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field.hh
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			/**
			* @file field.hh
			*
			* @author Till Junge <till.junge@epfl.ch>
			*
			* @date 07 Sep 2017
			*
			* @brief header-only implementation of a field for field collections
			*
			* Copyright © 2017 Till Junge
			*
			* µSpectre is free software; you can redistribute it and/or
			* modify it under the terms of the GNU General Public License as
			* published by the Free Software Foundation, either version 3, or (at
			* your option) any later version.
			*
			* µSpectre is distributed in the hope that it will be useful, but
			* WITHOUT ANY WARRANTY; without even the implied warranty of
			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
			* General Public License for more details.
			*
			* You should have received a copy of the GNU General Public License
			* along with GNU Emacs; see the file COPYING. If not, write to the
			* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
			* Boston, MA 02111-1307, USA.
			*/


			#ifndef FIELD_H
			#define FIELD_H

			#include "common/T4_map_proxy.hh"

			#include <Eigen/Dense>

			#include <string>
			#include <sstream>
			#include <utility>
			#include <typeinfo>
			#include <vector>
			#include <algorithm>
			#include <cmath>
			#include <memory>
			#include <type_traits>

			namespace muSpectre {

			/* ---------------------------------------------------------------------- */
			/**
			* base class for field collection-related exceptions
			*/
			class FieldCollectionError: public std::runtime_error {
			public:
			//! constructor
			explicit FieldCollectionError(const std::string& what)
			:std::runtime_error(what){}
			//! constructor
			explicit FieldCollectionError(const char * what)
			:std::runtime_error(what){}
			};

			/// base class for field-related exceptions
			class FieldError: public FieldCollectionError {
			using Parent = FieldCollectionError;
			public:
			//! constructor
			explicit FieldError(const std::string& what)
			:Parent(what){}
			//! constructor
			explicit FieldError(const char * what)
			:Parent(what){}
			};

			/**
			* Thrown when a associating a field map to and incompatible field
			* is attempted
			*/
			class FieldInterpretationError: public FieldError
			{
			public:
			//! constructor
			explicit FieldInterpretationError(const std::string & what)
			:FieldError(what){}
			//! constructor
			explicit FieldInterpretationError(const char * what)
			:FieldError(what){}
			};


			namespace internal {

			/* ---------------------------------------------------------------------- */
			/**
			* Virtual base class for all fields. A field represents meta-information
			* for the per-pixel storage for a scalar, vector or tensor quantity and
			* is therefore the abstract class defining the field. It is used for type
			* and size checking at runtime and for storage of polymorphic pointers to
			* fully typed and sized fields. `FieldBase` (and its children) are
			* templated with a specific `FieldCollection`. A `FieldCollection` stores
			* multiple fields that all apply to the same set of pixels. Allocating
			* and managing the data for all pixels is handled by the `FieldCollection`.
			* Note that `FieldBase` does not know anything about about mathematical
			* operations on the data or how to iterate over all pixels. Mapping the
			* raw data onto Eigen classes and iterating over those is handled by
			* the `FieldMap`.
			* `FieldBase` has the specialisation `TypedFieldBase`.
			*/
			template <class FieldCollection>
			class FieldBase
			{

			protected:
			//! constructor
			//! unique name (whithin Collection)
			//! number of components
			//! collection to which this field belongs (eg, material, system)
			FieldBase(std::string unique_name,
			size_t nb_components,
			FieldCollection & collection);

			public:
			using collection_t = FieldCollection; //!< for type checks

			//! Copy constructor
			FieldBase(const FieldBase &other) = delete;

			//! Move constructor
			FieldBase(FieldBase &&other) = delete;

			//! Destructor
			virtual ~FieldBase() = default;

			//! Copy assignment operator
			FieldBase& operator=(const FieldBase &other) = delete;

			//! Move assignment operator
			FieldBase& operator=(FieldBase &&other) = delete;

			/* ---------------------------------------------------------------------- */
			//!Identifying accessors
			//! return field name
			inline const std::string & get_name() const;
			//! return field type
			//inline const Field_t & get_type() const;
			//! return my collection (for iterating)
			inline const FieldCollection & get_collection() const;
			//! return my collection (for iterating)
			inline const size_t & get_nb_components() const;
			//! return type_id of stored type
			virtual const std::type_info & get_stored_typeid() const = 0;

			//! number of pixels in the field
			virtual size_t size() const = 0;

