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Diffstat (limited to 'unsupported/Eigen/CXX11/src/TensorSymmetry')
4 files changed, 1533 insertions, 0 deletions
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h new file mode 100644 index 000000000..bc4f2025f --- /dev/null +++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h @@ -0,0 +1,293 @@ +// 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; + */ diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h new file mode 100644 index 000000000..942293bd7 --- /dev/null +++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h @@ -0,0 +1,236 @@ +// 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_STATICSYMMETRY_H +#define EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H + +namespace Eigen { + +namespace internal { + +template<typename list> struct tensor_static_symgroup_permutate; + +template<int... nn> +struct tensor_static_symgroup_permutate<numeric_list<int, nn...>> +{ + constexpr static std::size_t N = sizeof...(nn); + + template<typename T> + constexpr static inline std::array<T, N> run(const std::array<T, N>& indices) + { + return {{indices[nn]...}}; + } +}; + +template<typename indices_, int flags_> +struct tensor_static_symgroup_element +{ + typedef indices_ indices; + constexpr static int flags = flags_; +}; + +template<typename Gen, int N> +struct tensor_static_symgroup_element_ctor +{ + typedef tensor_static_symgroup_element< + typename gen_numeric_list_swapped_pair<int, N, Gen::One, Gen::Two>::type, + Gen::Flags + > type; +}; + +template<int N> +struct tensor_static_symgroup_identity_ctor +{ + typedef tensor_static_symgroup_element< + typename gen_numeric_list<int, N>::type, + 0 + > type; +}; + +template<typename iib> +struct tensor_static_symgroup_multiply_helper +{ + template<int... iia> + constexpr static inline numeric_list<int, get<iia, iib>::value...> helper(numeric_list<int, iia...>) { + return numeric_list<int, get<iia, iib>::value...>(); + } +}; + +template<typename A, typename B> +struct tensor_static_symgroup_multiply +{ + private: + typedef typename A::indices iia; + typedef typename B::indices iib; + constexpr static int ffa = A::flags; + constexpr static int ffb = B::flags; + + public: + static_assert(iia::count == iib::count, "Cannot multiply symmetry elements with different number of indices."); + + typedef tensor_static_symgroup_element< + decltype(tensor_static_symgroup_multiply_helper<iib>::helper(iia())), + ffa ^ ffb + > type; +}; + +template<typename A, typename B> +struct tensor_static_symgroup_equality +{ + typedef typename A::indices iia; + typedef typename B::indices iib; + constexpr static int ffa = A::flags; + constexpr static int ffb = B::flags; + static_assert(iia::count == iib::count, "Cannot compare symmetry elements with different number of indices."); + + constexpr static bool value = is_same<iia, iib>::value; + + private: + /* this should be zero if they are identical, or else the tensor + * will be forced to be pure real, pure imaginary or even pure zero + */ + constexpr static int flags_cmp_ = ffa ^ ffb; + + /* either they are not equal, then we don't care whether the flags + * match, or they are equal, and then we have to check + */ + constexpr static bool is_zero = value && flags_cmp_ == NegationFlag; + constexpr static bool is_real = value && flags_cmp_ == ConjugationFlag; + constexpr static bool is_imag = value && flags_cmp_ == (NegationFlag | ConjugationFlag); + + public: + constexpr static int global_flags = + (is_real ? GlobalRealFlag : 0) | + (is_imag ? GlobalImagFlag : 0) | + (is_zero ? GlobalZeroFlag : 0); +}; + +template<std::size_t NumIndices, typename... Gen> +struct tensor_static_symgroup +{ + typedef StaticSGroup<Gen...> type; + constexpr static std::size_t size = type::static_size; +}; + +template<typename Index, std::size_t N, int... ii, int... jj> +constexpr static inline std::array<Index, N> tensor_static_symgroup_index_permute(std::array<Index, N> idx, internal::numeric_list<int, ii...>, internal::numeric_list<int, jj...>) +{ + return {{ idx[ii]..., idx[jj]... }}; +} + +template<typename Index, int... ii> +static inline std::vector<Index> tensor_static_symgroup_index_permute(std::vector<Index> idx, internal::numeric_list<int, ii...>) +{ + std::vector<Index> result{{ idx[ii]... }}; + std::size_t target_size = idx.size(); + for (std::size_t i = result.size(); i < target_size; i++) + result.push_back(idx[i]); + return result; +} + +template<typename T> struct tensor_static_symgroup_do_apply; + +template<typename first, typename... next> +struct tensor_static_symgroup_do_apply<internal::type_list<first, next...