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field_map_base.hh
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			/**
			* @file field_map.hh
			*
			* @author Till Junge <till.junge@epfl.ch>
			*
			* @date 12 Sep 2017
			*
			* @brief Defined a strongly defines proxy that iterates efficiently over a
			* field
			*
			* Copyright © 2017 Till Junge
			*
			* µSpectre is free software; you can redistribute it and/or
			* modify it under the terms of the GNU Lesser 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 Lesser General Public License
			* along with µSpectre; see the file COPYING. If not, write to the
			* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
			* * Boston, MA 02111-1307, USA.
			*
			* Additional permission under GNU GPL version 3 section 7
			*
			* If you modify this Program, or any covered work, by linking or combining it
			* with proprietary FFT implementations or numerical libraries, containing parts
			* covered by the terms of those libraries' licenses, the licensors of this
			* Program grant you additional permission to convey the resulting work.
			*/

			#ifndef SRC_COMMON_FIELD_MAP_BASE_HH_
			#define SRC_COMMON_FIELD_MAP_BASE_HH_

			#include "common/common.hh"
			#include "common/field.hh"
			#include "field_collection_base.hh"

			#include <unsupported/Eigen/CXX11/Tensor>

			#include <array>
			#include <memory>
			#include <string>

			namespace muSpectre {

			namespace internal {
			/**
			* Forward-declaration
			*/
			template <class FieldCollection, typename T, Dim_t NbComponents>
			class TypedSizedFieldBase;

			//! little helper to automate creation of const maps without duplication
			template <class T, bool isConst> struct const_corrector {
			//! non-const type
			using type = typename T::reference;
			};

			//! specialisation for constant case
			template <class T> struct const_corrector<T, true> {
			//! const type
			using type = typename T::const_reference;
			};

			//! convenience alias
			template <class T, bool isConst>
			using const_corrector_t = typename const_corrector<T, isConst>::type;

			//----------------------------------------------------------------------------//
			/**
			* `FieldMap` provides two central mechanisms:
			* - Map a field (that knows only about the size of the underlying object,
			* onto the mathematical object (reprensented by the respective Eigen class)
			* that provides linear algebra functionality.
			* - Provide an iterator that allows to iterate over all pixels.
			* A field is represented by `FieldBase` or a derived class.
			* `FieldMap` has the specialisations `MatrixLikeFieldMap`,
			* `ScalarFieldMap` and `TensorFieldMap`.
			*/
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			class FieldMap {
			static_assert((NbComponents != 0),
			"Fields with now components make no sense.");
			/*
			* Eigen::Dynamic is equal to -1, and is a legal value, hence
			* the following peculiar check
			*/
			static_assert(
			(NbComponents > -2),
			"Fields with a negative number of components make no sense.");

			public:
			//! Fundamental type stored
			using Scalar = T;
			//! number of scalars per entry
			constexpr static auto nb_components{NbComponents};
			//! non-constant version of field
			using TypedField_nc = std::conditional_t<
			(NbComponents >= 1),
			TypedSizedFieldBase<FieldCollection, T, NbComponents>,
			TypedField<FieldCollection, T>>;
			//! field type as seen from iterator
			using TypedField_t =
			std::conditional_t<ConstField, const TypedField_nc, TypedField_nc>;
			using Field = typename TypedField_nc::Base; //!< iterated field type
			//! const-correct field type
			using Field_c = std::conditional_t<ConstField, const Field, Field>;
			using size_type = std::size_t; //!< stl conformance
			using pointer = std::conditional_t<ConstField, const T *,
			T *>; //!< stl conformance
			//! Default constructor
			FieldMap() = delete;

			//! constructor
			explicit FieldMap(Field_c & field);

			//! constructor with run-time cost (for python and debugging)
			template <class FC, typename T2, Dim_t NbC>
			explicit FieldMap(TypedSizedFieldBase<FC, T2, NbC> & field);

			//! Copy constructor
			FieldMap(const FieldMap & other) = default;

			//! Move constructor
			FieldMap(FieldMap && other) = default;

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

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

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

			//! give human-readable field map type
			virtual std::string info_string() const = 0;

			//! return field name
			inline const std::string & get_name() const;

			//! return my collection (for iterating)
			inline const FieldCollection & get_collection() const;

			//! member access needs to be implemented by inheriting classes
			// inline value_type operator[](size_t index);
			// inline value_type operator[](Ccoord ccord);

