SpECTRE Documentation Coverage Report
Current view: top level - DataStructures - Variables.hpp Hit Total Coverage
Commit: 9f349d3c09e1c03107f00c2135ca40e209d3b84c Lines: 33 113 29.2 %
Date: 2023-06-09 21:05:06
Legend: Lines: hit not hit

          Line data    Source code
       1           1 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : /// \file
       5             : /// Defines class Variables
       6             : 
       7             : #pragma once
       8             : 
       9             : #include <algorithm>
      10             : #include <array>
      11             : #include <blaze/math/AlignmentFlag.h>
      12             : #include <blaze/math/CustomVector.h>
      13             : #include <blaze/math/DenseVector.h>
      14             : #include <blaze/math/GroupTag.h>
      15             : #include <blaze/math/PaddingFlag.h>
      16             : #include <blaze/math/TransposeFlag.h>
      17             : #include <blaze/math/Vector.h>
      18             : #include <limits>
      19             : #include <memory>
      20             : #include <ostream>
      21             : #include <pup.h>
      22             : #include <string>
      23             : #include <tuple>
      24             : 
      25             : #include "DataStructures/DataBox/PrefixHelpers.hpp"
      26             : #include "DataStructures/DataBox/Subitems.hpp"
      27             : #include "DataStructures/DataBox/Tag.hpp"
      28             : #include "DataStructures/DataBox/TagName.hpp"
      29             : #include "DataStructures/DataBox/TagTraits.hpp"
      30             : #include "DataStructures/DataVector.hpp"
      31             : #include "DataStructures/MathWrapper.hpp"
      32             : #include "DataStructures/Tensor/IndexType.hpp"
      33             : #include "DataStructures/Tensor/Tensor.hpp"
      34             : #include "Utilities/EqualWithinRoundoff.hpp"
      35             : #include "Utilities/ErrorHandling/Assert.hpp"
      36             : #include "Utilities/ForceInline.hpp"
      37             : #include "Utilities/Gsl.hpp"
      38             : #include "Utilities/Literals.hpp"
      39             : #include "Utilities/MakeSignalingNan.hpp"
      40             : #include "Utilities/MemoryHelpers.hpp"
      41             : #include "Utilities/PrettyType.hpp"
      42             : #include "Utilities/Requires.hpp"
      43             : #include "Utilities/TMPL.hpp"
      44             : #include "Utilities/TaggedTuple.hpp"
      45             : #include "Utilities/TypeTraits.hpp"
      46             : #include "Utilities/TypeTraits/IsA.hpp"
      47             : 
      48             : // IWYU pragma: no_forward_declare MakeWithValueImpl
      49             : // IWYU pragma: no_forward_declare Variables
      50             : 
      51             : /// \cond
      52             : template <typename X, typename Symm, typename IndexList>
      53             : class Tensor;
      54             : template <typename TagsList>
      55             : class Variables;
      56             : template <typename T, typename VectorType, size_t StaticSize>
      57             : class VectorImpl;
      58             : namespace Tags {
      59             : template <typename TagsList>
      60             : class Variables;
      61             : }  // namespace Tags
      62             : /// \endcond
      63             : 
      64             : /*!
      65             :  * \ingroup DataStructuresGroup
      66             :  * \brief A Variables holds a contiguous memory block with Tensors pointing
      67             :  * into it.
      68             :  *
      69             :  * The `Tags` are `struct`s that must have a public type alias `type` whose
      70             :  * value must be a `Tensor<DataVector, ...>`, a `static' method `name()` that
      71             :  * returns a `std::string` of the tag name, and must derive off of
      72             :  * `db::SimpleTag`. In general, they should be DataBoxTags that are not compute
      73             :  * items. For example,
      74             :  *
      75             :  * \snippet Helpers/DataStructures/TestTags.hpp simple_variables_tag
      76             :  *
      77             :  * Prefix tags can also be stored and their format is:
      78             :  *
      79             :  * \snippet Helpers/DataStructures/TestTags.hpp prefix_variables_tag
      80             :  *
      81             :  * #### Design Decisions
      82             :  *
      83             :  * The `Variables` class is designed to hold several different `Tensor`s
      84             :  * performing one memory allocation for all the `Tensor`s. The advantage is that
      85             :  * memory allocations are quite expensive, especially in a parallel environment.
      86             :  *
      87             :  * In Debug mode, or if the macro `SPECTRE_NAN_INIT` is defined, the contents
      88             :  * are initialized with `NaN`s.
      89             :  *
      90             :  * `Variables` stores the data it owns in a `std::unique_ptr<double[]>`
      91             :  * instead of a `std::vector` because `std::vector` value-initializes its
      92             :  * contents, which is very slow.
      93             :  */
      94             : template <typename... Tags>
      95           1 : class Variables<tmpl::list<Tags...>> {
      96             :  public:
      97           0 :   using size_type = size_t;
      98           0 :   using difference_type = std::ptrdiff_t;
      99           0 :   static constexpr auto transpose_flag = blaze::defaultTransposeFlag;
     100             : 
     101             :   /// A typelist of the Tags whose variables are held
     102           1 :   using tags_list = tmpl::list<Tags...>;
     103             :   static_assert(sizeof...(Tags) > 0,
     104             :                 "You must provide at least one tag to the Variables "
     105             :                 "for type inference");
     106             :   static_assert((db::is_simple_tag_v<Tags> and ...));
     107             :   static_assert(tmpl2::flat_all_v<tt::is_a_v<Tensor, typename Tags::type>...>);
     108             : 
     109             :  private:
     110           0 :   using first_tensors_type = typename tmpl::front<tags_list>::type::type;
     111             : 
     112             :  public:
     113             :   static_assert(tmpl2::flat_all_v<std::is_same_v<typename Tags::type::type,
     114             :                                                  first_tensors_type>...> or
     115             :                     tmpl2::flat_all_v<is_spin_weighted_of_same_type_v<
     116             :                         typename Tags::type::type, first_tensors_type>...>,
     117             :                 "All tensors stored in a single Variables must "
     118             :                 "have the same internal storage type.");
     119             : 
     120           0 :   using vector_type =
     121             :       tmpl::conditional_t<is_any_spin_weighted_v<first_tensors_type>,
     122             :                           typename first_tensors_type::value_type,
     123             :                           first_tensors_type>;
     124           0 :   using value_type = typename vector_type::value_type;
     125           0 :   using pointer = value_type*;
     126           0 :   using const_pointer = const value_type*;
     127           0 :   using allocator_type = std::allocator<value_type>;
     128           0 :   using pointer_type =
     129             :       blaze::CustomVector<value_type, blaze::AlignmentFlag::unaligned,
     130             :                           blaze::PaddingFlag::unpadded, transpose_flag,
     131             :                           blaze::GroupTag<0>, vector_type>;
     132             : 
     133             :   static_assert(
     134             :       std::is_fundamental_v<value_type> or tt::is_a_v<std::complex, value_type>,
     135             :       "`value_type` of the Variables (so the storage type of the vector type "
     136             :       "within the tensors in the Variables) must be either a fundamental type "
     137             :       "or a std::complex. If this constraint is relaxed, the value_type "
     138             :       "should be handled differently in the Variables, including pass by "
     139             :       "reference.");
     140             : 
     141             :   /// The number of variables of the Variables object is holding. E.g.
     142             :   /// \f$\psi_{ab}\f$ would be counted as one variable.
