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// 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/.
#ifndef EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
#define EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
namespace Eigen {
class DynamicSGroup
{
public:
inline explicit DynamicSGroup() : m_numIndices(1), m_elements(), m_generators(), m_globalFlags(0) { m_elements.push_back(ge(Generator(0, 0, 0))); }
inline DynamicSGroup(const DynamicSGroup& o) : m_numIndices(o.m_numIndices), m_elements(o.m_elements), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { }
inline DynamicSGroup(DynamicSGroup&& o) : m_numIndices(o.m_numIndices), m_elements(), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { std::swap(m_elements, o.m_elements); }
inline DynamicSGroup& operator=(const DynamicSGroup& o) { m_numIndices = o.m_numIndices; m_elements = o.m_elements; m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
inline DynamicSGroup& operator=(DynamicSGroup&& o) { m_numIndices = o.m_numIndices; std::swap(m_elements, o.m_elements); m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
void add(int one, int two, int flags = 0);
template<typename Gen_>
inline void add(Gen_) { add(Gen_::One, Gen_::Two, Gen_::Flags); }
inline void addSymmetry(int one, int two) { add(one, two, 0); }
inline void addAntiSymmetry(int one, int two) { add(one, two, NegationFlag); }
inline void addHermiticity(int one, int two) { add(one, two, ConjugationFlag); }
inline void addAntiHermiticity(int one, int two) { add(one, two, NegationFlag | ConjugationFlag); }
template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args) const
{
eigen_assert(N >= m_numIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
for (std::size_t i = 0; i < size(); i++)
initial = Op::run(h_permute(i, idx, typename internal::gen_numeric_list<int, N>::type()), m_elements[i].flags, initial, std::forward<Args>(args)...);
return initial;
}
template<typename Op, typename RV, typename Index, typename... Args>
inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args) const
{
eigen_assert(idx.size() >= m_numIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
for (std::size_t i = 0; i < size(); i++)
initial = Op::run(h_permute(i, idx), m_elements[i].flags, initial, std::forward<Args>(args)...);
return initial;
}
inline int globalFlags() const { return m_globalFlags; }
inline std::size_t size() const { return m_elements.size(); }
template<typename Tensor_, typename... IndexTypes>
inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const
{
static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices, "Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.");
return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});
}
template<typename Tensor_>
inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const
{
return internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup>(tensor, *this, indices);
}
private:
struct GroupElement {
std::vector<int> representation;
int flags;
bool isId() const
{
for (std::size_t i = 0; i < representation.size(); i++)
if (i != (size_t)representation[i])
return false;
return true;
}
};
struct Generator {
int one;
int two;
int flags;
constexpr inline Generator(int one_, int two_, int flags_) : one(one_), two(two_), flags(flags_) {}
};
std::size_t m_numIndices;
std::vector<GroupElement> m_elements;
std::vector<Generator> m_generators;
int m_globalFlags;
template<typename Index, std::size_t N, int... n>
inline std::array<Index, N> h_permute(std::size_t which, const std::array<Index, N>& idx, internal::numeric_list<int, n...>) const
{
return std::array<Index, N>{{ idx[n >= m_numIndices ? n : m_elements[which].representation[n]]... }};
}
template<typename Index>
inline std::vector<Index> h_permute(std::size_t which, std::vector<Index> idx) const
{
std::vector<Index> result;
result.reserve(idx.size());
for (auto k : m_elements[which].representation)
result.push_back(idx[k]);
for (std::size_t i = m_numIndices; i < idx.size(); i++)
result.push_back(idx[i]);
return result;
}
inline GroupElement ge(Generator const& g) const
{
GroupElement result;
result.representation.reserve(m_numIndices);
result.flags = g.flags;
for (std::size_t k = 0; k < m_numIndices; k++) {
if (k == (std::size_t)g.one)
result.representation.push_back(g.two);
else if (k == (std::size_t)g.two)
result.representation.push_back(g.one);
else
result.representation.push_back(int(k));
}
return result;
}
