boost/numeric/ublas/vector_expression.hpp
// // Copyright (c) 2000-2002 // Joerg Walter, Mathias Koch // // 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 // GeNeSys mbH & Co. KG in producing this work. // #ifndef _BOOST_UBLAS_VECTOR_EXPRESSION_ #define _BOOST_UBLAS_VECTOR_EXPRESSION_ #include <boost/numeric/ublas/expression_types.hpp> // Expression templates based on ideas of Todd Veldhuizen and Geoffrey Furnish // Iterators based on ideas of Jeremy Siek // // Classes that model the Vector Expression concept namespace boost { namespace numeric { namespace ublas { template<class E> class vector_reference: public vector_expression<vector_reference<E> > { typedef vector_reference<E> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using vector_expression<vector_reference<E> >::operator (); #endif typedef typename E::size_type size_type; typedef typename E::difference_type difference_type; typedef typename E::value_type value_type; typedef typename E::const_reference const_reference; typedef typename boost::mpl::if_<boost::is_const<E>, typename E::const_reference, typename E::reference>::type reference; typedef E referred_type; typedef const self_type const_closure_type; typedef self_type closure_type; typedef typename E::storage_category storage_category; // Construction and destruction BOOST_UBLAS_INLINE explicit vector_reference (referred_type &e): e_ (e) {} // Accessors BOOST_UBLAS_INLINE size_type size () const { return expression ().size (); } public: // Expression accessors - const correct BOOST_UBLAS_INLINE const referred_type &expression () const { return e_; } BOOST_UBLAS_INLINE referred_type &expression () { return e_; } public: // Element access #ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER BOOST_UBLAS_INLINE const_reference operator () (size_type i) const { return expression () (i); } BOOST_UBLAS_INLINE reference operator () (size_type i) { return expression () (i); } BOOST_UBLAS_INLINE const_reference operator [] (size_type i) const { return expression () [i]; } BOOST_UBLAS_INLINE reference operator [] (size_type i) { return expression () [i]; } #else BOOST_UBLAS_INLINE reference operator () (size_type i) const { return expression () (i); } BOOST_UBLAS_INLINE reference operator [] (size_type i) const { return expression () [i]; } #endif // Assignment BOOST_UBLAS_INLINE vector_reference &operator = (const vector_reference &v) { expression ().operator = (v); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &operator = (const vector_expression<AE> &ae) { expression ().operator = (ae); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &assign (const vector_expression<AE> &ae) { expression ().assign (ae); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &operator += (const vector_expression<AE> &ae) { expression ().operator += (ae); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &plus_assign (const vector_expression<AE> &ae) { expression ().plus_assign (ae); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &operator -= (const vector_expression<AE> &ae) { expression ().operator -= (ae); return *this; } template<class AE> BOOST_UBLAS_INLINE vector_reference &minus_assign (const vector_expression<AE> &ae) { expression ().minus_assign (ae); return *this; } template<class AT> BOOST_UBLAS_INLINE vector_reference &operator *= (const AT &at) { expression ().operator *= (at); return *this; } template<class AT> BOOST_UBLAS_INLINE vector_reference &operator /= (const AT &at) { expression ().operator /= (at); return *this; } // Swapping BOOST_UBLAS_INLINE void swap (vector_reference &v) { expression ().swap (v.expression ()); } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const vector_reference &vr) const { return &(*this).e_ == &vr.e_; } // Iterator types typedef typename E::const_iterator const_iterator; typedef typename boost::mpl::if_<boost::is_const<E>, typename E::const_iterator, typename E::iterator>::type iterator; // Element lookup BOOST_UBLAS_INLINE const_iterator find (size_type i) const { return expression ().find (i); } BOOST_UBLAS_INLINE iterator find (size_type i) { return expression ().find (i); } // Iterator is the iterator of the referenced expression. BOOST_UBLAS_INLINE const_iterator begin () const { return expression ().begin (); } BOOST_UBLAS_INLINE const_iterator end () const { return expression ().end (); } BOOST_UBLAS_INLINE iterator begin () { return expression ().begin (); } BOOST_UBLAS_INLINE iterator end () { return expression ().end (); } // Reverse iterator typedef reverse_iterator_base<const_iterator> const_reverse_iterator; typedef