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Commit: a6a8ee404306bec9d92da8ab89f636b037aefc25 Lines: 33 116 28.4 %
Date: 2024-07-26 22:35:59
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          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/SetNumberOfGridPoints.hpp"
      44             : #include "Utilities/TMPL.hpp"
      45             : #include "Utilities/TaggedTuple.hpp"
      46             : #include "Utilities/TypeTraits.hpp"
      47             : #include "Utilities/TypeTraits/IsA.hpp"
      48             : 
      49             : /// \cond
      50             : template <typename X, typename Symm, typename IndexList>
      51             : class Tensor;
      52             : template <typename TagsList>
      53             : class Variables;
      54             : template <typename T, typename VectorType, size_t StaticSize>
      55             : class VectorImpl;
      56             : namespace Tags {
      57             : template <typename TagsList>
      58             : class Variables;
      59             : }  // namespace Tags
      60             : /// \endcond
      61             : 
      62             : /*!
      63             :  * \ingroup DataStructuresGroup
      64             :  * \brief A Variables holds a contiguous memory block with Tensors pointing
      65             :  * into it.
      66             :  *
      67             :  * The `Tags` are `struct`s that must have a public type alias `type` whose
      68             :  * value must be a `Tensor<DataVector, ...>`, a `static' method `name()` that
      69             :  * returns a `std::string` of the tag name, and must derive off of
      70             :  * `db::SimpleTag`. In general, they should be DataBoxTags that are not compute
      71             :  * items. For example,
      72             :  *
      73             :  * \snippet Helpers/DataStructures/TestTags.hpp simple_variables_tag
      74             :  *
      75             :  * Prefix tags can also be stored and their format is:
      76             :  *
      77             :  * \snippet Helpers/DataStructures/TestTags.hpp prefix_variables_tag
      78             :  *
      79             :  * #### Design Decisions
      80             :  *
      81             :  * The `Variables` class is designed to hold several different `Tensor`s
      82             :  * performing one memory allocation for all the `Tensor`s. The advantage is that
      83             :  * memory allocations are quite expensive, especially in a parallel environment.
      84             :  *
      85             :  * In Debug mode, or if the macro `SPECTRE_NAN_INIT` is defined, the contents
      86             :  * are initialized with `NaN`s.
      87             :  *
      88             :  * `Variables` stores the data it owns in a `std::unique_ptr<double[]>`
      89             :  * instead of a `std::vector` because `std::vector` value-initializes its
      90             :  * contents, which is very slow.
      91             :  */
      92             : template <typename... Tags>
      93           1 : class Variables<tmpl::list<Tags...>> {
      94             :  public:
      95           0 :   using size_type = size_t;
      96           0 :   using difference_type = std::ptrdiff_t;
      97           0 :   static constexpr auto transpose_flag = blaze::defaultTransposeFlag;
      98             : 
      99             :   /// A typelist of the Tags whose variables are held
     100           1 :   using tags_list = tmpl::list<Tags...>;
     101             :   static_assert(sizeof...(Tags) > 0,
     102             :                 "You must provide at least one tag to the Variables "
     103             :                 "for type inference");
     104             :   static_assert((db::is_simple_tag_v<Tags> and ...));
     105             :   static_assert(tmpl2::flat_all_v<tt::is_a_v<Tensor, typename Tags::type>...>);
     106             : 
     107             :  private:
     108           0 :   using first_tensors_type = typename tmpl::front<tags_list>::type::type;
     109             : 
     110             :  public:
     111             :   static_assert(tmpl2::flat_all_v<std::is_same_v<typename Tags::type::type,
     112             :                                                  first_tensors_type>...> or
     113             :                     tmpl2::flat_all_v<is_spin_weighted_of_same_type_v<
     114             :                         typename Tags::type::type, first_tensors_type>...>,
     115             :                 "All tensors stored in a single Variables must "
     116             :                 "have the same internal storage type.");
     117             : 
     118           0 :   using vector_type =
     119             :       tmpl::conditional_t<is_any_spin_weighted_v<first_tensors_type>,
     120             :                           typename first_tensors_type::value_type,
     121             :                           first_tensors_type>;
     122           0 :   using value_type = typename vector_type::value_type;
     123           0 :   using pointer = value_type*;
     124           0 :   using const_pointer = const value_type*;
     125           0 :   using allocator_type = std::allocator<value_type>;
     126           0 :   using pointer_type =
     127             :       blaze::CustomVector<value_type, blaze::AlignmentFlag::unaligned,
     128             :                           blaze::PaddingFlag::unpadded, transpose_flag,
     129             :                           blaze::GroupTag<0>, vector_type>;
     130             : 
     131             :   static_assert(
     132             :       std::is_fundamental_v<value_type> or tt::is_a_v<std::complex, value_type>,
     133             :       "`value_type` of the Variables (so the storage type of the vector type "
     134             :       "within the tensors in the Variables) must be either a fundamental type "
     135             :       "or a std::complex. If this constraint is relaxed, the value_type "
     136             :       "should be handled differently in the Variables, including pass by "
     137             :       "reference.");
     138             : 
     139             :   /// The number of variables of the Variables object is holding. E.g.
     140             :   /// \f$\psi_{ab}\f$ would be counted as one variable.
     141           1 :   static constexpr auto number_of_variables = sizeof...(Tags);
     142             : 
     143             :   /// The total number of independent components of all the variables. E.g.
     144             :   /// a rank-2 symmetric spacetime Tensor \f$\psi_{ab}\f$ in 3 spatial
     145             :   /// dimensions would have 10 independent components.
     146           1 :   static constexpr size_t number_of_independent_components =
     147             :       (... + Tags::type::size());
     148             : 
     149             :   /// Default construct an empty Variables class, Charm++ needs this
     150           1 :   Variables();
     151             : 
     152           0 :   explicit Variables(size_t number_of_grid_points);
     153             : 
     154           0 :   Variables(size_t number_of_grid_points, value_type value);
     155             : 
     156             :   /// Construct a non-owning Variables that points to `start`. `size` is the
     157             :   /// size of the allocation, which must be
     158             :   /// `number_of_grid_points * Variables::number_of_independent_components`
     159           1 :   Variables(pointer start, size_t size);
     160             : 
     161           0 :   Variables(Variables&& rhs);
     162           0 :   Variables& operator=(Variables&& rhs);
     163             : 
     164           0 :   Variables(const Variables& rhs);
     165           0 :   Variables& operator=(const Variables& rhs);
     166             : 
     167             :   /// @{
     168             :   /// Copy and move semantics for wrapped variables
     169             :   template <typename... WrappedTags,
     170             :             Requires<tmpl2::flat_all<std::is_same<
     171             :                 db::remove_all_prefixes<WrappedTags>,
     172             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     173           1 :   explicit Variables(Variables<tmpl::list<WrappedTags...>>&& rhs);
     174             :   template <typename... WrappedTags,
     175             :             Requires<tmpl2::flat_all<std::is_same<
     176             :                 db::remove_all_prefixes<WrappedTags>,
     177             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     178           1 :   Variables& operator=(Variables<tmpl::list<WrappedTags...>>&& rhs);
     179             : 
     180             :   template <typename... WrappedTags,
     181             :             Requires<tmpl2::flat_all<std::is_same<
     182             :                 db::remove_all_prefixes<WrappedTags>,
     183             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     184           1 :   explicit Variables(const Variables<tmpl::list<WrappedTags...>>& rhs);
     185             :   template <typename... WrappedTags,
     186             :             Requires<tmpl2::flat_all<std::is_same<
     187             :                 db::remove_all_prefixes<WrappedTags>,
     188             :                 db::remove_all_prefixes<Tags>>::value...>::value> = nullptr>
     189           1 :   Variables& operator=(const Variables<tmpl::list<WrappedTags...>>& rhs);
     190             :   /// @}
     191             : 
     192             :   /// \cond HIDDEN_SYMBOLS
     193             :   ~Variables() = default;
     194             :   /// \endcond
     195             : 
     196             :   /// @{
     197             :   /// Initialize a Variables to the state it would have after calling
     198             :   /// the constructor with the same arguments.