			//! initialise field to zero (do more complicated initialisations through
			//! fully typed maps)
			virtual void set_zero() = 0;

			//! give access to collections
			friend FieldCollection;
			//! give access to collection's base class
			friend typename FieldCollection::Parent;

			protected:
			/* ---------------------------------------------------------------------- */
			//! allocate memory etc
			virtual void resize(size_t size) = 0;
			const std::string name; //!< the field's unique name
			const size_t nb_components; //!< number of components per entry
			//! reference to the collection this field belongs to
			const FieldCollection & collection;
			private:
			};


			/**
			* Dummy intermediate class to provide a run-time polymorphic
			* typed field. Mainly for binding Python. TypedFieldBase specifies methods
			* that return typed Eigen maps and vectors in addition to pointers to the
			* raw data.
			* `TypedFieldBase` has the specialisation `TypedSizedFieldBase`.
			*/
			template <class FieldCollection, typename T>
			class TypedFieldBase: public FieldBase<FieldCollection>
			{
			public:
			using Parent = FieldBase<FieldCollection>; //!< base class
			//! for type checks when mapping this field
			using collection_t = typename Parent::collection_t;
			using Scalar = T; //!< for type checks
			using Base = Parent; //!< for uniformity of interface
			//! Plain Eigen type to map
			using EigenRep = Eigen::Array<T, Eigen::Dynamic, Eigen::Dynamic>;
			//! map returned when iterating over field
			using EigenMap = Eigen::Map<EigenRep>;
			//! Plain eigen vector to map
			using EigenVec = Eigen::Map<Eigen::VectorXd>;
			//! vector map returned when iterating over field
			using EigenVecConst = Eigen::Map<const Eigen::VectorXd>;
			//! Default constructor
			TypedFieldBase() = delete;

			//! constructor
			TypedFieldBase(std::string unique_name,
			size_t nb_components,
			FieldCollection& collection);

			//! Copy constructor
			TypedFieldBase(const TypedFieldBase &other) = delete;

			//! Move constructor
			TypedFieldBase(TypedFieldBase &&other) = delete;

			//! Destructor
			virtual ~TypedFieldBase() = default;

			//! Copy assignment operator
			TypedFieldBase& operator=(const TypedFieldBase &other) = delete;

			//! Move assignment operator
			TypedFieldBase& operator=(TypedFieldBase &&other) = delete;

			//! return type_id of stored type
			virtual const std::type_info & get_stored_typeid() const override final;

			virtual size_t size() const override = 0;

			//! initialise field to zero (do more complicated initialisations through
			//! fully typed maps)
			virtual void set_zero() override = 0;

			//! raw pointer to content (e.g., for Eigen maps)
			virtual T* data() = 0;
			//! raw pointer to content (e.g., for Eigen maps)
			virtual const T* data() const = 0;

			//! return a map representing the entire field as a single `Eigen::Array`
			EigenMap eigen();
			//! return a map representing the entire field as a single Eigen vector
			EigenVec eigenvec();
			//! return a map representing the entire field as a single Eigen vector
			EigenVecConst eigenvec() const;

			protected:
			private:
			};

			/* ---------------------------------------------------------------------- */
			//! declaraton for friending
			template <class FieldCollection, typename T, Dim_t NbComponents, bool isConst>
			class FieldMap;

			/* ---------------------------------------------------------------------- */
			/**
			* A `TypedSizeFieldBase` is the base class for fields that contain
			* statically known number of scalars of a statically known type per pixel
			* in a `muSpectre::FieldCollection`. The actual data for all pixels is
			* stored in `TypedSizeFieldBase::values`.
			* `TypedSizedFieldBase` has the specialisations `MatrixField` and
			* `TensorField`.
			*/
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ArrayStore=false>
			class TypedSizedFieldBase: public TypedFieldBase<FieldCollection, T>
			{
			friend class FieldMap<FieldCollection, T, NbComponents, true>;
			friend class FieldMap<FieldCollection, T, NbComponents, false>;
			public:
			//! for compatibility checks
			constexpr static auto nb_components{NbComponents};
			using Parent = TypedFieldBase<FieldCollection, T>; //!< base class
			using Scalar = T; //!< for type checking
			using Base = typename Parent::Base; //!< root base class