			//! check compatibility (must be called by all inheriting classes at the
			//! end of their constructors
			inline void check_compatibility();

			//! convenience call to collection's size method
			inline size_t size() const;

			//! compile-time compatibility check
			template <class TypedField> struct is_compatible;

			/**
			* iterates over all pixels in the `muSpectre::FieldCollection`
			* and dereferences to an Eigen map to the currently used field.
			*/
			template <class FullyTypedFieldMap, bool ConstIter = false>
			class iterator;

			/**
			* Simple iterable proxy wrapper object around a FieldMap. When
			* iterated over, rather than dereferencing to the reference
			* type of iterator, it dereferences to a tuple of the pixel,
			* and the reference type of iterator
			*/
			template <class Iterator> class enumerator;

			TypedField_t & get_field() { return this->field; }

			protected:
			//! raw pointer to entry (for Eigen Map)
			inline pointer get_ptr_to_entry(size_t index);
			//! raw pointer to entry (for Eigen Map)
			inline const T * get_ptr_to_entry(size_t index) const;
			const FieldCollection & collection; //!< collection holding Field
			TypedField_t & field; //!< mapped Field

			private:
			};

			/**
			* iterates over all pixels in the `muSpectre::FieldCollection`
			* and dereferences to an Eigen map to the currently used field.
			*/
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			class FieldMap<FieldCollection, T, NbComponents, ConstField>::iterator {
			static_assert(!((ConstIter == false) && (ConstField == true)),
			"You can't have a non-const iterator over a const "
			"field");

			public:
			//! for use by enumerator
			using FullyTypedFieldMap_t = FullyTypedFieldMap;
			//! stl conformance
			using value_type = const_corrector_t<FullyTypedFieldMap, ConstIter>;
			//! stl conformance
			using const_value_type = const_corrector_t<FullyTypedFieldMap, true>;
			//! stl conformance
			using pointer = typename FullyTypedFieldMap::pointer;
			//! stl conformance
			using difference_type = std::ptrdiff_t;
			//! stl conformance
			using iterator_category = std::random_access_iterator_tag;
			//! cell coordinates type
			using Ccoord = typename FieldCollection::Ccoord;
			//! stl conformance
			using reference = typename FullyTypedFieldMap::reference;
			//! fully typed reference as seen by the iterator
			using TypedMap_t = std::conditional_t<ConstIter, const FullyTypedFieldMap,
			FullyTypedFieldMap>;

			//! Default constructor
			iterator() = delete;

			//! constructor
			inline iterator(TypedMap_t & fieldmap, bool begin = true);

			//! constructor for random access
			inline iterator(TypedMap_t & fieldmap, size_t index);

			//! Move constructor
			iterator(iterator && other) = default;

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

			//! Copy assignment operator
			iterator & operator=(const iterator & other) = default;

			//! Move assignment operator
			iterator & operator=(iterator && other) = default;

			//! pre-increment
			inline iterator & operator++();
			//! post-increment
			inline iterator operator++(int);
			//! dereference
			inline value_type operator*();
			//! dereference
			inline const_value_type operator*() const;
			//! member of pointer
			inline pointer operator->();
			//! pre-decrement
			inline iterator & operator--();
			//! post-decrement
			inline iterator operator--(int);
			//! access subscripting
			inline value_type operator[](difference_type diff);
			//! access subscripting
			inline const_value_type operator[](const difference_type diff) const;
			//! equality
			inline bool operator==(const iterator & other) const;
			//! inequality
			inline bool operator!=(const iterator & other) const;
			//! div. comparisons
			inline bool operator<(const iterator & other) const;
			//! div. comparisons
			inline bool operator<=(const iterator & other) const;
			//! div. comparisons
			inline bool operator>(const iterator & other) const;
			//! div. comparisons
			inline bool operator>=(const iterator & other) const;
			//! additions, subtractions and corresponding assignments
			inline iterator operator+(difference_type diff) const;
			//! additions, subtractions and corresponding assignments
			inline iterator operator-(difference_type diff) const;
			//! additions, subtractions and corresponding assignments
			inline iterator & operator+=(difference_type diff);
			//! additions, subtractions and corresponding assignments
			inline iterator & operator-=(difference_type diff);

			//! get pixel coordinates
			inline Ccoord get_ccoord() const;

