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third-party-mirror / eigen / eae6db0ca08e15a56faa194349561649dde541dd / . / unsupported / test / cxx11_tensor_symmetry.cpp
blob: 16173b94a486b04999fa77b03634c6c8ee246ee5 [file] [log] [blame]
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/CXX11/Tensor>
#include <Eigen/CXX11/TensorSymmetry>
#include <map>
#include <set>
using Eigen::AntiHermiticity;
using Eigen::AntiSymmetry;
using Eigen::DynamicSGroup;
using Eigen::Hermiticity;
using Eigen::SGroup;
using Eigen::StaticSGroup;
using Eigen::Symmetry;
using Eigen::Tensor;
using Eigen::ConjugationFlag;
using Eigen::GlobalImagFlag;
using Eigen::GlobalRealFlag;
using Eigen::GlobalZeroFlag;
using Eigen::NegationFlag;
// helper function to determine if the compiler intantiated a static
// or dynamic symmetry group
template <typename... Sym>
bool isDynGroup(StaticSGroup<Sym...> const& dummy) {
(void)dummy;
return false;
}
bool isDynGroup(DynamicSGroup const& dummy) {
(void)dummy;
return true;
}
// helper class for checking that the symmetry groups are correct
struct checkIdx {
template <typename ArrType>
static inline int doCheck_(ArrType e, int flags, int dummy, std::set<uint64_t>& found,
std::map<uint64_t, int> const& expected) {
// use decimal representation of value
uint64_t value = e[0];
for (std::size_t i = 1; i < e.size(); i++) value = value * 10 + e[i];
// we want to make sure that we find each element
auto it = expected.find(value);
VERIFY((it != expected.end()));
VERIFY_IS_EQUAL(it->second, flags);
// we want to make sure we only have each element once;
// set::insert returns true for the second part of the pair
// if the element was really inserted and not already there
auto p = found.insert(value);
VERIFY((p.second));
return dummy;
}
static inline int run(std::vector<int> e, int flags, int dummy, std::set<uint64_t>& found,
std::map<uint64_t, int> const& expected) {
return doCheck_(e, flags, dummy, found, expected);
}
template <std::size_t N>
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) {
return doCheck_(e, flags, dummy, found, expected);
}
};
static void test_symgroups_static() {
std::array<int, 7> identity{{0, 1, 2, 3, 4, 5, 6}};
// Simple static symmetry group
StaticSGroup<AntiSymmetry<0, 1>, Hermiticity<0, 2>> group;
std::set<uint64_t> found;
std::map<uint64_t, int> expected;
expected[123456] = 0;
expected[1023456] = NegationFlag;
expected[2103456] = ConjugationFlag;
expected[1203456] = ConjugationFlag | NegationFlag;
expected[2013456] = ConjugationFlag | NegationFlag;
expected[213456] = ConjugationFlag;
VERIFY_IS_EQUAL(group.size(), 6u);
VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
group.apply<checkIdx, int>(identity, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 6u);
}
static void test_symgroups_dynamic() {
std::vector<int> identity;
for (int i = 0; i <= 6; i++) identity.push_back(i);
// Simple dynamic symmetry group
DynamicSGroup group;
group.add(0, 1, NegationFlag);
group.add(0, 2, ConjugationFlag);
VERIFY_IS_EQUAL(group.size(), 6u);
VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
std::set<uint64_t> found;
std::map<uint64_t, int> expected;
expected[123456] = 0;
expected[1023456] = NegationFlag;
expected[2103456] = ConjugationFlag;
expected[1203456] = ConjugationFlag | NegationFlag;
expected[2013456] = ConjugationFlag | NegationFlag;
expected[213456] = ConjugationFlag;
VERIFY_IS_EQUAL(group.size(), 6u);
VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
group.apply<checkIdx, int>(identity, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 6u);
}
static void test_symgroups_selection() {
std::array<int, 7> identity7{{0, 1, 2, 3, 4, 5, 6}};
std::array<int, 10> identity10{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}};
{
// Do the same test as in test_symgroups_static but
// require selection via SGroup
SGroup<AntiSymmetry<0, 1>, Hermiticity<0, 2>> group;
std::set<uint64_t> found;
std::map<uint64_t, int> expected;
expected[123456] = 0;
expected[1023456] = NegationFlag;
expected[2103456] = ConjugationFlag;
expected[1203456] = ConjugationFlag | NegationFlag;
expected[2013456] = ConjugationFlag | NegationFlag;
expected[213456] = ConjugationFlag;
VERIFY(!isDynGroup(group));
VERIFY_IS_EQUAL(group.size(), 6u);
VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
group.apply<checkIdx, int>(identity7, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 6u);
}
{
// simple factorizing group: 5 generators, 2^5 = 32 elements
// selection should make this dynamic, although static group
// can still be reasonably generated
SGroup<Symmetry<0, 1>, Symmetry<2, 3>, Symmetry<4, 5>, Symmetry<6, 7>, Symmetry<8, 9>> group;
std::set<uint64_t> found;
std::map<uint64_t, int> expected;
expected[123456789] = 0;
expected[123456798] = 0;
expected[123457689] = 0;
expected[123457698] = 0;
expected[123546789] = 0;
expected[123546798] = 0;
expected[123547689] = 0;
expected[123547698] = 0;
expected[132456789] = 0;
expected[132456798] = 0;
expected[132457689] = 0;
expected[132457698] = 0;
expected[132546789] = 0;
expected[132546798] = 0;
expected[132547689] = 0;
expected[132547698] = 0;
expected[1023456789] = 0;
expected[1023456798] = 0;
expected[1023457689] = 0;
expected[1023457698] = 0;
expected[1023546789] = 0;
expected[1023546798] = 0;
expected[1023547689] = 0;
expected[1023547698] = 0;
expected[1032456789] = 0;
expected[1032456798] = 0;
expected[1032457689] = 0;
expected[1032457698] = 0;
expected[1032546789] = 0;
expected[1032546798] = 0;
expected[1032547689] = 0;
expected[1032547698] = 0;
VERIFY(isDynGroup(group));
VERIFY_IS_EQUAL(group.size(), 32u);
VERIFY_IS_EQUAL(group.globalFlags(), 0);
group.apply<checkIdx, int>(identity10, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 32u);
// no verify that we could also generate a static group
// with these generators
found.clear();
StaticSGroup<Symmetry<0, 1>, Symmetry<2, 3>, Symmetry<4, 5>, Symmetry<6, 7>, Symmetry<8, 9>> group_static;
VERIFY_IS_EQUAL(group_static.size(), 32u);
VERIFY_IS_EQUAL(group_static.globalFlags(), 0);
group_static.apply<checkIdx, int>(identity10, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 32u);
}
{
// try to create a HUGE group
SGroup<Symmetry<0, 1>, Symmetry<1, 2>, Symmetry<2, 3>, Symmetry<3, 4>, Symmetry<4, 5>, Symmetry<5, 6>> group;
std::set<uint64_t> found;
uint64_t pre_expected[5040] = {
123456, 1023456, 213456, 2013456, 1203456, 2103456, 132456, 1032456, 312456, 3012456, 1302456, 3102456,
231456, 2031456, 321456, 3021456, 2301456, 3201456, 1230456, 2130456, 1320456, 3120456, 2310456, 3210456,
124356, 1024356, 214356, 2014356, 1204356, 2104356, 142356, 1042356, 412356, 4012356, 1402356, 4102356,
241356, 2041356, 421356, 4021356, 2401356, 4201356, 1240356, 2140356, 1420356, 4120356, 2410356, 4210356,
134256, 1034256, 314256, 3014256, 1304256, 3104256, 143256, 1043256, 413256, 4013256, 1403256, 4103256,