>> +{ + template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args> + static inline RV run(const std::array<Index, NumIndices>& idx, RV initial, Args&&... args) + { + static_assert(NumIndices >= SGNumIndices, "Can only apply symmetry group to objects that have at least the required amount of indices."); + typedef typename internal::gen_numeric_list<int, NumIndices - SGNumIndices, SGNumIndices>::type remaining_indices; + initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices(), remaining_indices()), first::flags, initial, std::forward<Args>(args)...); + return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...); + } + + template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args> + static inline RV run(const std::vector<Index>& idx, RV initial, Args&&... args) + { + eigen_assert(idx.size() >= SGNumIndices && "Can only apply symmetry group to objects that have at least the required amount of indices."); + initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...); + return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...); + } +}; + +template<EIGEN_TPL_PP_SPEC_HACK_DEF(typename, empty)> +struct tensor_static_symgroup_do_apply<internal::type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>> +{ + template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args> + static inline RV run(const std::array<Index, NumIndices>&, RV initial, Args&&...) + { + // do nothing + return initial; + } + + template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args> + static inline RV run(const std::vector<Index>&, RV initial, Args&&...) + { + // do nothing + return initial; + } +}; + +} // end namespace internal + +template<typename... Gen> +class StaticSGroup +{ + constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value; + typedef internal::group_theory::enumerate_group_elements< + internal::tensor_static_symgroup_multiply, + internal::tensor_static_symgroup_equality, + typename internal::tensor_static_symgroup_identity_ctor<NumIndices>::type, + internal::type_list<typename internal::tensor_static_symgroup_element_ctor<Gen, NumIndices>::type...> + > group_elements; + typedef typename group_elements::type ge; + public: + constexpr inline StaticSGroup() {} + constexpr inline StaticSGroup(const StaticSGroup<Gen...>&) {} + constexpr inline StaticSGroup(StaticSGroup<Gen...>&&) {} + + template<typename Op, typename RV, typename Index, std::size_t N, typename... Args> + static inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args) + { + return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...); + } + + template<typename Op, typename RV, typename Index, typename... Args> + static inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args) + { + eigen_assert(idx.size() == NumIndices); + return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...); + } + + constexpr static std::size_t static_size = ge::count; + + constexpr static inline std::size_t size() { + return ge::count; + } + constexpr static inline int globalFlags() { return group_elements::global_flags; } + + template<typename Tensor_, typename... IndexTypes> + inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>> 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_, StaticSGroup<Gen...>> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const + { + return internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>(tensor, *this, indices); + } +}; + +} // end namespace Eigen + +#endif // EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H + +/* + * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle; + */ diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h new file mode 100644 index 000000000..879d6cd77 --- /dev/null +++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h @@ -0,0 +1,338 @@ +// 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_SYMMETRY_H +#define EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H + +namespace Eigen { + +enum { + NegationFlag = 0x01, + ConjugationFlag = 0x02 +}; + +enum { + GlobalRealFlag = 0x01, + GlobalImagFlag = 0x02, + GlobalZeroFlag = 0x03 +}; + +namespace internal { + +template<std::size_t NumIndices, typename... Sym> struct tensor_symmetry_pre_analysis; +template<std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup; +template<bool instantiate, std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup_if; +template<typename Tensor_> struct tensor_symmetry_calculate_flags; +template<typename Tensor_> struct tensor_symmetry_assign_value; +template<typename... Sym> struct tensor_symmetry_num_indices; + +} // end namespace internal + +template<int One_, int Two_> +struct Symmetry +{ + static_assert(One_ != Two_, "Symmetries must cover distinct indices."); + constexpr static int One = One_; + constexpr static int Two = Two_; + constexpr static int Flags = 0; +}; + +template<int One_, int Two_> +struct AntiSymmetry +{ + static_assert(One_ != Two_, "Symmetries must cover distinct indices."); + constexpr static int One = One_; + constexpr static int Two = Two_; + constexpr static int Flags = NegationFlag; +}; + +template<int One_, int Two_> +struct Hermiticity +{ + static_assert(One_ != Two_, "Symmetries must cover distinct indices."); + constexpr static int One = One_; + constexpr static int Two = Two_; + constexpr