     199             :   // this should be updated if we ever use a variables which has a `value_type`
     200             :   // larger than ~2 doubles in size.
     201           1 :   void initialize(size_t number_of_grid_points);
     202           1 :   void initialize(size_t number_of_grid_points, value_type value);
     203             :   /// @}
     204             : 
     205             :   /// @{
     206             :   /// Set the VectorImpl to be a reference to another VectorImpl object
     207           1 :   void set_data_ref(const gsl::not_null<Variables*> rhs) {
     208             :     set_data_ref(rhs->data(), rhs->size());
     209             :   }
     210             : 
     211           1 :   void set_data_ref(pointer const start, const size_t size) {
     212             :     variable_data_impl_dynamic_.reset();
     213             :     if (start == nullptr) {
     214             :       variable_data_ = pointer_type{};
     215             :       size_ = 0;
     216             :       number_of_grid_points_ = 0;
     217             :     } else {
     218             :       size_ = size;
     219             :       variable_data_.reset(start, size_);
     220             :       ASSERT(
     221             :           size_ % number_of_independent_components == 0,
     222             :           "The size (" << size_
     223             :                        << ") must be a multiple of the number of independent "
     224             :                           "components ("
     225             :                        << number_of_independent_components
     226             :                        << ") since we calculate the number of grid points from "
     227             :                           "the size and number of independent components.");
     228             :       number_of_grid_points_ = size_ / number_of_independent_components;
     229             :     }
     230             :     owning_ = false;
     231             :     add_reference_variable_data();
     232             :   }
     233             :   /// @}
     234             : 
     235           0 :   constexpr SPECTRE_ALWAYS_INLINE size_t number_of_grid_points() const {
     236             :     return number_of_grid_points_;
     237             :   }
     238             : 
     239             :   /// Number of grid points * number of independent components
     240           1 :   constexpr SPECTRE_ALWAYS_INLINE size_type size() const { return size_; }
     241             : 
     242             :   /// @{
     243             :   /// Access pointer to underlying data
     244           1 :   pointer data() { return variable_data_.data(); }
     245           1 :   const_pointer data() const { return variable_data_.data(); }
     246             :   /// @}
     247             : 
     248             :   /// \cond HIDDEN_SYMBOLS
     249             :   /// Needed because of limitations and inconsistency between compiler
     250             :   /// implementations of friend function templates with auto return type of
     251             :   /// class templates
     252             :   const auto& get_variable_data() const { return variable_data_; }
     253             :   /// \endcond
     254             : 
     255             :   /// Returns true if the class owns the data
     256           1 :   bool is_owning() const { return owning_; }
     257             : 
     258             :   // clang-tidy: redundant-declaration
     259             :   template <typename Tag, typename TagList>
     260           1 :   friend constexpr typename Tag::type& get(  // NOLINT
     261             :       Variables<TagList>& v);
     262             :   template <typename Tag, typename TagList>
     263           0 :   friend constexpr const typename Tag::type& get(  // NOLINT
     264             :       const Variables<TagList>& v);
     265             : 
     266             :   /// Serialization for Charm++.
     267             :   // NOLINTNEXTLINE(google-runtime-references)
     268           1 :   void pup(PUP::er& p);
     269             : 
     270             :   /// @{
     271             :   /// \brief Assign a subset of the `Tensor`s from another Variables or a
     272             :   /// tuples::TaggedTuple. Any tags that aren't in both containers are
     273             :   /// ignored.
     274             :   ///
     275             :   /// \note There is no need for an rvalue overload because we need to copy into
     276             :   /// the contiguous array anyway
     277             :   template <typename... SubsetOfTags>
     278           1 :   void assign_subset(const Variables<tmpl::list<SubsetOfTags...>>& vars) {
     279             :     EXPAND_PACK_LEFT_TO_RIGHT([this, &vars]() {
     280             :       if constexpr (tmpl::list_contains_v<tmpl::list<Tags...>, SubsetOfTags>) {
     281             :         get<SubsetOfTags>(*this) = get<SubsetOfTags>(vars);
     282             :       } else {
     283             :         (void)this;
     284             :         (void)vars;
     285             :       }
     286             :     }());
     287             :   }
     288             : 
     289             :   template <typename... SubsetOfTags>
     290           1 :   void assign_subset(const tuples::TaggedTuple<SubsetOfTags...>& vars) {
     291             :     EXPAND_PACK_LEFT_TO_RIGHT([this, &vars]() {
     292             :       if constexpr (tmpl::list_contains_v<tmpl::list<Tags...>, SubsetOfTags>) {
     293             :         get<SubsetOfTags>(*this) = get<SubsetOfTags>(vars);
     294             :       } else {
     295             :         (void)this;
     296             :         (void)vars;
     297             :       }
     298             :     }());
     299             :   }
     300             :   /// @}
     301             : 
     302             :   /// Create a Variables from a subset of the `Tensor`s in this
     303             :   /// Variables
     304             :   template <typename SubsetOfTags>
     305           1 :   Variables<SubsetOfTags> extract_subset() const {
     306             :     Variables<SubsetOfTags> sub_vars(number_of_grid_points());
     307             :     tmpl::for_each<SubsetOfTags>([&](const auto tag_v) {
     308             :       using tag = tmpl::type_from<decltype(tag_v)>;
     309             :       get<tag>(sub_vars) = get<tag>(*this);
     310             :     });
     311             :     return sub_vars;
     312             :   }
     313             : 
     314             :   /// Create a non-owning Variables referencing a subset of the
     315             :   /// `Tensor`s in this Variables.  The referenced tensors must be
     316             :   /// consecutive in this Variables's tags list.
     317             :   ///
     318             :   /// \warning As with other appearances of non-owning variables, this
     319             :   /// method can cast away constness.