			//! type stored if ArrayStore is true
			using StoredType = Eigen::Array<T, NbComponents, 1>;
			//! storage container
			using StorageType = std::conditional_t
			<ArrayStore,
			std::vector<StoredType,
			Eigen::aligned_allocator<StoredType>>,
			std::vector<T,Eigen::aligned_allocator<T>>>;

			//! Plain type that is being mapped (Eigen lingo)
			using EigenRep = Eigen::Array<T, NbComponents, Eigen::Dynamic>;
			//! maps returned when iterating over field
			using EigenMap = std::conditional_t<
			ArrayStore,
			Eigen::Map<EigenRep, Eigen::Aligned,
			Eigen::OuterStride<sizeof(StoredType)/sizeof(T)>>,
			Eigen::Map<EigenRep>>;

			//! maps returned when iterating over field
			using ConstEigenMap = std::conditional_t<
			ArrayStore,
			Eigen::Map<const EigenRep, Eigen::Aligned,
			Eigen::OuterStride<sizeof(StoredType)/sizeof(T)>>,
			Eigen::Map<const EigenRep>>;

			//! constructor
			TypedSizedFieldBase(std::string unique_name,
			FieldCollection& collection);
			virtual ~TypedSizedFieldBase() = default;

			//! initialise field to zero (do more complicated initialisations through
			//! fully typed maps)
			inline void set_zero() override final;

			//! add a new value at the end of the field
			template <bool isArrayStore = ArrayStore>
			inline void push_back(const
			std::enable_if_t<isArrayStore, StoredType> &
			value);

			//! add a new value at the end of the field
			template <bool componentStore = !ArrayStore>
			inline std::enable_if_t<componentStore> push_back(const StoredType & value);

			//! Number of stored arrays (i.e. total number of stored
			//! scalars/NbComponents)
			size_t size() const override final;

			/**
			* returns an upcasted reference to a field, or throws an
			* exception if the field is incompatible
			*/
			static TypedSizedFieldBase & check_ref(Base & other);
			/**
			* returns an upcasted reference to a field, or throws an
			* exception if the field is incompatible
			*/
			static const TypedSizedFieldBase & check_ref(const Base & other);

			//! return raw pointer to stored data (necessary for Eigen maps)
			inline T* data() override final {return this->get_ptr_to_entry(0);}
			//! return raw pointer to stored data (necessary for Eigen maps)
			inline const T* data() const override final {return this->get_ptr_to_entry(0);}

			//! return a map representing the entire field as a single `Eigen::Array`
			inline EigenMap eigen();
			//! return a map representing the entire field as a single `Eigen::Array`
			inline ConstEigenMap eigen() const;
			/**
			* return a map representing the entire field as a single
			* dynamically sized `Eigen::Array` (for python bindings)
			*/
			inline typename Parent::EigenMap dyn_eigen() {return Parent::eigen();}

			//! inner product between compatible fields
			template<typename otherT>
			inline Real inner_product(const TypedSizedFieldBase<FieldCollection, otherT, NbComponents,
			ArrayStore> & other) const;
			protected:

			//! returns a raw pointer to the entry, for `Eigen::Map`
			template <bool isArray=ArrayStore>
			inline std::enable_if_t<isArray, T*> get_ptr_to_entry(const size_t&& index);

			//! returns a raw pointer to the entry, for `Eigen::Map`
			template <bool isArray=ArrayStore>
			inline std::enable_if_t<isArray, const T*>
			get_ptr_to_entry(const size_t&& index) const;

			//! returns a raw pointer to the entry, for `Eigen::Map`
			template <bool noArray = !ArrayStore>
			inline T* get_ptr_to_entry(std::enable_if_t<noArray, const size_t&&> index);

			//! returns a raw pointer to the entry, for `Eigen::Map`
			template <bool noArray = !ArrayStore>
			inline const T*
			get_ptr_to_entry(std::enable_if_t<noArray, const size_t&&> index) const;

			//! set the storage size of this field
			inline virtual void resize(size_t size) override final;

			//! The actual storage container
			StorageType values{};
			};