static int Flags = ConjugationFlag; +}; + +template<int One_, int Two_> +struct AntiHermiticity +{ + static_assert(One_ != Two_, "Symmetries must cover distinct indices."); + constexpr static int One = One_; + constexpr static int Two = Two_; + constexpr static int Flags = ConjugationFlag | NegationFlag; +}; + +/** \class DynamicSGroup + * \ingroup TensorSymmetry_Module + * + * \brief Dynamic symmetry group + * + * The %DynamicSGroup class represents a symmetry group that need not be known at + * compile time. It is useful if one wants to support arbitrary run-time defineable + * symmetries for tensors, but it is also instantiated if a symmetry group is defined + * at compile time that would be either too large for the compiler to reasonably + * generate (using templates to calculate this at compile time is very inefficient) + * or that the compiler could generate the group but that it wouldn't make sense to + * unroll the loop for setting coefficients anymore. + */ +class DynamicSGroup; + +/** \internal + * + * \class DynamicSGroupFromTemplateArgs + * \ingroup TensorSymmetry_Module + * + * \brief Dynamic symmetry group, initialized from template arguments + * + * This class is a child class of DynamicSGroup. It uses the template arguments + * specified to initialize itself. + */ +template<typename... Gen> +class DynamicSGroupFromTemplateArgs; + +/** \class StaticSGroup + * \ingroup TensorSymmetry_Module + * + * \brief Static symmetry group + * + * This class represents a symmetry group that is known and resolved completely + * at compile time. Ideally, no run-time penalty is incurred compared to the + * manual unrolling of the symmetry. + * + * <b><i>CAUTION:</i></b> + * + * Do not use this class directly for large symmetry groups. The compiler + * may run into a limit, or segfault or in the very least will take a very, + * very, very long time to compile the code. Use the SGroup class instead + * if you want a static group. That class contains logic that will + * automatically select the DynamicSGroup class instead if the symmetry + * group becomes too large. (In that case, unrolling may not even be + * beneficial.) + */ +template<typename... Gen> +class StaticSGroup; + +/** \class SGroup + * \ingroup TensorSymmetry_Module + * + * \brief Symmetry group, initialized from template arguments + * + * This class represents a symmetry group whose generators are already + * known at compile time. It may or may not be resolved at compile time, + * depending on the estimated size of the group. + * + * \sa StaticSGroup + * \sa DynamicSGroup + */ +template<typename... Gen> +class SGroup : public internal::tensor_symmetry_pre_analysis<internal::tensor_symmetry_num_indices<Gen...>::value, Gen...>::root_type +{ + public: + constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value; + typedef typename internal::tensor_symmetry_pre_analysis<NumIndices, Gen...>::root_type Base; + + // make standard constructors + assignment operators public + inline SGroup() : Base() { } + inline SGroup(const SGroup<Gen...>& other) : Base(other) { } + inline SGroup(SGroup<Gen...>&& other) : Base(other) { } + inline SGroup<Gen...>& operator=(const SGroup<Gen...>& other) { Base::operator=(other); return *this; } + inline SGroup<Gen...>& operator=(SGroup<Gen...>&& other) { Base::operator=(other); return *this; } + + // all else is defined in the base class +}; + +namespace internal { + +template<typename... Sym> struct tensor_symmetry_num_indices +{ + constexpr static std::size_t value = 1; +}; + +template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> +{ +private: + constexpr static std::size_t One = static_cast<std::size_t>(One_); + constexpr static std::size_t Two = static_cast<std::size_t>(Two_); + constexpr static std::size_t Three = tensor_symmetry_num_indices<Sym...>::value; + + // don't use std::max, since it's not constexpr until C++14... + constexpr static std::size_t maxOneTwoPlusOne = ((One > Two) ? One : Two) + 1; +public: + constexpr static std::size_t value = (maxOneTwoPlusOne > Three) ? maxOneTwoPlusOne : Three; +}; + +template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiSymmetry<One_, Two_>, Sym...> + : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {}; +template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Hermiticity<One_, Two_>, Sym...> + : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {}; +template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiHermiticity<One_, Two_>, Sym...> + : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {}; + +/** \internal + * + * \class tensor_symmetry_pre_analysis + * \ingroup TensorSymmetry_Module + * + * \brief Pre-select whether to use a static or dynamic symmetry group + * + * When a symmetry group could in principle be determined at compile time, + * this template implements the logic whether to actually do that or whether + * to rather defer that to runtime. + * + * The logic is as follows: + * <dl> + * <dt><b>No generators (trivial symmetry):</b></dt> + * <dd>Use a trivial static group. Ideally, this has no performance impact + * compared to not using symmetry at all. In practice, this might not + * be the case.