     320             :   template <typename SubsetOfTags>
     321           1 :   Variables<SubsetOfTags> reference_subset() const {
     322             :     if constexpr (std::is_same_v<SubsetOfTags, tmpl::list<>>) {
     323             :       return {};
     324             :     } else {
     325             :       using subset_from_tags_list = tmpl::reverse_find<
     326             :           tmpl::find<
     327             :               tags_list,
     328             :               std::is_same<tmpl::_1, tmpl::pin<tmpl::front<SubsetOfTags>>>>,
     329             :           std::is_same<tmpl::_1, tmpl::pin<tmpl::back<SubsetOfTags>>>>;
     330             :       static_assert(std::is_same_v<subset_from_tags_list, SubsetOfTags>,
     331             :                     "Tags passed to reference_subset must be consecutive tags "
     332             :                     "in the original tags_list.");
     333             : 
     334             :       using preceeding_tags = tmpl::pop_back<tmpl::reverse_find<
     335             :           tags_list,
     336             :           std::is_same<tmpl::_1, tmpl::pin<tmpl::front<SubsetOfTags>>>>>;
     337             : 
     338             :       static constexpr auto count_components = [](auto... tags) {
     339             :         return (0_st + ... + tmpl::type_from<decltype(tags)>::type::size());
     340             :       };
     341             :       static constexpr size_t number_of_preceeding_components =
     342             :           tmpl::as_pack<preceeding_tags>(count_components);
     343             :       static constexpr size_t number_of_components_in_subset =
     344             :           tmpl::as_pack<SubsetOfTags>(count_components);
     345             : 
     346             :       return {const_cast<value_type*>(data()) +
     347             :                   number_of_grid_points() * number_of_preceeding_components,
     348             :               number_of_grid_points() * number_of_components_in_subset};
     349             :     }
     350             :   }
     351             : 
     352             :   /// Create a non-owning version of this Variables with different
     353             :   /// prefixes on the tensors.  Both sets of prefixes must have the
     354             :   /// same tensor types.
     355             :   ///
     356             :   /// \warning As with other appearances of non-owning variables, this
     357             :   /// method can cast away constness.
     358             :   template <typename WrappedVariables>
     359           1 :   WrappedVariables reference_with_different_prefixes() const {
     360             :     static_assert(
     361             :         tmpl::all<tmpl::transform<
     362             :             typename WrappedVariables::tags_list, tmpl::list<Tags...>,
     363             :             std::is_same<tmpl::bind<db::remove_all_prefixes, tmpl::_1>,
     364             :                          tmpl::bind<db::remove_all_prefixes, tmpl::_2>>>>::
     365             :             value,
     366             :         "Unprefixed tags do not match!");
     367             :     static_assert(
     368             :         tmpl::all<tmpl::transform<
     369             :             typename WrappedVariables::tags_list, tmpl::list<Tags...>,
     370             :             std::is_same<tmpl::bind<tmpl::type_from, tmpl::_1>,
     371             :                          tmpl::bind<tmpl::type_from, tmpl::_2>>>>::value,
     372             :         "Tensor types do not match!");
     373             :     return {const_cast<value_type*>(data()), size()};
     374             :   }
     375             : 
     376             :   /// Converting constructor for an expression to a Variables class
     377             :   // clang-tidy: mark as explicit (we want conversion to Variables)
     378             :   template <typename VT, bool VF>
     379           1 :   Variables(const blaze::DenseVector<VT, VF>& expression);  // NOLINT
     380             : 
     381             :   template <typename VT, bool VF>
     382           0 :   Variables& operator=(const blaze::DenseVector<VT, VF>& expression);
     383             : 
     384             :   // Prevent the previous two declarations from implicitly converting
     385             :   // DataVectors and similar to Variables.
     386             :   template <typename T, typename VectorType, size_t StaticSize>
     387           0 :   Variables(const VectorImpl<T, VectorType, StaticSize>&) = delete;
     388             :   template <typename T, typename VectorType, size_t StaticSize>
     389           0 :   Variables& operator=(const VectorImpl<T, VectorType, StaticSize>&) = delete;
     390             : 
     391             :   template <typename... WrappedTags,
     392             :             Requires<tmpl2::flat_all<std::is_same_v<
     393             :                 db::remove_all_prefixes<WrappedTags>,
     394             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     395           0 :   SPECTRE_ALWAYS_INLINE Variables& operator+=(
     396             :       const Variables<tmpl::list<WrappedTags...>>& rhs) {
     397             :     static_assert(
     398             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     399             :          ...),
     400             :         "Tensor types do not match!");
     401             :     variable_data_ += rhs.variable_data_;
     402             :     return *this;
     403             :   }
     404             :   template <typename VT, bool VF>
     405           0 :   SPECTRE_ALWAYS_INLINE Variables& operator+=(
     406             :       const blaze::Vector<VT, VF>& rhs) {
     407             :     variable_data_ += rhs;
     408             :     return *this;
     409             :   }
     410             : 
     411             :   template <typename... WrappedTags,
     412             :             Requires<tmpl2::flat_all<std::is_same_v<
     413             :                 db::remove_all_prefixes<WrappedTags>,
     414             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     415           0 :   SPECTRE_ALWAYS_INLINE Variables& operator-=(
     416             :       const Variables<tmpl::list<WrappedTags...>>& rhs) {
     417             :     static_assert(
     418             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     419             :          ...),
     420             :         "Tensor types do not match!");
     421             :     variable_data_ -= rhs.variable_data_;
     422             :     return *this;
     423             :   }
     424             :   template <typename VT, bool VF>
     425           0 :   SPECTRE_ALWAYS_INLINE Variables& operator-=(
     426             :       const blaze::Vector<VT, VF>& rhs) {
     427             :     variable_data_ -= rhs;
     428             :     return *this;
     429             :   }
     430             : 
     431           0 :   SPECTRE_ALWAYS_INLINE Variables& operator*=(const value_type& rhs) {
     432             :     variable_data_ *= rhs;
     433             :     return *this;
     434             :   }
     435             : 
     436           0 :   SPECTRE_ALWAYS_INLINE Variables& operator/=(const value_type& rhs) {
     437             :     variable_data_ /= rhs;
     438             :     return *this;
     439             :   }
     440             : 
     441             :   template <typename... WrappedTags,
     442             :             Requires<tmpl2::flat_all<std::is_same_v<
     443             :                 db::remove_all_prefixes<WrappedTags>,
     444             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     445           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     446             :       const Variables<tmpl::list<WrappedTags...>>& lhs, const Variables& rhs) {
     447             :     static_assert(
     448             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     449             :          ...),
     450             :         "Tensor types do not match!");
     451             :     return lhs.get_variable_data() + rhs.variable_data_;
     452             :   }
     453             :   template <typename VT, bool VF>
     454           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     455             :       const blaze::DenseVector<VT, VF>& lhs, const Variables& rhs) {
     456             :     return *lhs + rhs.variable_data_;
     457             :   }
     458             :   template <typename VT, bool VF>
     459           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(
     460             :       const Variables& lhs, const blaze::DenseVector<VT, VF>& rhs) {
     461             :     return lhs.variable_data_ + *rhs;
     462             :   }
     463             : 
     464             :   template <typename... WrappedTags,
     465             :             Requires<tmpl2::flat_all<std::is_same_v<
     466             :                 db::remove_all_prefixes<WrappedTags>,
     467             :                 db::remove_all_prefixes<Tags>>...>::value> = nullptr>
     468           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     469             :       const Variables<tmpl::list<WrappedTags...>>& lhs, const Variables& rhs) {
     470             :     static_assert(
     471             :         (std::is_same_v<typename Tags::type, typename WrappedTags::type> and
     472             :          ...),
     473             :         "Tensor types do not match!");
     474             :     return lhs.get_variable_data() - rhs.variable_data_;
     475             :   }
     476             :   template <typename VT, bool VF>
     477           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     478             :       const blaze::DenseVector<VT, VF>& lhs, const Variables& rhs) {
     479             :     return *lhs - rhs.variable_data_;
     480             :   }
     481             :   template <typename VT, bool VF>
     482           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(
     483             :       const Variables& lhs, const blaze::DenseVector<VT, VF>& rhs) {
     484             :     return lhs.variable_data_ - *rhs;
     485             :   }
     486             : 
     487           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator*(const Variables& lhs,
     488             :                                                         const value_type& rhs) {
     489             :     return lhs.variable_data_ * rhs;
     490             :   }
     491           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator*(const value_type& lhs,
     492             :                                                         const Variables& rhs) {
     493             :     return lhs * rhs.variable_data_;
     494             :   }
     495             : 
     496           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator/(const Variables& lhs,
     497             :                                                         const value_type& rhs) {
     498             :     return lhs.variable_data_ / rhs;
     499             :   }
     500             : 
     501           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator-(const Variables& lhs) {
     502             :     return -lhs.variable_data_;
     503             :   }
     504           0 :   friend SPECTRE_ALWAYS_INLINE decltype(auto) operator+(const Variables& lhs) {
     505             :     return lhs.variable_data_;
     506             :   }
     507             : 
     508             :  private:
     509             :   /// @{
     510             :   /*!
