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 //  Copyright (c) 2018-2019
 //  Cem Bassoy
 //
 //  Distributed under the Boost Software License, Version 1.0. (See
 //  accompanying file LICENSE_1_0.txt or copy at
 //  http://www.boost.org/LICENSE_1_0.txt)
 //
 //  The authors gratefully acknowledge the support of
 //  Fraunhofer and Google in producing this work
 //  which started as a Google Summer of Code project.
 //
 
 
 /// \file tensor.hpp Definition for the tensor template class
 
 #ifndef BOOST_UBLAS_TENSOR_IMPL_HPP
 #define BOOST_UBLAS_TENSOR_IMPL_HPP
 
 #include <boost/config.hpp>
 
 #include <initializer_list>
 
 #include "algorithms.hpp"
 #include "expression.hpp"
 #include "expression_evaluation.hpp"
 #include "extents.hpp"
 #include "strides.hpp"
 #include "index.hpp"
 
 namespace boost { namespace numeric { namespace ublas {
 
 template<class T, class F, class A>
 class tensor;
 
 template<class T, class F, class A>
 class matrix;
 
 template<class T, class A>
 class vector;
 
 ///** \brief Base class for Tensor container models
 // *
 // * it does not model the Tensor concept but all derived types should.
 // * The class defines a common base type and some common interface for all
 // * statically derived Tensor classes
 // * We implement the casts to the statically derived type.
 // */
 //template<class C>
 //class tensor_container:
 //      public detail::tensor_expression<C>
 //{
 //public:
 //  static const unsigned complexity = 0;
 //  typedef C container_type;
 //  typedef tensor_tag type_category;
 
 //  BOOST_UBLAS_INLINE
 //  const container_type &operator () () const {
 //          return *static_cast<const container_type *> (this);
 //  }
 //  BOOST_UBLAS_INLINE
 //  container_type &operator () () {
 //          return *static_cast<container_type *> (this);
 //  }
 //};
 
 
 
 /** @brief A dense tensor of values of type \c T.
         *
         * For a \f$n\f$-dimensional tensor \f$v\f$ and \f$0\leq i < n\f$ every element \f$v_i\f$ is mapped
         * to the \f$i\f$-th element of the container. A storage type \c A can be specified which defaults to \c unbounded_array.
         * Elements are constructed by \c A, which need not initialise their value.
         *
         * @tparam T type of the objects stored in the tensor (like int, double, complex,...)
         * @tparam A The type of the storage array of the tensor. Default is \c unbounded_array<T>. \c <bounded_array<T> and \c std::vector<T> can also be used
         */
 template<class T, class F = first_order, class A = std::vector<T,std::allocator<T>> >
 class tensor:
         public detail::tensor_expression<tensor<T, F, A>,tensor<T, F, A>>
 {
 
     static_assert( std::is_same<F,first_order>::value ||
                                  std::is_same<F,last_order >::value, "boost::numeric::tensor template class only supports first- or last-order storage formats.");
 
     using self_type  = tensor<T, F, A>;
 public:
 
 
 
     template<class derived_type>
     using tensor_expression_type = detail::tensor_expression<self_type,derived_type>;
 
     template<class derived_type>
     using matrix_expression_type = matrix_expression<derived_type>;
 
     template<class derived_type>
     using vector_expression_type = vector_expression<derived_type>;
 
     using super_type = tensor_expression_type<self_type>;
 
 //  static_assert(std::is_same_v<tensor_expression_type<self_type>, detail::tensor_expression<tensor<T,F,A>,tensor<T,F,A>>>, "tensor_expression_type<self_type>");
 
     using array_type  = A;
     using layout_type = F;
 
 
     using size_type       = typename array_type::size_type;
     using difference_type = typename array_type::difference_type;
     using value_type      = typename array_type::value_type;
 
     using reference       = typename array_type::reference;
     using const_reference = typename array_type::const_reference;
 
     using pointer         = typename array_type::pointer;
     using const_pointer   = typename array_type::const_pointer;
 
     using iterator        = typename array_type::iterator;
     using const_iterator  = typename array_type::const_iterator;
 
     using reverse_iterator        = typename array_type::reverse_iterator;
     using const_reverse_iterator  = typename array_type::const_reverse_iterator;
 
     using tensor_temporary_type = self_type;
     using storage_category = dense_tag;
 
     using strides_type = basic_strides<std::size_t,layout_type>;
     using extents_type = shape;
 
     using matrix_type     = matrix<value_type,layout_type,array_type>;
     using vector_type     = vector<value_type,array_type>;
 