</dd> + * <dt><b>More than 4 generators:</b></dt> + * <dd>Calculate the group at run time, it is likely far too large for the + * compiler to be able to properly generate it in a realistic time.</dd> + * <dt><b>Up to and including 4 generators:</b></dt> + * <dd>Actually enumerate all group elements, but then check how many there + * are. If there are more than 16, it is unlikely that unrolling the + * loop (as is done in the static compile-time case) is sensible, so + * use a dynamic group instead. If there are at most 16 elements, actually + * use that static group. Note that the largest group with 4 generators + * still compiles with reasonable resources.</dd> + * </dl> + * + * Note: Example compile time performance with g++-4.6 on an Intenl Core i5-3470 + * with 16 GiB RAM (all generators non-redundant and the subgroups don't + * factorize): + * + * # Generators -O0 -ggdb -O2 + * ------------------------------------------------------------------- + * 1 0.5 s / 250 MiB 0.45s / 230 MiB + * 2 0.5 s / 260 MiB 0.5 s / 250 MiB + * 3 0.65s / 310 MiB 0.62s / 310 MiB + * 4 2.2 s / 860 MiB 1.7 s / 770 MiB + * 5 130 s / 13000 MiB 120 s / 11000 MiB + * + * It is clear that everything is still very efficient up to 4 generators, then + * the memory and CPU requirements become unreasonable. Thus we only instantiate + * the template group theory logic if the number of generators supplied is 4 or + * lower, otherwise this will be forced to be done during runtime, where the + * algorithm is reasonably fast. + */ +template<std::size_t NumIndices> +struct tensor_symmetry_pre_analysis<NumIndices> +{ + typedef StaticSGroup<> root_type; +}; + +template<std::size_t NumIndices, typename Gen_, typename... Gens_> +struct tensor_symmetry_pre_analysis<NumIndices, Gen_, Gens_...> +{ + constexpr static std::size_t max_static_generators = 4; + constexpr static std::size_t max_static_elements = 16; + typedef tensor_static_symgroup_if<(sizeof...(Gens_) + 1 <= max_static_generators), NumIndices, Gen_, Gens_...> helper; + constexpr static std::size_t possible_size = helper::size; + + typedef typename conditional< + possible_size == 0 || possible_size >= max_static_elements, + DynamicSGroupFromTemplateArgs<Gen_, Gens_...>, + typename helper::type + >::type root_type; +}; + +template<bool instantiate, std::size_t NumIndices, typename... Gens> +struct tensor_static_symgroup_if +{ + constexpr static std::size_t size = 0; + typedef void type; +}; + +template<std::size_t NumIndices, typename... Gens> +struct tensor_static_symgroup_if<true, NumIndices, Gens...> : tensor_static_symgroup<NumIndices, Gens...> {}; + +template<typename Tensor_> +struct tensor_symmetry_assign_value +{ + typedef typename Tensor_::Index Index; + typedef typename Tensor_::Scalar Scalar; + constexpr static std::size_t NumIndices = Tensor_::NumIndices; + + static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transformation_flags, int dummy, Tensor_& tensor, const Scalar& value_) + { + Scalar value(value_); + if (transformation_flags & ConjugationFlag) + value = numext::conj(value); + if (transformation_flags & NegationFlag) + value = -value; + tensor.coeffRef(transformed_indices) = value; + return dummy; + } +}; + +template<typename Tensor_> +struct tensor_symmetry_calculate_flags +{ + typedef typename Tensor_::Index Index; + constexpr static std::size_t NumIndices = Tensor_::NumIndices; + + static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transform_flags, int current_flags, const std::array<Index, NumIndices>& orig_indices) + { + if (transformed_indices == orig_indices) { + if (transform_flags & (ConjugationFlag | NegationFlag)) + return current_flags | GlobalImagFlag; // anti-hermitian diagonal + else if (transform_flags & ConjugationFlag) + return current_flags | GlobalRealFlag; // hermitian diagonal + else if (transform_flags & NegationFlag) + return current_flags | GlobalZeroFlag; // anti-symmetric diagonal + } + return current_flags; + } +}; + +template<typename Tensor_, typename Symmetry_, int Flags = 0> +class tensor_symmetry_value_setter +{ + public: + typedef typename Tensor_::Index Index; + typedef typename Tensor_::Scalar Scalar; + constexpr static std::size_t NumIndices = Tensor_::NumIndices; + + inline tensor_symmetry_value_setter(Tensor_& tensor, Symmetry_ const& symmetry, std::array<Index, NumIndices> const& indices) + : m_tensor(tensor), m_symmetry(symmetry), m_indices(indices) { } + + inline tensor_symmetry_value_setter<Tensor_, Symmetry_, Flags>& operator=(Scalar const& value) + { + doAssign(value); + return *this; + } + private: + Tensor_& m_tensor; + Symmetry_ m_symmetry; + std::array<Index, NumIndices> m_indices; + + inline void doAssign(Scalar const& value) + { + #ifdef