     143           1 :   static constexpr auto number_of_variables = sizeof...(Tags);
     144             : 
     145             :   /// The total number of independent components of all the variables. E.g.
     146             :   /// a rank-2 symmetric spacetime Tensor \f$\psi_{ab}\f$ in 3 spatial
     147             :   /// dimensions would have 10 independent components.
     148           1 :   static constexpr size_t number_of_independent_components =
     149             :       (... + Tags::type::size());
     150             : 
     151             :   /// Default construct an empty Variables class, Charm++ needs this
     152           1 :   Variables();
     153             : 
     154           0 :   explicit Variables(size_t number_of_grid_points);
     155             : 
     156           0 :   Variables(size_t number_of_grid_points, value_type value);
     157             : 
     158             :   /// Construct a non-owning Variables that points to `start`. `size` is the
     159             :   /// size of the allocation, which must be
     160             :   /// `number_of_grid_points * Variables::number_of_independent_components`
     161           1 :   Variables(pointer start, size_t size);
     162             : 
     163           0 :   Variables(Variables&& rhs);
     164           0 :   Variables& operator=(Variables&& rhs);
     165             : 
     166           0 :   Variables(const Variables& rhs);
     167           0 :   Variables& operator=(const Variables& rhs);
     168             : 
     169             :   /// @{
     170             :   /// Copy and move semantics for wrapped variables
     171             :   template <typename... WrappedTags,
     172             :             Requires<tmpl2::flat_all<std::is_same<
     173             :                 db::remove_all_prefixes<WrappedTags>,
     174             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     175           1 :   explicit Variables(Variables<tmpl::list<WrappedTags...>>&& rhs);
     176             :   template <typename... WrappedTags,
     177             :             Requires<tmpl2::flat_all<std::is_same<
     178             :                 db::remove_all_prefixes<WrappedTags>,
     179             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     180           1 :   Variables& operator=(Variables<tmpl::list<WrappedTags...>>&& rhs);
     181             : 
     182             :   template <typename... WrappedTags,
     183             :             Requires<tmpl2::flat_all<std::is_same<
     184             :                 db::remove_all_prefixes<WrappedTags>,
     185             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     186           1 :   explicit Variables(const Variables<tmpl::list<WrappedTags...>>& rhs);
     187             :   template <typename... WrappedTags,
     188             :             Requires<tmpl2::flat_all<std::is_same<
     189             :                 db::remove_all_prefixes<WrappedTags>,
     190             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     191           1 :   Variables& operator=(const Variables<tmpl::list<WrappedTags...>>& rhs);
     192             :   /// @}
     193             : 
     194             :   /// \cond HIDDEN_SYMBOLS
     195             :   ~Variables() = default;
     196             :   /// \endcond
     197             : 
     198             :   /// @{
     199             :   /// Initialize a Variables to the state it would have after calling
     200             :   /// the constructor with the same arguments.
     201             :   // this should be updated if we ever use a variables which has a `value_type`
     202             :   // larger than ~2 doubles in size.
     203           1 :   void initialize(size_t number_of_grid_points);
     204           1 :   void initialize(size_t number_of_grid_points, value_type value);
     205             :   /// @}
     206             : 
     207             :   /// @{
     208             :   /// Set the VectorImpl to be a reference to another VectorImpl object
     209           1 :   void set_data_ref(const gsl::not_null<Variables*> rhs) {
     210             :     set_data_ref(rhs->data(), rhs->size());
     211             :   }
     212             : 
     213           1 :   void set_data_ref(pointer const start, const size_t size) {
     214             :     variable_data_impl_dynamic_.reset();
     215             :     if (start == nullptr) {
     216             :       variable_data_ = pointer_type{};
     217             :       size_ = 0;
     218             :       number_of_grid_points_ = 0;
     219             :     } else {
     220             :       size_ = size;
     221             :       variable_data_.reset(start, size_);
     222             :       ASSERT(
     223             :           size_ % number_of_independent_components == 0,
     224             :           "The size (" << size_
     225             :                        << ") must be a multiple of the number of independent "
     226             :                           "components ("
     227             :                        << number_of_independent_components
     228             :                        << ") since we calculate the number of grid points from "
     229             :                           "the size and number of independent components.");
     230             :       number_of_grid_points_ = size_ / number_of_independent_components;
     231             :     }
     232             :     owning_ = false;
     233             :     add_reference_variable_data();
     234             :   }
     235             :   /// @}
     236             : 
     237           0 :   constexpr SPECTRE_ALWAYS_INLINE size_t number_of_grid_points() const {
     238             :     return number_of_grid_points_;
     239             :   }
     240             : 
     241             :   /// Number of grid points * number of independent components
     242           1 :   constexpr SPECTRE_ALWAYS_INLINE size_type size() const { return size_; }
     243             : 
     244             :   /// @{
     245             :   /// Access pointer to underlying data
     246           1 :   pointer data() { return variable_data_.data(); }
     247           1 :   const_pointer data() const { return variable_data_.data(); }
     248             :   /// @}
     249             : 
     250             :   /// \cond HIDDEN_SYMBOLS
     251             :   /// Needed because of limitations and inconsistency between compiler
     252             :   /// implementations of friend function templates with auto return type of
     253             :   /// class templates
     254             :   const auto& get_variable_data() const { return variable_data_; }
     255             :   /// \endcond
     256             : 
     257             :   /// Returns true if the class owns the data
     258           1 :   bool is_owning() const { return owning_; }
     259             : 
     260             :   // clang-tidy: redundant-declaration
     261             :   template <typename Tag, typename TagList>
     262           1 :   friend constexpr typename Tag::type& get(  // NOLINT
     263             :       Variables<TagList>& v);
     264             :   template <typename Tag, typename TagList>
     265           0 :   friend constexpr const typename Tag::type& get(  // NOLINT
     266             :       const Variables<TagList>& v);
     267             : 
     268             :   /// Serialization for Charm++.
     269             :   // NOLINTNEXTLINE(google-runtime-references)
     270           1 :   void pup(PUP::er& p);
     271             : 
     272             :   /// @{
     273             :   /// \brief Assign a subset of the `Tensor`s from another Variables or a
     274             :   /// tuples::TaggedTuple. Any tags that aren't in both containers are
     275             :   /// ignored.
     276             :   ///
     277             :   /// \note There is no need for an rvalue overload because we need to copy into
     278             :   /// the contiguous array anyway
     279             :   template <typename... SubsetOfTags>
     280           1 :   void assign_subset(const Variables<tmpl::list<SubsetOfTags...>>& vars) {
     281             :     EXPAND_PACK_LEFT_TO_RIGHT([this, &vars]() {
     282             :       if constexpr (tmpl::list_contains_v<tmpl::list<Tags...>, SubsetOfTags>) {
     283             :         get<SubsetOfTags>(*this) = get<SubsetOfTags>(vars);
     284             :       } else {
     285             :         (void)this;
     286             :         (void)vars;
     287             :       }
     288             :     }());
     289             :   }
     290             : 
     291             :   template <typename... SubsetOfTags>
     292           1 :   void assign_subset(const tuples::TaggedTuple<SubsetOfTags...>& vars) {
     293             :     EXPAND_PACK_LEFT_TO_RIGHT([this, &vars]() {
     294             :       if constexpr (tmpl::list_contains_v<tmpl::list<Tags...>, SubsetOfTags>) {
     295             :         get<SubsetOfTags>(*this) = get<SubsetOfTags>(vars);
     296             :       } else {
     297             :         (void)this;
     298             :         (void)vars;
     299             :       }
     300             :     }());
     301             :   }
     302             :   /// @}
     303             : 
     304             :   /// Create a Variables from a subset of the `Tensor`s in this
     305             :   /// Variables
     306             :   template <typename SubsetOfTags>
     307           1 :   Variables<SubsetOfTags> extract_subset() const {
     308             :     Variables<SubsetOfTags> sub_vars(number_of_grid_points());
     309             :     tmpl::for_each<SubsetOfTags>([&](const auto tag_v) {
     310             :       using tag = tmpl::type_from<decltype(tag_v)>;
     311             :       get<tag>(sub_vars) = get<tag>(*this);
     312             :     });
     313             :     return sub_vars;
     314             :   }
     315             : 
     316             :   /// Create a non-owning Variables referencing a subset of the
     317             :   /// `Tensor`s in this Variables.  The referenced tensors must be
     318             :   /// consecutive in this Variables's tags list.