341256, 3041256, 431256, 4031256, 3401256, 4301256, 1340256, 3140256, 1430256, 4130256, 3410256, 4310256,
234156, 2034156, 324156, 3024156, 2304156, 3204156, 243156, 2043156, 423156, 4023156, 2403156, 4203156,
342156, 3042156, 432156, 4032156, 3402156, 4302156, 2340156, 3240156, 2430156, 4230156, 3420156, 4320156,
1234056, 2134056, 1324056, 3124056, 2314056, 3214056, 1243056, 2143056, 1423056, 4123056, 2413056, 4213056,
1342056, 3142056, 1432056, 4132056, 3412056, 4312056, 2341056, 3241056, 2431056, 4231056, 3421056, 4321056,
123546, 1023546, 213546, 2013546, 1203546, 2103546, 132546, 1032546, 312546, 3012546, 1302546, 3102546,
231546, 2031546, 321546, 3021546, 2301546, 3201546, 1230546, 2130546, 1320546, 3120546, 2310546, 3210546,
125346, 1025346, 215346, 2015346, 1205346, 2105346, 152346, 1052346, 512346, 5012346, 1502346, 5102346,
251346, 2051346, 521346, 5021346, 2501346, 5201346, 1250346, 2150346, 1520346, 5120346, 2510346, 5210346,
135246, 1035246, 315246, 3015246, 1305246, 3105246, 153246, 1053246, 513246, 5013246, 1503246, 5103246,
351246, 3051246, 531246, 5031246, 3501246, 5301246, 1350246, 3150246, 1530246, 5130246, 3510246, 5310246,
235146, 2035146, 325146, 3025146, 2305146, 3205146, 253146, 2053146, 523146, 5023146, 2503146, 5203146,
352146, 3052146, 532146, 5032146, 3502146, 5302146, 2350146, 3250146, 2530146, 5230146, 3520146, 5320146,
1235046, 2135046, 1325046, 3125046, 2315046, 3215046, 1253046, 2153046, 1523046, 5123046, 2513046, 5213046,
1352046, 3152046, 1532046, 5132046, 3512046, 5312046, 2351046, 3251046, 2531046, 5231046, 3521046, 5321046,
124536, 1024536, 214536, 2014536, 1204536, 2104536, 142536, 1042536, 412536, 4012536, 1402536, 4102536,
241536, 2041536, 421536, 4021536, 2401536, 4201536, 1240536, 2140536, 1420536, 4120536, 2410536, 4210536,
125436, 1025436, 215436, 2015436, 1205436, 2105436, 152436, 1052436, 512436, 5012436, 1502436, 5102436,
251436, 2051436, 521436, 5021436, 2501436, 5201436, 1250436, 2150436, 1520436, 5120436, 2510436, 5210436,
145236, 1045236, 415236, 4015236, 1405236, 4105236, 154236, 1054236, 514236, 5014236, 1504236, 5104236,
451236, 4051236, 541236, 5041236, 4501236, 5401236, 1450236, 4150236, 1540236, 5140236, 4510236, 5410236,
245136, 2045136, 425136, 4025136, 2405136, 4205136, 254136, 2054136, 524136, 5024136, 2504136, 5204136,
452136, 4052136, 542136, 5042136, 4502136, 5402136, 2450136, 4250136, 2540136, 5240136, 4520136, 5420136,
1245036, 2145036, 1425036, 4125036, 2415036, 4215036, 1254036, 2154036, 1524036, 5124036, 2514036, 5214036,
1452036, 4152036, 1542036, 5142036, 4512036, 5412036, 2451036, 4251036, 2541036, 5241036, 4521036, 5421036,
134526, 1034526, 314526, 3014526, 1304526, 3104526, 143526, 1043526, 413526, 4013526, 1403526, 4103526,
341526, 3041526, 431526, 4031526, 3401526, 4301526, 1340526, 3140526, 1430526, 4130526, 3410526, 4310526,
135426, 1035426, 315426, 3015426, 1305426, 3105426, 153426, 1053426, 513426, 5013426, 1503426, 5103426,
351426, 3051426, 531426, 5031426, 3501426, 5301426, 1350426, 3150426, 1530426, 5130426, 3510426, 5310426,
145326, 1045326, 415326, 4015326, 1405326, 4105326, 154326, 1054326, 514326, 5014326, 1504326, 5104326,
451326, 4051326, 541326, 5041326, 4501326, 5401326, 1450326, 4150326, 1540326, 5140326, 4510326, 5410326,
345126, 3045126, 435126, 4035126, 3405126, 4305126, 354126, 3054126, 534126, 5034126, 3504126, 5304126,
453126, 4053126, 543126, 5043126, 4503126, 5403126, 3450126, 4350126, 3540126, 5340126, 4530126, 5430126,
1345026, 3145026, 1435026, 4135026, 3415026, 4315026, 1354026, 3154026, 1534026, 5134026, 3514026, 5314026,
1453026, 4153026, 1543026, 5143026, 4513026, 5413026, 3451026, 4351026, 3541026, 5341026, 4531026, 5431026,
234516, 2034516, 324516, 3024516, 2304516, 3204516, 243516, 2043516, 423516, 4023516, 2403516, 4203516,
342516, 3042516, 432516, 4032516, 3402516, 4302516, 2340516, 3240516, 2430516, 4230516, 3420516, 4320516,
235416, 2035416, 325416, 3025416, 2305416, 3205416, 253416, 2053416, 523416, 5023416, 2503416, 5203416,
352416, 3052416, 532416, 5032416, 3502416, 5302416, 2350416, 3250416, 2530416, 5230416, 3520416, 5320416,
245316, 2045316, 425316, 4025316, 2405316, 4205316, 254316, 2054316, 524316, 5024316, 2504316, 5204316,
452316, 4052316, 542316, 5042316, 4502316, 5402316, 2450316, 4250316, 2540316, 5240316, 4520316, 5420316,
345216, 3045216, 435216, 4035216, 3405216, 4305216, 354216, 3054216, 534216, 5034216, 3504216, 5304216,
453216, 4053216, 543216, 5043216, 4503216, 5403216, 3450216, 4350216, 3540216, 5340216, 4530216, 5430216,
2345016, 3245016, 2435016, 4235016, 3425016, 4325016, 2354016, 3254016, 2534016, 5234016, 3524016, 5324016,
2453016, 4253016, 2543016, 5243016, 4523016, 5423016, 3452016, 4352016, 3542016, 5342016, 4532016, 5432016,
1234506, 2134506, 1324506, 3124506, 2314506, 3214506, 1243506, 2143506, 1423506, 4123506, 2413506, 4213506,
1342506, 3142506, 1432506, 4132506, 3412506, 4312506, 2341506, 3241506, 2431506, 4231506, 3421506, 4321506,
1235406, 2135406, 1325406, 3125406, 2315406, 3215406, 1253406, 2153406, 1523406, 5123406, 2513406, 5213406,
1352406, 3152406, 1532406, 5132406, 3512406, 5312406, 2351406, 3251406, 2531406, 5231406, 3521406, 5321406,
1245306, 2145306, 1425306, 4125306, 2415306, 4215306, 1254306, 2154306, 1524306, 5124306, 2514306, 5214306,
1452306, 4152306, 1542306, 5142306, 4512306, 5412306, 2451306, 4251306, 2541306, 5241306, 4521306, 5421306,
1345206, 3145206, 1435206, 4135206, 3415206, 4315206, 1354206, 3154206, 1534206, 5134206, 3514206, 5314206,
1453206, 4153206, 1543206, 5143206, 4513206, 5413206, 3451206, 4351206, 3541206, 5341206, 4531206, 5431206,
2345106, 3245106, 2435106, 4235106, 3425106, 4325106, 2354106, 3254106, 2534106, 5234106, 3524106, 5324106,
2453106, 4253106, 2543106, 5243106, 4523106, 5423106, 3452106, 4352106, 3542106, 5342106, 4532106, 5432106,
123465, 1023465, 213465, 2013465, 1203465, 2103465, 132465, 1032465, 312465, 3012465, 1302465, 3102465,
231465, 2031465, 321465, 3021465, 2301465, 3201465, 1230465, 2130465, 1320465, 3120465, 2310465, 3210465,
124365, 1024365, 214365, 2014365, 1204365, 2104365, 142365, 1042365, 412365, 4012365, 1402365, 4102365,
241365, 2041365, 421365, 4021365, 2401365, 4201365, 1240365, 2140365, 1420365, 4120365, 2410365, 4210365,
134265, 1034265, 314265, 3014265, 1304265, 3104265, 143265, 1043265, 413265, 4013265, 1403265, 4103265,
341265, 3041265, 431265, 4031265, 3401265, 4301265, 1340265, 3140265, 1430265, 4130265, 3410265, 4310265,
234165, 2034165, 324165, 3024165, 2304165, 3204165, 243165, 2043165, 423165, 4023165, 2403165, 4203165,
342165, 3042165, 432165, 4032165, 3402165, 4302165, 2340165, 3240165, 2430165, 4230165, 3420165, 4320165,
1234065, 2134065, 1324065, 3124065, 2314065, 3214065, 1243065, 2143065, 1423065, 4123065, 2413065, 4213065,
