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eigen/unsupported/test/cxx11_tensor_symmetry.cpp

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CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
C++11/Tensor: Fix copyright headers
2013-11-16 07:03:23 +08:00
// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
//
// 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::Tensor;
using Eigen::SGroup;
using Eigen::DynamicSGroup;
using Eigen::StaticSGroup;
using Eigen::Symmetry;
using Eigen::AntiSymmetry;
using Eigen::Hermiticity;
using Eigen::AntiHermiticity;
using Eigen::NegationFlag;
using Eigen::ConjugationFlag;
using Eigen::GlobalZeroFlag;
using Eigen::GlobalRealFlag;
using Eigen::GlobalImagFlag;
// helper function to determine if the compiler intantiated a static
// or dynamic symmetry group
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
template<typename... Sym>
bool isDynGroup(StaticSGroup<Sym...> const& dummy)
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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{
(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
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
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StaticSGroup<
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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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
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
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DynamicSGroup group;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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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
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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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
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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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();
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
StaticSGroup<
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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()
{
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
Tensor<int, 3> epsilon(3,3,3);
epsilon.setZero();
unsupported/TensorSymmetry: factor out completely from Tensor module Remove the symCoeff() method of the the Tensor module and move the functionality into a new operator() of the symmetry classes. This makes the Tensor module now completely self-contained without symmetry support (even though previously it was only a forward declaration and a otherwise harmless trivial templated method) and also removes the inconsistency with the rest of eigen w.r.t. the method's naming scheme.
2014-06-05 02:44:22 +08:00
sym(epsilon, 0, 1, 2) = 1;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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()
{
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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++) {
unsupported/TensorSymmetry: factor out completely from Tensor module Remove the symCoeff() method of the the Tensor module and move the functionality into a new operator() of the symmetry classes. This makes the Tensor module now completely self-contained without symmetry support (even though previously it was only a forward declaration and a otherwise harmless trivial templated method) and also removes the inconsistency with the rest of eigen w.r.t. the method's naming scheme.
2014-06-05 02:44:22 +08:00
sym(t, i, j, k, l) = (i + j) * (k + l);
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
}
}
}
}
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()
{
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<AntiSymmetry<0,1>, AntiSymmetry<2,3>> sym;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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++) {
unsupported/TensorSymmetry: factor out completely from Tensor module Remove the symCoeff() method of the the Tensor module and move the functionality into a new operator() of the symmetry classes. This makes the Tensor module now completely self-contained without symmetry support (even though previously it was only a forward declaration and a otherwise harmless trivial templated method) and also removes the inconsistency with the rest of eigen w.r.t. the method's naming scheme.
2014-06-05 02:44:22 +08:00
sym(t, i, j, k, l) = ((i * j) + (k * l));
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
}
}
}
}
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()
{
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
DynamicSGroup sym;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
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++) {
unsupported/TensorSymmetry: factor out completely from Tensor module Remove the symCoeff() method of the the Tensor module and move the functionality into a new operator() of the symmetry classes. This makes the Tensor module now completely self-contained without symmetry support (even though previously it was only a forward declaration and a otherwise harmless trivial templated method) and also removes the inconsistency with the rest of eigen w.r.t. the method's naming scheme.
2014-06-05 02:44:22 +08:00
sym(t, i, j, k, l) = (i + j) * (k + l);
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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}
}
}
}
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()
{
unsupported/TensorSymmetry: make symgroup construction autodetect number of indices When constructing a symmetry group, make the code automatically detect the number of indices required from the indices of the group's generators. Also, allow the symmetry group to be applied to lists of indices that are larger than the number of indices of the symmetry group. Before: SGroup<4, Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); After: SGroup<Symmetry<0, 1>, Symmetry<2,3>> group; group.apply<SomeOp, int>(std::array<int,4>{{0, 1, 2, 3}}, 0); group.apply<SomeOp, int>(std::array<int,5>{{0, 1, 2, 3, 4}}, 0); This should make the symmetry group easier to use - especially if one wants to reuse the same symmetry group for different tensors of maybe different rank. static/runtime asserts remain for the case where the length of the index list to which a symmetry group is to be applied is too small.
2014-06-05 02:27:42 +08:00
SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
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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);
unsupported/TensorSymmetry: factor out completely from Tensor module Remove the symCoeff() method of the the Tensor module and move the functionality into a new operator() of the symmetry classes. This makes the Tensor module now completely self-contained without symmetry support (even though previously it was only a forward declaration and a otherwise harmless trivial templated method) and also removes the inconsistency with the rest of eigen w.r.t. the method's naming scheme.
2014-06-05 02:44:22 +08:00
sym(t, i, j, k, l) = (i + j) * (k + l);
CXX11/TensorSymmetry: add symmetry support for Tensor class Add a symCoeff() method to the Tensor class template that allows the user of the class to set multiple elements of a tensor at once if they are connected by a symmetry operation with respect to the tensor's indices (symmetry/antisymmetry/hermiticity/antihermiticity under echange of two indices and combination thereof for different pairs of indices). A compile-time resolution of the required symmetry groups via meta templates is also implemented. For small enough groups this is used to unroll the loop that goes through all the elements of the Tensor that are connected by this group. For larger groups or groups where the symmetries are defined at run time, a standard run-time implementation of the same algorithm is provided. For example, the following code completely initializes all elements of the totally antisymmetric tensor in three dimensions ('epsilon tensor'): SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym; Eigen::Tensor<double, 3> epsilon(3,3,3); epsilon.setZero(); epsilon.symCoeff(sym, 0, 1, 2) = 1;
2013-11-15 06:35:11 +08:00
}
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)));
}
}
}
}
}
void 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;
*/
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