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Diffstat (limited to 'third_party/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h')
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diff --git a/third_party/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h b/third_party/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h deleted file mode 100644 index 0fe0b7c46d..0000000000 --- a/third_party/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h +++ /dev/null @@ -1,666 +0,0 @@ -// 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; - */ |