1342065, 3142065, 1432065, 4132065, 3412065, 4312065, 2341065, 3241065, 2431065, 4231065, 3421065, 4321065,
123645, 1023645, 213645, 2013645, 1203645, 2103645, 132645, 1032645, 312645, 3012645, 1302645, 3102645,
231645, 2031645, 321645, 3021645, 2301645, 3201645, 1230645, 2130645, 1320645, 3120645, 2310645, 3210645,
126345, 1026345, 216345, 2016345, 1206345, 2106345, 162345, 1062345, 612345, 6012345, 1602345, 6102345,
261345, 2061345, 621345, 6021345, 2601345, 6201345, 1260345, 2160345, 1620345, 6120345, 2610345, 6210345,
136245, 1036245, 316245, 3016245, 1306245, 3106245, 163245, 1063245, 613245, 6013245, 1603245, 6103245,
361245, 3061245, 631245, 6031245, 3601245, 6301245, 1360245, 3160245, 1630245, 6130245, 3610245, 6310245,
236145, 2036145, 326145, 3026145, 2306145, 3206145, 263145, 2063145, 623145, 6023145, 2603145, 6203145,
362145, 3062145, 632145, 6032145, 3602145, 6302145, 2360145, 3260145, 2630145, 6230145, 3620145, 6320145,
1236045, 2136045, 1326045, 3126045, 2316045, 3216045, 1263045, 2163045, 1623045, 6123045, 2613045, 6213045,
1362045, 3162045, 1632045, 6132045, 3612045, 6312045, 2361045, 3261045, 2631045, 6231045, 3621045, 6321045,
124635, 1024635, 214635, 2014635, 1204635, 2104635, 142635, 1042635, 412635, 4012635, 1402635, 4102635,
241635, 2041635, 421635, 4021635, 2401635, 4201635, 1240635, 2140635, 1420635, 4120635, 2410635, 4210635,
126435, 1026435, 216435, 2016435, 1206435, 2106435, 162435, 1062435, 612435, 6012435, 1602435, 6102435,
261435, 2061435, 621435, 6021435, 2601435, 6201435, 1260435, 2160435, 1620435, 6120435, 2610435, 6210435,
146235, 1046235, 416235, 4016235, 1406235, 4106235, 164235, 1064235, 614235, 6014235, 1604235, 6104235,
461235, 4061235, 641235, 6041235, 4601235, 6401235, 1460235, 4160235, 1640235, 6140235, 4610235, 6410235,
246135, 2046135, 426135, 4026135, 2406135, 4206135, 264135, 2064135, 624135, 6024135, 2604135, 6204135,
462135, 4062135, 642135, 6042135, 4602135, 6402135, 2460135, 4260135, 2640135, 6240135, 4620135, 6420135,
1246035, 2146035, 1426035, 4126035, 2416035, 4216035, 1264035, 2164035, 1624035, 6124035, 2614035, 6214035,
1462035, 4162035, 1642035, 6142035, 4612035, 6412035, 2461035, 4261035, 2641035, 6241035, 4621035, 6421035,
134625, 1034625, 314625, 3014625, 1304625, 3104625, 143625, 1043625, 413625, 4013625, 1403625, 4103625,
341625, 3041625, 431625, 4031625, 3401625, 4301625, 1340625, 3140625, 1430625, 4130625, 3410625, 4310625,
136425, 1036425, 316425, 3016425, 1306425, 3106425, 163425, 1063425, 613425, 6013425, 1603425, 6103425,
361425, 3061425, 631425, 6031425, 3601425, 6301425, 1360425, 3160425, 1630425, 6130425, 3610425, 6310425,
146325, 1046325, 416325, 4016325, 1406325, 4106325, 164325, 1064325, 614325, 6014325, 1604325, 6104325,
461325, 4061325, 641325, 6041325, 4601325, 6401325, 1460325, 4160325, 1640325, 6140325, 4610325, 6410325,
346125, 3046125, 436125, 4036125, 3406125, 4306125, 364125, 3064125, 634125, 6034125, 3604125, 6304125,
463125, 4063125, 643125, 6043125, 4603125, 6403125, 3460125, 4360125, 3640125, 6340125, 4630125, 6430125,
1346025, 3146025, 1436025, 4136025, 3416025, 4316025, 1364025, 3164025, 1634025, 6134025, 3614025, 6314025,
1463025, 4163025, 1643025, 6143025, 4613025, 6413025, 3461025, 4361025, 3641025, 6341025, 4631025, 6431025,
234615, 2034615, 324615, 3024615, 2304615, 3204615, 243615, 2043615, 423615, 4023615, 2403615, 4203615,
342615, 3042615, 432615, 4032615, 3402615, 4302615, 2340615, 3240615, 2430615, 4230615, 3420615, 4320615,
236415, 2036415, 326415, 3026415, 2306415, 3206415, 263415, 2063415, 623415, 6023415, 2603415, 6203415,
362415, 3062415, 632415, 6032415, 3602415, 6302415, 2360415, 3260415, 2630415, 6230415, 3620415, 6320415,
246315, 2046315, 426315, 4026315, 2406315, 4206315, 264315, 2064315, 624315, 6024315, 2604315, 6204315,
462315, 4062315, 642315, 6042315, 4602315, 6402315, 2460315, 4260315, 2640315, 6240315, 4620315, 6420315,
346215, 3046215, 436215, 4036215, 3406215, 4306215, 364215, 3064215, 634215, 6034215, 3604215, 6304215,
463215, 4063215, 643215, 6043215, 4603215, 6403215, 3460215, 4360215, 3640215, 6340215, 4630215, 6430215,
2346015, 3246015, 2436015, 4236015, 3426015, 4326015, 2364015, 3264015, 2634015, 6234015, 3624015, 6324015,
2463015, 4263015, 2643015, 6243015, 4623015, 6423015, 3462015, 4362015, 3642015, 6342015, 4632015, 6432015,
1234605, 2134605, 1324605, 3124605, 2314605, 3214605, 1243605, 2143605, 1423605, 4123605, 2413605, 4213605,
1342605, 3142605, 1432605, 4132605, 3412605, 4312605, 2341605, 3241605, 2431605, 4231605, 3421605, 4321605,
1236405, 2136405, 1326405, 3126405, 2316405, 3216405, 1263405, 2163405, 1623405, 6123405, 2613405, 6213405,
1362405, 3162405, 1632405, 6132405, 3612405, 6312405, 2361405, 3261405, 2631405, 6231405, 3621405, 6321405,
1246305, 2146305, 1426305, 4126305, 2416305, 4216305, 1264305, 2164305, 1624305, 6124305, 2614305, 6214305,
1462305, 4162305, 1642305, 6142305, 4612305, 6412305, 2461305, 4261305, 2641305, 6241305, 4621305, 6421305,
1346205, 3146205, 1436205, 4136205, 3416205, 4316205, 1364205, 3164205, 1634205, 6134205, 3614205, 6314205,
1463205, 4163205, 1643205, 6143205, 4613205, 6413205, 3461205, 4361205, 3641205, 6341205, 4631205, 6431205,
2346105, 3246105, 2436105, 4236105, 3426105, 4326105, 2364105, 3264105, 2634105, 6234105, 3624105, 6324105,
2463105, 4263105, 2643105, 6243105, 4623105, 6423105, 3462105, 4362105, 3642105, 6342105, 4632105, 6432105,
123564, 1023564, 213564, 2013564, 1203564, 2103564, 132564, 1032564, 312564, 3012564, 1302564, 3102564,
231564, 2031564, 321564, 3021564, 2301564, 3201564, 1230564, 2130564, 1320564, 3120564, 2310564, 3210564,
125364, 1025364, 215364, 2015364, 1205364, 2105364, 152364, 1052364, 512364, 5012364, 1502364, 5102364,
251364, 2051364, 521364, 5021364, 2501364, 5201364, 1250364, 2150364, 1520364, 5120364, 2510364, 5210364,
135264, 1035264, 315264, 3015264, 1305264, 3105264, 153264, 1053264, 513264, 5013264, 1503264, 5103264,
351264, 3051264, 531264, 5031264, 3501264, 5301264, 1350264, 3150264, 1530264, 5130264, 3510264, 5310264,
235164, 2035164, 325164, 3025164, 2305164, 3205164, 253164, 2053164, 523164, 5023164, 2503164, 5203164,
352164, 3052164, 532164, 5032164, 3502164, 5302164, 2350164, 3250164, 2530164, 5230164, 3520164, 5320164,
1235064, 2135064, 1325064, 3125064, 2315064, 3215064, 1253064, 2153064, 1523064, 5123064, 2513064, 5213064,
1352064, 3152064, 1532064, 5132064, 3512064, 5312064, 2351064, 3251064, 2531064, 5231064, 3521064, 5321064,
123654, 1023654, 213654, 2013654, 1203654, 2103654, 132654, 1032654, 312654, 3012654, 1302654, 3102654,
231654, 2031654, 321654, 3021654, 2301654, 3201654, 1230654, 2130654, 1320654, 3120654, 2310654, 3210654,
126354, 1026354, 216354, 2016354, 1206354, 2106354, 162354, 1062354, 612354, 6012354, 1602354, 6102354,