			} // internal


			/* ---------------------------------------------------------------------- */
			/**
			* The `TensorField` is a subclass of `muSpectre::internal::TypedSizedFieldBase`
			* that represents tensorial fields, i.e. arbitrary-dimensional arrays with
			* identical number of rows/columns (that typically correspond to the spatial
			* cartesian dimensions). It is defined by the stored scalar type @a T, the
			* tensorial order @a order (often also called degree or rank) and the
			* number of spatial dimensions @a dim.
			*/
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			class TensorField: public internal::TypedSizedFieldBase<FieldCollection,
			T,
			ipow(dim,order)>
			{
			public:
			//! base class
			using Parent = internal::TypedSizedFieldBase<FieldCollection,
			T,
			ipow(dim,order)>;
			using Base = typename Parent::Base; //!< root base class
			//! polymorphic base class
			using Field_p = typename FieldCollection::Field_p;
			using Scalar = typename Parent::Scalar; //!< for type checking
			//! Copy constructor
			TensorField(const TensorField &other) = delete;

			//! Move constructor
			TensorField(TensorField &&other) = delete;

			//! Destructor
			virtual ~TensorField() = default;

			//! Copy assignment operator
			TensorField& operator=(const TensorField &other) = delete;

			//! Move assignment operator
			TensorField& operator=(TensorField &&other) = delete;

			//! return the order of the stored tensor
			inline Dim_t get_order() const;
			//! return the dimension of the stored tensor
			inline Dim_t get_dim() const;


			//! factory function
			template<class FieldType, class CollectionType, typename... Args>
			friend FieldType& make_field(std::string unique_name,
			CollectionType & collection,
			Args&&... args);

			//! return a reference or throw an exception if `other` is incompatible
			static TensorField & check_ref(Base & other) {
			return static_cast<TensorField &>(Parent::check_ref(other));}
			//! return a reference or throw an exception if `other` is incompatible
			static const TensorField & check_ref(const Base & other) {
			return static_cast<const TensorField &>(Parent::check_ref(other));}

			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `MatrixFieldMap` with @a dim rows and one column if the tensorial
			* order @a order is unity.
			* - A `MatrixFieldMap` with @a dim rows and @a dim columns if the tensorial
			* order @a order is 2.
			* - A `T4MatrixFieldMap` if the tensorial order is 4.
			*/
			decltype(auto) get_map();
			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `MatrixFieldMap` with @a dim rows and one column if the tensorial
			* order @a order is unity.
			* - A `MatrixFieldMap` with @a dim rows and @a dim columns if the tensorial
			* order @a order is 2.
			* - A `T4MatrixFieldMap` if the tensorial order is 4.
			*/
			decltype(auto) get_const_map();
			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `MatrixFieldMap` with @a dim rows and one column if the tensorial
			* order @a order is unity.
			* - A `MatrixFieldMap` with @a dim rows and @a dim columns if the tensorial
			* order @a order is 2.
			* - A `T4MatrixFieldMap` if the tensorial order is 4.
			*/
			decltype(auto) get_map() const;

			protected:
			//! constructor protected!
			TensorField(std::string unique_name, FieldCollection & collection);

			private:
			};

			/* ---------------------------------------------------------------------- */
			/**
			* The `MatrixField` is subclass of `muSpectre::internal::TypedSizedFieldBase`
			* that represents matrix fields, i.e. a two dimensional arrays, defined by
			* the stored scalar type @a T and the number of rows @a NbRow and columns
			* @a NbCol of the matrix.
			*/
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol=NbRow>
			class MatrixField: public internal::TypedSizedFieldBase<FieldCollection,
			T,
			NbRow*NbCol>
			{
			public:
			//! base class
			using Parent = internal::TypedSizedFieldBase<FieldCollection,
			T,
			NbRow*NbCol>;
			using Base = typename Parent::Base; //!< root base class
			//! polymorphic base field ptr to store
			using Field_p = std::unique_ptr<internal::FieldBase<FieldCollection>>;
			//! Copy constructor
			MatrixField(const MatrixField &other) = delete;

			//! Move constructor
			MatrixField(MatrixField &&other) = delete;

			//! Destructor
			virtual ~MatrixField() = default;

			//! Copy assignment operator
			MatrixField& operator=(const MatrixField &other) = delete;

			//! Move assignment operator
			MatrixField& operator=(MatrixField &&other) = delete;

			//! returns the number of rows
			inline Dim_t get_nb_row() const;
			//! returns the number of columns
			inline Dim_t get_nb_col() const;


			//! factory function
			template<class FieldType, class CollectionType, typename... Args>
			friend FieldType& make_field(std::string unique_name,
			CollectionType & collection,
			Args&&... args);