 
     /** @brief Constructs a tensor.
      *
      * @note the tensor is empty.
      * @note the tensor needs to reshaped for further use.
      *
      */
     BOOST_UBLAS_INLINE
     constexpr tensor ()
         : tensor_expression_type<self_type>() // container_type
         , extents_()
         , strides_()
         , data_()
     {
     }
 
 
     /** @brief Constructs a tensor with an initializer list
      *
      * By default, its elements are initialized to 0.
      *
      * @code tensor<float> A{4,2,3}; @endcode
      *
      * @param l initializer list for setting the dimension extents of the tensor
      */
     explicit BOOST_UBLAS_INLINE
     tensor (std::initializer_list<size_type> l)
         : tensor_expression_type<self_type>()
         , extents_ (std::move(l))
         , strides_ (extents_)
         , data_    (extents_.product())
     {
     }
 
 
     /** @brief Constructs a tensor with a \c shape
      *
      * By default, its elements are initialized to 0.
      *
      * @code tensor<float> A{extents{4,2,3}}; @endcode
      *
      * @param s initial tensor dimension extents
      */
     explicit BOOST_UBLAS_INLINE
     tensor (extents_type const& s)
         : tensor_expression_type<self_type>() //tensor_container<self_type>()
         , extents_ (s)
         , strides_ (extents_)
         , data_    (extents_.product())
     {}
 
 
     /** @brief Constructs a tensor with a \c shape and initiates it with one-dimensional data
      *
      * @code tensor<float> A{extents{4,2,3}, array }; @endcode
      *
      *
      *  @param s initial tensor dimension extents
      *  @param a container of \c array_type that is copied according to the storage layout
      */
     BOOST_UBLAS_INLINE
     tensor (extents_type const& s, const array_type &a)
         : tensor_expression_type<self_type>() //tensor_container<self_type>()
         , extents_ (s)
         , strides_ (extents_)
         , data_    (a)
     {
         if(this->extents_.product() != this->data_.size())
             throw std::runtime_error("Error in boost::numeric::ublas::tensor: size of provided data and specified extents do not match.");
     }
 
 
 
     /** @brief Constructs a tensor using a shape tuple and initiates it with a value.
      *
      *  @code tensor<float> A{extents{4,2,3}, 1 }; @endcode
      *
      *  @param e initial tensor dimension extents
      *  @param i initial value of all elements of type \c value_type
      */
     BOOST_UBLAS_INLINE
     tensor (extents_type const& e, const value_type &i)
         : tensor_expression_type<self_type>() //tensor_container<self_type> ()
         , extents_ (e)
         , strides_ (extents_)
         , data_    (extents_.product(), i)
     {}
 
 
 
     /** @brief Constructs a tensor from another tensor
      *
      *  @param v tensor to be copied.
      */
     BOOST_UBLAS_INLINE
     tensor (const tensor &v)
         : tensor_expression_type<self_type>()
         , extents_ (v.extents_)
         , strides_ (v.strides_)
         , data_    (v.data_   )
     {}
 
 
 
     /** @brief Constructs a tensor from another tensor
      *
      *  @param v tensor to be moved.
      */
     BOOST_UBLAS_INLINE
     tensor (tensor &&v)
         : tensor_expression_type<self_type>() //tensor_container<self_type> ()
         , extents_ (std::move(v.extents_))
         , strides_ (std::move(v.strides_))
         , data_    (std::move(v.data_   ))
     {}
 
 
     /** @brief Constructs a tensor with a matrix
      *
      * \note Initially the tensor will be two-dimensional.
      *
      *  @param v matrix to be copied.
      */
     BOOST_UBLAS_INLINE
     tensor (const matrix_type &v)
         : tensor_expression_type<self_type>()
         , extents_ ()
         , strides_ ()
         , data_    (v.data())
     {
         if(!data_.empty()){
             extents_ = extents_type{v.size1(),v.size2()};
             strides_ = strides_type(extents_);
         }
     }
 