261354, 2061354, 621354, 6021354, 2601354, 6201354, 1260354, 2160354, 1620354, 6120354, 2610354, 6210354,
136254, 1036254, 316254, 3016254, 1306254, 3106254, 163254, 1063254, 613254, 6013254, 1603254, 6103254,
361254, 3061254, 631254, 6031254, 3601254, 6301254, 1360254, 3160254, 1630254, 6130254, 3610254, 6310254,
236154, 2036154, 326154, 3026154, 2306154, 3206154, 263154, 2063154, 623154, 6023154, 2603154, 6203154,
362154, 3062154, 632154, 6032154, 3602154, 6302154, 2360154, 3260154, 2630154, 6230154, 3620154, 6320154,
1236054, 2136054, 1326054, 3126054, 2316054, 3216054, 1263054, 2163054, 1623054, 6123054, 2613054, 6213054,
1362054, 3162054, 1632054, 6132054, 3612054, 6312054, 2361054, 3261054, 2631054, 6231054, 3621054, 6321054,
125634, 1025634, 215634, 2015634, 1205634, 2105634, 152634, 1052634, 512634, 5012634, 1502634, 5102634,
251634, 2051634, 521634, 5021634, 2501634, 5201634, 1250634, 2150634, 1520634, 5120634, 2510634, 5210634,
126534, 1026534, 216534, 2016534, 1206534, 2106534, 162534, 1062534, 612534, 6012534, 1602534, 6102534,
261534, 2061534, 621534, 6021534, 2601534, 6201534, 1260534, 2160534, 1620534, 6120534, 2610534, 6210534,
156234, 1056234, 516234, 5016234, 1506234, 5106234, 165234, 1065234, 615234, 6015234, 1605234, 6105234,
561234, 5061234, 651234, 6051234, 5601234, 6501234, 1560234, 5160234, 1650234, 6150234, 5610234, 6510234,
256134, 2056134, 526134, 5026134, 2506134, 5206134, 265134, 2065134, 625134, 6025134, 2605134, 6205134,
562134, 5062134, 652134, 6052134, 5602134, 6502134, 2560134, 5260134, 2650134, 6250134, 5620134, 6520134,
1256034, 2156034, 1526034, 5126034, 2516034, 5216034, 1265034, 2165034, 1625034, 6125034, 2615034, 6215034,
1562034, 5162034, 1652034, 6152034, 5612034, 6512034, 2561034, 5261034, 2651034, 6251034, 5621034, 6521034,
135624, 1035624, 315624, 3015624, 1305624, 3105624, 153624, 1053624, 513624, 5013624, 1503624, 5103624,
351624, 3051624, 531624, 5031624, 3501624, 5301624, 1350624, 3150624, 1530624, 5130624, 3510624, 5310624,
136524, 1036524, 316524, 3016524, 1306524, 3106524, 163524, 1063524, 613524, 6013524, 1603524, 6103524,
361524, 3061524, 631524, 6031524, 3601524, 6301524, 1360524, 3160524, 1630524, 6130524, 3610524, 6310524,
156324, 1056324, 516324, 5016324, 1506324, 5106324, 165324, 1065324, 615324, 6015324, 1605324, 6105324,
561324, 5061324, 651324, 6051324, 5601324, 6501324, 1560324, 5160324, 1650324, 6150324, 5610324, 6510324,
356124, 3056124, 536124, 5036124, 3506124, 5306124, 365124, 3065124, 635124, 6035124, 3605124, 6305124,
563124, 5063124, 653124, 6053124, 5603124, 6503124, 3560124, 5360124, 3650124, 6350124, 5630124, 6530124,
1356024, 3156024, 1536024, 5136024, 3516024, 5316024, 1365024, 3165024, 1635024, 6135024, 3615024, 6315024,
1563024, 5163024, 1653024, 6153024, 5613024, 6513024, 3561024, 5361024, 3651024, 6351024, 5631024, 6531024,
235614, 2035614, 325614, 3025614, 2305614, 3205614, 253614, 2053614, 523614, 5023614, 2503614, 5203614,
352614, 3052614, 532614, 5032614, 3502614, 5302614, 2350614, 3250614, 2530614, 5230614, 3520614, 5320614,
236514, 2036514, 326514, 3026514, 2306514, 3206514, 263514, 2063514, 623514, 6023514, 2603514, 6203514,
362514, 3062514, 632514, 6032514, 3602514, 6302514, 2360514, 3260514, 2630514, 6230514, 3620514, 6320514,
256314, 2056314, 526314, 5026314, 2506314, 5206314, 265314, 2065314, 625314, 6025314, 2605314, 6205314,
562314, 5062314, 652314, 6052314, 5602314, 6502314, 2560314, 5260314, 2650314, 6250314, 5620314, 6520314,
356214, 3056214, 536214, 5036214, 3506214, 5306214, 365214, 3065214, 635214, 6035214, 3605214, 6305214,
563214, 5063214, 653214, 6053214, 5603214, 6503214, 3560214, 5360214, 3650214, 6350214, 5630214, 6530214,
2356014, 3256014, 2536014, 5236014, 3526014, 5326014, 2365014, 3265014, 2635014, 6235014, 3625014, 6325014,
2563014, 5263014, 2653014, 6253014, 5623014, 6523014, 3562014, 5362014, 3652014, 6352014, 5632014, 6532014,
1235604, 2135604, 1325604, 3125604, 2315604, 3215604, 1253604, 2153604, 1523604, 5123604, 2513604, 5213604,
1352604, 3152604, 1532604, 5132604, 3512604, 5312604, 2351604, 3251604, 2531604, 5231604, 3521604, 5321604,
1236504, 2136504, 1326504, 3126504, 2316504, 3216504, 1263504, 2163504, 1623504, 6123504, 2613504, 6213504,
1362504, 3162504, 1632504, 6132504, 3612504, 6312504, 2361504, 3261504, 2631504, 6231504, 3621504, 6321504,
1256304, 2156304, 1526304, 5126304, 2516304, 5216304, 1265304, 2165304, 1625304, 6125304, 2615304, 6215304,
1562304, 5162304, 1652304, 6152304, 5612304, 6512304, 2561304, 5261304, 2651304, 6251304, 5621304, 6521304,
1356204, 3156204, 1536204, 5136204, 3516204, 5316204, 1365204, 3165204, 1635204, 6135204, 3615204, 6315204,
1563204, 5163204, 1653204, 6153204, 5613204, 6513204, 3561204, 5361204, 3651204, 6351204, 5631204, 6531204,
2356104, 3256104, 2536104, 5236104, 3526104, 5326104, 2365104, 3265104, 2635104, 6235104, 3625104, 6325104,
2563104, 5263104, 2653104, 6253104, 5623104, 6523104, 3562104, 5362104, 3652104, 6352104, 5632104, 6532104,
124563, 1024563, 214563, 2014563, 1204563, 2104563, 142563, 1042563, 412563, 4012563, 1402563, 4102563,
241563, 2041563, 421563, 4021563, 2401563, 4201563, 1240563, 2140563, 1420563, 4120563, 2410563, 4210563,
125463, 1025463, 215463, 2015463, 1205463, 2105463, 152463, 1052463, 512463, 5012463, 1502463, 5102463,
251463, 2051463, 521463, 5021463, 2501463, 5201463, 1250463, 2150463, 1520463, 5120463, 2510463, 5210463,
145263, 1045263, 415263, 4015263, 1405263, 4105263, 154263, 1054263, 514263, 5014263, 1504263, 5104263,
451263, 4051263, 541263, 5041263, 4501263, 5401263, 1450263, 4150263, 1540263, 5140263, 4510263, 5410263,
245163, 2045163, 425163, 4025163, 2405163, 4205163, 254163, 2054163, 524163, 5024163, 2504163, 5204163,
452163, 4052163, 542163, 5042163, 4502163, 5402163, 2450163, 4250163, 2540163, 5240163, 4520163, 5420163,
1245063, 2145063, 1425063, 4125063, 2415063, 4215063, 1254063, 2154063, 1524063, 5124063, 2514063, 5214063,
1452063, 4152063, 1542063, 5142063, 4512063, 5412063, 2451063, 4251063, 2541063, 5241063, 4521063, 5421063,
124653, 1024653, 214653, 2014653, 1204653, 2104653, 142653, 1042653, 412653, 4012653, 1402653, 4102653,
241653, 2041653, 421653, 4021653, 2401653, 4201653, 1240653, 2140653, 1420653, 4120653, 2410653, 4210653,
126453, 1026453, 216453, 2016453, 1206453, 2106453, 162453, 1062453, 612453, 6012453, 1602453, 6102453,
261453, 2061453, 621453, 6021453, 2601453, 6201453, 1260453, 2160453, 1620453, 6120453, 2610453, 6210453,
146253, 1046253, 416253, 4016253, 1406253, 4106253, 164253, 1064253, 614253, 6014253, 1604253, 6104253,
461253, 4061253, 641253, 6041253, 4601253, 6401253, 1460253, 4160253, 1640253, 6140253, 4610253, 6410253,
246153, 2046153, 426153, 4026153, 2406153, 4206153, 264153, 2064153, 624153, 6024153, 2604153, 6204153,
