cxx11_tensor_symmetry.cpp
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #include "main.h"
11 
12 #include <Eigen/CXX11/Tensor>
13 #include <Eigen/CXX11/TensorSymmetry>
14 
15 #include <map>
16 #include <set>
17 
18 using Eigen::Tensor;
19 using Eigen::SGroup;
20 using Eigen::DynamicSGroup;
21 using Eigen::StaticSGroup;
22 using Eigen::Symmetry;
23 using Eigen::AntiSymmetry;
24 using Eigen::Hermiticity;
25 using Eigen::AntiHermiticity;
26 
27 using Eigen::NegationFlag;
28 using Eigen::ConjugationFlag;
29 using Eigen::GlobalZeroFlag;
30 using Eigen::GlobalRealFlag;
31 using Eigen::GlobalImagFlag;
32 
33 // helper function to determine if the compiler intantiated a static
34 // or dynamic symmetry group
35 template<typename... Sym>
36 bool isDynGroup(StaticSGroup<Sym...> const& dummy)
37 {
38  (void)dummy;
39  return false;
40 }
41 
42 bool isDynGroup(DynamicSGroup const& dummy)
43 {
44  (void)dummy;
45  return true;
46 }
47 
48 // helper class for checking that the symmetry groups are correct
49 struct checkIdx {
50  template<typename ArrType>
51  static inline int doCheck_(ArrType e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
52  {
53  // use decimal representation of value
54  uint64_t value = e[0];
55  for (std::size_t i = 1; i < e.size(); i++)
56  value = value * 10 + e[i];
57 
58  // we want to make sure that we find each element
59  auto it = expected.find(value);
60  VERIFY((it != expected.end()));
61  VERIFY_IS_EQUAL(it->second, flags);
62 
63  // we want to make sure we only have each element once;
64  // set::insert returns true for the second part of the pair
65  // if the element was really inserted and not already there
66  auto p = found.insert(value);
67  VERIFY((p.second));
68 
69  return dummy;
70  }
71 
72  static inline int run(std::vector<int> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
73  {
74  return doCheck_(e, flags, dummy, found, expected);
75  }
76 
77  template<std::size_t N>
78  static inline int run(std::array<int, N> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
79  {
80  return doCheck_(e, flags, dummy, found, expected);
81  }
82 };
83 
84 static void test_symgroups_static()
85 {
86  std::array<int, 7> identity{{0,1,2,3,4,5,6}};
87 
88  // Simple static symmetry group
89  StaticSGroup<
90  AntiSymmetry<0,1>,
91  Hermiticity<0,2>
92  > group;
93 
94  std::set<uint64_t> found;
95  std::map<uint64_t, int> expected;
96  expected[ 123456] = 0;
97  expected[1023456] = NegationFlag;
98  expected[2103456] = ConjugationFlag;
99  expected[1203456] = ConjugationFlag | NegationFlag;
100  expected[2013456] = ConjugationFlag | NegationFlag;
101  expected[ 213456] = ConjugationFlag;
102 
103  VERIFY_IS_EQUAL(group.size(), 6u);
104  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
105  group.apply<checkIdx, int>(identity, 0, found, expected);
106  VERIFY_IS_EQUAL(found.size(), 6u);
107 }
108 
109 static void test_symgroups_dynamic()
110 {
111  std::vector<int> identity;
112  for (int i = 0; i <= 6; i++)
113  identity.push_back(i);
114 
115  // Simple dynamic symmetry group
116  DynamicSGroup group;
117  group.add(0,1,NegationFlag);
118  group.add(0,2,ConjugationFlag);
119 
120  VERIFY_IS_EQUAL(group.size(), 6u);
121  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
122 
123  std::set<uint64_t> found;
124  std::map<uint64_t, int> expected;
125  expected[ 123456] = 0;
126  expected[1023456] = NegationFlag;
127  expected[2103456] = ConjugationFlag;
128  expected[1203456] = ConjugationFlag | NegationFlag;
129  expected[2013456] = ConjugationFlag | NegationFlag;
130  expected[ 213456] = ConjugationFlag;
131 
132  VERIFY_IS_EQUAL(group.size(), 6u);
133  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
134  group.apply<checkIdx, int>(identity, 0, found, expected);
135  VERIFY_IS_EQUAL(found.size(), 6u);
136 }
137 
138 static void test_symgroups_selection()
139 {
140  std::array<int, 7> identity7{{0,1,2,3,4,5,6}};
141  std::array<int, 10> identity10{{0,1,2,3,4,5,6,7,8,9}};
142 
143  {
144  // Do the same test as in test_symgroups_static but
145  // require selection via SGroup
146  SGroup<
147  AntiSymmetry<0,1>,
148  Hermiticity<0,2>
149  > group;
150 
151  std::set<uint64_t> found;
152  std::map<uint64_t, int> expected;
153  expected[ 123456] = 0;
154  expected[1023456] = NegationFlag;
155  expected[2103456] = ConjugationFlag;
156  expected[1203456] = ConjugationFlag | NegationFlag;
157  expected[2013456] = ConjugationFlag | NegationFlag;
158  expected[ 213456] = ConjugationFlag;
159 
160  VERIFY(!isDynGroup(group));
161  VERIFY_IS_EQUAL(group.size(), 6u);
162  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
163  group.apply<checkIdx, int>(identity7, 0, found, expected);
164  VERIFY_IS_EQUAL(found.size(), 6u);
165  }
166 
167  {
168  // simple factorizing group: 5 generators, 2^5 = 32 elements
169  // selection should make this dynamic, although static group
170  // can still be reasonably generated
171  SGroup<
172  Symmetry<0,1>,
173  Symmetry<2,3>,
174  Symmetry<4,5>,
175  Symmetry<6,7>,
176  Symmetry<8,9>
177  > group;
178 
179  std::set<uint64_t> found;
180  std::map<uint64_t, int> expected;
181  expected[ 123456789] = 0; expected[ 123456798] = 0; expected[ 123457689] = 0; expected[ 123457698] = 0;
182  expected[ 123546789] = 0; expected[ 123546798] = 0; expected[ 123547689] = 0; expected[ 123547698] = 0;
183  expected[ 132456789] = 0; expected[ 132456798] = 0; expected[ 132457689] = 0; expected[ 132457698] = 0;
184  expected[ 132546789] = 0; expected[ 132546798] = 0; expected[ 132547689] = 0; expected[ 132547698] = 0;
185  expected[1023456789] = 0; expected[1023456798] = 0; expected[1023457689] = 0; expected[1023457698] = 0;
186  expected[1023546789] = 0; expected[1023546798] = 0; expected[1023547689] = 0; expected[1023547698] = 0;
187  expected[1032456789] = 0; expected[1032456798] = 0; expected[1032457689] = 0; expected[1032457698] = 0;
188  expected[1032546789] = 0; expected[1032546798] = 0; expected[1032547689] = 0; expected[1032547698] = 0;
189 
190  VERIFY(isDynGroup(group));
191  VERIFY_IS_EQUAL(group.size(), 32u);
192  VERIFY_IS_EQUAL(group.globalFlags(), 0);
193  group.apply<checkIdx, int>(identity10, 0, found, expected);
194  VERIFY_IS_EQUAL(found.size(), 32u);
195 
196  // no verify that we could also generate a static group
197  // with these generators
198  found.clear();
199  StaticSGroup<
200  Symmetry<0,1>,
201  Symmetry<2,3>,
202  Symmetry<4,5>,
203  Symmetry<6,7>,
204  Symmetry<8,9>
205  > group_static;
206  VERIFY_IS_EQUAL(group_static.size(), 32u);
207  VERIFY_IS_EQUAL(group_static.globalFlags(), 0);
208  group_static.apply<checkIdx, int>(identity10, 0, found, expected);
209  VERIFY_IS_EQUAL(found.size(), 32u);
210  }
211 
212  {
213  // try to create a HUGE group
214  SGroup<
215  Symmetry<0,1>,
216  Symmetry<1,2>,
217  Symmetry<2,3>,
218  Symmetry<3,4>,
219  Symmetry<4,5>,
220  Symmetry<5,6>
221  > group;
222 
223  std::set<uint64_t> found;
224  uint64_t pre_expected[5040] = {
225  123456, 1023456, 213456, 2013456, 1203456, 2103456, 132456, 1032456, 312456, 3012456, 1302456, 3102456,
226  231456, 2031456, 321456, 3021456, 2301456, 3201456, 1230456, 2130456, 1320456, 3120456, 2310456, 3210456,
227  124356, 1024356, 214356, 2014356, 1204356, 2104356, 142356, 1042356, 412356, 4012356, 1402356, 4102356,
228  241356, 2041356, 421356, 4021356, 2401356, 4201356, 1240356, 2140356, 1420356, 4120356, 2410356, 4210356,
229  134256, 1034256, 314256, 3014256, 1304256, 3104256, 143256, 1043256, 413256, 4013256, 1403256, 4103256,
230  341256, 3041256, 431256, 4031256, 3401256, 4301256, 1340256, 3140256, 1430256, 4130256, 3410256, 4310256,