     319             :   ///
     320             :   /// \warning As with other appearances of non-owning variables, this
     321             :   /// method can cast away constness.
     322             :   template <typename SubsetOfTags>
     323           1 :   Variables<SubsetOfTags> reference_subset() const {
     324             :     if constexpr (std::is_same_v<SubsetOfTags, tmpl::list<>>) {
     325             :       return {};
     326             :     } else {
     327             :       using subset_from_tags_list = tmpl::reverse_find<
     328             :           tmpl::find<
     329             :               tags_list,
     330             :               std::is_same<tmpl::_1, tmpl::pin<tmpl::front<SubsetOfTags>>>>,
     331             :           std::is_same<tmpl::_1, tmpl::pin<tmpl::back<SubsetOfTags>>>>;
     332             :       static_assert(std::is_same_v<subset_from_tags_list, SubsetOfTags>,
     333             :                     "Tags passed to reference_subset must be consecutive tags "
     334             :                     "in the original tags_list.");
     335             : 
     336             :       using preceeding_tags = tmpl::pop_back<tmpl::reverse_find<
     337             :           tags_list,
     338             :           std::is_same<tmpl::_1, tmpl::pin<tmpl::front<SubsetOfTags>>>>>;
     339             : 
     340             :       static constexpr auto count_components = [](auto... tags) {
     341             :         return (0_st + ... + tmpl::type_from<decltype(tags)>::type::size());
     342             :       };
     343             :       static constexpr size_t number_of_preceeding_components =
     344             :           tmpl::as_pack<preceeding_tags>(count_components);
     345             :       static constexpr size_t number_of_components_in_subset =
     346             :           tmpl::as_pack<SubsetOfTags>(count_components);
     347             : 
     348             :       return {const_cast<value_type*>(data()) +
     349             :                   number_of_grid_points() * number_of_preceeding_components,
     350             :               number_of_grid_points() * number_of_components_in_subset};
     351             :     }
     352             :   }
     353             : 
     354             :   /// Create a non-owning version of this Variables with different
     355             :   /// prefixes on the tensors.  Both sets of prefixes must have the
     356             :   /// same tensor types.
     357             :   ///
     358             :   /// \warning As with other appearances of non-owning variables, this
     359             :   /// method can cast away constness.
     360             :   template <typename WrappedVariables>
     361           1 :   WrappedVariables reference_with_different_prefixes() const {
     362             :     static_assert(
     363             :         tmpl::all<tmpl::transform<
     364             :             typename WrappedVariables::tags_list, tmpl::list<Tags...>,
     365             :             std::is_same<tmpl::bind<db::remove_all_prefixes, tmpl::_1>,
     366             :                          tmpl::bind<db::remove_all_prefixes, tmpl::_2>>>>::
     367             :             value,
     368             :         "Unprefixed tags do not match!");
     369             :     static_assert(
     370             :         tmpl::all<tmpl::transform<
     371             :             typename WrappedVariables::tags_list, tmpl::list<Tags...>,
     372             :             std::is_same<tmpl::bind<tmpl::type_from, tmpl::_1>,
     373             :                          tmpl::bind<tmpl::type_from, tmpl::_2>>>>::value,
     374             :         "Tensor types do not match!");
     375             :     return {const_cast<value_type*>(data()), size()};
     376             :   }
     377             : 
     378             :   /// Converting constructor for an expression to a Variables class
     379             :   // clang-tidy: mark as explicit (we want conversion to Variables)
     380             :   template <typename VT, bool VF>
     381           1 :   Variables(const blaze::DenseVector<VT, VF>& expression);  // NOLINT
     382             : 
     383             :   template <typename VT, bool VF>
     384           0 :   Variables& operator=(const blaze::DenseVector<VT, VF>& expression);
     385             : 
     386             :   // Prevent the previous two declarations from implicitly converting
     387             :   // DataVectors and similar to Variables.
     388             :   template <typename T, typename VectorType, size_t StaticSize>
     389           0 :   Variables(const VectorImpl<T, VectorType, StaticSize>&) = delete;
     390             :   template <typename T, typename VectorType, size_t StaticSize>
     391           0 :   Variables& operator=(const VectorImpl<T, VectorType, StaticSize>&) = delete;
     392             : 
     393             :   template <typename... WrappedTags,
     394             :             Requires<tmpl2::flat_all<std::is_same_v<
     395             :                 db::remove_all_prefixes<WrappedTags>,
     396             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     397           0 :   SPECTRE_ALWAYS_INLINE Variables& operator+=(
     398             :       const Variables<tmpl::list<WrappedTags...>>& rhs) {
     399             :     static_assert(
     400             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     401             :          ...),
     402             :         "Tensor types do not match!");
     403             :     variable_data_ += rhs.variable_data_;
     404             :     return *this;
     405             :   }
     406             :   template <typename VT, bool VF>
     407           0 :   SPECTRE_ALWAYS_INLINE Variables& operator+=(
     408             :       const blaze::Vector<VT, VF>& rhs) {
     409             :     variable_data_ += rhs;
     410             :     return *this;
     411             :   }
     412             : 
     413             :   template <typename... WrappedTags,
     414             :             Requires<tmpl2::flat_all<std::is_same_v<
     415             :                 db::remove_all_prefixes<WrappedTags>,
     416             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     417           0 :   SPECTRE_ALWAYS_INLINE Variables& operator-=(
     418             :       const Variables<tmpl::list<WrappedTags...>>& rhs) {
     419             :     static_assert(
     420             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     421             :          ...),
     422             :         "Tensor types do not match!");
     423             :     variable_data_ -= rhs.variable_data_;
     424             :     return *this;
     425             :   }
     426             :   template <typename VT, bool VF>
     427           0 :   SPECTRE_ALWAYS_INLINE Variables& operator-=(
     428             :       const blaze::Vector<VT, VF>& rhs) {
     429             :     variable_data_ -= rhs;
     430             :     return *this;
     431             :   }
     432             : 
     433           0 :   SPECTRE_ALWAYS_INLINE Variables& operator*=(const value_type& rhs) {
     434             :     variable_data_ *= rhs;
     435             :     return *this;
     436             :   }
     437             : 
     438           0 :   SPECTRE_ALWAYS_INLINE Variables& operator/=(const value_type& rhs) {
     439             :     variable_data_ /= rhs;
     440             :     return *this;
     441             :   }
     442             : 
     443             :   template <typename... WrappedTags,
     444             :             Requires<tmpl2::flat_all<std::is_same_v<
     445             :                 db::remove_all_prefixes<WrappedTags>,
     446             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     447           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     448             :       const Variables<tmpl::list<WrappedTags...>>& lhs, const Variables& rhs) {
     449             :     static_assert(
     450             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     451             :          ...),
     452             :         "Tensor types do not match!");
     453             :     return lhs.get_variable_data() + rhs.variable_data_;
     454             :   }
     455             :   template <typename VT, bool VF>
     456           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     457             :       const blaze::DenseVector<VT, VF>& lhs, const Variables& rhs) {