462153, 4062153, 642153, 6042153, 4602153, 6402153, 2460153, 4260153, 2640153, 6240153, 4620153, 6420153,
1246053, 2146053, 1426053, 4126053, 2416053, 4216053, 1264053, 2164053, 1624053, 6124053, 2614053, 6214053,
1462053, 4162053, 1642053, 6142053, 4612053, 6412053, 2461053, 4261053, 2641053, 6241053, 4621053, 6421053,
125643, 1025643, 215643, 2015643, 1205643, 2105643, 152643, 1052643, 512643, 5012643, 1502643, 5102643,
251643, 2051643, 521643, 5021643, 2501643, 5201643, 1250643, 2150643, 1520643, 5120643, 2510643, 5210643,
126543, 1026543, 216543, 2016543, 1206543, 2106543, 162543, 1062543, 612543, 6012543, 1602543, 6102543,
261543, 2061543, 621543, 6021543, 2601543, 6201543, 1260543, 2160543, 1620543, 6120543, 2610543, 6210543,
156243, 1056243, 516243, 5016243, 1506243, 5106243, 165243, 1065243, 615243, 6015243, 1605243, 6105243,
561243, 5061243, 651243, 6051243, 5601243, 6501243, 1560243, 5160243, 1650243, 6150243, 5610243, 6510243,
256143, 2056143, 526143, 5026143, 2506143, 5206143, 265143, 2065143, 625143, 6025143, 2605143, 6205143,
562143, 5062143, 652143, 6052143, 5602143, 6502143, 2560143, 5260143, 2650143, 6250143, 5620143, 6520143,
1256043, 2156043, 1526043, 5126043, 2516043, 5216043, 1265043, 2165043, 1625043, 6125043, 2615043, 6215043,
1562043, 5162043, 1652043, 6152043, 5612043, 6512043, 2561043, 5261043, 2651043, 6251043, 5621043, 6521043,
145623, 1045623, 415623, 4015623, 1405623, 4105623, 154623, 1054623, 514623, 5014623, 1504623, 5104623,
451623, 4051623, 541623, 5041623, 4501623, 5401623, 1450623, 4150623, 1540623, 5140623, 4510623, 5410623,
146523, 1046523, 416523, 4016523, 1406523, 4106523, 164523, 1064523, 614523, 6014523, 1604523, 6104523,
461523, 4061523, 641523, 6041523, 4601523, 6401523, 1460523, 4160523, 1640523, 6140523, 4610523, 6410523,
156423, 1056423, 516423, 5016423, 1506423, 5106423, 165423, 1065423, 615423, 6015423, 1605423, 6105423,
561423, 5061423, 651423, 6051423, 5601423, 6501423, 1560423, 5160423, 1650423, 6150423, 5610423, 6510423,
456123, 4056123, 546123, 5046123, 4506123, 5406123, 465123, 4065123, 645123, 6045123, 4605123, 6405123,
564123, 5064123, 654123, 6054123, 5604123, 6504123, 4560123, 5460123, 4650123, 6450123, 5640123, 6540123,
1456023, 4156023, 1546023, 5146023, 4516023, 5416023, 1465023, 4165023, 1645023, 6145023, 4615023, 6415023,
1564023, 5164023, 1654023, 6154023, 5614023, 6514023, 4561023, 5461023, 4651023, 6451023, 5641023, 6541023,
245613, 2045613, 425613, 4025613, 2405613, 4205613, 254613, 2054613, 524613, 5024613, 2504613, 5204613,
452613, 4052613, 542613, 5042613, 4502613, 5402613, 2450613, 4250613, 2540613, 5240613, 4520613, 5420613,
246513, 2046513, 426513, 4026513, 2406513, 4206513, 264513, 2064513, 624513, 6024513, 2604513, 6204513,
462513, 4062513, 642513, 6042513, 4602513, 6402513, 2460513, 4260513, 2640513, 6240513, 4620513, 6420513,
256413, 2056413, 526413, 5026413, 2506413, 5206413, 265413, 2065413, 625413, 6025413, 2605413, 6205413,
562413, 5062413, 652413, 6052413, 5602413, 6502413, 2560413, 5260413, 2650413, 6250413, 5620413, 6520413,
456213, 4056213, 546213, 5046213, 4506213, 5406213, 465213, 4065213, 645213, 6045213, 4605213, 6405213,
564213, 5064213, 654213, 6054213, 5604213, 6504213, 4560213, 5460213, 4650213, 6450213, 5640213, 6540213,
2456013, 4256013, 2546013, 5246013, 4526013, 5426013, 2465013, 4265013, 2645013, 6245013, 4625013, 6425013,
2564013, 5264013, 2654013, 6254013, 5624013, 6524013, 4562013, 5462013, 4652013, 6452013, 5642013, 6542013,
1245603, 2145603, 1425603, 4125603, 2415603, 4215603, 1254603, 2154603, 1524603, 5124603, 2514603, 5214603,
1452603, 4152603, 1542603, 5142603, 4512603, 5412603, 2451603, 4251603, 2541603, 5241603, 4521603, 5421603,
1246503, 2146503, 1426503, 4126503, 2416503, 4216503, 1264503, 2164503, 1624503, 6124503, 2614503, 6214503,
1462503, 4162503, 1642503, 6142503, 4612503, 6412503, 2461503, 4261503, 2641503, 6241503, 4621503, 6421503,
1256403, 2156403, 1526403, 5126403, 2516403, 5216403, 1265403, 2165403, 1625403, 6125403, 2615403, 6215403,
1562403, 5162403, 1652403, 6152403, 5612403, 6512403, 2561403, 5261403, 2651403, 6251403, 5621403, 6521403,
1456203, 4156203, 1546203, 5146203, 4516203, 5416203, 1465203, 4165203, 1645203, 6145203, 4615203, 6415203,
1564203, 5164203, 1654203, 6154203, 5614203, 6514203, 4561203, 5461203, 4651203, 6451203, 5641203, 6541203,
2456103, 4256103, 2546103, 5246103, 4526103, 5426103, 2465103, 4265103, 2645103, 6245103, 4625103, 6425103,
2564103, 5264103, 2654103, 6254103, 5624103, 6524103, 4562103, 5462103, 4652103, 6452103, 5642103, 6542103,
134562, 1034562, 314562, 3014562, 1304562, 3104562, 143562, 1043562, 413562, 4013562, 1403562, 4103562,
341562, 3041562, 431562, 4031562, 3401562, 4301562, 1340562, 3140562, 1430562, 4130562, 3410562, 4310562,
135462, 1035462, 315462, 3015462, 1305462, 3105462, 153462, 1053462, 513462, 5013462, 1503462, 5103462,
351462, 3051462, 531462, 5031462, 3501462, 5301462, 1350462, 3150462, 1530462, 5130462, 3510462, 5310462,
145362, 1045362, 415362, 4015362, 1405362, 4105362, 154362, 1054362, 514362, 5014362, 1504362, 5104362,
451362, 4051362, 541362, 5041362, 4501362, 5401362, 1450362, 4150362, 1540362, 5140362, 4510362, 5410362,
345162, 3045162, 435162, 4035162, 3405162, 4305162, 354162, 3054162, 534162, 5034162, 3504162, 5304162,
453162, 4053162, 543162, 5043162, 4503162, 5403162, 3450162, 4350162, 3540162, 5340162, 4530162, 5430162,
1345062, 3145062, 1435062, 4135062, 3415062, 4315062, 1354062, 3154062, 1534062, 5134062, 3514062, 5314062,
1453062, 4153062, 1543062, 5143062, 4513062, 5413062, 3451062, 4351062, 3541062, 5341062, 4531062, 5431062,
134652, 1034652, 314652, 3014652, 1304652, 3104652, 143652, 1043652, 413652, 4013652, 1403652, 4103652,
341652, 3041652, 431652, 4031652, 3401652, 4301652, 1340652, 3140652, 1430652, 4130652, 3410652, 4310652,
136452, 1036452, 316452, 3016452, 1306452, 3106452, 163452, 1063452, 613452, 6013452, 1603452, 6103452,
361452, 3061452, 631452, 6031452, 3601452, 6301452, 1360452, 3160452, 1630452, 6130452, 3610452, 6310452,
146352, 1046352, 416352, 4016352, 1406352, 4106352, 164352, 1064352, 614352, 6014352, 1604352, 6104352,
461352, 4061352, 641352, 6041352, 4601352, 6401352, 1460352, 4160352, 1640352, 6140352, 4610352, 6410352,
346152, 3046152, 436152, 4036152, 3406152, 4306152, 364152, 3064152, 634152, 6034152, 3604152, 6304152,
463152, 4063152, 643152, 6043152, 4603152, 6403152, 3460152, 4360152, 3640152, 6340152, 4630152, 6430152,
1346052, 3146052, 1436052, 4136052, 3416052, 4316052, 1364052, 3164052, 1634052, 6134052, 3614052, 6314052,
1463052, 4163052, 1643052, 6143052, 4613052, 6413052, 3461052, 4361052, 3641052, 6341052, 4631052, 6431052,
135642, 1035642, 315642, 3015642, 1305642, 3105642, 153642, 1053642, 513642, 5013642, 1503642, 5103642,