231  234156, 2034156, 324156, 3024156, 2304156, 3204156, 243156, 2043156, 423156, 4023156, 2403156, 4203156,
232  342156, 3042156, 432156, 4032156, 3402156, 4302156, 2340156, 3240156, 2430156, 4230156, 3420156, 4320156,
233  1234056, 2134056, 1324056, 3124056, 2314056, 3214056, 1243056, 2143056, 1423056, 4123056, 2413056, 4213056,
234  1342056, 3142056, 1432056, 4132056, 3412056, 4312056, 2341056, 3241056, 2431056, 4231056, 3421056, 4321056,
235  123546, 1023546, 213546, 2013546, 1203546, 2103546, 132546, 1032546, 312546, 3012546, 1302546, 3102546,
236  231546, 2031546, 321546, 3021546, 2301546, 3201546, 1230546, 2130546, 1320546, 3120546, 2310546, 3210546,
237  125346, 1025346, 215346, 2015346, 1205346, 2105346, 152346, 1052346, 512346, 5012346, 1502346, 5102346,
238  251346, 2051346, 521346, 5021346, 2501346, 5201346, 1250346, 2150346, 1520346, 5120346, 2510346, 5210346,
239  135246, 1035246, 315246, 3015246, 1305246, 3105246, 153246, 1053246, 513246, 5013246, 1503246, 5103246,
240  351246, 3051246, 531246, 5031246, 3501246, 5301246, 1350246, 3150246, 1530246, 5130246, 3510246, 5310246,
241  235146, 2035146, 325146, 3025146, 2305146, 3205146, 253146, 2053146, 523146, 5023146, 2503146, 5203146,
242  352146, 3052146, 532146, 5032146, 3502146, 5302146, 2350146, 3250146, 2530146, 5230146, 3520146, 5320146,
243  1235046, 2135046, 1325046, 3125046, 2315046, 3215046, 1253046, 2153046, 1523046, 5123046, 2513046, 5213046,
244  1352046, 3152046, 1532046, 5132046, 3512046, 5312046, 2351046, 3251046, 2531046, 5231046, 3521046, 5321046,
245  124536, 1024536, 214536, 2014536, 1204536, 2104536, 142536, 1042536, 412536, 4012536, 1402536, 4102536,
246  241536, 2041536, 421536, 4021536, 2401536, 4201536, 1240536, 2140536, 1420536, 4120536, 2410536, 4210536,
247  125436, 1025436, 215436, 2015436, 1205436, 2105436, 152436, 1052436, 512436, 5012436, 1502436, 5102436,
248  251436, 2051436, 521436, 5021436, 2501436, 5201436, 1250436, 2150436, 1520436, 5120436, 2510436, 5210436,
249  145236, 1045236, 415236, 4015236, 1405236, 4105236, 154236, 1054236, 514236, 5014236, 1504236, 5104236,
250  451236, 4051236, 541236, 5041236, 4501236, 5401236, 1450236, 4150236, 1540236, 5140236, 4510236, 5410236,
251  245136, 2045136, 425136, 4025136, 2405136, 4205136, 254136, 2054136, 524136, 5024136, 2504136, 5204136,
252  452136, 4052136, 542136, 5042136, 4502136, 5402136, 2450136, 4250136, 2540136, 5240136, 4520136, 5420136,
253  1245036, 2145036, 1425036, 4125036, 2415036, 4215036, 1254036, 2154036, 1524036, 5124036, 2514036, 5214036,
254  1452036, 4152036, 1542036, 5142036, 4512036, 5412036, 2451036, 4251036, 2541036, 5241036, 4521036, 5421036,
255  134526, 1034526, 314526, 3014526, 1304526, 3104526, 143526, 1043526, 413526, 4013526, 1403526, 4103526,
256  341526, 3041526, 431526, 4031526, 3401526, 4301526, 1340526, 3140526, 1430526, 4130526, 3410526, 4310526,
257  135426, 1035426, 315426, 3015426, 1305426, 3105426, 153426, 1053426, 513426, 5013426, 1503426, 5103426,
258  351426, 3051426, 531426, 5031426, 3501426, 5301426, 1350426, 3150426, 1530426, 5130426, 3510426, 5310426,
259  145326, 1045326, 415326, 4015326, 1405326, 4105326, 154326, 1054326, 514326, 5014326, 1504326, 5104326,
260  451326, 4051326, 541326, 5041326, 4501326, 5401326, 1450326, 4150326, 1540326, 5140326, 4510326, 5410326,
261  345126, 3045126, 435126, 4035126, 3405126, 4305126, 354126, 3054126, 534126, 5034126, 3504126, 5304126,
262  453126, 4053126, 543126, 5043126, 4503126, 5403126, 3450126, 4350126, 3540126, 5340126, 4530126, 5430126,
263  1345026, 3145026, 1435026, 4135026, 3415026, 4315026, 1354026, 3154026, 1534026, 5134026, 3514026, 5314026,
264  1453026, 4153026, 1543026, 5143026, 4513026, 5413026, 3451026, 4351026, 3541026, 5341026, 4531026, 5431026,
265  234516, 2034516, 324516, 3024516, 2304516, 3204516, 243516, 2043516, 423516, 4023516, 2403516, 4203516,
266  342516, 3042516, 432516, 4032516, 3402516, 4302516, 2340516, 3240516, 2430516, 4230516, 3420516, 4320516,
267  235416, 2035416, 325416, 3025416, 2305416, 3205416, 253416, 2053416, 523416, 5023416, 2503416, 5203416,
268  352416, 3052416, 532416, 5032416, 3502416, 5302416, 2350416, 3250416, 2530416, 5230416, 3520416, 5320416,
269  245316, 2045316, 425316, 4025316, 2405316, 4205316, 254316, 2054316, 524316, 5024316, 2504316, 5204316,
270  452316, 4052316, 542316, 5042316, 4502316, 5402316, 2450316, 4250316, 2540316, 5240316, 4520316, 5420316,
271  345216, 3045216, 435216, 4035216, 3405216, 4305216, 354216, 3054216, 534216, 5034216, 3504216, 5304216,
272  453216, 4053216, 543216, 5043216, 4503216, 5403216, 3450216, 4350216, 3540216, 5340216, 4530216, 5430216,
273  2345016, 3245016, 2435016, 4235016, 3425016, 4325016, 2354016, 3254016, 2534016, 5234016, 3524016, 5324016,
274  2453016, 4253016, 2543016, 5243016, 4523016, 5423016, 3452016, 4352016, 3542016, 5342016, 4532016, 5432016,
275  1234506, 2134506, 1324506, 3124506, 2314506, 3214506, 1243506, 2143506, 1423506, 4123506, 2413506, 4213506,
276  1342506, 3142506, 1432506, 4132506, 3412506, 4312506, 2341506, 3241506, 2431506, 4231506, 3421506, 4321506,
277  1235406, 2135406, 1325406, 3125406, 2315406, 3215406, 1253406, 2153406, 1523406, 5123406, 2513406, 5213406,
278  1352406, 3152406, 1532406, 5132406, 3512406, 5312406, 2351406, 3251406, 2531406, 5231406, 3521406, 5321406,
279  1245306, 2145306, 1425306, 4125306, 2415306, 4215306, 1254306, 2154306, 1524306, 5124306, 2514306, 5214306,
280  1452306, 4152306, 1542306, 5142306, 4512306, 5412306, 2451306, 4251306, 2541306, 5241306, 4521306, 5421306,
281  1345206, 3145206, 1435206, 4135206, 3415206, 4315206, 1354206, 3154206, 1534206, 5134206, 3514206, 5314206,
282  1453206, 4153206, 1543206, 5143206, 4513206, 5413206, 3451206, 4351206, 3541206, 5341206, 4531206, 5431206,
283  2345106, 3245106, 2435106, 4235106, 3425106, 4325106, 2354106, 3254106, 2534106, 5234106, 3524106, 5324106,
284  2453106, 4253106, 2543106, 5243106, 4523106, 5423106, 3452106, 4352106, 3542106, 5342106, 4532106, 5432106,
285  123465, 1023465, 213465, 2013465, 1203465, 2103465, 132465, 1032465, 312465, 3012465, 1302465, 3102465,
286  231465, 2031465, 321465, 3021465, 2301465, 3201465, 1230465, 2130465, 1320465, 3120465, 2310465, 3210465,
287  124365, 1024365, 214365, 2014365, 1204365, 2104365, 142365, 1042365, 412365, 4012365, 1402365, 4102365,
288  241365, 2041365, 421365, 4021365, 2401365, 4201365, 1240365, 2140365, 1420365, 4120365, 2410365, 4210365,
289  134265, 1034265, 314265, 3014265, 1304265, 3104265, 143265, 1043265, 413265, 4013265, 1403265, 4103265,
290  341265, 3041265, 431265, 4031265, 3401265, 4301265, 1340265, 3140265, 1430265, 4130265, 3410265, 4310265,
291  234165, 2034165, 324165, 3024165, 2304165, 3204165, 243165, 2043165, 423165, 4023165, 2403165, 4203165,
292  342165, 3042165, 432165, 4032165, 3402165, 4302165, 2340165, 3240165, 2430165, 4230165, 3420165, 4320165,
293  1234065, 2134065, 1324065, 3124065, 2314065, 3214065, 1243065, 2143065, 1423065, 4123065, 2413065, 4213065,
294  1342065, 3142065, 1432065, 4132065, 3412065, 4312065, 2341065, 3241065, 2431065, 4231065, 3421065, 4321065,
295  123645, 1023645, 213645, 2013645, 1203645, 2103645, 132645, 1032645, 312645, 3012645, 1302645, 3102645,
296  231645, 2031645, 321645, 3021645, 2301645, 3201645, 1230645, 2130645, 1320645, 3120645, 2310645, 3210645,
297  126345, 1026345, 216345, 2016345, 1206345, 2106345, 162345, 1062345, 612345, 6012345, 1602345, 6102345,
298  261345, 2061345, 621345, 6021345, 2601345, 6201345, 1260345, 2160345, 1620345, 6120345, 2610345, 6210345,
299  136245, 1036245, 316245, 3016245, 1306245, 3106245, 163245, 1063245, 613245, 6013245, 1603245, 6103245,
300  361245, 3061245, 631245, 6031245, 3601245, 6301245, 1360245, 3160245, 1630245, 6130245, 3610245, 6310245,