EIGEN_TENSOR_SYMMETRY_CHECK_VALUES + int value_flags = m_symmetry.template apply<internal::tensor_symmetry_calculate_flags<Tensor_>, int>(m_indices, m_symmetry.globalFlags(), m_indices); + if (value_flags & GlobalRealFlag) + eigen_assert(numext::imag(value) == 0); + if (value_flags & GlobalImagFlag) + eigen_assert(numext::real(value) == 0); + #endif + m_symmetry.template apply<internal::tensor_symmetry_assign_value<Tensor_>, int>(m_indices, 0, m_tensor, value); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H + +/* + * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle; + */ diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h new file mode 100644 index 000000000..0fe0b7c46 --- /dev/null +++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h @@ -0,0 +1,666 @@ +// 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_TEMPLATEGROUPTHEORY_H +#define EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H + +namespace Eigen { + +namespace internal { + +namespace group_theory { + +/** \internal + * \file CXX11/Tensor/util/TemplateGroupTheory.h + * This file contains C++ templates that implement group theory algorithms. + * + * The algorithms allow for a compile-time analysis of finite groups. + * + * Currently only Dimino's algorithm is implemented, which returns a list + * of all elements in a group given a set of (possibly redundant) generators. + * (One could also do that with the so-called orbital algorithm, but that + * is much more expensive and usually has no advantages.) + */ + +/********************************************************************** + * "Ok kid, here is where it gets complicated." + * - Amelia Pond in the "Doctor Who" episode + * "The Big Bang" + * + * Dimino's algorithm + * ================== + * + * The following is Dimino's algorithm in sequential form: + * + * Input: identity element, list of generators, equality check, + * multiplication operation + * Output: list of group elements + * + * 1. add identity element + * 2. remove identities from list of generators + * 3. add all powers of first generator that aren't the + * identity element + * 4. go through all remaining generators: + * a. if generator is already in the list of elements + * -> do nothing + * b. otherwise + * i. remember current # of elements + * (i.e. the size of the current subgroup) + * ii. add all current elements (which includes + * the identity) each multiplied from right + * with the current generator to the group + * iii. add all remaining cosets that are generated + * by products of the new generator with itself + * and all other generators seen so far + * + * In functional form, this is implemented as a long set of recursive + * templates that have a complicated relationship. + * + * The main interface for Dimino's algorithm is the template + * enumerate_group_elements. All lists are implemented as variadic + * type_list<typename...> and numeric_list<typename = int, int...> + * templates. + * + * 'Calling' templates is usually done via typedefs. + * + * This algorithm is an extended version of the basic version. The + * extension consists in the fact that each group element has a set + * of flags associated with it. Multiplication of two group elements + * with each other results in a group element whose flags are the + * XOR of the flags of the previous elements. Each time the algorithm + * notices that a group element it just calculated is already in the + * list of current elements, the flags of both will be compared and + * added to the so-called 'global flags' of the group. + * + * The rationale behind this extension is that this allows not only + * for the description of symmetries between tensor indices, but + * also allows for the description of hermiticity, antisymmetry and + * antihermiticity. Negation and conjugation each are specific bit + * in the flags value and if two different ways to reach a group + * element lead to two different flags, this poses a constraint on + * the allowed values of the resulting tensor. For example, if a + * group element is reach both with and without the conjugation + * flags, it is clear that the resulting tensor has to be real. + * + * Note that this flag mechanism is quite generic and may have other + * uses beyond tensor properties. + * + * IMPORTANT: + * This algorithm assumes the group to be finite. If you try to + * run it with a group that's infinite, the algorithm will only + * terminate once you hit a compiler limit (max template depth). + * Also note that trying to use this implementation to create a + * very large group will probably either make you hit the same + * limit, cause the compiler to segfault or at the very least + * take a *really* long time (hours, days, weeks - sic!) to + * compile. It is not recommended to plug in more than 4 + * generators, unless they are independent of each other. + */ + +/** \internal + * + * \class strip_identities + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Cleanse a list of group elements of the identity element + * + * This template is used to make a first pass through all initial + * generators of Dimino's algorithm and remove the identity + * elements. + * + * \sa enumerate_group_elements + */ +template<template<typename, typename> class Equality, typename id, typename L> struct strip_identities; + +template< + template<typename, typename> class Equality, + typename id, + typename t, + typename... ts +> +struct strip_identities<Equality, id, type_list<t, ts...