351642, 3051642, 531642, 5031642, 3501642, 5301642, 1350642, 3150642, 1530642, 5130642, 3510642, 5310642,
136542, 1036542, 316542, 3016542, 1306542, 3106542, 163542, 1063542, 613542, 6013542, 1603542, 6103542,
361542, 3061542, 631542, 6031542, 3601542, 6301542, 1360542, 3160542, 1630542, 6130542, 3610542, 6310542,
156342, 1056342, 516342, 5016342, 1506342, 5106342, 165342, 1065342, 615342, 6015342, 1605342, 6105342,
561342, 5061342, 651342, 6051342, 5601342, 6501342, 1560342, 5160342, 1650342, 6150342, 5610342, 6510342,
356142, 3056142, 536142, 5036142, 3506142, 5306142, 365142, 3065142, 635142, 6035142, 3605142, 6305142,
563142, 5063142, 653142, 6053142, 5603142, 6503142, 3560142, 5360142, 3650142, 6350142, 5630142, 6530142,
1356042, 3156042, 1536042, 5136042, 3516042, 5316042, 1365042, 3165042, 1635042, 6135042, 3615042, 6315042,
1563042, 5163042, 1653042, 6153042, 5613042, 6513042, 3561042, 5361042, 3651042, 6351042, 5631042, 6531042,
145632, 1045632, 415632, 4015632, 1405632, 4105632, 154632, 1054632, 514632, 5014632, 1504632, 5104632,
451632, 4051632, 541632, 5041632, 4501632, 5401632, 1450632, 4150632, 1540632, 5140632, 4510632, 5410632,
146532, 1046532, 416532, 4016532, 1406532, 4106532, 164532, 1064532, 614532, 6014532, 1604532, 6104532,
461532, 4061532, 641532, 6041532, 4601532, 6401532, 1460532, 4160532, 1640532, 6140532, 4610532, 6410532,
156432, 1056432, 516432, 5016432, 1506432, 5106432, 165432, 1065432, 615432, 6015432, 1605432, 6105432,
561432, 5061432, 651432, 6051432, 5601432, 6501432, 1560432, 5160432, 1650432, 6150432, 5610432, 6510432,
456132, 4056132, 546132, 5046132, 4506132, 5406132, 465132, 4065132, 645132, 6045132, 4605132, 6405132,
564132, 5064132, 654132, 6054132, 5604132, 6504132, 4560132, 5460132, 4650132, 6450132, 5640132, 6540132,
1456032, 4156032, 1546032, 5146032, 4516032, 5416032, 1465032, 4165032, 1645032, 6145032, 4615032, 6415032,
1564032, 5164032, 1654032, 6154032, 5614032, 6514032, 4561032, 5461032, 4651032, 6451032, 5641032, 6541032,
345612, 3045612, 435612, 4035612, 3405612, 4305612, 354612, 3054612, 534612, 5034612, 3504612, 5304612,
453612, 4053612, 543612, 5043612, 4503612, 5403612, 3450612, 4350612, 3540612, 5340612, 4530612, 5430612,
346512, 3046512, 436512, 4036512, 3406512, 4306512, 364512, 3064512, 634512, 6034512, 3604512, 6304512,
463512, 4063512, 643512, 6043512, 4603512, 6403512, 3460512, 4360512, 3640512, 6340512, 4630512, 6430512,
356412, 3056412, 536412, 5036412, 3506412, 5306412, 365412, 3065412, 635412, 6035412, 3605412, 6305412,
563412, 5063412, 653412, 6053412, 5603412, 6503412, 3560412, 5360412, 3650412, 6350412, 5630412, 6530412,
456312, 4056312, 546312, 5046312, 4506312, 5406312, 465312, 4065312, 645312, 6045312, 4605312, 6405312,
564312, 5064312, 654312, 6054312, 5604312, 6504312, 4560312, 5460312, 4650312, 6450312, 5640312, 6540312,
3456012, 4356012, 3546012, 5346012, 4536012, 5436012, 3465012, 4365012, 3645012, 6345012, 4635012, 6435012,
3564012, 5364012, 3654012, 6354012, 5634012, 6534012, 4563012, 5463012, 4653012, 6453012, 5643012, 6543012,
1345602, 3145602, 1435602, 4135602, 3415602, 4315602, 1354602, 3154602, 1534602, 5134602, 3514602, 5314602,
1453602, 4153602, 1543602, 5143602, 4513602, 5413602, 3451602, 4351602, 3541602, 5341602, 4531602, 5431602,
1346502, 3146502, 1436502, 4136502, 3416502, 4316502, 1364502, 3164502, 1634502, 6134502, 3614502, 6314502,
1463502, 4163502, 1643502, 6143502, 4613502, 6413502, 3461502, 4361502, 3641502, 6341502, 4631502, 6431502,
1356402, 3156402, 1536402, 5136402, 3516402, 5316402, 1365402, 3165402, 1635402, 6135402, 3615402, 6315402,
1563402, 5163402, 1653402, 6153402, 5613402, 6513402, 3561402, 5361402, 3651402, 6351402, 5631402, 6531402,
1456302, 4156302, 1546302, 5146302, 4516302, 5416302, 1465302, 4165302, 1645302, 6145302, 4615302, 6415302,
1564302, 5164302, 1654302, 6154302, 5614302, 6514302, 4561302, 5461302, 4651302, 6451302, 5641302, 6541302,
3456102, 4356102, 3546102, 5346102, 4536102, 5436102, 3465102, 4365102, 3645102, 6345102, 4635102, 6435102,
3564102, 5364102, 3654102, 6354102, 5634102, 6534102, 4563102, 5463102, 4653102, 6453102, 5643102, 6543102,
234561, 2034561, 324561, 3024561, 2304561, 3204561, 243561, 2043561, 423561, 4023561, 2403561, 4203561,
342561, 3042561, 432561, 4032561, 3402561, 4302561, 2340561, 3240561, 2430561, 4230561, 3420561, 4320561,
235461, 2035461, 325461, 3025461, 2305461, 3205461, 253461, 2053461, 523461, 5023461, 2503461, 5203461,
352461, 3052461, 532461, 5032461, 3502461, 5302461, 2350461, 3250461, 2530461, 5230461, 3520461, 5320461,
245361, 2045361, 425361, 4025361, 2405361, 4205361, 254361, 2054361, 524361, 5024361, 2504361, 5204361,
452361, 4052361, 542361, 5042361, 4502361, 5402361, 2450361, 4250361, 2540361, 5240361, 4520361, 5420361,
345261, 3045261, 435261, 4035261, 3405261, 4305261, 354261, 3054261, 534261, 5034261, 3504261, 5304261,
453261, 4053261, 543261, 5043261, 4503261, 5403261, 3450261, 4350261, 3540261, 5340261, 4530261, 5430261,
2345061, 3245061, 2435061, 4235061, 3425061, 4325061, 2354061, 3254061, 2534061, 5234061, 3524061, 5324061,
2453061, 4253061, 2543061, 5243061, 4523061, 5423061, 3452061, 4352061, 3542061, 5342061, 4532061, 5432061,
234651, 2034651, 324651, 3024651, 2304651, 3204651, 243651, 2043651, 423651, 4023651, 2403651, 4203651,
342651, 3042651, 432651, 4032651, 3402651, 4302651, 2340651, 3240651, 2430651, 4230651, 3420651, 4320651,
236451, 2036451, 326451, 3026451, 2306451, 3206451, 263451, 2063451, 623451, 6023451, 2603451, 6203451,
362451, 3062451, 632451, 6032451, 3602451, 6302451, 2360451, 3260451, 2630451, 6230451, 3620451, 6320451,
246351, 2046351, 426351, 4026351, 2406351, 4206351, 264351, 2064351, 624351, 6024351, 2604351, 6204351,
462351, 4062351, 642351, 6042351, 4602351, 6402351, 2460351, 4260351, 2640351, 6240351, 4620351, 6420351,
346251, 3046251, 436251, 4036251, 3406251, 4306251, 364251, 3064251, 634251, 6034251, 3604251, 6304251,
463251, 4063251, 643251, 6043251, 4603251, 6403251, 3460251, 4360251, 3640251, 6340251, 4630251, 6430251,
2346051, 3246051, 2436051, 4236051, 3426051, 4326051, 2364051, 3264051, 2634051, 6234051, 3624051, 6324051,
2463051, 4263051, 2643051, 6243051, 4623051, 6423051, 3462051, 4362051, 3642051, 6342051, 4632051, 6432051,
235641, 2035641, 325641, 3025641, 2305641, 3205641, 253641, 2053641, 523641, 5023641, 2503641, 5203641,
352641, 3052641, 532641, 5032641, 3502641, 5302641, 2350641, 3250641, 2530641, 5230641, 3520641, 5320641,
236541, 2036541, 326541, 3026541, 2306541, 3206541, 263541, 2063541, 623541, 6023541, 2603541, 6203541,
362541, 3062541, 632541, 6032541, 3602541, 6302541, 2360541, 3260541, 2630541, 6230541, 3620541, 6320541,
256341, 2056341, 526341, 5026341, 2506341, 5206341, 265341, 2065341, 625341, 6025341, 2605341, 6205341,
562341, 5062341, 652341, 6052341, 5602341, 6502341, 2560341, 5260341, 2650341, 6250341, 5620341, 6520341,