301  236145, 2036145, 326145, 3026145, 2306145, 3206145, 263145, 2063145, 623145, 6023145, 2603145, 6203145,
302  362145, 3062145, 632145, 6032145, 3602145, 6302145, 2360145, 3260145, 2630145, 6230145, 3620145, 6320145,
303  1236045, 2136045, 1326045, 3126045, 2316045, 3216045, 1263045, 2163045, 1623045, 6123045, 2613045, 6213045,
304  1362045, 3162045, 1632045, 6132045, 3612045, 6312045, 2361045, 3261045, 2631045, 6231045, 3621045, 6321045,
305  124635, 1024635, 214635, 2014635, 1204635, 2104635, 142635, 1042635, 412635, 4012635, 1402635, 4102635,
306  241635, 2041635, 421635, 4021635, 2401635, 4201635, 1240635, 2140635, 1420635, 4120635, 2410635, 4210635,
307  126435, 1026435, 216435, 2016435, 1206435, 2106435, 162435, 1062435, 612435, 6012435, 1602435, 6102435,
308  261435, 2061435, 621435, 6021435, 2601435, 6201435, 1260435, 2160435, 1620435, 6120435, 2610435, 6210435,
309  146235, 1046235, 416235, 4016235, 1406235, 4106235, 164235, 1064235, 614235, 6014235, 1604235, 6104235,
310  461235, 4061235, 641235, 6041235, 4601235, 6401235, 1460235, 4160235, 1640235, 6140235, 4610235, 6410235,
311  246135, 2046135, 426135, 4026135, 2406135, 4206135, 264135, 2064135, 624135, 6024135, 2604135, 6204135,
312  462135, 4062135, 642135, 6042135, 4602135, 6402135, 2460135, 4260135, 2640135, 6240135, 4620135, 6420135,
313  1246035, 2146035, 1426035, 4126035, 2416035, 4216035, 1264035, 2164035, 1624035, 6124035, 2614035, 6214035,
314  1462035, 4162035, 1642035, 6142035, 4612035, 6412035, 2461035, 4261035, 2641035, 6241035, 4621035, 6421035,
315  134625, 1034625, 314625, 3014625, 1304625, 3104625, 143625, 1043625, 413625, 4013625, 1403625, 4103625,
316  341625, 3041625, 431625, 4031625, 3401625, 4301625, 1340625, 3140625, 1430625, 4130625, 3410625, 4310625,
317  136425, 1036425, 316425, 3016425, 1306425, 3106425, 163425, 1063425, 613425, 6013425, 1603425, 6103425,
318  361425, 3061425, 631425, 6031425, 3601425, 6301425, 1360425, 3160425, 1630425, 6130425, 3610425, 6310425,
319  146325, 1046325, 416325, 4016325, 1406325, 4106325, 164325, 1064325, 614325, 6014325, 1604325, 6104325,
320  461325, 4061325, 641325, 6041325, 4601325, 6401325, 1460325, 4160325, 1640325, 6140325, 4610325, 6410325,
321  346125, 3046125, 436125, 4036125, 3406125, 4306125, 364125, 3064125, 634125, 6034125, 3604125, 6304125,
322  463125, 4063125, 643125, 6043125, 4603125, 6403125, 3460125, 4360125, 3640125, 6340125, 4630125, 6430125,
323  1346025, 3146025, 1436025, 4136025, 3416025, 4316025, 1364025, 3164025, 1634025, 6134025, 3614025, 6314025,
324  1463025, 4163025, 1643025, 6143025, 4613025, 6413025, 3461025, 4361025, 3641025, 6341025, 4631025, 6431025,
325  234615, 2034615, 324615, 3024615, 2304615, 3204615, 243615, 2043615, 423615, 4023615, 2403615, 4203615,
326  342615, 3042615, 432615, 4032615, 3402615, 4302615, 2340615, 3240615, 2430615, 4230615, 3420615, 4320615,
327  236415, 2036415, 326415, 3026415, 2306415, 3206415, 263415, 2063415, 623415, 6023415, 2603415, 6203415,
328  362415, 3062415, 632415, 6032415, 3602415, 6302415, 2360415, 3260415, 2630415, 6230415, 3620415, 6320415,
329  246315, 2046315, 426315, 4026315, 2406315, 4206315, 264315, 2064315, 624315, 6024315, 2604315, 6204315,
330  462315, 4062315, 642315, 6042315, 4602315, 6402315, 2460315, 4260315, 2640315, 6240315, 4620315, 6420315,
331  346215, 3046215, 436215, 4036215, 3406215, 4306215, 364215, 3064215, 634215, 6034215, 3604215, 6304215,
332  463215, 4063215, 643215, 6043215, 4603215, 6403215, 3460215, 4360215, 3640215, 6340215, 4630215, 6430215,
333  2346015, 3246015, 2436015, 4236015, 3426015, 4326015, 2364015, 3264015, 2634015, 6234015, 3624015, 6324015,
334  2463015, 4263015, 2643015, 6243015, 4623015, 6423015, 3462015, 4362015, 3642015, 6342015, 4632015, 6432015,
335  1234605, 2134605, 1324605, 3124605, 2314605, 3214605, 1243605, 2143605, 1423605, 4123605, 2413605, 4213605,
336  1342605, 3142605, 1432605, 4132605, 3412605, 4312605, 2341605, 3241605, 2431605, 4231605, 3421605, 4321605,
337  1236405, 2136405, 1326405, 3126405, 2316405, 3216405, 1263405, 2163405, 1623405, 6123405, 2613405, 6213405,
338  1362405, 3162405, 1632405, 6132405, 3612405, 6312405, 2361405, 3261405, 2631405, 6231405, 3621405, 6321405,
339  1246305, 2146305, 1426305, 4126305, 2416305, 4216305, 1264305, 2164305, 1624305, 6124305, 2614305, 6214305,
340  1462305, 4162305, 1642305, 6142305, 4612305, 6412305, 2461305, 4261305, 2641305, 6241305, 4621305, 6421305,
341  1346205, 3146205, 1436205, 4136205, 3416205, 4316205, 1364205, 3164205, 1634205, 6134205, 3614205, 6314205,
342  1463205, 4163205, 1643205, 6143205, 4613205, 6413205, 3461205, 4361205, 3641205, 6341205, 4631205, 6431205,
343  2346105, 3246105, 2436105, 4236105, 3426105, 4326105, 2364105, 3264105, 2634105, 6234105, 3624105, 6324105,
344  2463105, 4263105, 2643105, 6243105, 4623105, 6423105, 3462105, 4362105, 3642105, 6342105, 4632105, 6432105,
345  123564, 1023564, 213564, 2013564, 1203564, 2103564, 132564, 1032564, 312564, 3012564, 1302564, 3102564,
346  231564, 2031564, 321564, 3021564, 2301564, 3201564, 1230564, 2130564, 1320564, 3120564, 2310564, 3210564,
347  125364, 1025364, 215364, 2015364, 1205364, 2105364, 152364, 1052364, 512364, 5012364, 1502364, 5102364,
348  251364, 2051364, 521364, 5021364, 2501364, 5201364, 1250364, 2150364, 1520364, 5120364, 2510364, 5210364,
349  135264, 1035264, 315264, 3015264, 1305264, 3105264, 153264, 1053264, 513264, 5013264, 1503264, 5103264,
350  351264, 3051264, 531264, 5031264, 3501264, 5301264, 1350264, 3150264, 1530264, 5130264, 3510264, 5310264,
351  235164, 2035164, 325164, 3025164, 2305164, 3205164, 253164, 2053164, 523164, 5023164, 2503164, 5203164,
352  352164, 3052164, 532164, 5032164, 3502164, 5302164, 2350164, 3250164, 2530164, 5230164, 3520164, 5320164,
353  1235064, 2135064, 1325064, 3125064, 2315064, 3215064, 1253064, 2153064, 1523064, 5123064, 2513064, 5213064,
354  1352064, 3152064, 1532064, 5132064, 3512064, 5312064, 2351064, 3251064, 2531064, 5231064, 3521064, 5321064,
355  123654, 1023654, 213654, 2013654, 1203654, 2103654, 132654, 1032654, 312654, 3012654, 1302654, 3102654,
356  231654, 2031654, 321654, 3021654, 2301654, 3201654, 1230654, 2130654, 1320654, 3120654, 2310654, 3210654,
357  126354, 1026354, 216354, 2016354, 1206354, 2106354, 162354, 1062354, 612354, 6012354, 1602354, 6102354,
358  261354, 2061354, 621354, 6021354, 2601354, 6201354, 1260354, 2160354, 1620354, 6120354, 2610354, 6210354,
359  136254, 1036254, 316254, 3016254, 1306254, 3106254, 163254, 1063254, 613254, 6013254, 1603254, 6103254,
360  361254, 3061254, 631254, 6031254, 3601254, 6301254, 1360254, 3160254, 1630254, 6130254, 3610254, 6310254,
361  236154, 2036154, 326154, 3026154, 2306154, 3206154, 263154, 2063154, 623154, 6023154, 2603154, 6203154,
362  362154, 3062154, 632154, 6032154, 3602154, 6302154, 2360154, 3260154, 2630154, 6230154, 3620154, 6320154,
363  1236054, 2136054, 1326054, 3126054, 2316054, 3216054, 1263054, 2163054, 1623054, 6123054, 2613054, 6213054,
364  1362054, 3162054, 1632054, 6132054, 3612054, 6312054, 2361054, 3261054, 2631054, 6231054, 3621054, 6321054,
365  125634, 1025634, 215634, 2015634, 1205634, 2105634, 152634, 1052634, 512634, 5012634, 1502634, 5102634,
366  251634, 2051634, 521634, 5021634, 2501634, 5201634, 1250634, 2150634, 1520634, 5120634, 2510634, 5210634,
367  126534, 1026534, 216534, 2016534, 1206534, 2106534, 162534, 1062534, 612534, 6012534, 1602534, 6102534,
368  261534, 2061534, 621534, 6021534, 2601534, 6201534, 1260534, 2160534, 1620534, 6120534, 2610534, 6210534,
369  156234, 1056234, 516234, 5016234, 1506234, 5106234, 165234, 1065234, 615234, 6015234, 1605234, 6105234,