     458             :     return *lhs + rhs.variable_data_;
     459             :   }
     460             :   template <typename VT, bool VF>
     461           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     462             :       const Variables& lhs, const blaze::DenseVector<VT, VF>& rhs) {
     463             :     return lhs.variable_data_ + *rhs;
     464             :   }
     465             : 
     466             :   template <typename... WrappedTags,
     467             :             Requires<tmpl2::flat_all<std::is_same_v<
     468             :                 db::remove_all_prefixes<WrappedTags>,
     469             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     470           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     471             :       const Variables<tmpl::list<WrappedTags...>>& lhs, const Variables& rhs) {
     472             :     static_assert(
     473             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     474             :          ...),
     475             :         "Tensor types do not match!");
     476             :     return lhs.get_variable_data() - rhs.variable_data_;
     477             :   }
     478             :   template <typename VT, bool VF>
     479           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     480             :       const blaze::DenseVector<VT, VF>& lhs, const Variables& rhs) {
     481             :     return *lhs - rhs.variable_data_;
     482             :   }
     483             :   template <typename VT, bool VF>
     484           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     485             :       const Variables& lhs, const blaze::DenseVector<VT, VF>& rhs) {
     486             :     return lhs.variable_data_ - *rhs;
     487             :   }
     488             : 
     489           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator*(const Variables& lhs,
     490             :                                                         const value_type& rhs) {
     491             :     return lhs.variable_data_ * rhs;
     492             :   }
     493           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator*(const value_type& lhs,
     494             :                                                         const Variables& rhs) {
     495             :     return lhs * rhs.variable_data_;
     496             :   }
     497             : 
     498           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator/(const Variables& lhs,
     499             :                                                         const value_type& rhs) {
     500             :     return lhs.variable_data_ / rhs;
     501             :   }
     502             : 
     503           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(const Variables& lhs) {
     504             :     return -lhs.variable_data_;
     505             :   }
     506           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(const Variables& lhs) {
     507             :     return lhs.variable_data_;
     508             :   }
     509             : 
     510             :  private:
     511             :   /// @{
     512             :   /*!
     513             :    * \brief Subscript operator
     514             :    *
     515             :    * The subscript operator is private since it should not be used directly.
     516             :    * Mathematical operations should be done using the math operators provided.
     517             :    * Since the internal ordering of variables is implementation defined there
     518             :    * is no safe way to perform any operation that is not a linear combination of
     519             :    * Variables. Retrieving a Tensor must be done via the `get()` function.
     520             :    *
     521             :    *  \requires `i >= 0 and i < size()`
     522             :    */
     523           1 :   SPECTRE_ALWAYS_INLINE value_type& operator[](const size_type i) {
     524             :     return variable_data_[i];
     525             :   }
     526           1 :   SPECTRE_ALWAYS_INLINE const value_type& operator[](const size_type i) const {
     527             :     return variable_data_[i];
     528             :   }
     529             :   /// @}
     530             : 
     531           0 :   void add_reference_variable_data();
     532             : 
     533           0 :   friend bool operator==(const Variables& lhs, const Variables& rhs) {
     534             :     return blaze::equal<blaze::strict>(lhs.variable_data_, rhs.variable_data_);
     535             :   }
     536             : 
     537             :   template <typename VT, bool TF>
     538           0 :   friend bool operator==(const Variables& lhs,
     539             :                          const blaze::DenseVector<VT, TF>& rhs) {
     540             :     return blaze::equal<blaze::strict>(lhs.variable_data_, *rhs);
     541             :   }
     542             : 
     543             :   template <typename VT, bool TF>
     544           0 :   friend bool operator==(const blaze::DenseVector<VT, TF>& lhs,
     545             :                          const Variables& rhs) {
     546             :     return blaze::equal<blaze::strict>(*lhs, rhs.variable_data_);
     547             :   }
     548             : 
     549             :   template <class FriendTags>
     550           0 :   friend class Variables;
     551             : 
     552             :   std::array<value_type, number_of_independent_components>
     553           0 :       variable_data_impl_static_;
     554           0 :   std::unique_ptr<value_type[]> variable_data_impl_dynamic_{};
     555           0 :   bool owning_{true};
     556           0 :   size_t size_ = 0;
     557           0 :   size_t number_of_grid_points_ = 0;
     558             : 
     559           0 :   pointer_type variable_data_;
     560           0 :   tuples::TaggedTuple<Tags...> reference_variable_data_;
     561             : };
     562             : 
     563             : // The above Variables implementation doesn't work for an empty parameter pack,
     564             : // so specialize here.
     565             : template <>
     566           0 : class Variables<tmpl::list<>> {
     567             :  public:
     568           0 :   using tags_list = tmpl::list<>;
     569           0 :   static constexpr size_t number_of_independent_components = 0;
     570           0 :   Variables() = default;
     571           0 :   explicit Variables(const size_t /*number_of_grid_points*/) {}
     572             :   template <typename T>
     573           0 :   Variables(const T* /*pointer*/, const size_t /*size*/) {}
     574           0 :   static constexpr size_t size() { return 0; }
     575             : };
     576             : 
     577             : // gcc8 screams when the empty Variables has pup as a member function, so we
     578             : // declare pup as a free function here.
     579             : // clang-tidy: runtime-references
     580           0 : SPECTRE_ALWAYS_INLINE void pup(
     581             :     PUP::er& /*p*/,                           // NOLINT
     582             :     Variables<tmpl::list<>>& /* unused */) {  // NOLINT
     583             : }
     584           0 : SPECTRE_ALWAYS_INLINE void operator|(
     585             :     PUP::er& /*p*/, Variables<tmpl::list<>>& /* unused */) {  // NOLINT
     586             : }
     587             : 
     588           0 : SPECTRE_ALWAYS_INLINE bool operator==(const Variables<tmpl::list<>>& /*lhs*/,
     589             :                                       const Variables<tmpl::list<>>& /*rhs*/) {
     590             :   return true;
     591             : }
     592           0 : SPECTRE_ALWAYS_INLINE bool operator!=(const Variables<tmpl::list<>>& /*lhs*/,
     593             :                                       const Variables<tmpl::list<>>& /*rhs*/) {
     594             :   return false;
     595             : }
     596             : 
     597           0 : inline std::ostream& operator<<(std::ostream& os,
     598             :                                 const Variables<tmpl::list<>>& /*d*/) {
     599             :   return os << "{}";
     600             : }
     601             : 
     602             : template <typename... Tags>
     603             : Variables<tmpl::list<Tags...>>::Variables() {
     604             :   // This makes an assertion trigger if one tries to assign to
     605             :   // components of a default-constructed Variables.