reverse_iterator_base<iterator> reverse_iterator; BOOST_UBLAS_INLINE const_reverse_iterator rbegin () const { return const_reverse_iterator (end ()); } BOOST_UBLAS_INLINE const_reverse_iterator rend () const { return const_reverse_iterator (begin ()); } BOOST_UBLAS_INLINE reverse_iterator rbegin () { return reverse_iterator (end ()); } BOOST_UBLAS_INLINE reverse_iterator rend () { return reverse_iterator (begin ()); } private: referred_type &e_; }; template<class E, class F> class vector_unary: public vector_expression<vector_unary<E, F> > { typedef F functor_type; typedef typename boost::mpl::if_<boost::is_same<F, scalar_identity<typename E::value_type> >, E, const E>::type expression_type; typedef typename boost::mpl::if_<boost::is_const<expression_type>, typename E::const_closure_type, typename E::closure_type>::type expression_closure_type; typedef vector_unary<E, F> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using vector_expression<vector_unary<E, F> >::operator (); #endif typedef typename E::size_type size_type; typedef typename E::difference_type difference_type; typedef typename F::result_type value_type; typedef value_type const_reference; typedef typename boost::mpl::if_<boost::is_same<F, scalar_identity<value_type> >, typename E::reference, value_type>::type reference; typedef const self_type const_closure_type; typedef self_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE // May be used as mutable expression. explicit vector_unary (expression_type &e): e_ (e) {} // Accessors BOOST_UBLAS_INLINE size_type size () const { return e_.size (); } public: // Expression accessors BOOST_UBLAS_INLINE const expression_closure_type &expression () const { return e_; } public: // Element access BOOST_UBLAS_INLINE const_reference operator () (size_type i) const { return functor_type::apply (e_ (i)); } BOOST_UBLAS_INLINE reference operator () (size_type i) { BOOST_STATIC_ASSERT ((boost::is_same<functor_type, scalar_identity<value_type > >::value)); return e_ (i); } BOOST_UBLAS_INLINE const_reference operator [] (size_type i) const { return functor_type::apply (e_ [i]); } BOOST_UBLAS_INLINE reference operator [] (size_type i) { BOOST_STATIC_ASSERT ((boost::is_same<functor_type, scalar_identity<value_type > >::value)); return e_ [i]; } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const vector_unary &vu) const { return (*this).expression ().same_closure (vu.expression ()); } // Iterator types private: typedef typename E::const_iterator const_subiterator_type; typedef const value_type *const_pointer; public: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef indexed_const_iterator<const_closure_type, typename const_subiterator_type::iterator_category> const_iterator; typedef const_iterator iterator; #else class const_iterator; typedef const_iterator iterator; #endif // Element lookup BOOST_UBLAS_INLINE const_iterator find (size_type i) const { #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR const_subiterator_type it (e_.find (i)); return const_iterator (*this, it.index ()); #else return const_iterator (*this, e_.find (i)); #endif } // Iterator enhances the iterator of the referenced expression // with the unary functor. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator: public container_const_reference<vector_unary>, public iterator_base_traits<typename E::const_iterator::iterator_category>::template iterator_base<const_iterator, value_type>::type { public: typedef typename E::const_iterator::iterator_category iterator_category; typedef typename vector_unary::difference_type difference_type; typedef typename vector_unary::value_type value_type; typedef typename vector_unary::const_reference reference; typedef typename vector_unary::const_pointer pointer; // Construction and destruction BOOST_UBLAS_INLINE const_iterator (): container_const_reference<self_type> (), it_ () {} BOOST_UBLAS_INLINE const_iterator (const self_type &vu, const const_subiterator_type &it): container_const_reference<self_type> (vu), it_ (it) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator &operator ++ () { ++ it_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -- () { -- it_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator += (difference_type n) { it_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -= (difference_type n) { it_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return it_ - it.it_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return functor_type::apply (*it_); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } // Index BOOST_UBLAS_INLINE size_type index () const { return it_.index (); } // Assignment BOOST_UBLAS_INLINE const_iterator &operator = (const const_iterator &it) { container_const_reference<self_type>::assign (&it ()); it_ = it.it_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return it_ == it.it_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return it_ < it.it_; } private: const_subiterator_type it_; }; #endif BOOST_UBLAS_INLINE const_iterator begin () const { return find (0); } BOOST_UBLAS_INLINE const_iterator end () const { return find (size ()); } // Reverse iterator typedef reverse_iterator_base<const_iterator> const_reverse_iterator; BOOST_UBLAS_INLINE const_reverse_iterator rbegin () const { return const_reverse_iterator (end ()); } BOOST_UBLAS_INLINE const_reverse_iterator rend () const { return const_reverse_iterator (begin ()); } private: expression_closure_type e_; }; template<class E, class F> struct vector_unary_traits { typedef vector_unary<E, F> expression_type; //FIXME // #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG typedef expression_type result_type; // #else // typedef typename E::vector_temporary_type result_type; // #endif }; // (- v) [i] = - v [i] template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type operator - (const vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } // (conj v) [i] = conj (v [i]) template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type conj (const vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } // (real v) [i] = real (v [i]) template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type real (const vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_real<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } // (imag v) [i] = imag (v [i]) template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type imag (const vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } // (trans v) [i] = v [i] template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<const E, scalar_identity<typename E::value_type> >::result_type trans (const vector_expression<E> &e) { typedef typename vector_unary_traits<const E, scalar_identity<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type trans (vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } // (herm v) [i] = conj (v [i]) template<class E> BOOST_UBLAS_INLINE typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type herm (const vector_expression<E> &e) { typedef typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::expression_type expression_type; return expression_type (e ()); } template<class E1, class E2, class F> class vector_binary: public vector_expression<vector_binary<E1, E2, F> > { typedef E1 expression1_type; typedef E2 expression2_type; typedef F functor_type; typedef typename E1::const_closure_type expression1_closure_type; typedef typename E2::const_closure_type expression2_closure_type; typedef vector_binary<E1, E2, F> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using vector_expression<vector_binary<E1, E2, F> >::operator (); #endif typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type; typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type; typedef typename F::result_type value_type; typedef value_type const_reference; typedef const_reference reference; typedef const self_type const_closure_type; typedef const_closure_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE vector_binary (const expression1_type &e1, const expression2_type &e2): e1_ (e1), e2_ (e2) {} // Accessors BOOST_UBLAS_INLINE size_type size () const { return BOOST_UBLAS_SAME (e1_.size (), e2_.size ()); } private: // Accessors BOOST_UBLAS_INLINE const expression1_closure_type &expression1 () const { return e1_; } BOOST_UBLAS_INLINE const expression2_closure_type &expression2 () const { return e2_; } public: // Element access BOOST_UBLAS_INLINE const_reference operator () (size_type i) const { return functor_type::apply (e1_ (i), e2_ (i)); } BOOST_UBLAS_INLINE const_reference operator [] (size_type i) const { return functor_type::apply (e1_ [i], e2_ [i]); } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const vector_binary &vb) const { return (*this).expression1 ().same_closure (vb.expression1 ()) && (*this).expression2 ().same_closure (vb.expression2 ()); } // Iterator types private: typedef typename E1::const_iterator const_subiterator1_type; typedef typename E2::const_iterator const_subiterator2_type; typedef const value_type *const_pointer; public: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef typename iterator_restrict_traits<typename const_subiterator1_type::iterator_category, typename