     511             :    * \brief Subscript operator
     512             :    *
     513             :    * The subscript operator is private since it should not be used directly.
     514             :    * Mathematical operations should be done using the math operators provided.
     515             :    * Since the internal ordering of variables is implementation defined there
     516             :    * is no safe way to perform any operation that is not a linear combination of
     517             :    * Variables. Retrieving a Tensor must be done via the `get()` function.
     518             :    *
     519             :    *  \requires `i >= 0 and i < size()`
     520             :    */
     521           1 :   SPECTRE_ALWAYS_INLINE value_type& operator[](const size_type i) {
     522             :     return variable_data_[i];
     523             :   }
     524           1 :   SPECTRE_ALWAYS_INLINE const value_type& operator[](const size_type i) const {
     525             :     return variable_data_[i];
     526             :   }
     527             :   /// @}
     528             : 
     529           0 :   void add_reference_variable_data();
     530             : 
     531           0 :   friend bool operator==(const Variables& lhs, const Variables& rhs) {
     532             :     return blaze::equal<blaze::strict>(lhs.variable_data_, rhs.variable_data_);
     533             :   }
     534             : 
     535             :   template <typename VT, bool TF>
     536           0 :   friend bool operator==(const Variables& lhs,
     537             :                          const blaze::DenseVector<VT, TF>& rhs) {
     538             :     return blaze::equal<blaze::strict>(lhs.variable_data_, *rhs);
     539             :   }
     540             : 
     541             :   template <typename VT, bool TF>
     542           0 :   friend bool operator==(const blaze::DenseVector<VT, TF>& lhs,
     543             :                          const Variables& rhs) {
     544             :     return blaze::equal<blaze::strict>(*lhs, rhs.variable_data_);
     545             :   }
     546             : 
     547             :   template <class FriendTags>
     548           0 :   friend class Variables;
     549             : 
     550             :   std::array<value_type, number_of_independent_components>
     551           0 :       variable_data_impl_static_;
     552           0 :   std::unique_ptr<value_type[]> variable_data_impl_dynamic_{};
     553           0 :   bool owning_{true};
     554           0 :   size_t size_ = 0;
     555           0 :   size_t number_of_grid_points_ = 0;
     556             : 
     557           0 :   pointer_type variable_data_;
     558           0 :   tuples::TaggedTuple<Tags...> reference_variable_data_;
     559             : };
     560             : 
     561             : // The above Variables implementation doesn't work for an empty parameter pack,
     562             : // so specialize here.
     563             : template <>
     564           0 : class Variables<tmpl::list<>> {
     565             :  public:
     566           0 :   using tags_list = tmpl::list<>;
     567           0 :   static constexpr size_t number_of_independent_components = 0;
     568           0 :   Variables() = default;
     569           0 :   explicit Variables(const size_t /*number_of_grid_points*/) {}
     570             :   template <typename T>
     571           0 :   Variables(const T* /*pointer*/, const size_t /*size*/) {}
     572           0 :   static constexpr size_t size() { return 0; }
     573             : };
     574             : 
     575             : // gcc8 screams when the empty Variables has pup as a member function, so we
     576             : // declare pup as a free function here.
     577             : // clang-tidy: runtime-references
     578           0 : SPECTRE_ALWAYS_INLINE void pup(
     579             :     PUP::er& /*p*/,                           // NOLINT
     580             :     Variables<tmpl::list<>>& /* unused */) {  // NOLINT
     581             : }
     582           0 : SPECTRE_ALWAYS_INLINE void operator|(
     583             :     PUP::er& /*p*/, Variables<tmpl::list<>>& /* unused */) {  // NOLINT
     584             : }
     585             : 
     586           0 : SPECTRE_ALWAYS_INLINE bool operator==(const Variables<tmpl::list<>>& /*lhs*/,
     587             :                                       const Variables<tmpl::list<>>& /*rhs*/) {
     588             :   return true;
     589             : }
     590           0 : SPECTRE_ALWAYS_INLINE bool operator!=(const Variables<tmpl::list<>>& /*lhs*/,
     591             :                                       const Variables<tmpl::list<>>& /*rhs*/) {
     592             :   return false;
     593             : }
     594             : 
     595           0 : inline std::ostream& operator<<(std::ostream& os,
     596             :                                 const Variables<tmpl::list<>>& /*d*/) {
     597             :   return os << "{}";
     598             : }
     599             : 
     600             : template <typename... Tags>
     601             : Variables<tmpl::list<Tags...>>::Variables() {
     602             :   // This makes an assertion trigger if one tries to assign to
     603             :   // components of a default-constructed Variables.