     606             :   const auto set_refs = [](auto& var) {
     607             :     for (auto& dv : var) {
     608             :       dv.set_data_ref(nullptr, 0);
     609             :     }
     610             :     return 0;
     611             :   };
     612             :   (void)set_refs;
     613             :   expand_pack(set_refs(tuples::get<Tags>(reference_variable_data_))...);
     614             : }
     615             : 
     616             : template <typename... Tags>
     617             : Variables<tmpl::list<Tags...>>::Variables(const size_t number_of_grid_points) {
     618             :   initialize(number_of_grid_points);
     619             : }
     620             : 
     621             : template <typename... Tags>
     622             : Variables<tmpl::list<Tags...>>::Variables(const size_t number_of_grid_points,
     623             :                                           const value_type value) {
     624             :   initialize(number_of_grid_points, value);
     625             : }
     626             : 
     627             : template <typename... Tags>
     628             : void Variables<tmpl::list<Tags...>>::initialize(
     629             :     const size_t number_of_grid_points) {
     630             :   if (number_of_grid_points_ == 0) {
     631             :     variable_data_impl_dynamic_.reset();
     632             :     size_ = 0;
     633             :     number_of_grid_points_ = 0;
     634             :   }
     635             :   if (number_of_grid_points_ == number_of_grid_points) {
     636             :     return;
     637             :   }
     638             :   if (UNLIKELY(not is_owning())) {
     639             :     ERROR("Variables::initialize cannot be called on a non-owning Variables.  "
     640             :           "This likely happened because of an attempted resize.  The current "
     641             :           "number of grid points is " << number_of_grid_points_ << " and the "
     642             :           "requested number is " << number_of_grid_points << ".");
     643             :   }
     644             :   number_of_grid_points_ = number_of_grid_points;
     645             :   size_ = number_of_grid_points * number_of_independent_components;
     646             :   if (size_ > 0) {
     647             :     if (number_of_grid_points_ == 1) {
     648             :       variable_data_impl_dynamic_.reset();
     649             :     } else {
     650             :       variable_data_impl_dynamic_ =
     651             :           cpp20::make_unique_for_overwrite<value_type[]>(size_);
     652             :     }
     653             :     add_reference_variable_data();
     654             : #if defined(SPECTRE_DEBUG) || defined(SPECTRE_NAN_INIT)
     655             :     std::fill(variable_data_.data(), variable_data_.data() + size_,
     656             :               make_signaling_NaN<value_type>());
     657             : #endif  // SPECTRE_DEBUG
     658             :   }
     659             : }
     660             : 
     661             : template <typename... Tags>
     662             : void Variables<tmpl::list<Tags...>>::initialize(
     663             :     const size_t number_of_grid_points, const value_type value) {
     664             :   initialize(number_of_grid_points);
     665             :   std::fill(variable_data_.data(), variable_data_.data() + size_, value);
     666             : }
     667             : 
     668             : /// \cond HIDDEN_SYMBOLS
     669             : template <typename... Tags>
     670             : Variables<tmpl::list<Tags...>>::Variables(
     671             :     const Variables<tmpl::list<Tags...>>& rhs) {
     672             :   initialize(rhs.number_of_grid_points());
     673             :   variable_data_ =
     674             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     675             :           rhs.variable_data_);
     676             : }
     677             : 
     678             : template <typename... Tags>
     679             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     680             :     const Variables<tmpl::list<Tags...>>& rhs) {
     681             :   if (&rhs == this) {
     682             :     return *this;
     683             :   }
     684             :   initialize(rhs.number_of_grid_points());
     685             :   variable_data_ =
     686             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     687             :           rhs.variable_data_);
     688             :   return *this;
     689             : }
     690             : 
     691             : template <typename... Tags>
     692             : Variables<tmpl::list<Tags...>>::Variables(Variables<tmpl::list<Tags...>>&& rhs)
     693             :     : variable_data_impl_dynamic_(std::move(rhs.variable_data_impl_dynamic_)),
     694             :       owning_(rhs.owning_),
     695             :       size_(rhs.size()),
     696             :       number_of_grid_points_(rhs.number_of_grid_points()),
     697             :       variable_data_(std::move(rhs.variable_data_)) {
     698             :   if (number_of_grid_points_ == 1) {
     699             : #if defined(__GNUC__) and not defined(__clang__)
     700             : #pragma GCC diagnostic push
     701             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     702             : #endif  // defined(__GNUC__) and not defined(__clang__)
     703             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     704             : #if defined(__GNUC__) and not defined(__clang__)
     705             : #pragma GCC diagnostic pop
     706             : #endif  // defined(__GNUC__) and not defined(__clang__)
     707             :   }
     708             :   rhs.variable_data_impl_dynamic_.reset();
     709             :   rhs.owning_ = true;
     710             :   rhs.size_ = 0;
     711             :   rhs.number_of_grid_points_ = 0;
     712             :   add_reference_variable_data();
     713             : }
     714             : 
     715             : template <typename... Tags>
     716             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     717             :     Variables<tmpl::list<Tags...>>&& rhs) {
     718             :   if (this == &rhs) {
     719             :     return *this;
     720             :   }
     721             :   owning_ = rhs.owning_;
     722             :   size_ = rhs.size_;
     723             :   number_of_grid_points_ = std::move(rhs.number_of_grid_points_);
     724             :   variable_data_ = std::move(rhs.variable_data_);
     725             :   variable_data_impl_dynamic_ = std::move(rhs.variable_data_impl_dynamic_);
     726             :   if (number_of_grid_points_ == 1) {
     727             : #if defined(__GNUC__) and not defined(__clang__)
     728             : #pragma GCC diagnostic push
     729             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     730             : #endif  // defined(__GNUC__) and not defined(__clang__)
     731             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     732             : #if defined(__GNUC__) and not defined(__clang__)
     733             : #pragma GCC diagnostic pop
     734             : #endif  // defined(__GNUC__) and not defined(__clang__)
     735             :   }
     736             : 
     737             :   rhs.variable_data_impl_dynamic_.reset();
     738             :   rhs.owning_ = true;
     739             :   rhs.size_ = 0;
     740             :   rhs.number_of_grid_points_ = 0;
     741             :   add_reference_variable_data();
     742             :   return *this;
     743             : }
     744             : 
     745             : template <typename... Tags>
     746             : template <typename... WrappedTags,
     747             :           Requires<tmpl2::flat_all<
     748             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     749             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     750             : Variables<tmpl::list<Tags...>>::Variables(
     751             :     const Variables<tmpl::list<WrappedTags...>>& rhs) {
     752             :   static_assert(
     753             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     754             :       "Tensor types do not match!");
     755             :   initialize(rhs.number_of_grid_points());
     756             :   variable_data_ =
     757             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     758             :           rhs.variable_data_);
     759             : }
     760             : 
     761             : template <typename... Tags>
     762             : template <typename... WrappedTags,
     763             :           Requires<tmpl2::flat_all<
     764             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     765             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     766             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     767             :     const Variables<tmpl::list<WrappedTags...>>& rhs) {
     768             :   static_assert(
     769             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     770             :       "Tensor types do not match!");
     771             :   initialize(rhs.number_of_grid_points());
     772             :   variable_data_ =
     773             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     774             :           rhs.variable_data_);
     775             :   return *this;
     776             : }
     777             : 
     778             : template <typename... Tags>
     779             : template <typename... WrappedTags,
     780             :           Requires<tmpl2::flat_all<
     781             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     782             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     783             : Variables<tmpl::list<Tags...>>::Variables(
     784             :     Variables<tmpl::list<WrappedTags...>>&& rhs)
     785             :     : variable_data_impl_dynamic_(std::move(rhs.variable_data_impl_dynamic_)),