			//! returns a `MatrixField` reference if `other` is a compatible field
			static MatrixField & check_ref(Base & other) {
			return static_cast<MatrixField &>(Parent::check_ref(other));}
			//! returns a `MatrixField` reference if `other` is a compatible field
			static const MatrixField & check_ref(const Base & other) {
			return static_cast<const MatrixField &>(Parent::check_ref(other));}

			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `ScalarFieldMap` if @a NbRows and @a NbCols are unity.
			* - A `MatrixFieldMap` with @a NbRows rows and @a NbCols columns
			* otherwise.
			*/
			decltype(auto) get_map();
			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `ScalarFieldMap` if @a NbRows and @a NbCols are unity.
			* - A `MatrixFieldMap` with @a NbRows rows and @a NbCols columns
			* otherwise.
			*/
			decltype(auto) get_const_map();
			/**
			* Convenience functions to return a map onto this field. A map allows
			* iteration over all pixels. The map's iterator returns an object that
			* represents the underlying mathematical structure of the field and
			* implements common linear algebra operations on it.
			* Specifically, this function returns
			* - A `ScalarFieldMap` if @a NbRows and @a NbCols are unity.
			* - A `MatrixFieldMap` with @a NbRows rows and @a NbCols columns
			* otherwise.
			*/
			decltype(auto) get_map() const;


			protected:
			//! constructor protected!
			MatrixField(std::string unique_name, FieldCollection & collection);

			private:
			};

			/* ---------------------------------------------------------------------- */
			//! convenience alias (
			template <class FieldCollection, typename T>
			using ScalarField = MatrixField<FieldCollection, T, 1, 1>;
			/* ---------------------------------------------------------------------- */
			// Implementations
			namespace internal {
			/* ---------------------------------------------------------------------- */
			template <class FieldCollection>
			FieldBase<FieldCollection>::FieldBase(std::string unique_name,
			size_t nb_components_,
			FieldCollection & collection_)
			:name(unique_name), nb_components(nb_components_),
			collection(collection_) {}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection>
			inline const std::string & FieldBase<FieldCollection>::get_name() const {
			return this->name;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection>
			inline const FieldCollection & FieldBase<FieldCollection>::
			get_collection() const {
			return this->collection;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection>
			inline const size_t & FieldBase<FieldCollection>::
			get_nb_components() const {
			return this->nb_components;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T>
			TypedFieldBase<FieldCollection, T>::
			TypedFieldBase(std::string unique_name, size_t nb_components,
			FieldCollection & collection)
			:Parent(unique_name, nb_components, collection)
			{}

			/* ---------------------------------------------------------------------- */
			//! return type_id of stored type
			template <class FieldCollection, typename T>
			const std::type_info & TypedFieldBase<FieldCollection, T>::
			get_stored_typeid() const {
			return typeid(T);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T>
			typename TypedFieldBase<FieldCollection, T>::EigenMap
			TypedFieldBase<FieldCollection, T>::
			eigen() {
			return EigenMap(this->data(), this->get_nb_components(), this->size());
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T>
			typename TypedFieldBase<FieldCollection, T>::EigenVec
			TypedFieldBase<FieldCollection, T>::
			eigenvec() {
			return EigenVec(this->data(), this->get_nb_components() * this->size());
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T>
			typename TypedFieldBase<FieldCollection, T>::EigenVecConst
			TypedFieldBase<FieldCollection, T>::
			eigenvec() const{
			return EigenVecConst(this->data(), this->get_nb_components() * this->size());
			}


			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			TypedSizedFieldBase(std::string unique_name, FieldCollection & collection)
			:Parent(unique_name, NbComponents, collection){
			static_assert
			((std::is_arithmetic<T>::value \|\|
			std::is_same<T, Complex>::value),
			"Use TypedSizedFieldBase for integer, real or complex scalars for T");
			static_assert(NbComponents > 0,
			"Only fields with more than 0 components");
			}

