DynamicSymmetry.h

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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
 
// IWYU pragma: private
#include "./InternalHeaderCheck.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
 
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