GroupElement mul(GroupElement, GroupElement) const;
inline GroupElement mul(Generator g1, GroupElement g2) const
{
return mul(ge(g1), g2);
}
inline GroupElement mul(GroupElement g1, Generator g2) const
{
return mul(g1, ge(g2));
}
inline GroupElement mul(Generator g1, Generator g2) const
{
return mul(ge(g1), ge(g2));
}
inline int findElement(GroupElement e) const
{
for (auto ee : m_elements) {
if (ee.representation == e.representation)
return ee.flags ^ e.flags;
}
return -1;
}
void updateGlobalFlags(int flagDiffOfSameGenerator);
};
// dynamic symmetry group that auto-adds the template parameters in the constructor
template<typename... Gen>
class DynamicSGroupFromTemplateArgs : public DynamicSGroup
{
public:
inline DynamicSGroupFromTemplateArgs() : DynamicSGroup()
{
add_all(internal::type_list<Gen...>());
}
inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs const& other) : DynamicSGroup(other) { }
inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs&& other) : DynamicSGroup(other) { }
inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(const DynamicSGroupFromTemplateArgs<Gen...>& o) { DynamicSGroup::operator=(o); return *this; }
inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(DynamicSGroupFromTemplateArgs<Gen...>&& o) { DynamicSGroup::operator=(o); return *this; }
private:
template<typename Gen1, typename... GenNext>
inline void add_all(internal::type_list<Gen1, GenNext...>)
{
add(Gen1());
add_all(internal::type_list<GenNext...>());
}
inline void add_all(internal::type_list<>)
{
}
};
inline DynamicSGroup::GroupElement DynamicSGroup::mul(GroupElement g1, GroupElement g2) const
{
eigen_internal_assert(g1.representation.size() == m_numIndices);
eigen_internal_assert(g2.representation.size() == m_numIndices);
GroupElement result;
result.representation.reserve(m_numIndices);
for (std::size_t i = 0; i < m_numIndices; i++) {
int v = g2.representation[g1.representation[i]];
eigen_assert(v >= 0);
result.representation.push_back(v);
}
result.flags = g1.flags ^ g2.flags;
return result;
}
inline void DynamicSGroup::add(int one, int two, int flags)
{
eigen_assert(one >= 0);
eigen_assert(two >= 0);
eigen_assert(one != two);
if ((std::size_t)one >= m_numIndices || (std::size_t)two >= m_numIndices) {
std::size_t newNumIndices = (one > two) ? one : two + 1;
for (auto& gelem : m_elements) {
gelem.representation.reserve(newNumIndices);
for (std::size_t i = m_numIndices; i < newNumIndices; i++)
gelem.representation.push_back(i);
}
m_numIndices = newNumIndices;
}
Generator g{one, two, flags};
GroupElement e = ge(g);
/* special case for first generator */
if (m_elements.size() == 1) {
while (!e.isId()) {
m_elements.push_back(e);
e = mul(e, g);
}
if (e.flags > 0)
updateGlobalFlags(e.flags);
// only add in case we didn't have identity
if (m_elements.size() > 1)
m_generators.push_back(g);
return;
}
int p = findElement(e);
if (p >= 0) {
updateGlobalFlags(p);
return;
}
std::size_t coset_order = m_elements.size();
m_elements.push_back(e);
for (std::size_t i = 1; i < coset_order; i++)
m_elements.push_back(mul(m_elements[i], e));
m_generators.push_back(g);
std::size_t coset_rep = coset_order;
do {
for (auto g : m_generators) {
e = mul(m_elements[coset_rep], g);
p = findElement(e);
if (p < 0) {
// element not yet in group
m_elements.push_back(e);
for (std::size_t i = 1; i < coset_order; i++)
m_elements.push_back(mul(m_elements[i], e));
} else if (p > 0) {
updateGlobalFlags(p);
}
}
coset_rep += coset_order;
} while (coset_rep < m_elements.size());
}
inline void DynamicSGroup::updateGlobalFlags(int flagDiffOfSameGenerator)
{
switch (flagDiffOfSameGenerator) {
case 0:
default:
// nothing happened
break;
case NegationFlag:
// every element is it's own negative => whole tensor is zero
m_globalFlags |= GlobalZeroFlag;
break;
case ConjugationFlag:
// every element is it's own conjugate => whole tensor is real
m_globalFlags |= GlobalRealFlag;
break;
case (NegationFlag | ConjugationFlag):
// every element is it's own negative conjugate => whole tensor is imaginary
m_globalFlags |= GlobalImagFlag;
break;
/* NOTE:
* since GlobalZeroFlag == GlobalRealFlag | GlobalImagFlag, if one generator
* causes the tensor to be real and the next one to be imaginary, this will
* trivially give the correct result
*/
}
}
} // end namespace Eigen
#endif // EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
/*
* kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
*/
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