smash
Definition: action.h:24
smash::ClebschGordan::ThreeSpinHash
This is one of the possible ways to prepare a hashing mechanism to use a custom object in a std::unor...
Definition: clebschgordan_lookup.h:101
smash::ClebschGordan::ThreeSpinHash::operator()
std::size_t operator()(const ThreeSpins &in) const noexcept
The overload of the operator() is the only needed ingredient to make this class ready to be used as h...
Definition: clebschgordan_lookup.h:163
smash::ClebschGordan::ThreeSpins
Auxiliary struct to be used as key in the look up table of Clebsch-Gordan coefficients.
Definition: clebschgordan_lookup.h:41
smash::ClebschGordan::ThreeSpins::m2
int m2
z component of second isospin
Definition: clebschgordan_lookup.h:46
smash::ClebschGordan::ThreeSpins::m1
int m1
z component of first isospin
Definition: clebschgordan_lookup.h:45
smash::ClebschGordan::ThreeSpins::operator==
bool operator==(const ThreeSpins &other) const
Comparison operator between two set of spin information.
Definition: clebschgordan_lookup.h:68
smash::ClebschGordan::ThreeSpins::m3
int m3
z component of third isospin
Definition: clebschgordan_lookup.h:47
smash::ClebschGordan::ThreeSpins::tied
auto tied() const
A utility function to avoid duplication in comparison operator(s).
Definition: clebschgordan_lookup.h:57