			/* ---------------------------------------------------------------------- */
			template<class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			void
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			set_zero() {
			std::fill(this->values.begin(), this->values.end(), T{});
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			size_t TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			size() const {
			if (ArrayStore) {
			return this->values.size();
			} else {
			return this->values.size()/NbComponents;
			}
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore> &
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			check_ref(Base & other) {
			if (typeid(T).hash_code() != other.get_stored_typeid().hash_code()) {
			std::string err ="Cannot create a Reference of requested type " +(
			"for field '" + other.get_name() + "' of type '" +
			other.get_stored_typeid().name() + "'");
			throw std::runtime_error
			(err);
			}
			//check size compatibility
			if (NbComponents != other.get_nb_components()) {
			throw std::runtime_error
			("Cannot create a Reference to a field with " +
			std::to_string(NbComponents) + " components " +
			"for field '" + other.get_name() + "' with " +
			std::to_string(other.get_nb_components()) + " components");
			}
			return static_cast<TypedSizedFieldBase&>(other);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ArrayStore>
			const TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore> &
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			check_ref(const Base & other) {
			if (typeid(T).hash_code() != other.get_stored_typeid().hash_code()) {
			std::stringstream err_str{};
			err_str << "Cannot create a Reference of requested type "
			<< "for field '" << other.get_name() << "' of type '"
			<< other.get_stored_typeid().name() << "'";
			throw std::runtime_error
			(err_str.str());
			}
			//check size compatibility
			if (NbComponents != other.get_nb_components()) {
			throw std::runtime_error
			("Cannot create a Reference to a field with " +
			std::to_string(NbComponents) + " components " +
			"for field '" + other.get_name() + "' with " +
			std::to_string(other.get_nb_components()) + " components");
			}
			return static_cast<const TypedSizedFieldBase&>(other);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ArrayStore>
			typename TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::EigenMap
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			eigen() {
			return EigenMap(this->data(), NbComponents, this->size());
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ArrayStore>
			typename TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::ConstEigenMap
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			eigen() const {
			return ConstEigenMap(this->data(), NbComponents, this->size());
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ArrayStore>
			template<typename otherT>
			Real
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			inner_product(const TypedSizedFieldBase<FieldCollection, otherT, NbComponents,
			ArrayStore> & other) const {
			return (this->eigen() * other.eigen()).sum();
			}


			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool isArray>
			std::enable_if_t<isArray, T*>
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			get_ptr_to_entry(const size_t&& index) {
			static_assert (isArray == ArrayStore, "SFINAE");
			return &this->values[std::move(index)](0, 0);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool noArray>
			T* TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			get_ptr_to_entry(std::enable_if_t<noArray, const size_t&&> index) {
			static_assert (noArray != ArrayStore, "SFINAE");
			return &this->values[NbComponents*std::move(index)];
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool isArray>
			std::enable_if_t<isArray, const T*>
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			get_ptr_to_entry(const size_t&& index) const {
			static_assert (isArray == ArrayStore, "SFINAE");
			return &this->values[std::move(index)](0, 0);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool noArray>
			const T* TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			get_ptr_to_entry(std::enable_if_t<noArray, const size_t&&> index) const {
			static_assert (noArray != ArrayStore, "SFINAE");
			return &this->values[NbComponents*std::move(index)];
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			void TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			resize(size_t size) {
			if (ArrayStore) {
			this->values.resize(size);
			} else {
			this->values.resize(size*NbComponents);
			}
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool isArrayStore>
			void
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			push_back(const std::enable_if_t<isArrayStore,StoredType> & value) {
			static_assert(isArrayStore == ArrayStore, "SFINAE");
			this->values.push_back(value);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents, bool ArrayStore>
			template <bool componentStore>
			std::enable_if_t<componentStore>
			TypedSizedFieldBase<FieldCollection, T, NbComponents, ArrayStore>::
			push_back(const StoredType & value) {
			static_assert(componentStore != ArrayStore, "SFINAE");
			for (Dim_t i = 0; i < NbComponents; ++i) {
			this->values.push_back(value(i));
			}
			}

			} // internal

			/* ---------------------------------------------------------------------- */
			//! Factory function, guarantees that only fields get created that are
			//! properly registered and linked to a collection.
			template<class FieldType, class FieldCollection, typename... Args>
			FieldType &
			make_field(std::string unique_name,
			FieldCollection & collection,
			Args&&... args) {
			auto ptr = std::unique_ptr<FieldType>{
			new FieldType(unique_name, collection, args...)};
			auto& retref = *ptr;
			collection.register_field(std::move(ptr));
			return retref;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			TensorField<FieldCollection, T, order, dim>::
			TensorField(std::string unique_name, FieldCollection & collection)
			:Parent(unique_name, collection) {}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			Dim_t TensorField<FieldCollection, T, order, dim>::
			get_order() const {
			return order;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			Dim_t TensorField<FieldCollection, T, order, dim>::
			get_dim() const {
			return dim;
			}