370  561234, 5061234, 651234, 6051234, 5601234, 6501234, 1560234, 5160234, 1650234, 6150234, 5610234, 6510234,
371  256134, 2056134, 526134, 5026134, 2506134, 5206134, 265134, 2065134, 625134, 6025134, 2605134, 6205134,
372  562134, 5062134, 652134, 6052134, 5602134, 6502134, 2560134, 5260134, 2650134, 6250134, 5620134, 6520134,
373  1256034, 2156034, 1526034, 5126034, 2516034, 5216034, 1265034, 2165034, 1625034, 6125034, 2615034, 6215034,
374  1562034, 5162034, 1652034, 6152034, 5612034, 6512034, 2561034, 5261034, 2651034, 6251034, 5621034, 6521034,
375  135624, 1035624, 315624, 3015624, 1305624, 3105624, 153624, 1053624, 513624, 5013624, 1503624, 5103624,
376  351624, 3051624, 531624, 5031624, 3501624, 5301624, 1350624, 3150624, 1530624, 5130624, 3510624, 5310624,
377  136524, 1036524, 316524, 3016524, 1306524, 3106524, 163524, 1063524, 613524, 6013524, 1603524, 6103524,
378  361524, 3061524, 631524, 6031524, 3601524, 6301524, 1360524, 3160524, 1630524, 6130524, 3610524, 6310524,
379  156324, 1056324, 516324, 5016324, 1506324, 5106324, 165324, 1065324, 615324, 6015324, 1605324, 6105324,
380  561324, 5061324, 651324, 6051324, 5601324, 6501324, 1560324, 5160324, 1650324, 6150324, 5610324, 6510324,
381  356124, 3056124, 536124, 5036124, 3506124, 5306124, 365124, 3065124, 635124, 6035124, 3605124, 6305124,
382  563124, 5063124, 653124, 6053124, 5603124, 6503124, 3560124, 5360124, 3650124, 6350124, 5630124, 6530124,
383  1356024, 3156024, 1536024, 5136024, 3516024, 5316024, 1365024, 3165024, 1635024, 6135024, 3615024, 6315024,
384  1563024, 5163024, 1653024, 6153024, 5613024, 6513024, 3561024, 5361024, 3651024, 6351024, 5631024, 6531024,
385  235614, 2035614, 325614, 3025614, 2305614, 3205614, 253614, 2053614, 523614, 5023614, 2503614, 5203614,
386  352614, 3052614, 532614, 5032614, 3502614, 5302614, 2350614, 3250614, 2530614, 5230614, 3520614, 5320614,
387  236514, 2036514, 326514, 3026514, 2306514, 3206514, 263514, 2063514, 623514, 6023514, 2603514, 6203514,
388  362514, 3062514, 632514, 6032514, 3602514, 6302514, 2360514, 3260514, 2630514, 6230514, 3620514, 6320514,
389  256314, 2056314, 526314, 5026314, 2506314, 5206314, 265314, 2065314, 625314, 6025314, 2605314, 6205314,
390  562314, 5062314, 652314, 6052314, 5602314, 6502314, 2560314, 5260314, 2650314, 6250314, 5620314, 6520314,
391  356214, 3056214, 536214, 5036214, 3506214, 5306214, 365214, 3065214, 635214, 6035214, 3605214, 6305214,
392  563214, 5063214, 653214, 6053214, 5603214, 6503214, 3560214, 5360214, 3650214, 6350214, 5630214, 6530214,
393  2356014, 3256014, 2536014, 5236014, 3526014, 5326014, 2365014, 3265014, 2635014, 6235014, 3625014, 6325014,
394  2563014, 5263014, 2653014, 6253014, 5623014, 6523014, 3562014, 5362014, 3652014, 6352014, 5632014, 6532014,
395  1235604, 2135604, 1325604, 3125604, 2315604, 3215604, 1253604, 2153604, 1523604, 5123604, 2513604, 5213604,
396  1352604, 3152604, 1532604, 5132604, 3512604, 5312604, 2351604, 3251604, 2531604, 5231604, 3521604, 5321604,
397  1236504, 2136504, 1326504, 3126504, 2316504, 3216504, 1263504, 2163504, 1623504, 6123504, 2613504, 6213504,
398  1362504, 3162504, 1632504, 6132504, 3612504, 6312504, 2361504, 3261504, 2631504, 6231504, 3621504, 6321504,
399  1256304, 2156304, 1526304, 5126304, 2516304, 5216304, 1265304, 2165304, 1625304, 6125304, 2615304, 6215304,
400  1562304, 5162304, 1652304, 6152304, 5612304, 6512304, 2561304, 5261304, 2651304, 6251304, 5621304, 6521304,
401  1356204, 3156204, 1536204, 5136204, 3516204, 5316204, 1365204, 3165204, 1635204, 6135204, 3615204, 6315204,
402  1563204, 5163204, 1653204, 6153204, 5613204, 6513204, 3561204, 5361204, 3651204, 6351204, 5631204, 6531204,
403  2356104, 3256104, 2536104, 5236104, 3526104, 5326104, 2365104, 3265104, 2635104, 6235104, 3625104, 6325104,
404  2563104, 5263104, 2653104, 6253104, 5623104, 6523104, 3562104, 5362104, 3652104, 6352104, 5632104, 6532104,
405  124563, 1024563, 214563, 2014563, 1204563, 2104563, 142563, 1042563, 412563, 4012563, 1402563, 4102563,
406  241563, 2041563, 421563, 4021563, 2401563, 4201563, 1240563, 2140563, 1420563, 4120563, 2410563, 4210563,
407  125463, 1025463, 215463, 2015463, 1205463, 2105463, 152463, 1052463, 512463, 5012463, 1502463, 5102463,
408  251463, 2051463, 521463, 5021463, 2501463, 5201463, 1250463, 2150463, 1520463, 5120463, 2510463, 5210463,
409  145263, 1045263, 415263, 4015263, 1405263, 4105263, 154263, 1054263, 514263, 5014263, 1504263, 5104263,
410  451263, 4051263, 541263, 5041263, 4501263, 5401263, 1450263, 4150263, 1540263, 5140263, 4510263, 5410263,
411  245163, 2045163, 425163, 4025163, 2405163, 4205163, 254163, 2054163, 524163, 5024163, 2504163, 5204163,
412  452163, 4052163, 542163, 5042163, 4502163, 5402163, 2450163, 4250163, 2540163, 5240163, 4520163, 5420163,
413  1245063, 2145063, 1425063, 4125063, 2415063, 4215063, 1254063, 2154063, 1524063, 5124063, 2514063, 5214063,
414  1452063, 4152063, 1542063, 5142063, 4512063, 5412063, 2451063, 4251063, 2541063, 5241063, 4521063, 5421063,
415  124653, 1024653, 214653, 2014653, 1204653, 2104653, 142653, 1042653, 412653, 4012653, 1402653, 4102653,
416  241653, 2041653, 421653, 4021653, 2401653, 4201653, 1240653, 2140653, 1420653, 4120653, 2410653, 4210653,
417  126453, 1026453, 216453, 2016453, 1206453, 2106453, 162453, 1062453, 612453, 6012453, 1602453, 6102453,
418  261453, 2061453, 621453, 6021453, 2601453, 6201453, 1260453, 2160453, 1620453, 6120453, 2610453, 6210453,
419  146253, 1046253, 416253, 4016253, 1406253, 4106253, 164253, 1064253, 614253, 6014253, 1604253, 6104253,
420  461253, 4061253, 641253, 6041253, 4601253, 6401253, 1460253, 4160253, 1640253, 6140253, 4610253, 6410253,
421  246153, 2046153, 426153, 4026153, 2406153, 4206153, 264153, 2064153, 624153, 6024153, 2604153, 6204153,
422  462153, 4062153, 642153, 6042153, 4602153, 6402153, 2460153, 4260153, 2640153, 6240153, 4620153, 6420153,
423  1246053, 2146053, 1426053, 4126053, 2416053, 4216053, 1264053, 2164053, 1624053, 6124053, 2614053, 6214053,
424  1462053, 4162053, 1642053, 6142053, 4612053, 6412053, 2461053, 4261053, 2641053, 6241053, 4621053, 6421053,
425  125643, 1025643, 215643, 2015643, 1205643, 2105643, 152643, 1052643, 512643, 5012643, 1502643, 5102643,
426  251643, 2051643, 521643, 5021643, 2501643, 5201643, 1250643, 2150643, 1520643, 5120643, 2510643, 5210643,
427  126543, 1026543, 216543, 2016543, 1206543, 2106543, 162543, 1062543, 612543, 6012543, 1602543, 6102543,
428  261543, 2061543, 621543, 6021543, 2601543, 6201543, 1260543, 2160543, 1620543, 6120543, 2610543, 6210543,
429  156243, 1056243, 516243, 5016243, 1506243, 5106243, 165243, 1065243, 615243, 6015243, 1605243, 6105243,
430  561243, 5061243, 651243, 6051243, 5601243, 6501243, 1560243, 5160243, 1650243, 6150243, 5610243, 6510243,
431  256143, 2056143, 526143, 5026143, 2506143, 5206143, 265143, 2065143, 625143, 6025143, 2605143, 6205143,
432  562143, 5062143, 652143, 6052143, 5602143, 6502143, 2560143, 5260143, 2650143, 6250143, 5620143, 6520143,
433  1256043, 2156043, 1526043, 5126043, 2516043, 5216043, 1265043, 2165043, 1625043, 6125043, 2615043, 6215043,
434  1562043, 5162043, 1652043, 6152043, 5612043, 6512043, 2561043, 5261043, 2651043, 6251043, 5621043, 6521043,
435  145623, 1045623, 415623, 4015623, 1405623, 4105623, 154623, 1054623, 514623, 5014623, 1504623, 5104623,
436  451623, 4051623, 541623, 5041623, 4501623, 5401623, 1450623, 4150623, 1540623, 5140623, 4510623, 5410623,
437  146523, 1046523, 416523, 4016523, 1406523, 4106523, 164523, 1064523, 614523, 6014523, 1604523, 6104523,
438  461523, 4061523, 641523, 6041523, 4601523, 6401523, 1460523, 4160523, 1640523, 6140523, 4610523, 6410523,
439  156423, 1056423, 516423, 5016423, 1506423, 5106423, 165423, 1065423, 615423, 6015423, 1605423, 6105423,