     604             :   const auto set_refs = [](auto& var) {
     605             :     for (auto& dv : var) {
     606             :       dv.set_data_ref(nullptr, 0);
     607             :     }
     608             :     return 0;
     609             :   };
     610             :   (void)set_refs;
     611             :   expand_pack(set_refs(tuples::get<Tags>(reference_variable_data_))...);
     612             : }
     613             : 
     614             : template <typename... Tags>
     615             : Variables<tmpl::list<Tags...>>::Variables(const size_t number_of_grid_points) {
     616             :   initialize(number_of_grid_points);
     617             : }
     618             : 
     619             : template <typename... Tags>
     620             : Variables<tmpl::list<Tags...>>::Variables(const size_t number_of_grid_points,
     621             :                                           const value_type value) {
     622             :   initialize(number_of_grid_points, value);
     623             : }
     624             : 
     625             : template <typename... Tags>
     626             : void Variables<tmpl::list<Tags...>>::initialize(
     627             :     const size_t number_of_grid_points) {
     628             :   if (number_of_grid_points_ == 0) {
     629             :     variable_data_impl_dynamic_.reset();
     630             :     size_ = 0;
     631             :     number_of_grid_points_ = 0;
     632             :   }
     633             :   if (number_of_grid_points_ == number_of_grid_points) {
     634             :     return;
     635             :   }
     636             :   if (UNLIKELY(not is_owning())) {
     637             :     ERROR("Variables::initialize cannot be called on a non-owning Variables.  "
     638             :           "This likely happened because of an attempted resize.  The current "
     639             :           "number of grid points is " << number_of_grid_points_ << " and the "
     640             :           "requested number is " << number_of_grid_points << ".");
     641             :   }
     642             :   number_of_grid_points_ = number_of_grid_points;
     643             :   size_ = number_of_grid_points * number_of_independent_components;
     644             :   if (size_ > 0) {
     645             :     if (number_of_grid_points_ == 1) {
     646             :       variable_data_impl_dynamic_.reset();
     647             :     } else {
     648             :       variable_data_impl_dynamic_ =
     649             :           cpp20::make_unique_for_overwrite<value_type[]>(size_);
     650             :     }
     651             :     add_reference_variable_data();
     652             : #if defined(SPECTRE_DEBUG) || defined(SPECTRE_NAN_INIT)
     653             :     std::fill(variable_data_.data(), variable_data_.data() + size_,
     654             :               make_signaling_NaN<value_type>());
     655             : #endif  // SPECTRE_DEBUG
     656             :   }
     657             : }
     658             : 
     659             : template <typename... Tags>
     660             : void Variables<tmpl::list<Tags...>>::initialize(
     661             :     const size_t number_of_grid_points, const value_type value) {
     662             :   initialize(number_of_grid_points);
     663             :   std::fill(variable_data_.data(), variable_data_.data() + size_, value);
     664             : }
     665             : 
     666             : /// \cond HIDDEN_SYMBOLS
     667             : template <typename... Tags>
     668             : Variables<tmpl::list<Tags...>>::Variables(
     669             :     const Variables<tmpl::list<Tags...>>& rhs) {
     670             :   initialize(rhs.number_of_grid_points());
     671             :   variable_data_ =
     672             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     673             :           rhs.variable_data_);
     674             : }
     675             : 
     676             : template <typename... Tags>
     677             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     678             :     const Variables<tmpl::list<Tags...>>& rhs) {
     679             :   if (&rhs == this) {
     680             :     return *this;
     681             :   }
     682             :   initialize(rhs.number_of_grid_points());
     683             :   variable_data_ =
     684             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     685             :           rhs.variable_data_);
     686             :   return *this;
     687             : }
     688             : 
     689             : template <typename... Tags>
     690             : Variables<tmpl::list<Tags...>>::Variables(Variables<tmpl::list<Tags...>>&& rhs)
     691             :     : variable_data_impl_dynamic_(std::move(rhs.variable_data_impl_dynamic_)),
     692             :       owning_(rhs.owning_),
     693             :       size_(rhs.size()),
     694             :       number_of_grid_points_(rhs.number_of_grid_points()),
     695             :       variable_data_(std::move(rhs.variable_data_)) {
     696             :   if (number_of_grid_points_ == 1) {
     697             : #if defined(__GNUC__) and not defined(__clang__)
     698             : #pragma GCC diagnostic push
     699             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     700             : #endif  // defined(__GNUC__) and not defined(__clang__)
     701             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     702             : #if defined(__GNUC__) and not defined(__clang__)
     703             : #pragma GCC diagnostic pop
     704             : #endif  // defined(__GNUC__) and not defined(__clang__)
     705             :   }
     706             :   rhs.variable_data_impl_dynamic_.reset();
     707             :   rhs.owning_ = true;
     708             :   rhs.size_ = 0;
     709             :   rhs.number_of_grid_points_ = 0;
     710             :   add_reference_variable_data();
     711             : }
     712             : 
     713             : template <typename... Tags>
     714             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     715             :     Variables<tmpl::list<Tags...>>&& rhs) {
     716             :   if (this == &rhs) {
     717             :     return *this;
     718             :   }
     719             :   owning_ = rhs.owning_;
     720             :   size_ = rhs.size_;
     721             :   number_of_grid_points_ = std::move(rhs.number_of_grid_points_);
     722             :   variable_data_ = std::move(rhs.variable_data_);
     723             :   variable_data_impl_dynamic_ = std::move(rhs.variable_data_impl_dynamic_);
     724             :   if (number_of_grid_points_ == 1) {
     725             : #if defined(__GNUC__) and not defined(__clang__)
     726             : #pragma GCC diagnostic push
     727             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     728             : #endif  // defined(__GNUC__) and not defined(__clang__)
     729             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     730             : #if defined(__GNUC__) and not defined(__clang__)
     731             : #pragma GCC diagnostic pop
     732             : #endif  // defined(__GNUC__) and not defined(__clang__)
     733             :   }
     734             : 
     735             :   rhs.variable_data_impl_dynamic_.reset();
     736             :   rhs.owning_ = true;
     737             :   rhs.size_ = 0;
     738             :   rhs.number_of_grid_points_ = 0;
     739             :   add_reference_variable_data();
     740             :   return *this;
     741             : }
     742             : 
     743             : template <typename... Tags>
     744             : template <typename... WrappedTags,
     745             :           Requires<tmpl2::flat_all<
     746             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     747             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     748             : Variables<tmpl::list<Tags...>>::Variables(
     749             :     const Variables<tmpl::list<WrappedTags...>>& rhs) {
     750             :   static_assert(
     751             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     752             :       "Tensor types do not match!");
     753             :   initialize(rhs.number_of_grid_points());
     754             :   variable_data_ =
     755             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     756             :           rhs.variable_data_);
     757             : }
     758             : 
     759             : template <typename... Tags>
     760             : template <typename... WrappedTags,
     761             :           Requires<tmpl2::flat_all<
     762             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     763             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     764             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     765             :     const Variables<tmpl::list<WrappedTags...>>& rhs) {
     766             :   static_assert(
     767             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     768             :       "Tensor types do not match!");
     769             :   initialize(rhs.number_of_grid_points());
     770             :   variable_data_ =
     771             :       static_cast<const blaze::Vector<pointer_type, transpose_flag>&>(
     772             :           rhs.variable_data_);
     773             :   return *this;
     774             : }
     775             : 
     776             : template <typename... Tags>
     777             : template <typename... WrappedTags,
     778             :           Requires<tmpl2::flat_all<
     779             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     780             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     781             : Variables<tmpl::list<Tags...>>::Variables(
     782             :     Variables<tmpl::list<WrappedTags...>>&& rhs)
     783             :     : variable_data_impl_dynamic_(std::move(rhs.variable_data_impl_dynamic_)),
     784             :       owning_(rhs.owning_),
     785             :       size_(rhs.size()),
     786             :       number_of_grid_points_(rhs.number_of_grid_points()),