			//! ostream operator (mainly for debugging)
			friend std::ostream & operator<<(std::ostream & os, const iterator & it) {
			if (ConstIter) {
			os << "const ";
			}
			os << "iterator on field '" << it.fieldmap.get_name() << "', entry "
			<< it.index;
			return os;
			}

			protected:
			//! Copy constructor
			iterator(const iterator & other) = default;

			const FieldCollection & collection; //!< collection of the field
			TypedMap_t & fieldmap; //!< ref to the field itself
			size_t index; //!< index of currently pointed-to pixel

			private:
			};

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class Iterator>
			class FieldMap<FieldCollection, T, NbComponents, ConstField>::enumerator {
			public:
			//! fully typed reference as seen by the iterator
			using TypedMap_t = typename Iterator::TypedMap_t;

			//! Default constructor
			enumerator() = delete;

			//! constructor with field mapped
			enumerator(TypedMap_t & field_map) : field_map{field_map} {}

			/**
			* similar to iterators of the field map, but dereferences to a
			* tuple containing the cell coordinates and teh corresponding
			* entry
			*/
			class iterator;

			iterator begin() { return iterator(this->field_map); }
			iterator end() { return iterator(this->field_map, false); }

			protected:
			TypedMap_t & field_map;
			};

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class SimpleIterator>
			class FieldMap<FieldCollection, T, NbComponents,
			ConstField>::enumerator<SimpleIterator>::iterator {
			public:
			//! cell coordinates type
			using Ccoord = typename FieldCollection::Ccoord;
			//! stl conformance
			using value_type =
			std::tuple<Ccoord, typename SimpleIterator::value_type>;
			//! stl conformance
			using const_value_type =
			std::tuple<Ccoord, typename SimpleIterator::const_value_type>;
			//! stl conformance
			using difference_type = std::ptrdiff_t;
			//! stl conformance
			using iterator_category = std::random_access_iterator_tag;
			//! stl conformance
			using reference =
			std::tuple<Ccoord,
			typename SimpleIterator::FullyTypedFieldMap_t::reference>;

			//! Default constructor
			iterator() = delete;

			//! constructor for begin/end
			iterator(TypedMap_t & fieldmap, bool begin = true)
			: it{fieldmap, begin} {}

			//! constructor for random access
			iterator(TypedMap_t & fieldmap, size_t index) : it{fieldmap, index} {}

			//! constructor from iterator
			iterator(const SimpleIterator & it) : it{it} {}

			//! Copy constructor
			iterator(const iterator & other) = default;

			//! Move constructor
			iterator(iterator && other) = default;

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

			//! Copy assignment operator
			iterator & operator=(const iterator & other) = default;

			//! Move assignment operator
			iterator & operator=(iterator && other) = default;

			//! pre-increment
			iterator & operator++() {
			++(this->it);
			return *this;
			}

			//! post-increment
			iterator operator++(int) {
			iterator current = *this;
			++(this->it);
			return current;
			}

			//! dereference
			value_type operator() { return value_type{it.get_ccoord(), this->it}; }

			//! dereference
			const_value_type operator*() const {
			return const_value_type{it.get_ccoord(), *this->it};
			}

			//! pre-decrement
			iterator & operator--() {
			--(this->it);
			return *this;
			}

			//! post-decrement
			iterator operator--(int) {
			iterator current = *this;
			--(this->it);
			return current;
			}

			//! access subscripting
			value_type operator[](difference_type diff) {
			SimpleIterator accessed{this->it + diff};
			return *accessed;
			}

			//! access subscripting
			const_value_type operator[](const difference_type diff) const {
			SimpleIterator accessed{this->it + diff};
			return *accessed;
			}

			//! equality
			bool operator==(const iterator & other) const {
			return this->it == other.it;
			}

			//! inequality
			bool operator!=(const iterator & other) const {
			return this->it != other.it;
			}

			//! div. comparisons
			bool operator<(const iterator & other) const {
			return this->it < other.it;
			}

			//! div. comparisons
			bool operator<=(const iterator & other) const {
			return this->it <= other.it;
			}

			//! div. comparisons
			bool operator>(const iterator & other) const {
			return this->it > other.it;
			}

			//! div. comparisons
			bool operator>=(const iterator & other) const {
			return this->it >= other.it;
			}

			//! additions, subtractions and corresponding assignments
			iterator operator+(difference_type diff) const {
			return iterator{this->it + diff};
			}