     /** @brief Constructs a tensor with a matrix
      *
      * \note Initially the tensor will be two-dimensional.
      *
      *  @param v matrix to be moved.
      */
     BOOST_UBLAS_INLINE
     tensor (matrix_type &&v)
         : tensor_expression_type<self_type>()
         , extents_ {}
         , strides_ {}
         , data_    {}
     {
         if(v.size1()*v.size2() != 0){
             extents_ = extents_type{v.size1(),v.size2()};
             strides_ = strides_type(extents_);
             data_    = std::move(v.data());
         }
     }
 
     /** @brief Constructs a tensor using a \c vector
      *
      * @note It is assumed that vector is column vector
      * @note Initially the tensor will be one-dimensional.
      *
      *  @param v vector to be copied.
      */
     BOOST_UBLAS_INLINE
     tensor (const vector_type &v)
         : tensor_expression_type<self_type>()
         , extents_ ()
         , strides_ ()
         , data_    (v.data())
     {
         if(!data_.empty()){
             extents_ = extents_type{data_.size(),1};
             strides_ = strides_type(extents_);
         }
     }
 
     /** @brief Constructs a tensor using a \c vector
      *
      *  @param v vector to be moved.
      */
     BOOST_UBLAS_INLINE
     tensor (vector_type &&v)
         : tensor_expression_type<self_type>()
         , extents_ {}
         , strides_ {}
         , data_    {}
     {
         if(v.size() != 0){
             extents_ = extents_type{v.size(),1};
             strides_ = strides_type(extents_);
             data_    = std::move(v.data());
         }
     }
 
 
     /** @brief Constructs a tensor with another tensor with a different layout
      *
      * @param other tensor with a different layout to be copied.
      */
     BOOST_UBLAS_INLINE
     template<class other_layout>
     tensor (const tensor<value_type, other_layout> &other)
         : tensor_expression_type<self_type> ()
         , extents_ (other.extents())
         , strides_ (other.extents())
         , data_    (other.extents().product())
     {
         copy(this->rank(), this->extents().data(),
                  this->data(), this->strides().data(),
                  other.data(), other.strides().data());
     }
 
     /** @brief Constructs a tensor with an tensor expression
      *
      * @code tensor<float> A = B + 3 * C; @endcode
      *
      * @note type must be specified of tensor must be specified.
      * @note dimension extents are extracted from tensors within the expression.
      *
      * @param expr tensor expression
      */
     BOOST_UBLAS_INLINE
     template<class derived_type>
     tensor (const tensor_expression_type<derived_type> &expr)
         : tensor_expression_type<self_type> ()
         , extents_ ( detail::retrieve_extents(expr) )
         , strides_ ( extents_ )
         , data_    ( extents_.product() )
     {
         static_assert( detail::has_tensor_types<self_type, tensor_expression_type<derived_type>>::value,
                                      "Error in boost::numeric::ublas::tensor: expression does not contain a tensor. cannot retrieve shape.");
         detail::eval( *this, expr );
     }
 
     /** @brief Constructs a tensor with a matrix expression
      *
      * @code tensor<float> A = B + 3 * C; @endcode
      *
      * @note matrix expression is evaluated and pushed into a temporary matrix before assignment.
      * @note extents are automatically extracted from the temporary matrix
      *
      * @param expr matrix expression
      */
     BOOST_UBLAS_INLINE
     template<class derived_type>
     tensor (const matrix_expression_type<derived_type> &expr)
         : tensor(  matrix_type ( expr )  )
     {
     }
 
     /** @brief Constructs a tensor with a vector expression
      *
      * @code tensor<float> A = b + 3 * b; @endcode
      *
      * @note matrix expression is evaluated and pushed into a temporary matrix before assignment.
      * @note extents are automatically extracted from the temporary matrix
      *
      * @param expr vector expression
      */
     BOOST_UBLAS_INLINE
     template<class derived_type>
     tensor (const vector_expression_type<derived_type> &expr)
         : tensor(  vector_type ( expr )  )
     {
     }
 
     /** @brief Evaluates the tensor_expression and assigns the results to the tensor
      *
      * @code A = B + C * 2;  @endcode
      *
      * @note rank and dimension extents of the tensors in the expressions must conform with this tensor.
      *
      * @param expr expression that is evaluated.
      */
     BOOST_UBLAS_INLINE
     template<class derived_type>
     tensor &operator = (const tensor_expression_type<derived_type> &expr)
     {
         detail::eval(*this, expr);
         return *this;
     }
 
     tensor& operator=(tensor other)
     {
         swap (*this, other);
         return *this;
     }
 
     tensor& operator=(const_reference v)
     {
         std::fill(this->begin(), this->end(), v);
         return *this;
     }
 