     786             :       owning_(rhs.owning_),
     787             :       size_(rhs.size()),
     788             :       number_of_grid_points_(rhs.number_of_grid_points()),
     789             :       variable_data_(std::move(rhs.variable_data_)) {
     790             :   static_assert(
     791             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     792             :       "Tensor types do not match!");
     793             :   if (number_of_grid_points_ == 1) {
     794             : #if defined(__GNUC__) and not defined(__clang__)
     795             : #pragma GCC diagnostic push
     796             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     797             : #endif  // defined(__GNUC__) and not defined(__clang__)
     798             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     799             : #if defined(__GNUC__) and not defined(__clang__)
     800             : #pragma GCC diagnostic pop
     801             : #endif  // defined(__GNUC__) and not defined(__clang__)
     802             :   }
     803             :   rhs.variable_data_impl_dynamic_.reset();
     804             :   rhs.size_ = 0;
     805             :   rhs.owning_ = true;
     806             :   rhs.number_of_grid_points_ = 0;
     807             :   add_reference_variable_data();
     808             : }
     809             : 
     810             : template <typename... Tags>
     811             : template <typename... WrappedTags,
     812             :           Requires<tmpl2::flat_all<
     813             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     814             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     815             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     816             :     Variables<tmpl::list<WrappedTags...>>&& rhs) {
     817             :   static_assert(
     818             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     819             :       "Tensor types do not match!");
     820             :   variable_data_ = std::move(rhs.variable_data_);
     821             :   owning_ = rhs.owning_;
     822             :   size_ = rhs.size_;
     823             :   number_of_grid_points_ = std::move(rhs.number_of_grid_points_);
     824             :   variable_data_impl_dynamic_ = std::move(rhs.variable_data_impl_dynamic_);
     825             :   if (number_of_grid_points_ == 1) {
     826             : #if defined(__GNUC__) and not defined(__clang__)
     827             : #pragma GCC diagnostic push
     828             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     829             : #endif  // defined(__GNUC__) and not defined(__clang__)
     830             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     831             : #if defined(__GNUC__) and not defined(__clang__)
     832             : #pragma GCC diagnostic pop
     833             : #endif  // defined(__GNUC__) and not defined(__clang__)
     834             :   }
     835             : 
     836             :   rhs.variable_data_impl_dynamic_.reset();
     837             :   rhs.size_ = 0;
     838             :   rhs.owning_ = true;
     839             :   rhs.number_of_grid_points_ = 0;
     840             :   add_reference_variable_data();
     841             :   return *this;
     842             : }
     843             : 
     844             : template <typename... Tags>
     845             : Variables<tmpl::list<Tags...>>::Variables(const pointer start,
     846             :                                           const size_t size) {
     847             :   set_data_ref(start, size);
     848             : }
     849             : 
     850             : template <typename... Tags>
     851             : void Variables<tmpl::list<Tags...>>::pup(PUP::er& p) {
     852             :   ASSERT(
     853             :       owning_,
     854             :       "Cannot pup a non-owning Variables! It may be reasonable to pack a "
     855             :       "non-owning Variables, but not to unpack one. This should be discussed "
     856             :       "in an issue with the core devs if the feature seems necessary.");
     857             :   size_t number_of_grid_points = number_of_grid_points_;
     858             :   p | number_of_grid_points;
     859             :   if (p.isUnpacking()) {
     860             :     initialize(number_of_grid_points);
     861             :   }
     862             :   PUParray(p, variable_data_.data(), size_);
     863             : }
     864             : /// \endcond
     865             : 
     866             : /// @{
     867             : /*!
     868             :  * \ingroup DataStructuresGroup
     869             :  * \brief Return Tag::type pointing into the contiguous array
     870             :  *
     871             :  * \tparam Tag the variable to return
     872             :  */
     873             : template <typename Tag, typename TagList>
     874           1 : constexpr typename Tag::type& get(Variables<TagList>& v) {
     875             :   static_assert(tmpl::list_contains_v<TagList, Tag>,
     876             :                 "Could not retrieve Tag from Variables. See the first "
     877             :                 "template parameter of the instantiation for what Tag is "
     878             :                 "being retrieved and the second template parameter for "
     879             :                 "what Tags are available.");
     880             :   return tuples::get<Tag>(v.reference_variable_data_);
     881             : }
     882             : template <typename Tag, typename TagList>
     883           1 : constexpr const typename Tag::type& get(const Variables<TagList>& v) {
     884             :   static_assert(tmpl::list_contains_v<TagList, Tag>,
     885             :                 "Could not retrieve Tag from Variables. See the first "
     886             :                 "template parameter of the instantiation for what Tag is "
     887             :                 "being retrieved and the second template parameter for "
     888             :                 "what Tags are available.");
     889             :   return tuples::get<Tag>(v.reference_variable_data_);
     890             : }
     891             : /// @}
     892             : 
     893             : template <typename... Tags>
     894             : template <typename VT, bool VF>
     895             : Variables<tmpl::list<Tags...>>::Variables(
     896             :     const blaze::DenseVector<VT, VF>& expression) {
     897             :   ASSERT((*expression).size() % number_of_independent_components == 0,
     898             :          "Invalid size " << (*expression).size() << " for a Variables with "
     899             :          << number_of_independent_components << " components.");
     900             :   initialize((*expression).size() / number_of_independent_components);
     901             :   variable_data_ = expression;
     902             : }
     903             : 
     904             : /// \cond
     905             : template <typename... Tags>
     906             : template <typename VT, bool VF>
     907             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     908             :     const blaze::DenseVector<VT, VF>& expression) {
     909             :   ASSERT((*expression).size() % number_of_independent_components == 0,
     910             :          "Invalid size " << (*expression).size() << " for a Variables with "
     911             :          << number_of_independent_components << " components.");
     912             :   initialize((*expression).size() / number_of_independent_components);
     913             :   variable_data_ = expression;
     914             :   return *this;
     915             : }
     916             : /// \endcond
     917             : 
     918             : /// \cond HIDDEN_SYMBOLS
     919             : template <typename... Tags>
     920             : void Variables<tmpl::list<Tags...>>::add_reference_variable_data() {
     921             :   if (size_ == 0) {
     922             :     return;
     923             :   }
     924             :   if (is_owning()) {
     925             :     if (number_of_grid_points_ == 1) {
     926             :       variable_data_.reset(variable_data_impl_static_.data(), size_);
     927             :     } else {
     928             :       variable_data_.reset(variable_data_impl_dynamic_.get(), size_);
     929             :     }
     930             :   }
     931             :   ASSERT(variable_data_.size() == size_ and
     932             :              size_ == number_of_grid_points_ * number_of_independent_components,
     933             :          "Size mismatch: variable_data_.size() = "
     934             :              << variable_data_.size() << " size_ = " << size_ << " should be: "
     935             :              << number_of_grid_points_ * number_of_independent_components
     936             :              << "\nThis is an internal inconsistency bug in Variables. Please "
     937             :                 "file an issue.");
     938             :   size_t variable_offset = 0;
     939             :   tmpl::for_each<tags_list>([this, &variable_offset](auto tag_v) {
     940             :     using Tag = tmpl::type_from<decltype(tag_v)>;
     941             :     auto& var = tuples::get<Tag>(reference_variable_data_);
     942             :     for (size_t i = 0; i < Tag::type::size(); ++i) {
     943             :       var[i].set_data_ref(
     944             :           &variable_data_[variable_offset++ * number_of_grid_points_],
     945             :           number_of_grid_points_);
     946             :     }
     947             :   });
     948             : }
     949             : /// \endcond
     950             : 
     951             : template <typename... Tags>
     952           0 : Variables<tmpl::list<Tags...>>& operator*=(
     953             :     Variables<tmpl::list<Tags...>>& lhs,