>> +{ + typedef typename conditional< + Equality<id, t>::value, + typename strip_identities<Equality, id, type_list<ts...>>::type, + typename concat<type_list<t>, typename strip_identities<Equality, id, type_list<ts...>>::type>::type + >::type type; + constexpr static int global_flags = Equality<id, t>::global_flags | strip_identities<Equality, id, type_list<ts...>>::global_flags; +}; + +template< + template<typename, typename> class Equality, + typename id + EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, ts) +> +struct strip_identities<Equality, id, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(ts)>> +{ + typedef type_list<> type; + constexpr static int global_flags = 0; +}; + +/** \internal + * + * \class dimino_first_step_elements_helper + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Recursive template that adds powers of the first generator to the list of group elements + * + * This template calls itself recursively to add powers of the first + * generator to the list of group elements. It stops if it reaches + * the identity element again. + * + * \sa enumerate_group_elements, dimino_first_step_elements + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename g, + typename current_element, + typename elements, + bool dont_add_current_element // = false +> +struct dimino_first_step_elements_helper : + public dimino_first_step_elements_helper< + Multiply, + Equality, + id, + g, + typename Multiply<current_element, g>::type, + typename concat<elements, type_list<current_element>>::type, + Equality<typename Multiply<current_element, g>::type, id>::value + > {}; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename g, + typename current_element, + typename elements +> +struct dimino_first_step_elements_helper<Multiply, Equality, id, g, current_element, elements, true> +{ + typedef elements type; + constexpr static int global_flags = Equality<current_element, id>::global_flags; +}; + +/** \internal + * + * \class dimino_first_step_elements + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Add all powers of the first generator to the list of group elements + * + * This template takes the first non-identity generator and generates the initial + * list of elements which consists of all powers of that generator. For a group + * with just one generated, it would be enumerated after this. + * + * \sa enumerate_group_elements + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename generators +> +struct dimino_first_step_elements +{ + typedef typename get<0, generators>::type first_generator; + typedef typename skip<1, generators>::type next_generators; + typedef type_list<first_generator> generators_done; + + typedef dimino_first_step_elements_helper< + Multiply, + Equality, + id, + first_generator, + first_generator, + type_list<id>, + false + > helper; + typedef typename helper::type type; + constexpr static int global_flags = helper::global_flags; +}; + +/** \internal + * + * \class dimino_get_coset_elements + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Generate all elements of a specific coset + * + * This template generates all the elements of a specific coset by + * multiplying all elements in the given subgroup with the new + * coset representative. Note that the first element of the + * subgroup is always the identity element, so the first element of + * ther result of this template is going to be the coset + * representative itself. + * + * Note that this template accepts an additional boolean parameter + * that specifies whether to actually generate the coset (true) or + * just return an empty list (false). + * + * \sa enumerate_group_elements, dimino_add_cosets_for_rep + */ +template< + template<typename, typename> class Multiply, + typename sub_group_elements, + typename new_coset_rep, + bool generate_coset // = true +> +struct dimino_get_coset_elements +{ + typedef typename apply_op_from_right<Multiply, new_coset_rep, sub_group_elements>::type type; +}; + +template< + template<typename, typename> class Multiply, + typename sub_group_elements, + typename new_coset_rep +> +struct dimino_get_coset_elements<Multiply, sub_group_elements, new_coset_rep, false> +{ + typedef type_list<> type; +}; + +/** \internal + * + * \class dimino_add_cosets_for_rep + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Recursive template for adding coset spaces + * + * This template multiplies the coset representative