			//! additions, subtractions and corresponding assignments
			iterator operator-(difference_type diff) const {
			return iterator{this->it - diff};
			}

			//! additions, subtractions and corresponding assignments
			iterator & operator+=(difference_type diff) { this->it += diff; }

			//! additions, subtractions and corresponding assignments
			iterator & operator-=(difference_type diff) { this->it -= diff; }

			protected:
			SimpleIterator it;

			private:
			};

			} // namespace internal

			namespace internal {

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			FieldMap<FieldCollection, T, NbComponents, ConstField>::FieldMap(
			Field_c & field)
			: collection(field.get_collection()),
			field(static_cast<TypedField_t &>(field)) {
			static_assert((NbComponents > 0) or (NbComponents == Eigen::Dynamic),
			"Only fields with more than 0 components allowed");
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FC, typename T2, Dim_t NbC>
			FieldMap<FieldCollection, T, NbComponents, ConstField>::FieldMap(
			TypedSizedFieldBase<FC, T2, NbC> & field)
			: collection(field.get_collection()),
			field(static_cast<TypedField_t &>(field)) {
			static_assert(
			std::is_same<FC, FieldCollection>::value,
			"The field does not have the expected FieldCollection type");
			static_assert(std::is_same<T2, T>::value,
			"The field does not have the expected Scalar type");
			static_assert(
			(NbC == NbComponents),
			"The field does not have the expected number of components");
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			void FieldMap<FieldCollection, T, NbComponents,
			ConstField>::check_compatibility() {
			if (typeid(T).hash_code() !=
			this->field.get_stored_typeid().hash_code()) {
			std::string err{"Cannot create a Map of type '" + this->info_string() +
			"' for field '" + this->field.get_name() +
			"' of type '" + this->field.get_stored_typeid().name() +
			"'"};
			throw FieldInterpretationError(err);
			}
			// check size compatibility
			if ((NbComponents != Dim_t(this->field.get_nb_components())) and
			(NbComponents != Eigen::Dynamic)) {
			throw FieldInterpretationError(
			"Cannot create a Map of type '" + this->info_string() +
			"' for field '" + this->field.get_name() + "' with " +
			std::to_string(this->field.get_nb_components()) + " components");
			}
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			size_t
			FieldMap<FieldCollection, T, NbComponents, ConstField>::size() const {
			return this->collection.size();
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class myField>
			struct FieldMap<FieldCollection, T, NbComponents,
			ConstField>::is_compatible {
			//! creates a more readable compile error
			constexpr static bool explain() {
			static_assert(
			std::is_same<typename myField::collection_t,
			FieldCollection>::value,
			"The field does not have the expected FieldCollection type");
			static_assert(std::is_same<typename myField::Scalar, T>::value,
			"The // field does not have the expected Scalar type");
			static_assert(
			(TypedField_t::nb_components == NbComponents),
			"The field does not have the expected number of components");
			// The static asserts wouldn't pass in the incompatible case, so this is
			// it
			return true;
			}
			//! evaluated compatibility
			constexpr static bool value{
			std::is_base_of<TypedField_t, myField>::value};
			};

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			const std::string &
			FieldMap<FieldCollection, T, NbComponents, ConstField>::get_name() const {
			return this->field.get_name();
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			const FieldCollection &
			FieldMap<FieldCollection, T, NbComponents, ConstField>::get_collection()
			const {
			return this->collection;
			}

			/* ---------------------------------------------------------------------- */
			/* ---------------------------------------------------------------------- */
			// Iterator implementations
			//! constructor
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			FieldMap<FieldCollection, T, NbComponents, ConstField>::iterator<
			FullyTypedFieldMap, ConstIter>::iterator(TypedMap_t & fieldmap,
			bool begin)
			: collection(fieldmap.get_collection()), fieldmap(fieldmap),
			index(begin ? 0 : fieldmap.field.size()) {}

			/* ---------------------------------------------------------------------- */
			//! constructor for random access
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			FieldMap<FieldCollection, T, NbComponents, ConstField>::iterator<
			FullyTypedFieldMap, ConstIter>::iterator(TypedMap_t & fieldmap,
			size_t index)
			: collection(fieldmap.collection), fieldmap(fieldmap), index(index) {}

			/* ---------------------------------------------------------------------- */
			//! pre-increment
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter> &
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator++() {
			this->index++;
			return *this;
			}