356241, 3056241, 536241, 5036241, 3506241, 5306241, 365241, 3065241, 635241, 6035241, 3605241, 6305241,
563241, 5063241, 653241, 6053241, 5603241, 6503241, 3560241, 5360241, 3650241, 6350241, 5630241, 6530241,
2356041, 3256041, 2536041, 5236041, 3526041, 5326041, 2365041, 3265041, 2635041, 6235041, 3625041, 6325041,
2563041, 5263041, 2653041, 6253041, 5623041, 6523041, 3562041, 5362041, 3652041, 6352041, 5632041, 6532041,
245631, 2045631, 425631, 4025631, 2405631, 4205631, 254631, 2054631, 524631, 5024631, 2504631, 5204631,
452631, 4052631, 542631, 5042631, 4502631, 5402631, 2450631, 4250631, 2540631, 5240631, 4520631, 5420631,
246531, 2046531, 426531, 4026531, 2406531, 4206531, 264531, 2064531, 624531, 6024531, 2604531, 6204531,
462531, 4062531, 642531, 6042531, 4602531, 6402531, 2460531, 4260531, 2640531, 6240531, 4620531, 6420531,
256431, 2056431, 526431, 5026431, 2506431, 5206431, 265431, 2065431, 625431, 6025431, 2605431, 6205431,
562431, 5062431, 652431, 6052431, 5602431, 6502431, 2560431, 5260431, 2650431, 6250431, 5620431, 6520431,
456231, 4056231, 546231, 5046231, 4506231, 5406231, 465231, 4065231, 645231, 6045231, 4605231, 6405231,
564231, 5064231, 654231, 6054231, 5604231, 6504231, 4560231, 5460231, 4650231, 6450231, 5640231, 6540231,
2456031, 4256031, 2546031, 5246031, 4526031, 5426031, 2465031, 4265031, 2645031, 6245031, 4625031, 6425031,
2564031, 5264031, 2654031, 6254031, 5624031, 6524031, 4562031, 5462031, 4652031, 6452031, 5642031, 6542031,
345621, 3045621, 435621, 4035621, 3405621, 4305621, 354621, 3054621, 534621, 5034621, 3504621, 5304621,
453621, 4053621, 543621, 5043621, 4503621, 5403621, 3450621, 4350621, 3540621, 5340621, 4530621, 5430621,
346521, 3046521, 436521, 4036521, 3406521, 4306521, 364521, 3064521, 634521, 6034521, 3604521, 6304521,
463521, 4063521, 643521, 6043521, 4603521, 6403521, 3460521, 4360521, 3640521, 6340521, 4630521, 6430521,
356421, 3056421, 536421, 5036421, 3506421, 5306421, 365421, 3065421, 635421, 6035421, 3605421, 6305421,
563421, 5063421, 653421, 6053421, 5603421, 6503421, 3560421, 5360421, 3650421, 6350421, 5630421, 6530421,
456321, 4056321, 546321, 5046321, 4506321, 5406321, 465321, 4065321, 645321, 6045321, 4605321, 6405321,
564321, 5064321, 654321, 6054321, 5604321, 6504321, 4560321, 5460321, 4650321, 6450321, 5640321, 6540321,
3456021, 4356021, 3546021, 5346021, 4536021, 5436021, 3465021, 4365021, 3645021, 6345021, 4635021, 6435021,
3564021, 5364021, 3654021, 6354021, 5634021, 6534021, 4563021, 5463021, 4653021, 6453021, 5643021, 6543021,
2345601, 3245601, 2435601, 4235601, 3425601, 4325601, 2354601, 3254601, 2534601, 5234601, 3524601, 5324601,
2453601, 4253601, 2543601, 5243601, 4523601, 5423601, 3452601, 4352601, 3542601, 5342601, 4532601, 5432601,
2346501, 3246501, 2436501, 4236501, 3426501, 4326501, 2364501, 3264501, 2634501, 6234501, 3624501, 6324501,
2463501, 4263501, 2643501, 6243501, 4623501, 6423501, 3462501, 4362501, 3642501, 6342501, 4632501, 6432501,
2356401, 3256401, 2536401, 5236401, 3526401, 5326401, 2365401, 3265401, 2635401, 6235401, 3625401, 6325401,
2563401, 5263401, 2653401, 6253401, 5623401, 6523401, 3562401, 5362401, 3652401, 6352401, 5632401, 6532401,
2456301, 4256301, 2546301, 5246301, 4526301, 5426301, 2465301, 4265301, 2645301, 6245301, 4625301, 6425301,
2564301, 5264301, 2654301, 6254301, 5624301, 6524301, 4562301, 5462301, 4652301, 6452301, 5642301, 6542301,
3456201, 4356201, 3546201, 5346201, 4536201, 5436201, 3465201, 4365201, 3645201, 6345201, 4635201, 6435201,
3564201, 5364201, 3654201, 6354201, 5634201, 6534201, 4563201, 5463201, 4653201, 6453201, 5643201, 6543201,
1234560, 2134560, 1324560, 3124560, 2314560, 3214560, 1243560, 2143560, 1423560, 4123560, 2413560, 4213560,
1342560, 3142560, 1432560, 4132560, 3412560, 4312560, 2341560, 3241560, 2431560, 4231560, 3421560, 4321560,
1235460, 2135460, 1325460, 3125460, 2315460, 3215460, 1253460, 2153460, 1523460, 5123460, 2513460, 5213460,
1352460, 3152460, 1532460, 5132460, 3512460, 5312460, 2351460, 3251460, 2531460, 5231460, 3521460, 5321460,
1245360, 2145360, 1425360, 4125360, 2415360, 4215360, 1254360, 2154360, 1524360, 5124360, 2514360, 5214360,
1452360, 4152360, 1542360, 5142360, 4512360, 5412360, 2451360, 4251360, 2541360, 5241360, 4521360, 5421360,
1345260, 3145260, 1435260, 4135260, 3415260, 4315260, 1354260, 3154260, 1534260, 5134260, 3514260, 5314260,
1453260, 4153260, 1543260, 5143260, 4513260, 5413260, 3451260, 4351260, 3541260, 5341260, 4531260, 5431260,
2345160, 3245160, 2435160, 4235160, 3425160, 4325160, 2354160, 3254160, 2534160, 5234160, 3524160, 5324160,
2453160, 4253160, 2543160, 5243160, 4523160, 5423160, 3452160, 4352160, 3542160, 5342160, 4532160, 5432160,
1234650, 2134650, 1324650, 3124650, 2314650, 3214650, 1243650, 2143650, 1423650, 4123650, 2413650, 4213650,
1342650, 3142650, 1432650, 4132650, 3412650, 4312650, 2341650, 3241650, 2431650, 4231650, 3421650, 4321650,
1236450, 2136450, 1326450, 3126450, 2316450, 3216450, 1263450, 2163450, 1623450, 6123450, 2613450, 6213450,
1362450, 3162450, 1632450, 6132450, 3612450, 6312450, 2361450, 3261450, 2631450, 6231450, 3621450, 6321450,
1246350, 2146350, 1426350, 4126350, 2416350, 4216350, 1264350, 2164350, 1624350, 6124350, 2614350, 6214350,
1462350, 4162350, 1642350, 6142350, 4612350, 6412350, 2461350, 4261350, 2641350, 6241350, 4621350, 6421350,
1346250, 3146250, 1436250, 4136250, 3416250, 4316250, 1364250, 3164250, 1634250, 6134250, 3614250, 6314250,
1463250, 4163250, 1643250, 6143250, 4613250, 6413250, 3461250, 4361250, 3641250, 6341250, 4631250, 6431250,
2346150, 3246150, 2436150, 4236150, 3426150, 4326150, 2364150, 3264150, 2634150, 6234150, 3624150, 6324150,
2463150, 4263150, 2643150, 6243150, 4623150, 6423150, 3462150, 4362150, 3642150, 6342150, 4632150, 6432150,
1235640, 2135640, 1325640, 3125640, 2315640, 3215640, 1253640, 2153640, 1523640, 5123640, 2513640, 5213640,
1352640, 3152640, 1532640, 5132640, 3512640, 5312640, 2351640, 3251640, 2531640, 5231640, 3521640, 5321640,
1236540, 2136540, 1326540, 3126540, 2316540, 3216540, 1263540, 2163540, 1623540, 6123540, 2613540, 6213540,
1362540, 3162540, 1632540, 6132540, 3612540, 6312540, 2361540, 3261540, 2631540, 6231540, 3621540, 6321540,
1256340, 2156340, 1526340, 5126340, 2516340, 5216340, 1265340, 2165340, 1625340, 6125340, 2615340, 6215340,
1562340, 5162340, 1652340, 6152340, 5612340, 6512340, 2561340, 5261340, 2651340, 6251340, 5621340, 6521340,
1356240, 3156240, 1536240, 5136240, 3516240, 5316240, 1365240, 3165240, 1635240, 6135240, 3615240, 6315240,
1563240, 5163240, 1653240, 6153240, 5613240, 6513240, 3561240, 5361240, 3651240, 6351240, 5631240, 6531240,
2356140, 3256140, 2536140, 5236140, 3526140, 5326140, 2365140, 3265140, 2635140, 6235140, 3625140, 6325140,