440  561423, 5061423, 651423, 6051423, 5601423, 6501423, 1560423, 5160423, 1650423, 6150423, 5610423, 6510423,
441  456123, 4056123, 546123, 5046123, 4506123, 5406123, 465123, 4065123, 645123, 6045123, 4605123, 6405123,
442  564123, 5064123, 654123, 6054123, 5604123, 6504123, 4560123, 5460123, 4650123, 6450123, 5640123, 6540123,
443  1456023, 4156023, 1546023, 5146023, 4516023, 5416023, 1465023, 4165023, 1645023, 6145023, 4615023, 6415023,
444  1564023, 5164023, 1654023, 6154023, 5614023, 6514023, 4561023, 5461023, 4651023, 6451023, 5641023, 6541023,
445  245613, 2045613, 425613, 4025613, 2405613, 4205613, 254613, 2054613, 524613, 5024613, 2504613, 5204613,
446  452613, 4052613, 542613, 5042613, 4502613, 5402613, 2450613, 4250613, 2540613, 5240613, 4520613, 5420613,
447  246513, 2046513, 426513, 4026513, 2406513, 4206513, 264513, 2064513, 624513, 6024513, 2604513, 6204513,
448  462513, 4062513, 642513, 6042513, 4602513, 6402513, 2460513, 4260513, 2640513, 6240513, 4620513, 6420513,
449  256413, 2056413, 526413, 5026413, 2506413, 5206413, 265413, 2065413, 625413, 6025413, 2605413, 6205413,
450  562413, 5062413, 652413, 6052413, 5602413, 6502413, 2560413, 5260413, 2650413, 6250413, 5620413, 6520413,
451  456213, 4056213, 546213, 5046213, 4506213, 5406213, 465213, 4065213, 645213, 6045213, 4605213, 6405213,
452  564213, 5064213, 654213, 6054213, 5604213, 6504213, 4560213, 5460213, 4650213, 6450213, 5640213, 6540213,
453  2456013, 4256013, 2546013, 5246013, 4526013, 5426013, 2465013, 4265013, 2645013, 6245013, 4625013, 6425013,
454  2564013, 5264013, 2654013, 6254013, 5624013, 6524013, 4562013, 5462013, 4652013, 6452013, 5642013, 6542013,
455  1245603, 2145603, 1425603, 4125603, 2415603, 4215603, 1254603, 2154603, 1524603, 5124603, 2514603, 5214603,
456  1452603, 4152603, 1542603, 5142603, 4512603, 5412603, 2451603, 4251603, 2541603, 5241603, 4521603, 5421603,
457  1246503, 2146503, 1426503, 4126503, 2416503, 4216503, 1264503, 2164503, 1624503, 6124503, 2614503, 6214503,
458  1462503, 4162503, 1642503, 6142503, 4612503, 6412503, 2461503, 4261503, 2641503, 6241503, 4621503, 6421503,
459  1256403, 2156403, 1526403, 5126403, 2516403, 5216403, 1265403, 2165403, 1625403, 6125403, 2615403, 6215403,
460  1562403, 5162403, 1652403, 6152403, 5612403, 6512403, 2561403, 5261403, 2651403, 6251403, 5621403, 6521403,
461  1456203, 4156203, 1546203, 5146203, 4516203, 5416203, 1465203, 4165203, 1645203, 6145203, 4615203, 6415203,
462  1564203, 5164203, 1654203, 6154203, 5614203, 6514203, 4561203, 5461203, 4651203, 6451203, 5641203, 6541203,
463  2456103, 4256103, 2546103, 5246103, 4526103, 5426103, 2465103, 4265103, 2645103, 6245103, 4625103, 6425103,
464  2564103, 5264103, 2654103, 6254103, 5624103, 6524103, 4562103, 5462103, 4652103, 6452103, 5642103, 6542103,
465  134562, 1034562, 314562, 3014562, 1304562, 3104562, 143562, 1043562, 413562, 4013562, 1403562, 4103562,
466  341562, 3041562, 431562, 4031562, 3401562, 4301562, 1340562, 3140562, 1430562, 4130562, 3410562, 4310562,
467  135462, 1035462, 315462, 3015462, 1305462, 3105462, 153462, 1053462, 513462, 5013462, 1503462, 5103462,
468  351462, 3051462, 531462, 5031462, 3501462, 5301462, 1350462, 3150462, 1530462, 5130462, 3510462, 5310462,
469  145362, 1045362, 415362, 4015362, 1405362, 4105362, 154362, 1054362, 514362, 5014362, 1504362, 5104362,
470  451362, 4051362, 541362, 5041362, 4501362, 5401362, 1450362, 4150362, 1540362, 5140362, 4510362, 5410362,
471  345162, 3045162, 435162, 4035162, 3405162, 4305162, 354162, 3054162, 534162, 5034162, 3504162, 5304162,
472  453162, 4053162, 543162, 5043162, 4503162, 5403162, 3450162, 4350162, 3540162, 5340162, 4530162, 5430162,
473  1345062, 3145062, 1435062, 4135062, 3415062, 4315062, 1354062, 3154062, 1534062, 5134062, 3514062, 5314062,
474  1453062, 4153062, 1543062, 5143062, 4513062, 5413062, 3451062, 4351062, 3541062, 5341062, 4531062, 5431062,
475  134652, 1034652, 314652, 3014652, 1304652, 3104652, 143652, 1043652, 413652, 4013652, 1403652, 4103652,
476  341652, 3041652, 431652, 4031652, 3401652, 4301652, 1340652, 3140652, 1430652, 4130652, 3410652, 4310652,
477  136452, 1036452, 316452, 3016452, 1306452, 3106452, 163452, 1063452, 613452, 6013452, 1603452, 6103452,
478  361452, 3061452, 631452, 6031452, 3601452, 6301452, 1360452, 3160452, 1630452, 6130452, 3610452, 6310452,
479  146352, 1046352, 416352, 4016352, 1406352, 4106352, 164352, 1064352, 614352, 6014352, 1604352, 6104352,
480  461352, 4061352, 641352, 6041352, 4601352, 6401352, 1460352, 4160352, 1640352, 6140352, 4610352, 6410352,
481  346152, 3046152, 436152, 4036152, 3406152, 4306152, 364152, 3064152, 634152, 6034152, 3604152, 6304152,
482  463152, 4063152, 643152, 6043152, 4603152, 6403152, 3460152, 4360152, 3640152, 6340152, 4630152, 6430152,
483  1346052, 3146052, 1436052, 4136052, 3416052, 4316052, 1364052, 3164052, 1634052, 6134052, 3614052, 6314052,
484  1463052, 4163052, 1643052, 6143052, 4613052, 6413052, 3461052, 4361052, 3641052, 6341052, 4631052, 6431052,
485  135642, 1035642, 315642, 3015642, 1305642, 3105642, 153642, 1053642, 513642, 5013642, 1503642, 5103642,
486  351642, 3051642, 531642, 5031642, 3501642, 5301642, 1350642, 3150642, 1530642, 5130642, 3510642, 5310642,
487  136542, 1036542, 316542, 3016542, 1306542, 3106542, 163542, 1063542, 613542, 6013542, 1603542, 6103542,
488  361542, 3061542, 631542, 6031542, 3601542, 6301542, 1360542, 3160542, 1630542, 6130542, 3610542, 6310542,
489  156342, 1056342, 516342, 5016342, 1506342, 5106342, 165342, 1065342, 615342, 6015342, 1605342, 6105342,
490  561342, 5061342, 651342, 6051342, 5601342, 6501342, 1560342, 5160342, 1650342, 6150342, 5610342, 6510342,
491  356142, 3056142, 536142, 5036142, 3506142, 5306142, 365142, 3065142, 635142, 6035142, 3605142, 6305142,
492  563142, 5063142, 653142, 6053142, 5603142, 6503142, 3560142, 5360142, 3650142, 6350142, 5630142, 6530142,
493  1356042, 3156042, 1536042, 5136042, 3516042, 5316042, 1365042, 3165042, 1635042, 6135042, 3615042, 6315042,
494  1563042, 5163042, 1653042, 6153042, 5613042, 6513042, 3561042, 5361042, 3651042, 6351042, 5631042, 6531042,
495  145632, 1045632, 415632, 4015632, 1405632, 4105632, 154632, 1054632, 514632, 5014632, 1504632, 5104632,
496  451632, 4051632, 541632, 5041632, 4501632, 5401632, 1450632, 4150632, 1540632, 5140632, 4510632, 5410632,
497  146532, 1046532, 416532, 4016532, 1406532, 4106532, 164532, 1064532, 614532, 6014532, 1604532, 6104532,
498  461532, 4061532, 641532, 6041532, 4601532, 6401532, 1460532, 4160532, 1640532, 6140532, 4610532, 6410532,
499  156432, 1056432, 516432, 5016432, 1506432, 5106432, 165432, 1065432, 615432, 6015432, 1605432, 6105432,
500  561432, 5061432, 651432, 6051432, 5601432, 6501432, 1560432, 5160432, 1650432, 6150432, 5610432, 6510432,
501  456132, 4056132, 546132, 5046132, 4506132, 5406132, 465132, 4065132, 645132, 6045132, 4605132, 6405132,
502  564132, 5064132, 654132, 6054132, 5604132, 6504132, 4560132, 5460132, 4650132, 6450132, 5640132, 6540132,
503  1456032, 4156032, 1546032, 5146032, 4516032, 5416032, 1465032, 4165032, 1645032, 6145032, 4615032, 6415032,
504  1564032, 5164032, 1654032, 6154032, 5614032, 6514032, 4561032, 5461032, 4651032, 6451032, 5641032, 6541032,
505  345612, 3045612, 435612, 4035612, 3405612, 4305612, 354612, 3054612, 534612, 5034612, 3504612, 5304612,
506  453612, 4053612, 543612, 5043612, 4503612, 5403612, 3450612, 4350612, 3540612, 5340612, 4530612, 5430612,
507  346512, 3046512, 436512, 4036512, 3406512, 4306512, 364512, 3064512, 634512, 6034512, 3604512, 6304512,
508  463512, 4063512, 643512, 6043512, 4603512, 6403512, 3460512, 4360512, 3640512, 6340512, 4630512, 6430512,