     954             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     955             :   using value_type = typename Variables<tmpl::list<Tags...>>::value_type;
     956             :   ASSERT(lhs.number_of_grid_points() == rhs.size(),
     957             :          "Size mismatch in multiplication: " << lhs.number_of_grid_points()
     958             :                                              << " and " << rhs.size());
     959             :   value_type* const lhs_data = lhs.data();
     960             :   const value_type* const rhs_data = rhs.data();
     961             :   for (size_t c = 0; c < lhs.number_of_independent_components; ++c) {
     962             :     for (size_t s = 0; s < lhs.number_of_grid_points(); ++s) {
     963             :       // clang-tidy: do not use pointer arithmetic
     964             :       lhs_data[c * lhs.number_of_grid_points() + s] *= rhs_data[s];  // NOLINT
     965             :     }
     966             :   }
     967             :   return lhs;
     968             : }
     969             : 
     970             : template <typename... Tags>
     971           0 : Variables<tmpl::list<Tags...>> operator*(
     972             :     const Variables<tmpl::list<Tags...>>& lhs,
     973             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     974             :   auto result = lhs;
     975             :   result *= rhs;
     976             :   return result;
     977             : }
     978             : 
     979             : template <typename... Tags>
     980           0 : Variables<tmpl::list<Tags...>> operator*(
     981             :     const typename Variables<tmpl::list<Tags...>>::vector_type& lhs,
     982             :     const Variables<tmpl::list<Tags...>>& rhs) {
     983             :   auto result = rhs;
     984             :   result *= lhs;
     985             :   return result;
     986             : }
     987             : 
     988             : template <typename... Tags>
     989           0 : Variables<tmpl::list<Tags...>>& operator/=(
     990             :     Variables<tmpl::list<Tags...>>& lhs,
     991             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     992             :   ASSERT(lhs.number_of_grid_points() == rhs.size(),
     993             :          "Size mismatch in multiplication: " << lhs.number_of_grid_points()
     994             :                                              << " and " << rhs.size());
     995             :   using value_type = typename Variables<tmpl::list<Tags...>>::value_type;
     996             :   value_type* const lhs_data = lhs.data();
     997             :   const value_type* const rhs_data = rhs.data();
     998             :   for (size_t c = 0; c < lhs.number_of_independent_components; ++c) {
     999             :     for (size_t s = 0; s < lhs.number_of_grid_points(); ++s) {
    1000             :       // clang-tidy: do not use pointer arithmetic
    1001             :       lhs_data[c * lhs.number_of_grid_points() + s] /= rhs_data[s];  // NOLINT
    1002             :     }
    1003             :   }
    1004             :   return lhs;
    1005             : }
    1006             : 
    1007             : template <typename... Tags>
    1008           0 : Variables<tmpl::list<Tags...>> operator/(
    1009             :     const Variables<tmpl::list<Tags...>>& lhs,
    1010             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
    1011             :   auto result = lhs;
    1012             :   result /= rhs;
    1013             :   return result;
    1014             : }
    1015             : 
    1016             : template <typename... Tags, Requires<sizeof...(Tags) != 0> = nullptr>
    1017           0 : std::ostream& operator<<(std::ostream& os,
    1018             :                          const Variables<tmpl::list<Tags...>>& d) {
    1019             :   size_t count = 0;
    1020             :   const auto helper = [&os, &d, &count](auto tag_v) {
    1021             :     count++;
    1022             :     using Tag = typename decltype(tag_v)::type;
    1023             :     os << db::tag_name<Tag>() << ":\n";
    1024             :     os << get<Tag>(d);
    1025             :     if (count < sizeof...(Tags)) {
    1026             :       os << "\n\n";
    1027             :     }
    1028             :   };
    1029             :   EXPAND_PACK_LEFT_TO_RIGHT(helper(tmpl::type_<Tags>{}));
    1030             :   return os;
    1031             : }
    1032             : 
    1033             : template <typename TagsList>
    1034           0 : bool operator!=(const Variables<TagsList>& lhs,
    1035             :                 const Variables<TagsList>& rhs) {
    1036             :   return not(lhs == rhs);
    1037             : }
    1038             : 
    1039             : template <typename... TagsLhs, typename... TagsRhs,
    1040             :           Requires<not std::is_same<tmpl::list<TagsLhs...>,
    1041             :                                     tmpl::list<TagsRhs...>>::value> = nullptr>
    1042           0 : void swap(Variables<tmpl::list<TagsLhs...>>& lhs,
    1043             :           Variables<tmpl::list<TagsRhs...>>& rhs) {
    1044             :   Variables<tmpl::list<TagsLhs...>> temp{std::move(lhs)};
    1045             :   lhs = std::move(rhs);
    1046             :   rhs = std::move(temp);
    1047             : }
    1048             : 
    1049             : /// \ingroup DataStructuresGroup
    1050             : /// Construct a variables from the `Tensor`s in a `TaggedTuple`.
    1051             : template <typename... Tags>
    1052           1 : Variables<tmpl::list<Tags...>> variables_from_tagged_tuple(
    1053             :     const tuples::TaggedTuple<Tags...>& tuple) {
    1054             :   auto result = make_with_value<Variables<tmpl::list<Tags...>>>(
    1055             :       get<tmpl::front<tmpl::list<Tags...>>>(tuple), 0.0);
    1056             :   result.assign_subset(tuple);
    1057             :   return result;
    1058             : }
    1059             : 
    1060             : namespace MakeWithValueImpls {
    1061             : template <typename TagList>
    1062           0 : struct MakeWithSize<Variables<TagList>> {
    1063           0 :   static SPECTRE_ALWAYS_INLINE Variables<TagList> apply(
    1064             :       const size_t size, const typename Variables<TagList>::value_type value) {
    1065             :     return Variables<TagList>(size, value);
    1066             :   }
    1067             : };
    1068             : 
    1069             : template <typename TagList>
    1070           0 : struct NumberOfPoints<Variables<TagList>> {
    1071           0 :   static SPECTRE_ALWAYS_INLINE size_t apply(const Variables<TagList>& input) {
    1072             :     return input.number_of_grid_points();
    1073             :   }
    1074             : };
    1075             : }  // namespace MakeWithValueImpls
    1076             : 
    1077           1 : namespace EqualWithinRoundoffImpls {
    1078             : // It would be nice to use `blaze::equal` in these implementations, but it
    1079             : // doesn't currently allow to specify a tolerance. See upstream issue:
    1080             : // https://bitbucket.org/blaze-lib/blaze/issues/417/adjust-relaxed-equal-accuracy
    1081             : template <typename TagList, typename Floating>
    1082             : struct EqualWithinRoundoffImpl<Variables<TagList>, Floating,
    1083             :                                Requires<std::is_floating_point_v<Floating>>> {
    1084             :   static bool apply(const Variables<TagList>& lhs, const Floating& rhs,
    1085             :                     const double eps, const double scale) {
    1086             :     for (size_t i = 0; i < lhs.size(); ++i) {
    1087             :       if (not equal_within_roundoff(lhs.data()[i], rhs, eps, scale)) {
    1088             :         return false;
    1089             :       }
    1090             :     }
    1091             :     return true;
    1092             :   }
    1093             : };
    1094             : template <typename TagList, typename Floating>
    1095             : struct EqualWithinRoundoffImpl<Floating, Variables<TagList>,
    1096             :                                Requires<std::is_floating_point_v<Floating>>> {
    1097             :   static SPECTRE_ALWAYS_INLINE bool apply(const Floating& lhs,
    1098             :                                           const Variables<TagList>& rhs,
    1099             :                                           const double eps,
    1100             :                                           const double scale) {
    1101             :     return equal_within_roundoff(rhs, lhs, eps, scale);
    1102             :   }
    1103             : };
    1104             : template <typename LhsTagList, typename RhsTagList>
    1105           0 : struct EqualWithinRoundoffImpl<Variables<LhsTagList>, Variables<RhsTagList>> {
    1106           0 :   static bool apply(const Variables<LhsTagList>& lhs,
    1107             :                     const Variables<RhsTagList>& rhs, const double eps,
    1108             :                     const double scale) {
    1109             :     ASSERT(lhs.size() == rhs.size(),
    1110             :            "Can only compare two Variables of the same size, but lhs has size "
    1111             :                << lhs.size() << " and rhs has size " << rhs.size() << ".");
    1112             :     for (size_t i = 0; i < lhs.size(); ++i) {
    1113             :       if (not equal_within_roundoff(lhs.data()[i], rhs.data()[i], eps, scale)) {
    1114             :         return false;
    1115             :       }
    1116             :     }
    1117             :     return true;
    1118             :   }
    1119             : };
    1120             : }  // namespace EqualWithinRoundoffImpls
    1121             : 
    1122             : namespace db {
    1123             : // Enable subitems for ::Tags::Variables and derived tags (e.g. compute tags).