			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			MatrixField<FieldCollection, T, NbRow, NbCol>::
			MatrixField(std::string unique_name, FieldCollection & collection)
			:Parent(unique_name, collection) {}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			Dim_t MatrixField<FieldCollection, T, NbRow, NbCol>::
			get_nb_col() const {
			return NbCol;
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			Dim_t MatrixField<FieldCollection, T, NbRow, NbCol>::
			get_nb_row() const {
			return NbRow;
			}

			} // muSpectre

			#include "common/field_map.hh"

			namespace muSpectre {

			namespace internal {

			/* ---------------------------------------------------------------------- */
			/**
			* defines the default mapped type obtained when calling
			* `muSpectre::TensorField::get_map()`
			*/
			template <class FieldCollection, typename T, size_t order, Dim_t dim,
			bool ConstMap>
			struct tensor_map_type {
			};

			/// specialisation for vectors
			template <class FieldCollection, typename T, Dim_t dim, bool ConstMap>
			struct tensor_map_type<FieldCollection, T, firstOrder, dim, ConstMap> {
			//! use this type
			using type = MatrixFieldMap<FieldCollection, T, dim, 1, ConstMap>;
			};

			/// specialisation to second-order tensors (matrices)
			template <class FieldCollection, typename T, Dim_t dim, bool ConstMap>
			struct tensor_map_type<FieldCollection, T, secondOrder, dim, ConstMap> {
			//! use this type
			using type = MatrixFieldMap<FieldCollection, T, dim, dim, ConstMap>;
			};

			/// specialisation to fourth-order tensors
			template <class FieldCollection, typename T, Dim_t dim, bool ConstMap>
			struct tensor_map_type<FieldCollection, T, fourthOrder, dim, ConstMap> {
			//! use this type
			using type = T4MatrixFieldMap<FieldCollection, T, dim, ConstMap>;
			};

			/* ---------------------------------------------------------------------- */
			/**
			* defines the default mapped type obtained when calling
			* `muSpectre::MatrixField::get_map()`
			*/
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol,
			bool ConstMap>
			struct matrix_map_type {
			//! mapping type
			using type =
			MatrixFieldMap<FieldCollection, T, NbRow, NbCol, ConstMap>;
			};

			//! specialisation to scalar fields
			template <class FieldCollection, typename T, bool ConstMap>
			struct matrix_map_type<FieldCollection, T, oneD, oneD, ConstMap> {
			//! mapping type
			using type = ScalarFieldMap<FieldCollection, T, ConstMap>;
			};

			} // internal

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			decltype(auto) TensorField<FieldCollection, T, order, dim>::
			get_map() {
			constexpr bool map_constness{false};
			using RawMap_t =
			typename internal::tensor_map_type<FieldCollection, T, order, dim,
			map_constness>::type;
			return RawMap_t(*this);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			decltype(auto) TensorField<FieldCollection, T, order, dim>::
			get_const_map() {
			constexpr bool map_constness{true};
			using RawMap_t =
			typename internal::tensor_map_type<FieldCollection, T, order, dim,
			map_constness>::type;
			return RawMap_t(*this);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t order, Dim_t dim>
			decltype(auto) TensorField<FieldCollection, T, order, dim>::
			get_map() const {
			constexpr bool map_constness{true};
			using RawMap_t =
			typename internal::tensor_map_type<FieldCollection, T, order, dim,
			map_constness>::type;
			return RawMap_t(*this);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			decltype(auto) MatrixField<FieldCollection, T, NbRow, NbCol>::
			get_map() {
			constexpr bool map_constness{false};
			using RawMap_t =
			typename internal::matrix_map_type<FieldCollection, T, NbRow, NbCol,
			map_constness>::type;
			return RawMap_t(*this);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			decltype(auto) MatrixField<FieldCollection, T, NbRow, NbCol>::
			get_const_map() {
			constexpr bool map_constness{true};
			using RawMap_t =
			typename internal::matrix_map_type<FieldCollection, T, NbRow, NbCol,
			map_constness>::type;
			return RawMap_t(*this);
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbRow, Dim_t NbCol>
			decltype(auto) MatrixField<FieldCollection, T, NbRow, NbCol>::
			get_map() const {
			constexpr bool map_constness{true};
			using RawMap_t =
			typename internal::matrix_map_type<FieldCollection, T, NbRow, NbCol,
			map_constness>::type;
			return RawMap_t(*this);
			}


			} // muSpectre

			#endif /* FIELD_H */

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