509  356412, 3056412, 536412, 5036412, 3506412, 5306412, 365412, 3065412, 635412, 6035412, 3605412, 6305412,
510  563412, 5063412, 653412, 6053412, 5603412, 6503412, 3560412, 5360412, 3650412, 6350412, 5630412, 6530412,
511  456312, 4056312, 546312, 5046312, 4506312, 5406312, 465312, 4065312, 645312, 6045312, 4605312, 6405312,
512  564312, 5064312, 654312, 6054312, 5604312, 6504312, 4560312, 5460312, 4650312, 6450312, 5640312, 6540312,
513  3456012, 4356012, 3546012, 5346012, 4536012, 5436012, 3465012, 4365012, 3645012, 6345012, 4635012, 6435012,
514  3564012, 5364012, 3654012, 6354012, 5634012, 6534012, 4563012, 5463012, 4653012, 6453012, 5643012, 6543012,
515  1345602, 3145602, 1435602, 4135602, 3415602, 4315602, 1354602, 3154602, 1534602, 5134602, 3514602, 5314602,
516  1453602, 4153602, 1543602, 5143602, 4513602, 5413602, 3451602, 4351602, 3541602, 5341602, 4531602, 5431602,
517  1346502, 3146502, 1436502, 4136502, 3416502, 4316502, 1364502, 3164502, 1634502, 6134502, 3614502, 6314502,
518  1463502, 4163502, 1643502, 6143502, 4613502, 6413502, 3461502, 4361502, 3641502, 6341502, 4631502, 6431502,
519  1356402, 3156402, 1536402, 5136402, 3516402, 5316402, 1365402, 3165402, 1635402, 6135402, 3615402, 6315402,
520  1563402, 5163402, 1653402, 6153402, 5613402, 6513402, 3561402, 5361402, 3651402, 6351402, 5631402, 6531402,
521  1456302, 4156302, 1546302, 5146302, 4516302, 5416302, 1465302, 4165302, 1645302, 6145302, 4615302, 6415302,
522  1564302, 5164302, 1654302, 6154302, 5614302, 6514302, 4561302, 5461302, 4651302, 6451302, 5641302, 6541302,
523  3456102, 4356102, 3546102, 5346102, 4536102, 5436102, 3465102, 4365102, 3645102, 6345102, 4635102, 6435102,
524  3564102, 5364102, 3654102, 6354102, 5634102, 6534102, 4563102, 5463102, 4653102, 6453102, 5643102, 6543102,
525  234561, 2034561, 324561, 3024561, 2304561, 3204561, 243561, 2043561, 423561, 4023561, 2403561, 4203561,
526  342561, 3042561, 432561, 4032561, 3402561, 4302561, 2340561, 3240561, 2430561, 4230561, 3420561, 4320561,
527  235461, 2035461, 325461, 3025461, 2305461, 3205461, 253461, 2053461, 523461, 5023461, 2503461, 5203461,
528  352461, 3052461, 532461, 5032461, 3502461, 5302461, 2350461, 3250461, 2530461, 5230461, 3520461, 5320461,
529  245361, 2045361, 425361, 4025361, 2405361, 4205361, 254361, 2054361, 524361, 5024361, 2504361, 5204361,
530  452361, 4052361, 542361, 5042361, 4502361, 5402361, 2450361, 4250361, 2540361, 5240361, 4520361, 5420361,
531  345261, 3045261, 435261, 4035261, 3405261, 4305261, 354261, 3054261, 534261, 5034261, 3504261, 5304261,
532  453261, 4053261, 543261, 5043261, 4503261, 5403261, 3450261, 4350261, 3540261, 5340261, 4530261, 5430261,
533  2345061, 3245061, 2435061, 4235061, 3425061, 4325061, 2354061, 3254061, 2534061, 5234061, 3524061, 5324061,
534  2453061, 4253061, 2543061, 5243061, 4523061, 5423061, 3452061, 4352061, 3542061, 5342061, 4532061, 5432061,
535  234651, 2034651, 324651, 3024651, 2304651, 3204651, 243651, 2043651, 423651, 4023651, 2403651, 4203651,
536  342651, 3042651, 432651, 4032651, 3402651, 4302651, 2340651, 3240651, 2430651, 4230651, 3420651, 4320651,
537  236451, 2036451, 326451, 3026451, 2306451, 3206451, 263451, 2063451, 623451, 6023451, 2603451, 6203451,
538  362451, 3062451, 632451, 6032451, 3602451, 6302451, 2360451, 3260451, 2630451, 6230451, 3620451, 6320451,
539  246351, 2046351, 426351, 4026351, 2406351, 4206351, 264351, 2064351, 624351, 6024351, 2604351, 6204351,
540  462351, 4062351, 642351, 6042351, 4602351, 6402351, 2460351, 4260351, 2640351, 6240351, 4620351, 6420351,
541  346251, 3046251, 436251, 4036251, 3406251, 4306251, 364251, 3064251, 634251, 6034251, 3604251, 6304251,
542  463251, 4063251, 643251, 6043251, 4603251, 6403251, 3460251, 4360251, 3640251, 6340251, 4630251, 6430251,
543  2346051, 3246051, 2436051, 4236051, 3426051, 4326051, 2364051, 3264051, 2634051, 6234051, 3624051, 6324051,
544  2463051, 4263051, 2643051, 6243051, 4623051, 6423051, 3462051, 4362051, 3642051, 6342051, 4632051, 6432051,
545  235641, 2035641, 325641, 3025641, 2305641, 3205641, 253641, 2053641, 523641, 5023641, 2503641, 5203641,
546  352641, 3052641, 532641, 5032641, 3502641, 5302641, 2350641, 3250641, 2530641, 5230641, 3520641, 5320641,
547  236541, 2036541, 326541, 3026541, 2306541, 3206541, 263541, 2063541, 623541, 6023541, 2603541, 6203541,
548  362541, 3062541, 632541, 6032541, 3602541, 6302541, 2360541, 3260541, 2630541, 6230541, 3620541, 6320541,
549  256341, 2056341, 526341, 5026341, 2506341, 5206341, 265341, 2065341, 625341, 6025341, 2605341, 6205341,
550  562341, 5062341, 652341, 6052341, 5602341, 6502341, 2560341, 5260341, 2650341, 6250341, 5620341, 6520341,
551  356241, 3056241, 536241, 5036241, 3506241, 5306241, 365241, 3065241, 635241, 6035241, 3605241, 6305241,
552  563241, 5063241, 653241, 6053241, 5603241, 6503241, 3560241, 5360241, 3650241, 6350241, 5630241, 6530241,
553  2356041, 3256041, 2536041, 5236041, 3526041, 5326041, 2365041, 3265041, 2635041, 6235041, 3625041, 6325041,
554  2563041, 5263041, 2653041, 6253041, 5623041, 6523041, 3562041, 5362041, 3652041, 6352041, 5632041, 6532041,
555  245631, 2045631, 425631, 4025631, 2405631, 4205631, 254631, 2054631, 524631, 5024631, 2504631, 5204631,
556  452631, 4052631, 542631, 5042631, 4502631, 5402631, 2450631, 4250631, 2540631, 5240631, 4520631, 5420631,
557  246531, 2046531, 426531, 4026531, 2406531, 4206531, 264531, 2064531, 624531, 6024531, 2604531, 6204531,
558  462531, 4062531, 642531, 6042531, 4602531, 6402531, 2460531, 4260531, 2640531, 6240531, 4620531, 6420531,
559  256431, 2056431, 526431, 5026431, 2506431, 5206431, 265431, 2065431, 625431, 6025431, 2605431, 6205431,
560  562431, 5062431, 652431, 6052431, 5602431, 6502431, 2560431, 5260431, 2650431, 6250431, 5620431, 6520431,
561  456231, 4056231, 546231, 5046231, 4506231, 5406231, 465231, 4065231, 645231, 6045231, 4605231, 6405231,
562  564231, 5064231, 654231, 6054231, 5604231, 6504231, 4560231, 5460231, 4650231, 6450231, 5640231, 6540231,
563  2456031, 4256031, 2546031, 5246031, 4526031, 5426031, 2465031, 4265031, 2645031, 6245031, 4625031, 6425031,
564  2564031, 5264031, 2654031, 6254031, 5624031, 6524031, 4562031, 5462031, 4652031, 6452031, 5642031, 6542031,
565  345621, 3045621, 435621, 4035621, 3405621, 4305621, 354621, 3054621, 534621, 5034621, 3504621, 5304621,
566  453621, 4053621, 543621, 5043621, 4503621, 5403621, 3450621, 4350621, 3540621, 5340621, 4530621, 5430621,
567  346521, 3046521, 436521, 4036521, 3406521, 4306521, 364521, 3064521, 634521, 6034521, 3604521, 6304521,
568  463521, 4063521, 643521, 6043521, 4603521, 6403521, 3460521, 4360521, 3640521, 6340521, 4630521, 6430521,
569  356421, 3056421, 536421, 5036421, 3506421, 5306421, 365421, 3065421, 635421, 6035421, 3605421, 6305421,
570  563421, 5063421, 653421, 6053421, 5603421, 6503421, 3560421, 5360421, 3650421, 6350421, 5630421, 6530421,
571  456321, 4056321, 546321, 5046321, 4506321, 5406321, 465321, 4065321, 645321, 6045321, 4605321, 6405321,
572  564321, 5064321, 654321, 6054321, 5604321, 6504321, 4560321, 5460321, 4650321, 6450321, 5640321, 6540321,
573  3456021, 4356021, 3546021, 5346021, 4536021, 5436021, 3465021, 4365021, 3645021, 6345021, 4635021, 6435021,
574  3564021, 5364021, 3654021, 6354021, 5634021, 6534021, 4563021, 5463021, 4653021, 6453021, 5643021, 6543021,
575  2345601, 3245601, 2435601, 4235601, 3425601, 4325601, 2354601, 3254601, 2534601, 5234601, 3524601, 5324601,
576  2453601, 4253601, 2543601, 5243601, 4523601, 5423601, 3452601, 4352601, 3542601, 5342601, 4532601, 5432601,
577  2346501, 3246501, 2436501, 4236501, 3426501, 4326501, 2364501, 3264501, 2634501, 6234501, 3624501, 6324501,