     787             :       variable_data_(std::move(rhs.variable_data_)) {
     788             :   static_assert(
     789             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     790             :       "Tensor types do not match!");
     791             :   if (number_of_grid_points_ == 1) {
     792             : #if defined(__GNUC__) and not defined(__clang__)
     793             : #pragma GCC diagnostic push
     794             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     795             : #endif  // defined(__GNUC__) and not defined(__clang__)
     796             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     797             : #if defined(__GNUC__) and not defined(__clang__)
     798             : #pragma GCC diagnostic pop
     799             : #endif  // defined(__GNUC__) and not defined(__clang__)
     800             :   }
     801             :   rhs.variable_data_impl_dynamic_.reset();
     802             :   rhs.size_ = 0;
     803             :   rhs.owning_ = true;
     804             :   rhs.number_of_grid_points_ = 0;
     805             :   add_reference_variable_data();
     806             : }
     807             : 
     808             : template <typename... Tags>
     809             : template <typename... WrappedTags,
     810             :           Requires<tmpl2::flat_all<
     811             :               std::is_same<db::remove_all_prefixes<WrappedTags>,
     812             :                            db::remove_all_prefixes<Tags>>::value...>::value>>
     813             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     814             :     Variables<tmpl::list<WrappedTags...>>&& rhs) {
     815             :   static_assert(
     816             :       (std::is_same_v<typename Tags::type, typename WrappedTags::type> and ...),
     817             :       "Tensor types do not match!");
     818             :   variable_data_ = std::move(rhs.variable_data_);
     819             :   owning_ = rhs.owning_;
     820             :   size_ = rhs.size_;
     821             :   number_of_grid_points_ = std::move(rhs.number_of_grid_points_);
     822             :   variable_data_impl_dynamic_ = std::move(rhs.variable_data_impl_dynamic_);
     823             :   if (number_of_grid_points_ == 1) {
     824             : #if defined(__GNUC__) and not defined(__clang__)
     825             : #pragma GCC diagnostic push
     826             : #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
     827             : #endif  // defined(__GNUC__) and not defined(__clang__)
     828             :     variable_data_impl_static_ = std::move(rhs.variable_data_impl_static_);
     829             : #if defined(__GNUC__) and not defined(__clang__)
     830             : #pragma GCC diagnostic pop
     831             : #endif  // defined(__GNUC__) and not defined(__clang__)
     832             :   }
     833             : 
     834             :   rhs.variable_data_impl_dynamic_.reset();
     835             :   rhs.size_ = 0;
     836             :   rhs.owning_ = true;
     837             :   rhs.number_of_grid_points_ = 0;
     838             :   add_reference_variable_data();
     839             :   return *this;
     840             : }
     841             : 
     842             : template <typename... Tags>
     843             : Variables<tmpl::list<Tags...>>::Variables(const pointer start,
     844             :                                           const size_t size) {
     845             :   set_data_ref(start, size);
     846             : }
     847             : 
     848             : template <typename... Tags>
     849             : void Variables<tmpl::list<Tags...>>::pup(PUP::er& p) {
     850             :   ASSERT(
     851             :       owning_,
     852             :       "Cannot pup a non-owning Variables! It may be reasonable to pack a "
     853             :       "non-owning Variables, but not to unpack one. This should be discussed "
     854             :       "in an issue with the core devs if the feature seems necessary.");
     855             :   size_t number_of_grid_points = number_of_grid_points_;
     856             :   p | number_of_grid_points;
     857             :   if (p.isUnpacking()) {
     858             :     initialize(number_of_grid_points);
     859             :   }
     860             :   PUParray(p, variable_data_.data(), size_);
     861             : }
     862             : /// \endcond
     863             : 
     864             : /// @{
     865             : /*!
     866             :  * \ingroup DataStructuresGroup
     867             :  * \brief Return Tag::type pointing into the contiguous array
     868             :  *
     869             :  * \tparam Tag the variable to return
     870             :  */
     871             : template <typename Tag, typename TagList>
     872           1 : constexpr typename Tag::type& get(Variables<TagList>& v) {
     873             :   static_assert(tmpl::list_contains_v<TagList, Tag>,
     874             :                 "Could not retrieve Tag from Variables. See the first "
     875             :                 "template parameter of the instantiation for what Tag is "
     876             :                 "being retrieved and the second template parameter for "
     877             :                 "what Tags are available.");
     878             :   return tuples::get<Tag>(v.reference_variable_data_);
     879             : }
     880             : template <typename Tag, typename TagList>
     881           1 : constexpr const typename Tag::type& get(const Variables<TagList>& v) {
     882             :   static_assert(tmpl::list_contains_v<TagList, Tag>,
     883             :                 "Could not retrieve Tag from Variables. See the first "
     884             :                 "template parameter of the instantiation for what Tag is "
     885             :                 "being retrieved and the second template parameter for "
     886             :                 "what Tags are available.");
     887             :   return tuples::get<Tag>(v.reference_variable_data_);
     888             : }
     889             : /// @}
     890             : 
     891             : template <typename... Tags>
     892             : template <typename VT, bool VF>
     893             : Variables<tmpl::list<Tags...>>::Variables(
     894             :     const blaze::DenseVector<VT, VF>& expression) {
     895             :   ASSERT((*expression).size() % number_of_independent_components == 0,
     896             :          "Invalid size " << (*expression).size() << " for a Variables with "
     897             :          << number_of_independent_components << " components.");
     898             :   initialize((*expression).size() / number_of_independent_components);
     899             :   variable_data_ = expression;
     900             : }
     901             : 
     902             : /// \cond
     903             : template <typename... Tags>
     904             : template <typename VT, bool VF>
     905             : Variables<tmpl::list<Tags...>>& Variables<tmpl::list<Tags...>>::operator=(
     906             :     const blaze::DenseVector<VT, VF>& expression) {
     907             :   ASSERT((*expression).size() % number_of_independent_components == 0,
     908             :          "Invalid size " << (*expression).size() << " for a Variables with "
     909             :          << number_of_independent_components << " components.");
     910             :   initialize((*expression).size() / number_of_independent_components);
     911             :   variable_data_ = expression;
     912             :   return *this;
     913             : }
     914             : /// \endcond
     915             : 
     916             : /// \cond HIDDEN_SYMBOLS
     917             : template <typename... Tags>
     918             : void Variables<tmpl::list<Tags...>>::add_reference_variable_data() {
     919             :   if (size_ == 0) {
     920             :     return;
     921             :   }
     922             :   if (is_owning()) {
     923             :     if (number_of_grid_points_ == 1) {
     924             :       variable_data_.reset(variable_data_impl_static_.data(), size_);
     925             :     } else {
     926             :       variable_data_.reset(variable_data_impl_dynamic_.get(), size_);
     927             :     }
     928             :   }
     929             :   ASSERT(variable_data_.size() == size_ and
     930             :              size_ == number_of_grid_points_ * number_of_independent_components,
     931             :          "Size mismatch: variable_data_.size() = "
     932             :              << variable_data_.size() << " size_ = " << size_ << " should be: "
     933             :              << number_of_grid_points_ * number_of_independent_components
     934             :              << "\nThis is an internal inconsistency bug in Variables. Please "
     935             :                 "file an issue.");
     936             :   size_t variable_offset = 0;
     937             :   tmpl::for_each<tags_list>([this, &variable_offset](auto tag_v) {
     938             :     using Tag = tmpl::type_from<decltype(tag_v)>;
     939             :     auto& var = tuples::get<Tag>(reference_variable_data_);
     940             :     for (size_t i = 0; i < Tag::type::size(); ++i) {
     941             :       var[i].set_data_ref(
     942             :           &variable_data_[variable_offset++ * number_of_grid_points_],
     943             :           number_of_grid_points_);
     944             :     }
     945             :   });
     946             : }
     947             : /// \endcond
     948             : 
     949             : template <typename... Tags>
     950           0 : Variables<tmpl::list<Tags...>>& operator*=(
     951             :     Variables<tmpl::list<Tags...>>& lhs,
     952             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     953             :   using value_type = typename Variables<tmpl::list<Tags...>>::value_type;
     954             :   ASSERT(lhs.number_of_grid_points() == rhs.size(),
     955             :          "Size mismatch in multiplication: " << lhs.number_of_grid_points()