     /** @brief Returns true if the tensor is empty (\c size==0) */
     BOOST_UBLAS_INLINE
     bool empty () const {
         return this->data_.empty();
     }
 
 
     /** @brief Returns the size of the tensor */
     BOOST_UBLAS_INLINE
     size_type size () const {
         return this->data_.size ();
     }
 
     /** @brief Returns the size of the tensor */
     BOOST_UBLAS_INLINE
     size_type size (size_type r) const {
         return this->extents_.at(r);
     }
 
     /** @brief Returns the number of dimensions/modes of the tensor */
     BOOST_UBLAS_INLINE
     size_type rank () const {
         return this->extents_.size();
     }
 
     /** @brief Returns the number of dimensions/modes of the tensor */
     BOOST_UBLAS_INLINE
     size_type order () const {
         return this->extents_.size();
     }
 
     /** @brief Returns the strides of the tensor */
     BOOST_UBLAS_INLINE
     strides_type const& strides () const {
         return this->strides_;
     }
 
     /** @brief Returns the extents of the tensor */
     BOOST_UBLAS_INLINE
     extents_type const& extents () const {
         return this->extents_;
     }
 
 
     /** @brief Returns a \c const reference to the container. */
     BOOST_UBLAS_INLINE
     const_pointer data () const {
         return this->data_.data();
     }
 
     /** @brief Returns a \c const reference to the container. */
     BOOST_UBLAS_INLINE
     pointer data () {
         return this->data_.data();
     }
 
     /** @brief Element access using a single index.
      *
      *  @code auto a = A[i]; @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size()
      */
     BOOST_UBLAS_INLINE
     const_reference operator [] (size_type i) const {
         return this->data_[i];
     }
 
     /** @brief Element access using a single index.
      *
      *
      *  @code A[i] = a; @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size()
      */
     BOOST_UBLAS_INLINE
     reference operator [] (size_type i)
     {
         return this->data_[i];
     }
 
 
     /** @brief Element access using a multi-index or single-index.
      *
      *
      *  @code auto a = A.at(i,j,k); @endcode or
      *  @code auto a = A.at(i);     @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size() if sizeof...(is) == 0, else 0<= i < this->size(0)
      *  @param is zero-based indices where 0 <= is[r] < this->size(r) where  0 < r < this->rank()
      */
     template<class ... size_types>
     BOOST_UBLAS_INLINE
     const_reference at (size_type i, size_types ... is) const {
         if constexpr (sizeof...(is) == 0)
             return this->data_[i];
         else
             return this->data_[detail::access<0ul>(size_type(0),this->strides_,i,std::forward<size_types>(is)...)];
     }
 
     /** @brief Element access using a multi-index or single-index.
      *
      *
      *  @code A.at(i,j,k) = a; @endcode or
      *  @code A.at(i) = a;     @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size() if sizeof...(is) == 0, else 0<= i < this->size(0)
      *  @param is zero-based indices where 0 <= is[r] < this->size(r) where  0 < r < this->rank()
      */
     BOOST_UBLAS_INLINE
     template<class ... size_types>
     reference at (size_type i, size_types ... is) {
         if constexpr (sizeof...(is) == 0)
             return this->data_[i];
         else
             return this->data_[detail::access<0ul>(size_type(0),this->strides_,i,std::forward<size_types>(is)...)];
     }
 
 
 
 
     /** @brief Element access using a single index.
      *
      *
      *  @code A(i) = a; @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size()
      */
     BOOST_UBLAS_INLINE
     const_reference operator()(size_type i) const {
         return this->data_[i];
     }
 
 
     /** @brief Element access using a single index.
      *
      *  @code A(i) = a; @endcode
      *
      *  @param i zero-based index where 0 <= i < this->size()
      */
     BOOST_UBLAS_INLINE
     reference operator()(size_type i){
         return this->data_[i];
     }
 
 
 
 
     /** @brief Generates a tensor index for tensor contraction
      *
      *
      *  @code auto Ai = A(_i,_j,k); @endcode
      *
      *  @param i placeholder
      *  @param is zero-based indices where 0 <= is[r] < this->size(r) where  0 < r < this->rank()
      */
     BOOST_UBLAS_INLINE
     template<std::size_t I, class ... index_types>
     decltype(auto) operator() (index::index_type<I> p, index_types ... ps) const
     {
         constexpr auto N = sizeof...(ps)+1;
         if( N != this->rank() )
             throw std::runtime_error("Error in boost::numeric::ublas::operator(): size of provided index_types does not match with the rank.");
 
         return std::make_pair( std::cref(*this),  std::make_tuple( p, std::forward<index_types>(ps)... ) );
     }
 