578  2463501, 4263501, 2643501, 6243501, 4623501, 6423501, 3462501, 4362501, 3642501, 6342501, 4632501, 6432501,
579  2356401, 3256401, 2536401, 5236401, 3526401, 5326401, 2365401, 3265401, 2635401, 6235401, 3625401, 6325401,
580  2563401, 5263401, 2653401, 6253401, 5623401, 6523401, 3562401, 5362401, 3652401, 6352401, 5632401, 6532401,
581  2456301, 4256301, 2546301, 5246301, 4526301, 5426301, 2465301, 4265301, 2645301, 6245301, 4625301, 6425301,
582  2564301, 5264301, 2654301, 6254301, 5624301, 6524301, 4562301, 5462301, 4652301, 6452301, 5642301, 6542301,
583  3456201, 4356201, 3546201, 5346201, 4536201, 5436201, 3465201, 4365201, 3645201, 6345201, 4635201, 6435201,
584  3564201, 5364201, 3654201, 6354201, 5634201, 6534201, 4563201, 5463201, 4653201, 6453201, 5643201, 6543201,
585  1234560, 2134560, 1324560, 3124560, 2314560, 3214560, 1243560, 2143560, 1423560, 4123560, 2413560, 4213560,
586  1342560, 3142560, 1432560, 4132560, 3412560, 4312560, 2341560, 3241560, 2431560, 4231560, 3421560, 4321560,
587  1235460, 2135460, 1325460, 3125460, 2315460, 3215460, 1253460, 2153460, 1523460, 5123460, 2513460, 5213460,
588  1352460, 3152460, 1532460, 5132460, 3512460, 5312460, 2351460, 3251460, 2531460, 5231460, 3521460, 5321460,
589  1245360, 2145360, 1425360, 4125360, 2415360, 4215360, 1254360, 2154360, 1524360, 5124360, 2514360, 5214360,
590  1452360, 4152360, 1542360, 5142360, 4512360, 5412360, 2451360, 4251360, 2541360, 5241360, 4521360, 5421360,
591  1345260, 3145260, 1435260, 4135260, 3415260, 4315260, 1354260, 3154260, 1534260, 5134260, 3514260, 5314260,
592  1453260, 4153260, 1543260, 5143260, 4513260, 5413260, 3451260, 4351260, 3541260, 5341260, 4531260, 5431260,
593  2345160, 3245160, 2435160, 4235160, 3425160, 4325160, 2354160, 3254160, 2534160, 5234160, 3524160, 5324160,
594  2453160, 4253160, 2543160, 5243160, 4523160, 5423160, 3452160, 4352160, 3542160, 5342160, 4532160, 5432160,
595  1234650, 2134650, 1324650, 3124650, 2314650, 3214650, 1243650, 2143650, 1423650, 4123650, 2413650, 4213650,
596  1342650, 3142650, 1432650, 4132650, 3412650, 4312650, 2341650, 3241650, 2431650, 4231650, 3421650, 4321650,
597  1236450, 2136450, 1326450, 3126450, 2316450, 3216450, 1263450, 2163450, 1623450, 6123450, 2613450, 6213450,
598  1362450, 3162450, 1632450, 6132450, 3612450, 6312450, 2361450, 3261450, 2631450, 6231450, 3621450, 6321450,
599  1246350, 2146350, 1426350, 4126350, 2416350, 4216350, 1264350, 2164350, 1624350, 6124350, 2614350, 6214350,
600  1462350, 4162350, 1642350, 6142350, 4612350, 6412350, 2461350, 4261350, 2641350, 6241350, 4621350, 6421350,
601  1346250, 3146250, 1436250, 4136250, 3416250, 4316250, 1364250, 3164250, 1634250, 6134250, 3614250, 6314250,
602  1463250, 4163250, 1643250, 6143250, 4613250, 6413250, 3461250, 4361250, 3641250, 6341250, 4631250, 6431250,
603  2346150, 3246150, 2436150, 4236150, 3426150, 4326150, 2364150, 3264150, 2634150, 6234150, 3624150, 6324150,
604  2463150, 4263150, 2643150, 6243150, 4623150, 6423150, 3462150, 4362150, 3642150, 6342150, 4632150, 6432150,
605  1235640, 2135640, 1325640, 3125640, 2315640, 3215640, 1253640, 2153640, 1523640, 5123640, 2513640, 5213640,
606  1352640, 3152640, 1532640, 5132640, 3512640, 5312640, 2351640, 3251640, 2531640, 5231640, 3521640, 5321640,
607  1236540, 2136540, 1326540, 3126540, 2316540, 3216540, 1263540, 2163540, 1623540, 6123540, 2613540, 6213540,
608  1362540, 3162540, 1632540, 6132540, 3612540, 6312540, 2361540, 3261540, 2631540, 6231540, 3621540, 6321540,
609  1256340, 2156340, 1526340, 5126340, 2516340, 5216340, 1265340, 2165340, 1625340, 6125340, 2615340, 6215340,
610  1562340, 5162340, 1652340, 6152340, 5612340, 6512340, 2561340, 5261340, 2651340, 6251340, 5621340, 6521340,
611  1356240, 3156240, 1536240, 5136240, 3516240, 5316240, 1365240, 3165240, 1635240, 6135240, 3615240, 6315240,
612  1563240, 5163240, 1653240, 6153240, 5613240, 6513240, 3561240, 5361240, 3651240, 6351240, 5631240, 6531240,
613  2356140, 3256140, 2536140, 5236140, 3526140, 5326140, 2365140, 3265140, 2635140, 6235140, 3625140, 6325140,
614  2563140, 5263140, 2653140, 6253140, 5623140, 6523140, 3562140, 5362140, 3652140, 6352140, 5632140, 6532140,
615  1245630, 2145630, 1425630, 4125630, 2415630, 4215630, 1254630, 2154630, 1524630, 5124630, 2514630, 5214630,
616  1452630, 4152630, 1542630, 5142630, 4512630, 5412630, 2451630, 4251630, 2541630, 5241630, 4521630, 5421630,
617  1246530, 2146530, 1426530, 4126530, 2416530, 4216530, 1264530, 2164530, 1624530, 6124530, 2614530, 6214530,
618  1462530, 4162530, 1642530, 6142530, 4612530, 6412530, 2461530, 4261530, 2641530, 6241530, 4621530, 6421530,
619  1256430, 2156430, 1526430, 5126430, 2516430, 5216430, 1265430, 2165430, 1625430, 6125430, 2615430, 6215430,
620  1562430, 5162430, 1652430, 6152430, 5612430, 6512430, 2561430, 5261430, 2651430, 6251430, 5621430, 6521430,
621  1456230, 4156230, 1546230, 5146230, 4516230, 5416230, 1465230, 4165230, 1645230, 6145230, 4615230, 6415230,
622  1564230, 5164230, 1654230, 6154230, 5614230, 6514230, 4561230, 5461230, 4651230, 6451230, 5641230, 6541230,
623  2456130, 4256130, 2546130, 5246130, 4526130, 5426130, 2465130, 4265130, 2645130, 6245130, 4625130, 6425130,
624  2564130, 5264130, 2654130, 6254130, 5624130, 6524130, 4562130, 5462130, 4652130, 6452130, 5642130, 6542130,
625  1345620, 3145620, 1435620, 4135620, 3415620, 4315620, 1354620, 3154620, 1534620, 5134620, 3514620, 5314620,
626  1453620, 4153620, 1543620, 5143620, 4513620, 5413620, 3451620, 4351620, 3541620, 5341620, 4531620, 5431620,
627  1346520, 3146520, 1436520, 4136520, 3416520, 4316520, 1364520, 3164520, 1634520, 6134520, 3614520, 6314520,
628  1463520, 4163520, 1643520, 6143520, 4613520, 6413520, 3461520, 4361520, 3641520, 6341520, 4631520, 6431520,
629  1356420, 3156420, 1536420, 5136420, 3516420, 5316420, 1365420, 3165420, 1635420, 6135420, 3615420, 6315420,
630  1563420, 5163420, 1653420, 6153420, 5613420, 6513420, 3561420, 5361420, 3651420, 6351420, 5631420, 6531420,
631  1456320, 4156320, 1546320, 5146320, 4516320, 5416320, 1465320, 4165320, 1645320, 6145320, 4615320, 6415320,
632  1564320, 5164320, 1654320, 6154320, 5614320, 6514320, 4561320, 5461320, 4651320, 6451320, 5641320, 6541320,
633  3456120, 4356120, 3546120, 5346120, 4536120, 5436120, 3465120, 4365120, 3645120, 6345120, 4635120, 6435120,
634  3564120, 5364120, 3654120, 6354120, 5634120, 6534120, 4563120, 5463120, 4653120, 6453120, 5643120, 6543120,
635  2345610, 3245610, 2435610, 4235610, 3425610, 4325610, 2354610, 3254610, 2534610, 5234610, 3524610, 5324610,
636  2453610, 4253610, 2543610, 5243610, 4523610, 5423610, 3452610, 4352610, 3542610, 5342610, 4532610, 5432610,
637  2346510, 3246510, 2436510, 4236510, 3426510, 4326510, 2364510, 3264510, 2634510, 6234510, 3624510, 6324510,
638  2463510, 4263510, 2643510, 6243510, 4623510, 6423510, 3462510, 4362510, 3642510, 6342510, 4632510, 6432510,
639  2356410, 3256410, 2536410, 5236410, 3526410, 5326410, 2365410, 3265410, 2635410, 6235410, 3625410, 6325410,
640  2563410, 5263410, 2653410, 6253410, 5623410, 6523410, 3562410, 5362410, 3652410, 6352410, 5632410, 6532410,
641  2456310, 4256310, 2546310, 5246310, 4526310, 5426310, 2465310, 4265310, 2645310, 6245310, 4625310, 6425310,
642  2564310, 5264310, 2654310, 6254310, 5624310, 6524310, 4562310, 5462310, 4652310, 6452310, 5642310, 6542310,
643  3456210, 4356210, 3546210, 5346210, 4536210, 5436210, 3465210, 4365210, 3645210, 6345210, 4635210, 6435210,
644  3564210, 5364210, 3654210, 6354210, 5634210, 6534210, 4563210, 5463210, 4653210, 6453210, 5643210, 6543210
645  };
646  std::map<uint64_t, int> expected;
647  for (std::size_t i = 0; i < 5040; i++)
648  expected[pre_expected[i]] = 0; // flags are 0, everything is symmetric here