     956             :                                              << " and " << rhs.size());
     957             :   value_type* const lhs_data = lhs.data();
     958             :   const value_type* const rhs_data = rhs.data();
     959             :   for (size_t c = 0; c < lhs.number_of_independent_components; ++c) {
     960             :     for (size_t s = 0; s < lhs.number_of_grid_points(); ++s) {
     961             :       // clang-tidy: do not use pointer arithmetic
     962             :       lhs_data[c * lhs.number_of_grid_points() + s] *= rhs_data[s];  // NOLINT
     963             :     }
     964             :   }
     965             :   return lhs;
     966             : }
     967             : 
     968             : template <typename... Tags>
     969           0 : Variables<tmpl::list<Tags...>> operator*(
     970             :     const Variables<tmpl::list<Tags...>>& lhs,
     971             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     972             :   auto result = lhs;
     973             :   result *= rhs;
     974             :   return result;
     975             : }
     976             : 
     977             : template <typename... Tags>
     978           0 : Variables<tmpl::list<Tags...>> operator*(
     979             :     const typename Variables<tmpl::list<Tags...>>::vector_type& lhs,
     980             :     const Variables<tmpl::list<Tags...>>& rhs) {
     981             :   auto result = rhs;
     982             :   result *= lhs;
     983             :   return result;
     984             : }
     985             : 
     986             : template <typename... Tags>
     987           0 : Variables<tmpl::list<Tags...>>& operator/=(
     988             :     Variables<tmpl::list<Tags...>>& lhs,
     989             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
     990             :   ASSERT(lhs.number_of_grid_points() == rhs.size(),
     991             :          "Size mismatch in multiplication: " << lhs.number_of_grid_points()
     992             :                                              << " and " << rhs.size());
     993             :   using value_type = typename Variables<tmpl::list<Tags...>>::value_type;
     994             :   value_type* const lhs_data = lhs.data();
     995             :   const value_type* const rhs_data = rhs.data();
     996             :   for (size_t c = 0; c < lhs.number_of_independent_components; ++c) {
     997             :     for (size_t s = 0; s < lhs.number_of_grid_points(); ++s) {
     998             :       // clang-tidy: do not use pointer arithmetic
     999             :       lhs_data[c * lhs.number_of_grid_points() + s] /= rhs_data[s];  // NOLINT
    1000             :     }
    1001             :   }
    1002             :   return lhs;
    1003             : }
    1004             : 
    1005             : template <typename... Tags>
    1006           0 : Variables<tmpl::list<Tags...>> operator/(
    1007             :     const Variables<tmpl::list<Tags...>>& lhs,
    1008             :     const typename Variables<tmpl::list<Tags...>>::vector_type& rhs) {
    1009             :   auto result = lhs;
    1010             :   result /= rhs;
    1011             :   return result;
    1012             : }
    1013             : 
    1014             : template <typename... Tags, Requires<sizeof...(Tags) != 0> = nullptr>
    1015           0 : std::ostream& operator<<(std::ostream& os,
    1016             :                          const Variables<tmpl::list<Tags...>>& d) {
    1017             :   size_t count = 0;
    1018             :   const auto helper = [&os, &d, &count](auto tag_v) {
    1019             :     count++;
    1020             :     using Tag = typename decltype(tag_v)::type;
    1021             :     os << db::tag_name<Tag>() << ":\n";
    1022             :     os << get<Tag>(d);
    1023             :     if (count < sizeof...(Tags)) {
    1024             :       os << "\n\n";
    1025             :     }
    1026             :   };
    1027             :   EXPAND_PACK_LEFT_TO_RIGHT(helper(tmpl::type_<Tags>{}));
    1028             :   return os;
    1029             : }
    1030             : 
    1031             : template <typename TagsList>
    1032           0 : bool operator!=(const Variables<TagsList>& lhs,
    1033             :                 const Variables<TagsList>& rhs) {
    1034             :   return not(lhs == rhs);
    1035             : }
    1036             : 
    1037             : template <typename... TagsLhs, typename... TagsRhs,
    1038             :           Requires<not std::is_same<tmpl::list<TagsLhs...>,
    1039             :                                     tmpl::list<TagsRhs...>>::value> = nullptr>
    1040           0 : void swap(Variables<tmpl::list<TagsLhs...>>& lhs,
    1041             :           Variables<tmpl::list<TagsRhs...>>& rhs) {
    1042             :   Variables<tmpl::list<TagsLhs...>> temp{std::move(lhs)};
    1043             :   lhs = std::move(rhs);
    1044             :   rhs = std::move(temp);
    1045             : }
    1046             : 
    1047             : /// \ingroup DataStructuresGroup
    1048             : /// Construct a variables from the `Tensor`s in a `TaggedTuple`.
    1049             : template <typename... Tags>
    1050           1 : Variables<tmpl::list<Tags...>> variables_from_tagged_tuple(
    1051             :     const tuples::TaggedTuple<Tags...>& tuple) {
    1052             :   auto result = make_with_value<Variables<tmpl::list<Tags...>>>(
    1053             :       get<tmpl::front<tmpl::list<Tags...>>>(tuple), 0.0);
    1054             :   result.assign_subset(tuple);
    1055             :   return result;
    1056             : }
    1057             : 
    1058             : namespace MakeWithValueImpls {
    1059             : template <typename TagList>
    1060           0 : struct MakeWithSize<Variables<TagList>> {
    1061           0 :   static SPECTRE_ALWAYS_INLINE Variables<TagList> apply(
    1062             :       const size_t size, const typename Variables<TagList>::value_type value) {
    1063             :     return Variables<TagList>(size, value);
    1064             :   }
    1065             : };
    1066             : 
    1067             : template <typename TagList>
    1068           0 : struct NumberOfPoints<Variables<TagList>> {
    1069           0 :   static SPECTRE_ALWAYS_INLINE size_t apply(const Variables<TagList>& input) {
    1070             :     return input.number_of_grid_points();
    1071             :   }
    1072             : };
    1073             : }  // namespace MakeWithValueImpls
    1074             : 
    1075             : template <typename TagList>
    1076           0 : struct SetNumberOfGridPointsImpls::SetNumberOfGridPointsImpl<
    1077             :     Variables<TagList>> {
    1078           0 :   static constexpr bool is_trivial = false;
    1079           0 :   static SPECTRE_ALWAYS_INLINE void apply(
    1080             :       const gsl::not_null<Variables<TagList>*> result, const size_t size) {
    1081             :     result->initialize(size);
    1082             :   }
    1083             : };
    1084             : 
    1085           1 : namespace EqualWithinRoundoffImpls {
    1086             : // It would be nice to use `blaze::equal` in these implementations, but it
    1087             : // doesn't currently allow to specify a tolerance. See upstream issue:
    1088             : // https://bitbucket.org/blaze-lib/blaze/issues/417/adjust-relaxed-equal-accuracy
    1089             : template <typename TagList, typename Floating>
    1090             : struct EqualWithinRoundoffImpl<Variables<TagList>, Floating,
    1091             :                                Requires<std::is_floating_point_v<Floating>>> {
    1092             :   static bool apply(const Variables<TagList>& lhs, const Floating& rhs,
    1093             :                     const double eps, const double scale) {
    1094             :     for (size_t i = 0; i < lhs.size(); ++i) {
    1095             :       if (not equal_within_roundoff(lhs.data()[i], rhs, eps, scale)) {
    1096             :         return false;
    1097             :       }
    1098             :     }
    1099             :     return true;
    1100             :   }
    1101             : };
    1102             : template <typename TagList, typename Floating>
    1103             : struct EqualWithinRoundoffImpl<Floating, Variables<TagList>,
    1104             :                                Requires<std::is_floating_point_v<Floating>>> {
    1105             :   static SPECTRE_ALWAYS_INLINE bool apply(const Floating& lhs,
    1106             :                                           const Variables<TagList>& rhs,
    1107             :                                           const double eps,
    1108             :                                           const double scale) {
    1109             :     return equal_within_roundoff(rhs, lhs, eps, scale);
    1110             :   }
    1111             : };
    1112             : template <typename LhsTagList, typename RhsTagList>
    1113           0 : struct EqualWithinRoundoffImpl<Variables<LhsTagList>, Variables<RhsTagList>> {
    1114           0 :   static bool apply(const Variables<LhsTagList>& lhs,
    1115             :                     const Variables<RhsTagList>& rhs, const double eps,
    1116             :                     const double scale) {
    1117             :     ASSERT(lhs.size() == rhs.size(),
    1118             :            "Can only compare two Variables of the same size, but lhs has size "
    1119             :                << lhs.size() << " and rhs has size " << rhs.size() << ".");
    1120             :     for (size_t i = 0; i < lhs.size(); ++i) {
    1121             :       if (not equal_within_roundoff(lhs.data()[i], rhs.data()[i], eps, scale)) {
    1122             :         return false;
    1123             :       }
    1124             :     }
    1125             :     return true;
    1126             :   }
    1127             : };
    1128             : }  // namespace EqualWithinRoundoffImpls
    1129             : 
    1130             : namespace db {
    1131             : // Enable subitems for ::Tags::Variables and derived tags (e.g. compute tags).