2563140, 5263140, 2653140, 6253140, 5623140, 6523140, 3562140, 5362140, 3652140, 6352140, 5632140, 6532140,
1245630, 2145630, 1425630, 4125630, 2415630, 4215630, 1254630, 2154630, 1524630, 5124630, 2514630, 5214630,
1452630, 4152630, 1542630, 5142630, 4512630, 5412630, 2451630, 4251630, 2541630, 5241630, 4521630, 5421630,
1246530, 2146530, 1426530, 4126530, 2416530, 4216530, 1264530, 2164530, 1624530, 6124530, 2614530, 6214530,
1462530, 4162530, 1642530, 6142530, 4612530, 6412530, 2461530, 4261530, 2641530, 6241530, 4621530, 6421530,
1256430, 2156430, 1526430, 5126430, 2516430, 5216430, 1265430, 2165430, 1625430, 6125430, 2615430, 6215430,
1562430, 5162430, 1652430, 6152430, 5612430, 6512430, 2561430, 5261430, 2651430, 6251430, 5621430, 6521430,
1456230, 4156230, 1546230, 5146230, 4516230, 5416230, 1465230, 4165230, 1645230, 6145230, 4615230, 6415230,
1564230, 5164230, 1654230, 6154230, 5614230, 6514230, 4561230, 5461230, 4651230, 6451230, 5641230, 6541230,
2456130, 4256130, 2546130, 5246130, 4526130, 5426130, 2465130, 4265130, 2645130, 6245130, 4625130, 6425130,
2564130, 5264130, 2654130, 6254130, 5624130, 6524130, 4562130, 5462130, 4652130, 6452130, 5642130, 6542130,
1345620, 3145620, 1435620, 4135620, 3415620, 4315620, 1354620, 3154620, 1534620, 5134620, 3514620, 5314620,
1453620, 4153620, 1543620, 5143620, 4513620, 5413620, 3451620, 4351620, 3541620, 5341620, 4531620, 5431620,
1346520, 3146520, 1436520, 4136520, 3416520, 4316520, 1364520, 3164520, 1634520, 6134520, 3614520, 6314520,
1463520, 4163520, 1643520, 6143520, 4613520, 6413520, 3461520, 4361520, 3641520, 6341520, 4631520, 6431520,
1356420, 3156420, 1536420, 5136420, 3516420, 5316420, 1365420, 3165420, 1635420, 6135420, 3615420, 6315420,
1563420, 5163420, 1653420, 6153420, 5613420, 6513420, 3561420, 5361420, 3651420, 6351420, 5631420, 6531420,
1456320, 4156320, 1546320, 5146320, 4516320, 5416320, 1465320, 4165320, 1645320, 6145320, 4615320, 6415320,
1564320, 5164320, 1654320, 6154320, 5614320, 6514320, 4561320, 5461320, 4651320, 6451320, 5641320, 6541320,
3456120, 4356120, 3546120, 5346120, 4536120, 5436120, 3465120, 4365120, 3645120, 6345120, 4635120, 6435120,
3564120, 5364120, 3654120, 6354120, 5634120, 6534120, 4563120, 5463120, 4653120, 6453120, 5643120, 6543120,
2345610, 3245610, 2435610, 4235610, 3425610, 4325610, 2354610, 3254610, 2534610, 5234610, 3524610, 5324610,
2453610, 4253610, 2543610, 5243610, 4523610, 5423610, 3452610, 4352610, 3542610, 5342610, 4532610, 5432610,
2346510, 3246510, 2436510, 4236510, 3426510, 4326510, 2364510, 3264510, 2634510, 6234510, 3624510, 6324510,
2463510, 4263510, 2643510, 6243510, 4623510, 6423510, 3462510, 4362510, 3642510, 6342510, 4632510, 6432510,
2356410, 3256410, 2536410, 5236410, 3526410, 5326410, 2365410, 3265410, 2635410, 6235410, 3625410, 6325410,
2563410, 5263410, 2653410, 6253410, 5623410, 6523410, 3562410, 5362410, 3652410, 6352410, 5632410, 6532410,
2456310, 4256310, 2546310, 5246310, 4526310, 5426310, 2465310, 4265310, 2645310, 6245310, 4625310, 6425310,
2564310, 5264310, 2654310, 6254310, 5624310, 6524310, 4562310, 5462310, 4652310, 6452310, 5642310, 6542310,
3456210, 4356210, 3546210, 5346210, 4536210, 5436210, 3465210, 4365210, 3645210, 6345210, 4635210, 6435210,
3564210, 5364210, 3654210, 6354210, 5634210, 6534210, 4563210, 5463210, 4653210, 6453210, 5643210, 6543210};
std::map<uint64_t, int> expected;
for (std::size_t i = 0; i < 5040; i++) expected[pre_expected[i]] = 0; // flags are 0, everything is symmetric here
VERIFY(isDynGroup(group));
VERIFY_IS_EQUAL(group.size(), 5040u);
VERIFY_IS_EQUAL(group.globalFlags(), 0);
group.apply<checkIdx, int>(identity7, 0, found, expected);
VERIFY_IS_EQUAL(found.size(), 5040u);
}
}
static void test_tensor_epsilon() {
SGroup<AntiSymmetry<0, 1>, AntiSymmetry<1, 2>> sym;
Tensor<int, 3> epsilon(3, 3, 3);
epsilon.setZero();
sym(epsilon, 0, 1, 2) = 1;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
VERIFY_IS_EQUAL((epsilon(i, j, k)), (-(j - i) * (k - j) * (i - k) / 2));
}
}
}
}
static void test_tensor_sym() {
SGroup<Symmetry<0, 1>, Symmetry<2, 3>> sym;
Tensor<int, 4> t(10, 10, 10, 10);
t.setZero();
for (int l = 0; l < 10; l++) {
for (int k = l; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = j; i < 10; i++) {
sym(t, i, j, k, l) = (i + j) * (k + l);
}
}
}
}
for (int l = 0; l < 10; l++) {
for (int k = 0; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = 0; i < 10; i++) {
VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
}
}
}
}
}
static void test_tensor_asym() {
SGroup<AntiSymmetry<0, 1>, AntiSymmetry<2, 3>> sym;
Tensor<int, 4> t(10, 10, 10, 10);
t.setZero();
for (int l = 0; l < 10; l++) {
for (int k = l + 1; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = j + 1; i < 10; i++) {
sym(t, i, j, k, l) = ((i * j) + (k * l));
}
}
}
}
for (int l = 0; l < 10; l++) {
for (int k = 0; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = 0; i < 10; i++) {
if (i < j && k < l)
VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
else if (i > j && k > l)
VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
else if (i < j && k > l)
VERIFY_IS_EQUAL((t(i, j, k, l)), (-((i * j) + (k * l))));
else if (i > j && k < l)
VERIFY_IS_EQUAL((t(i, j, k, l)), (-((i * j) + (k * l))));
else
VERIFY_IS_EQUAL((t(i, j, k, l)), 0);
}
}
}
}
}
static void test_tensor_dynsym() {
DynamicSGroup sym;
sym.addSymmetry(0, 1);
sym.addSymmetry(2, 3);
Tensor<int, 4> t(10, 10, 10, 10);
t.setZero();
for (int l = 0; l < 10; l++) {
for (int k = l; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = j; i < 10; i++) {
sym(t, i, j, k, l) = (i + j) * (k + l);
}
}
}
}
for (int l = 0; l < 10; l++) {
for (int k = 0; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = 0; i < 10; i++) {
VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
}
}
}
}
}
static void test_tensor_randacc() {
SGroup<Symmetry<0, 1>, Symmetry<2, 3>> sym;
Tensor<int, 4> t(10, 10, 10, 10);
t.setZero();
// set elements 1 million times, that way we access the
// entire matrix
for (int n = 0; n < 1000000; n++) {
int i = rand() % 10;
int j = rand() % 10;
int k = rand() % 10;
int l = rand() % 10;
// only access those indices in a given order
if (i < j) std::swap(i, j);
if (k < l) std::swap(k, l);
sym(t, i, j, k, l) = (i + j) * (k + l);
}
for (int l = 0; l < 10; l++) {
for (int k = 0; k < 10; k++) {
for (int j = 0; j < 10; j++) {
for (int i = 0; i < 10; i++) {
VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
}
}
}
}
}
EIGEN_DECLARE_TEST(cxx11_tensor_symmetry) {
CALL_SUBTEST(test_symgroups_static());
CALL_SUBTEST(test_symgroups_dynamic());
CALL_SUBTEST(test_symgroups_selection());
CALL_SUBTEST(test_tensor_epsilon());
CALL_SUBTEST(test_tensor_sym());
CALL_SUBTEST(test_tensor_asym());
CALL_SUBTEST(test_tensor_dynsym());
CALL_SUBTEST(test_tensor_randacc());
}
/*
* kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
*/