 
 
 
 
     /** @brief Reshapes the tensor
      *
      *
      * (1) @code A.reshape(extents{m,n,o});     @endcode or
      * (2) @code A.reshape(extents{m,n,o},4);   @endcode
      *
      * If the size of this smaller than the specified extents than
      * default constructed (1) or specified (2) value is appended.
      *
      * @note rank of the tensor might also change.
      *
      * @param e extents with which the tensor is reshaped.
      * @param v value which is appended if the tensor is enlarged.
      */
     BOOST_UBLAS_INLINE
     void reshape (extents_type const& e, value_type v = value_type{})
     {
         this->extents_ = e;
         this->strides_ = strides_type(this->extents_);
 
         if(e.product() != this->size())
             this->data_.resize (this->extents_.product(), v);
     }
 
 
 
 
 
     friend void swap(tensor& lhs, tensor& rhs) {
         std::swap(lhs.data_   , rhs.data_   );
         std::swap(lhs.extents_, rhs.extents_);
         std::swap(lhs.strides_, rhs.strides_);
     }
 
 
     /// \brief return an iterator on the first element of the tensor
     BOOST_UBLAS_INLINE
     const_iterator begin () const {
         return data_.begin ();
     }
 
     /// \brief return an iterator on the first element of the tensor
     BOOST_UBLAS_INLINE
     const_iterator cbegin () const {
         return data_.cbegin ();
     }
 
     /// \brief return an iterator after the last element of the tensor
     BOOST_UBLAS_INLINE
     const_iterator end () const {
         return data_.end();
     }
 
     /// \brief return an iterator after the last element of the tensor
     BOOST_UBLAS_INLINE
     const_iterator cend () const {
         return data_.cend ();
     }
 
     /// \brief Return an iterator on the first element of the tensor
     BOOST_UBLAS_INLINE
     iterator begin () {
         return data_.begin();
     }
 
     /// \brief Return an iterator at the end of the tensor
     BOOST_UBLAS_INLINE
     iterator end () {
         return data_.end();
     }
 
     /// \brief Return a const reverse iterator before the first element of the reversed tensor (i.e. end() of normal tensor)
     BOOST_UBLAS_INLINE
     const_reverse_iterator rbegin () const {
         return data_.rbegin();
     }
 
     /// \brief Return a const reverse iterator before the first element of the reversed tensor (i.e. end() of normal tensor)
     BOOST_UBLAS_INLINE
     const_reverse_iterator crbegin () const {
         return data_.crbegin();
     }
 
     /// \brief Return a const reverse iterator on the end of the reverse tensor (i.e. first element of the normal tensor)
     BOOST_UBLAS_INLINE
     const_reverse_iterator rend () const {
         return data_.rend();
     }
 
     /// \brief Return a const reverse iterator on the end of the reverse tensor (i.e. first element of the normal tensor)
     BOOST_UBLAS_INLINE
     const_reverse_iterator crend () const {
         return data_.crend();
     }
 
     /// \brief Return a const reverse iterator before the first element of the reversed tensor (i.e. end() of normal tensor)
     BOOST_UBLAS_INLINE
     reverse_iterator rbegin () {
         return data_.rbegin();
     }
 
     /// \brief Return a const reverse iterator on the end of the reverse tensor (i.e. first element of the normal tensor)
     BOOST_UBLAS_INLINE
     reverse_iterator rend () {
         return data_.rend();
     }
 
 
 #if 0
     // -------------
     // Serialization
     // -------------
 
     /// Serialize a tensor into and archive as defined in Boost
     /// \param ar Archive object. Can be a flat file, an XML file or any other stream
     /// \param file_version Optional file version (not yet used)
     template<class Archive>
     void serialize(Archive & ar, const unsigned int /* file_version */){
         ar & serialization::make_nvp("data",data_);
     }
 #endif
 
 
 
 private:
 
     extents_type extents_;
     strides_type strides_;
     array_type data_;
 };
 
 }}} // namespaces
 
 
 
 
 
 #endif

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