    1132             : // Other tags that hold a `Variables` don't expose the constituent tensors as
    1133             : // subitems by default.
    1134             : namespace Variables_detail {
    1135             : // Check if the argument is a `::Tags::Variables`, or derived from it. Can't use
    1136             : // `tt:is_a_v` because we also want to match derived classes. Can't use
    1137             : // `std::is_base_of` because `::Tags::Variables` is a template.
    1138             : template <typename TagsList>
    1139             : constexpr std::true_type is_a_variables_tag(::Tags::Variables<TagsList>&&) {
    1140             :   return {};
    1141             : }
    1142             : constexpr std::false_type is_a_variables_tag(...) { return {}; }
    1143             : template <typename Tag>
    1144             : static constexpr bool is_a_variables_tag_v =
    1145             :     decltype(is_a_variables_tag(std::declval<Tag>()))::value;
    1146             : }  // namespace Variables_detail
    1147             : template <typename Tag>
    1148             : struct Subitems<Tag, Requires<Variables_detail::is_a_variables_tag_v<Tag>>> {
    1149             :   using type = typename Tag::type::tags_list;
    1150             : 
    1151             :   template <typename Subtag, typename LocalTag = Tag>
    1152             :   static void create_item(
    1153             :       const gsl::not_null<typename LocalTag::type*> parent_value,
    1154             :       const gsl::not_null<typename Subtag::type*> sub_value) {
    1155             :     auto& vars = get<Subtag>(*parent_value);
    1156             :     // Only update the Tensor if the Variables has changed its allocation
    1157             :     if constexpr (not is_any_spin_weighted_v<typename Subtag::type::type>) {
    1158             :       if (vars.begin()->data() != sub_value->begin()->data()) {
    1159             :         for (auto vars_it = vars.begin(), sub_var_it = sub_value->begin();
    1160             :              vars_it != vars.end(); ++vars_it, ++sub_var_it) {
    1161             :           sub_var_it->set_data_ref(make_not_null(&*vars_it));
    1162             :         }
    1163             :       }
    1164             :     } else {
    1165             :       if (vars.begin()->data().data() != sub_value->begin()->data().data()) {
    1166             :         for (auto vars_it = vars.begin(), sub_var_it = sub_value->begin();
    1167             :              vars_it != vars.end(); ++vars_it, ++sub_var_it) {
    1168             :           sub_var_it->set_data_ref(make_not_null(&*vars_it));
    1169             :         }
    1170             :       }
    1171             :     }
    1172             :   }
    1173             : 
    1174             :   template <typename Subtag>
    1175             :   static const typename Subtag::type& create_compute_item(
    1176             :       const typename Tag::type& parent_value) {
    1177             :     return get<Subtag>(parent_value);
    1178             :   }
    1179             : };
    1180             : }  // namespace db
    1181             : 
    1182             : namespace Variables_detail {
    1183             : template <typename Tags>
    1184             : using MathWrapperVectorType = tmpl::conditional_t<
    1185             :     std::is_same_v<typename Variables<Tags>::value_type, double>, DataVector,
    1186             :     ComplexDataVector>;
    1187             : }  // namespace Variables_detail
    1188             : 
    1189             : template <typename Tags>
    1190           0 : auto make_math_wrapper(const gsl::not_null<Variables<Tags>*> data) {
    1191             :   using Vector = Variables_detail::MathWrapperVectorType<Tags>;
    1192             :   Vector referencing(data->data(), data->size());
    1193             :   return make_math_wrapper(&referencing);
    1194             : }
    1195             : 
    1196             : template <typename Tags>
    1197           0 : auto make_math_wrapper(const Variables<Tags>& data) {
    1198             :   using Vector = Variables_detail::MathWrapperVectorType<Tags>;
    1199             :   const Vector referencing(
    1200             :       const_cast<typename Vector::value_type*>(data.data()), data.size());
    1201             :   return make_math_wrapper(referencing);
    1202             : }
    1203             : 
    1204             : /// \cond
    1205             : template <size_t I, class... Tags>
    1206             : inline constexpr typename tmpl::at_c<tmpl::list<Tags...>, I>::type&& get(
    1207             :     Variables<tmpl::list<Tags...>>&& t) {
    1208             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1209             : }
    1210             : 
    1211             : template <size_t I, class... Tags>
    1212             : inline constexpr const typename tmpl::at_c<tmpl::list<Tags...>, I>::type& get(
    1213             :     const Variables<tmpl::list<Tags...>>& t) {
    1214             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1215             : }
    1216             : 
    1217             : template <size_t I, class... Tags>
    1218             : inline constexpr typename tmpl::at_c<tmpl::list<Tags...>, I>::type& get(
    1219             :     Variables<tmpl::list<Tags...>>& t) {
    1220             :   return get<tmpl::at_c<tmpl::list<Tags...>, I>>(t);
    1221             : }
    1222             : /// \endcond
    1223             : 
    1224             : namespace std {
    1225             : template <typename... Tags>
    1226             : struct tuple_size<Variables<tmpl::list<Tags...>>>
    1227             :     : std::integral_constant<int, sizeof...(Tags)> {};
    1228             : template <size_t I, typename... Tags>
    1229             : struct tuple_element<I, Variables<tmpl::list<Tags...>>> {
    1230             :   using type = typename tmpl::at_c<tmpl::list<Tags...>, I>::type;
    1231             : };
    1232             : }  // namespace std
    1233             : 
    1234             : template <typename TagsList>
    1235           0 : bool contains_allocations(const Variables<TagsList>& value) {
    1236             :   return value.number_of_grid_points() > 1;
    1237             : }
    1238             : 
    1239           0 : inline bool contains_allocations(const Variables<tmpl::list<>>& /*value*/) {
    1240             :   return false;
    1241             : }

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