649 
650  VERIFY(isDynGroup(group));
651  VERIFY_IS_EQUAL(group.size(), 5040u);
652  VERIFY_IS_EQUAL(group.globalFlags(), 0);
653  group.apply<checkIdx, int>(identity7, 0, found, expected);
654  VERIFY_IS_EQUAL(found.size(), 5040u);
655  }
656 }
657 
658 static void test_tensor_epsilon()
659 {
660  SGroup<AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;
661  Tensor<int, 3> epsilon(3,3,3);
662 
663  epsilon.setZero();
664  sym(epsilon, 0, 1, 2) = 1;
665 
666  for (int i = 0; i < 3; i++) {
667  for (int j = 0; j < 3; j++) {
668  for (int k = 0; k < 3; k++) {
669  VERIFY_IS_EQUAL((epsilon(i,j,k)), (- (j - i) * (k - j) * (i - k) / 2) );
670  }
671  }
672  }
673 }
674 
675 static void test_tensor_sym()
676 {
677  SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
678  Tensor<int, 4> t(10,10,10,10);
679 
680  t.setZero();
681 
682  for (int l = 0; l < 10; l++) {
683  for (int k = l; k < 10; k++) {
684  for (int j = 0; j < 10; j++) {
685  for (int i = j; i < 10; i++) {
686  sym(t, i, j, k, l) = (i + j) * (k + l);
687  }
688  }
689  }
690  }
691 
692  for (int l = 0; l < 10; l++) {
693  for (int k = 0; k < 10; k++) {
694  for (int j = 0; j < 10; j++) {
695  for (int i = 0; i < 10; i++) {
696  VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
697  }
698  }
699  }
700  }
701 
702 }
703 
704 static void test_tensor_asym()
705 {
706  SGroup<AntiSymmetry<0,1>, AntiSymmetry<2,3>> sym;
707  Tensor<int, 4> t(10,10,10,10);
708 
709  t.setZero();
710 
711  for (int l = 0; l < 10; l++) {
712  for (int k = l + 1; k < 10; k++) {
713  for (int j = 0; j < 10; j++) {
714  for (int i = j + 1; i < 10; i++) {
715  sym(t, i, j, k, l) = ((i * j) + (k * l));
716  }
717  }
718  }
719  }
720 
721  for (int l = 0; l < 10; l++) {
722  for (int k = 0; k < 10; k++) {
723  for (int j = 0; j < 10; j++) {
724  for (int i = 0; i < 10; i++) {
725  if (i < j && k < l)
726  VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
727  else if (i > j && k > l)
728  VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
729  else if (i < j && k > l)
730  VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
731  else if (i > j && k < l)
732  VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
733  else
734  VERIFY_IS_EQUAL((t(i, j, k, l)), 0);
735  }
736  }
737  }
738  }
739 }
740 
741 static void test_tensor_dynsym()
742 {
743  DynamicSGroup sym;
744  sym.addSymmetry(0,1);
745  sym.addSymmetry(2,3);
746  Tensor<int, 4> t(10,10,10,10);
747 
748  t.setZero();
749 
750  for (int l = 0; l < 10; l++) {
751  for (int k = l; k < 10; k++) {
752  for (int j = 0; j < 10; j++) {
753  for (int i = j; i < 10; i++) {
754  sym(t, i, j, k, l) = (i + j) * (k + l);
755  }
756  }
757  }
758  }
759 
760  for (int l = 0; l < 10; l++) {
761  for (int k = 0; k < 10; k++) {
762  for (int j = 0; j < 10; j++) {
763  for (int i = 0; i < 10; i++) {
764  VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
765  }
766  }
767  }
768  }
769 }
770 
771 static void test_tensor_randacc()
772 {
773  SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
774  Tensor<int, 4> t(10,10,10,10);
775 
776  t.setZero();
777 
778  // set elements 1 million times, that way we access the
779  // entire matrix
780  for (int n = 0; n < 1000000; n++) {
781  int i = rand() % 10;
782  int j = rand() % 10;
783  int k = rand() % 10;
784  int l = rand() % 10;
785  // only access those indices in a given order
786  if (i < j)
787  std::swap(i, j);
788  if (k < l)
789  std::swap(k, l);
790  sym(t, i, j, k, l) = (i + j) * (k + l);
791  }
792 
793  for (int l = 0; l < 10; l++) {
794  for (int k = 0; k < 10; k++) {
795  for (int j = 0; j < 10; j++) {
796  for (int i = 0; i < 10; i++) {
797  VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
798  }
799  }
800  }
801  }
802 }
803 
804 void test_cxx11_tensor_symmetry()
805 {
806  CALL_SUBTEST(test_symgroups_static());
807  CALL_SUBTEST(test_symgroups_dynamic());
808  CALL_SUBTEST(test_symgroups_selection());
809  CALL_SUBTEST(test_tensor_epsilon());
810  CALL_SUBTEST(test_tensor_sym());
811  CALL_SUBTEST(test_tensor_asym());
812  CALL_SUBTEST(test_tensor_dynsym());
813  CALL_SUBTEST(test_tensor_randacc());
814 }
815 
816 /*
817  * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
818  */
Eigen::DynamicSGroup::apply
RV apply(const std::array< Index, N > &idx, RV initial, Args &&...args) const
Definition: DynamicSymmetry.h:34
test_tensor_sym
static void test_tensor_sym()
Definition: cxx11_tensor_symmetry.cpp:675
cholesky::expected
Matrix expected
Definition: testMatrix.cpp:974
Eigen::DynamicSGroup::size
std::size_t size() const
Definition: DynamicSymmetry.h:52
Eigen::SGroup
Symmetry group, initialized from template arguments.
Definition: Symmetry.h:136
test_symgroups_dynamic
static void test_symgroups_dynamic()
Definition: cxx11_tensor_symmetry.cpp:109
n
int n
Definition: BiCGSTAB_simple.cpp:1
checkIdx::run
static int run(std::vector< int > e, int flags, int dummy, std::set< uint64_t > &found, std::map< uint64_t, int > const &expected)
Definition: cxx11_tensor_symmetry.cpp:72
epsilon
static double epsilon
Definition: testRot3.cpp:39
test_symgroups_selection
static void test_symgroups_selection()
Definition: cxx11_tensor_symmetry.cpp:138
test_tensor_epsilon
static void test_tensor_epsilon()
Definition: cxx11_tensor_symmetry.cpp:658
l
static const Line3 l(Rot3(), 1, 1)
VERIFY_IS_EQUAL
#define VERIFY_IS_EQUAL(a, b)
Definition: main.h:331
Eigen::StaticSGroup
Static symmetry group.
Definition: StaticSymmetry.h:181
Eigen::DynamicSGroup::globalFlags
int globalFlags() const
Definition: DynamicSymmetry.h:51
test_tensor_dynsym
static void test_tensor_dynsym()
Definition: cxx11_tensor_symmetry.cpp:741
test_callbacks.value
value
Definition: test_callbacks.py:116
test_tensor_randacc
static void test_tensor_randacc()
Definition: cxx11_tensor_symmetry.cpp:771
test_symgroups_static
static void test_symgroups_static()
Definition: cxx11_tensor_symmetry.cpp:84
uint64_t
unsigned __int64 uint64_t
Definition: ms_stdint.h:95
e
Array< double, 1, 3 > e(1./3., 0.5, 2.)
isDynGroup
bool isDynGroup(StaticSGroup< Sym... > const &dummy)
Definition: cxx11_tensor_symmetry.cpp:36
checkIdx::run
static int run(std::array< int, N > e, int flags, int dummy, std::set< uint64_t > &found, std::map< uint64_t, int > const &expected)
Definition: cxx11_tensor_symmetry.cpp:78
Eigen::DynamicSGroup::addSymmetry
void addSymmetry(int one, int two)
Definition: DynamicSymmetry.h:28
test_tensor_asym
static void test_tensor_asym()
Definition: cxx11_tensor_symmetry.cpp:704
test_cxx11_tensor_symmetry
void test_cxx11_tensor_symmetry()
Definition: cxx11_tensor_symmetry.cpp:804
CALL_SUBTEST
#define CALL_SUBTEST(FUNC)
Definition: main.h:342
VERIFY
#define VERIFY(a)
Definition: main.h:325
p
float * p
Definition: Tutorial_Map_using.cpp:9
Eigen::DynamicSGroup::add
void add(int one, int two, int flags=0)
Definition: DynamicSymmetry.h:195
Eigen::DynamicSGroup
Dynamic symmetry group.
Definition: DynamicSymmetry.h:15
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9
checkIdx::doCheck_
static int doCheck_(ArrType e, int flags, int dummy, std::set< uint64_t > &found, std::map< uint64_t, int > const &expected)
Definition: cxx11_tensor_symmetry.cpp:51
std::swap
void swap(mpfr::mpreal &x, mpfr::mpreal &y)
Definition: mpreal.h:2986
j
std::ptrdiff_t j
Definition: tut_arithmetic_redux_minmax.cpp:2
Eigen::TensorBase< Tensor< Scalar_, NumIndices_, Options_, IndexType_ > >::setZero
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor< Scalar_, NumIndices_, Options_, IndexType_ > & setZero()
Definition: TensorBase.h:842
Eigen::Tensor
The tensor class.
Definition: Tensor.h:63
align_3::t
Point2 t(10, 10)

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