with a generator + * from the list of previous generators. If the new element is not in + * the group already, it adds the corresponding coset. Finally it + * proceeds to call itself with the next generator from the list. + * + * \sa enumerate_group_elements, dimino_add_all_coset_spaces + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename sub_group_elements, + typename elements, + typename generators, + typename rep_element, + int sub_group_size +> +struct dimino_add_cosets_for_rep; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename sub_group_elements, + typename elements, + typename g, + typename... gs, + typename rep_element, + int sub_group_size +> +struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<g, gs...>, rep_element, sub_group_size> +{ + typedef typename Multiply<rep_element, g>::type new_coset_rep; + typedef contained_in_list_gf<Equality, new_coset_rep, elements> _cil; + constexpr static bool add_coset = !_cil::value; + + typedef typename dimino_get_coset_elements< + Multiply, + sub_group_elements, + new_coset_rep, + add_coset + >::type coset_elements; + + typedef dimino_add_cosets_for_rep< + Multiply, + Equality, + id, + sub_group_elements, + typename concat<elements, coset_elements>::type, + type_list<gs...>, + rep_element, + sub_group_size + > _helper; + + typedef typename _helper::type type; + constexpr static int global_flags = _cil::global_flags | _helper::global_flags; + + /* Note that we don't have to update global flags here, since + * we will only add these elements if they are not part of + * the group already. But that only happens if the coset rep + * is not already in the group, so the check for the coset rep + * will catch this. + */ +}; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename sub_group_elements, + typename elements + EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty), + typename rep_element, + int sub_group_size +> +struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, rep_element, sub_group_size> +{ + typedef elements type; + constexpr static int global_flags = 0; +}; + +/** \internal + * + * \class dimino_add_all_coset_spaces + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Recursive template for adding all coset spaces for a new generator + * + * This template tries to go through the list of generators (with + * the help of the dimino_add_cosets_for_rep template) as long as + * it still finds elements that are not part of the group and add + * the corresponding cosets. + * + * \sa enumerate_group_elements, dimino_add_cosets_for_rep + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename sub_group_elements, + typename elements, + typename generators, + int sub_group_size, + int rep_pos, + bool stop_condition // = false +> +struct dimino_add_all_coset_spaces +{ + typedef typename get<rep_pos, elements>::type rep_element; + typedef dimino_add_cosets_for_rep< + Multiply, + Equality, + id, + sub_group_elements, + elements, + generators, + rep_element, + sub_group_elements::count + > _ac4r; + typedef typename _ac4r::type new_elements; + + constexpr static int new_rep_pos = rep_pos + sub_group_elements::count; + constexpr static bool new_stop_condition = new_rep_pos >= new_elements::count; + + typedef dimino_add_all_coset_spaces< + Multiply, + Equality, + id, + sub_group_elements, + new_elements, + generators, + sub_group_size, + new_rep_pos, + new_stop_condition + > _helper; + + typedef typename _helper::type type; + constexpr static int global_flags = _helper::global_flags | _ac4r::global_flags; +}; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename sub_group_elements, + typename elements, + typename generators, + int sub_group_size, + int rep_pos +> +struct dimino_add_all_coset_spaces<Multiply, Equality, id, sub_group_elements, elements, generators, sub_group_size, rep_pos, true> +{ + typedef elements type; + constexpr static int global_flags = 0; +}; + +/** \internal + * + * \class dimino_add_generator + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Enlarge the group by adding a new generator. + * + * It accepts a boolean parameter that determines if the generator is redundant, + * i.e. was already seen in the group. In that case, it reduces to a no-op. + * + * \sa enumerate_group_elements, dimino_add_all_coset_spaces + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename elements, + typename generators_done, + typename current_generator, + bool redundant // = false +> +struct dimino_add_generator +{ + /* this template is only called if the generator is not redundant + * => all elements of the group multiplied with the new generator + * are going to be new elements of the most trivial coset space + */ + typedef typename apply_op_from_right<Multiply, current_generator, elements>::type multiplied_elements; + typedef typename concat<elements, multiplied_elements>::type new_elements; + + constexpr static int rep_pos = elements::count; + + typedef