			/* ---------------------------------------------------------------------- */
			//! post-increment
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator++(int) {
			iterator current = *this;
			this->index++;
			return current;
			}

			/* ---------------------------------------------------------------------- */
			//! dereference
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>::value_type
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator*() {
			return this->fieldmap.operator[](this->index);
			}

			/* ---------------------------------------------------------------------- */
			//! dereference
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>::const_value_type
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator*() const {
			return this->fieldmap.operator[](this->index);
			}

			/* ---------------------------------------------------------------------- */
			//! member of pointer
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FullyTypedFieldMap::pointer
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator->() {
			return this->fieldmap.ptr_to_val_t(this->index);
			}

			/* ---------------------------------------------------------------------- */
			//! pre-decrement
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter> &
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator--() {
			this->index--;
			return *this;
			}

			/* ---------------------------------------------------------------------- */
			//! post-decrement
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator--(int) {
			iterator current = *this;
			this->index--;
			return current;
			}

			/* ---------------------------------------------------------------------- */
			//! Access subscripting
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>::value_type
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator[](difference_type diff) {
			return this->fieldmap[this->index + diff];
			}

			/* ---------------------------------------------------------------------- */
			//! Access subscripting
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>::const_value_type
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator[](const difference_type diff) const {
			return this->fieldmap[this->index + diff];
			}

			/* ---------------------------------------------------------------------- */
			//! equality
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator==(const iterator & other) const {
			return (this->index == other.index);
			}

			/* ---------------------------------------------------------------------- */
			//! inquality
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator!=(const iterator & other) const {
			return !(*this == other);
			}

			/* ---------------------------------------------------------------------- */
			//! div. comparisons
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator<(const iterator & other) const {
			return (this->index < other.index);
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator<=(const iterator & other) const {
			return (this->index <= other.index);
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator>(const iterator & other) const {
			return (this->index > other.index);
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			bool FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator>=(const iterator & other) const {
			return (this->index >= other.index);
			}

			/* ---------------------------------------------------------------------- */
			//! additions, subtractions and corresponding assignments
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator+(difference_type diff) const {
			return iterator(this->fieldmap, this->index + diff);
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter>
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator-(difference_type diff) const {
			return iterator(this->fieldmap, this->index - diff);
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter> &
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator+=(difference_type diff) {
			this->index += diff;
			return *this;
			}
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			template iterator<FullyTypedFieldMap, ConstIter> &
			FieldMap<FieldCollection, T, NbComponents,
			ConstField>::iterator<FullyTypedFieldMap, ConstIter>::
			operator-=(difference_type diff) {
			this->index -= diff;
			return *this;
			}

			/* ---------------------------------------------------------------------- */
			//! get pixel coordinates
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			template <class FullyTypedFieldMap, bool ConstIter>
			typename FieldCollection::Ccoord
			FieldMap<FieldCollection, T, NbComponents, ConstField>::iterator<
			FullyTypedFieldMap, ConstIter>::get_ccoord() const {
			return this->collection.get_ccoord(this->index);
			}

			////----------------------------------------------------------------------------//
			// template<class FieldCollection, typename T, Dim_t NbComponents, class
			// FullyTypedFieldMap> std::ostream & operator << (std::ostream &os,
			// const typename FieldMap<FieldCollection, T, NbComponents, ConstField>::
			// template iterator<FullyTypedFieldMap, ConstIter> & it) {
			// os << "iterator on field '"
			// << it.field.get_name()
			// << "', entry " << it.index;
			// return os;
			//}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			typename FieldMap<FieldCollection, T, NbComponents, ConstField>::pointer
			FieldMap<FieldCollection, T, NbComponents, ConstField>::get_ptr_to_entry(
			size_t index) {
			return this->field.get_ptr_to_entry(std::move(index));
			}

			/* ---------------------------------------------------------------------- */
			template <class FieldCollection, typename T, Dim_t NbComponents,
			bool ConstField>
			const T *
			FieldMap<FieldCollection, T, NbComponents, ConstField>::get_ptr_to_entry(
			size_t index) const {
			return this->field.get_ptr_to_entry(std::move(index));
			}

			} // namespace internal

			} // namespace muSpectre

			#endif // SRC_COMMON_FIELD_MAP_BASE_HH_

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muSpectre/src/common/field_map_base.hh
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