    1124             : // Other tags that hold a `Variables` don't expose the constituent tensors as
    1125             : // subitems by default.
    1126             : namespace Variables_detail {
    1127             : // Check if the argument is a `::Tags::Variables`, or derived from it. Can't use
    1128             : // `tt:is_a_v` because we also want to match derived classes. Can't use
    1129             : // `std::is_base_of` because `::Tags::Variables` is a template.
    1130             : template <typename TagsList>
    1131             : constexpr std::true_type is_a_variables_tag(::Tags::Variables<TagsList>&&) {
    1132             :   return {};
    1133             : }
    1134             : constexpr std::false_type is_a_variables_tag(...) { return {}; }
    1135             : template <typename Tag>
    1136             : static constexpr bool is_a_variables_tag_v =
    1137             :     decltype(is_a_variables_tag(std::declval<Tag>()))::value;
    1138             : }  // namespace Variables_detail
    1139             : template <typename Tag>
    1140             : struct Subitems<Tag, Requires<Variables_detail::is_a_variables_tag_v<Tag>>> {
    1141             :   using type = typename Tag::type::tags_list;
    1142             : 
    1143             :   template <typename Subtag, typename LocalTag = Tag>
    1144             :   static void create_item(
    1145             :       const gsl::not_null<typename LocalTag::type*> parent_value,
    1146             :       const gsl::not_null<typename Subtag::type*> sub_value) {
    1147             :     auto& vars = get<Subtag>(*parent_value);
    1148             :     // Only update the Tensor if the Variables has changed its allocation
    1149             :     if constexpr (not is_any_spin_weighted_v<typename Subtag::type::type>) {
    1150             :       if (vars.begin()->data() != sub_value->begin()->data()) {
    1151             :         for (auto vars_it = vars.begin(), sub_var_it = sub_value->begin();
    1152             :              vars_it != vars.end(); ++vars_it, ++sub_var_it) {
    1153             :           sub_var_it->set_data_ref(make_not_null(&*vars_it));
    1154             :         }
    1155             :       }
    1156             :     } else {
    1157             :       if (vars.begin()->data().data() != sub_value->begin()->data().data()) {
    1158             :         for (auto vars_it = vars.begin(), sub_var_it = sub_value->begin();
    1159             :              vars_it != vars.end(); ++vars_it, ++sub_var_it) {
    1160             :           sub_var_it->set_data_ref(make_not_null(&*vars_it));
    1161             :         }
    1162             :       }
    1163             :     }
    1164             :   }
    1165             : 
    1166             :   template <typename Subtag>
    1167             :   static const typename Subtag::type& create_compute_item(
    1168             :       const typename Tag::type& parent_value) {
    1169             :     return get<Subtag>(parent_value);
    1170             :   }
    1171             : };
    1172             : }  // namespace db
    1173             : 
    1174             : namespace Variables_detail {
    1175             : template <typename Tags>
    1176             : using MathWrapperVectorType = tmpl::conditional_t<
    1177             :     std::is_same_v<typename Variables<Tags>::value_type, double>, DataVector,
    1178             :     ComplexDataVector>;
    1179             : }  // namespace Variables_detail
    1180             : 
    1181             : template <typename Tags>
    1182           0 : auto make_math_wrapper(const gsl::not_null<Variables<Tags>*> data) {
    1183             :   using Vector = Variables_detail::MathWrapperVectorType<Tags>;
    1184             :   Vector referencing(data->data(), data->size());
    1185             :   return make_math_wrapper(&referencing);
    1186             : }
    1187             : 
    1188             : template <typename Tags>
    1189           0 : auto make_math_wrapper(const Variables<Tags>& data) {
    1190             :   using Vector = Variables_detail::MathWrapperVectorType<Tags>;
    1191             :   const Vector referencing(
    1192             :       const_cast<typename Vector::value_type*>(data.data()), data.size());
    1193             :   return make_math_wrapper(referencing);
    1194             : }
    1195             : 
    1196             : /// \cond
    1197             : template <size_t I, class... Tags>
    1198             : inline constexpr typename tmpl::at_c<tmpl::list<Tags...>, I>::type&& get(
    1199             :     Variables<tmpl::list<Tags...>>&& t) {
    1200             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1201             : }
    1202             : 
    1203             : template <size_t I, class... Tags>
    1204             : inline constexpr const typename tmpl::at_c<tmpl::list<Tags...>, I>::type& get(
    1205             :     const Variables<tmpl::list<Tags...>>& t) {
    1206             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1207             : }
    1208             : 
    1209             : template <size_t I, class... Tags>
    1210             : inline constexpr typename tmpl::at_c<tmpl::list<Tags...>, I>::type& get(
    1211             :     Variables<tmpl::list<Tags...>>& t) {
    1212             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1213             : }
    1214             : /// \endcond
    1215             : 
    1216             : namespace std {
    1217             : template <typename... Tags>
    1218             : struct tuple_size<Variables<tmpl::list<Tags...>>>
    1219             :     : std::integral_constant<int, sizeof...(Tags)> {};
    1220             : template <size_t I, typename... Tags>
    1221             : struct tuple_element<I, Variables<tmpl::list<Tags...>>> {
    1222             :   using type = typename tmpl::at_c<tmpl::list<Tags...>, I>::type;
    1223             : };
    1224             : }  // namespace std
    1225             : 
    1226             : template <typename TagsList>
    1227           0 : bool contains_allocations(const Variables<TagsList>& value) {
    1228             :   return value.number_of_grid_points() > 1;
    1229             : }
    1230             : 
    1231           0 : inline bool contains_allocations(const Variables<tmpl::list<>>& /*value*/) {
    1232             :   return false;
    1233             : }

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