dimino_add_all_coset_spaces< + Multiply, + Equality, + id, + elements, // elements of previous subgroup + new_elements, + typename concat<generators_done, type_list<current_generator>>::type, + elements::count, // size of previous subgroup + rep_pos, + false // don't stop (because rep_pos >= new_elements::count is always false at this point) + > _helper; + typedef typename _helper::type type; + constexpr static int global_flags = _helper::global_flags; +}; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename elements, + typename generators_done, + typename current_generator +> +struct dimino_add_generator<Multiply, Equality, id, elements, generators_done, current_generator, true> +{ + // redundant case + typedef elements type; + constexpr static int global_flags = 0; +}; + +/** \internal + * + * \class dimino_add_remaining_generators + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Recursive template that adds all remaining generators to a group + * + * Loop through the list of generators that remain and successively + * add them to the group. + * + * \sa enumerate_group_elements, dimino_add_generator + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename generators_done, + typename remaining_generators, + typename elements +> +struct dimino_add_remaining_generators +{ + typedef typename get<0, remaining_generators>::type first_generator; + typedef typename skip<1, remaining_generators>::type next_generators; + + typedef contained_in_list_gf<Equality, first_generator, elements> _cil; + + typedef dimino_add_generator< + Multiply, + Equality, + id, + elements, + generators_done, + first_generator, + _cil::value + > _helper; + + typedef typename _helper::type new_elements; + + typedef dimino_add_remaining_generators< + Multiply, + Equality, + id, + typename concat<generators_done, type_list<first_generator>>::type, + next_generators, + new_elements + > _next_iter; + + typedef typename _next_iter::type type; + constexpr static int global_flags = + _cil::global_flags | + _helper::global_flags | + _next_iter::global_flags; +}; + +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename generators_done, + typename elements +> +struct dimino_add_remaining_generators<Multiply, Equality, id, generators_done, type_list<>, elements> +{ + typedef elements type; + constexpr static int global_flags = 0; +}; + +/** \internal + * + * \class enumerate_group_elements_noid + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Helper template that implements group element enumeration + * + * This is a helper template that implements the actual enumeration + * of group elements. This has been split so that the list of + * generators can be cleansed of the identity element before + * performing the actual operation. + * + * \sa enumerate_group_elements + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename generators, + int initial_global_flags = 0 +> +struct enumerate_group_elements_noid +{ + typedef dimino_first_step_elements<Multiply, Equality, id, generators> first_step; + typedef typename first_step::type first_step_elements; + + typedef dimino_add_remaining_generators< + Multiply, + Equality, + id, + typename first_step::generators_done, + typename first_step::next_generators, // remaining_generators + typename first_step::type // first_step elements + > _helper; + + typedef typename _helper::type type; + constexpr static int global_flags = + initial_global_flags | + first_step::global_flags | + _helper::global_flags; +}; + +// in case when no generators are specified +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + int initial_global_flags +> +struct enumerate_group_elements_noid<Multiply, Equality, id, type_list<>, initial_global_flags> +{ + typedef type_list<id> type; + constexpr static int global_flags = initial_global_flags; +}; + +/** \internal + * + * \class enumerate_group_elements + * \ingroup CXX11_TensorSymmetry_Module + * + * \brief Enumerate all elements in a finite group + * + * This template enumerates all elements in a finite group. It accepts + * the following template parameters: + * + * \tparam Multiply The multiplication operation that multiplies two group elements + * with each other. + * \tparam Equality The equality check operation that checks if two group elements + * are equal to another. + * \tparam id The identity element + * \tparam _generators A list of (possibly redundant) generators of the group + */ +template< + template<typename, typename> class Multiply, + template<typename, typename> class Equality, + typename id, + typename _generators +> +struct enumerate_group_elements + : public enumerate_group_elements_noid< + Multiply, + Equality, + id, + typename strip_identities<Equality, id, _generators>::type, + strip_identities<Equality, id, _generators>::global_flags + > +{ +}; + +} // end namespace group_theory + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H + +/* + * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle; + */ |