const_subiterator2_type::iterator_category>::iterator_category iterator_category; typedef indexed_const_iterator<const_closure_type, iterator_category> const_iterator; typedef const_iterator iterator; #else class const_iterator; typedef const_iterator iterator; #endif // Element lookup BOOST_UBLAS_INLINE const_iterator find (size_type i) const { const_subiterator1_type it1 (e1_.find (i)); const_subiterator1_type it1_end (e1_.find (size ())); const_subiterator2_type it2 (e2_.find (i)); const_subiterator2_type it2_end (e2_.find (size ())); i = (std::min) (it1 != it1_end ? it1.index () : size (), it2 != it2_end ? it2.index () : size ()); #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR return const_iterator (*this, i); #else return const_iterator (*this, i, it1, it1_end, it2, it2_end); #endif } // Iterator merges the iterators of the referenced expressions and // enhances them with the binary functor. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator: public container_const_reference<vector_binary>, public iterator_base_traits<typename iterator_restrict_traits<typename E1::const_iterator::iterator_category, typename E2::const_iterator::iterator_category>::iterator_category>::template iterator_base<const_iterator, value_type>::type { public: typedef typename iterator_restrict_traits<typename E1::const_iterator::iterator_category, typename E2::const_iterator::iterator_category>::iterator_category iterator_category; typedef typename vector_binary::difference_type difference_type; typedef typename vector_binary::value_type value_type; typedef typename vector_binary::const_reference reference; typedef typename vector_binary::const_pointer pointer; // Construction and destruction BOOST_UBLAS_INLINE const_iterator (): container_const_reference<self_type> (), i_ (), it1_ (), it1_end_ (), it2_ (), it2_end_ () {} BOOST_UBLAS_INLINE const_iterator (const self_type &vb, size_type i, const const_subiterator1_type &it1, const const_subiterator1_type &it1_end, const const_subiterator2_type &it2, const const_subiterator2_type &it2_end): container_const_reference<self_type> (vb), i_ (i), it1_ (it1), it1_end_ (it1_end), it2_ (it2), it2_end_ (it2_end) {} private: // Dense specializations BOOST_UBLAS_INLINE void increment (dense_random_access_iterator_tag) { ++ i_; ++ it1_; ++ it2_; } BOOST_UBLAS_INLINE void decrement (dense_random_access_iterator_tag) { -- i_; -- it1_; -- it2_; } BOOST_UBLAS_INLINE void increment (dense_random_access_iterator_tag, difference_type n) { i_ += n; it1_ += n; it2_ += n; } BOOST_UBLAS_INLINE void decrement (dense_random_access_iterator_tag, difference_type n) { i_ -= n; it1_ -= n; it2_ -= n; } BOOST_UBLAS_INLINE value_type dereference (dense_random_access_iterator_tag) const { return functor_type::apply (*it1_, *it2_); } // Packed specializations BOOST_UBLAS_INLINE void increment (packed_random_access_iterator_tag) { if (it1_ != it1_end_) if (it1_.index () <= i_) ++ it1_; if (it2_ != it2_end_) if (it2_.index () <= i_) ++ it2_; ++ i_; } BOOST_UBLAS_INLINE void decrement (packed_random_access_iterator_tag) { if (it1_ != it1_end_) if (i_ <= it1_.index ()) -- it1_; if (it2_ != it2_end_) if (i_ <= it2_.index ()) -- it2_; -- i_; } BOOST_UBLAS_INLINE void increment (packed_random_access_iterator_tag, difference_type n) { while (n > 0) { increment (packed_random_access_iterator_tag ()); --n; } while (n < 0) { decrement (packed_random_access_iterator_tag ()); ++n; } } BOOST_UBLAS_INLINE void decrement (packed_random_access_iterator_tag, difference_type n) { while (n > 0) { decrement (packed_random_access_iterator_tag ()); --n; } while (n < 0) { increment (packed_random_access_iterator_tag ()); ++n; } } BOOST_UBLAS_INLINE value_type dereference (packed_random_access_iterator_tag) const { value_type t1 = value_type/*zero*/(); if (it1_ != it1_end_) if (it1_.index () == i_) t1 = *it1_; value_type t2 = value_type/*zero*/(); if (it2_ != it2_end_) if (it2_.index () == i_) t2 = *it2_; return functor_type::apply (t1, t2); } // Sparse specializations BOOST_UBLAS_INLINE void increment (sparse_bidirectional_iterator_tag) { size_type index1 = (*this) ().size (); if (it1_ != it1_end_) { if (it1_.index () <= i_) ++ it1_; if (it1_ != it1_end_) index1 = it1_.index (); } size_type index2 = (*this) ().size (); if (it2_ != it2_end_) { if (it2_.index () <= i_) ++ it2_; if (it2_ != it2_end_) index2 = it2_.index (); } i_ = (std::min) (index1, index2); } BOOST_UBLAS_INLINE void decrement (sparse_bidirectional_iterator_tag) { size_type index1 = (*this) ().size (); if (it1_ != it1_end_) { if (i_ <= it1_.index ()) -- it1_; if (it1_ != it1_end_) index1 = it1_.index (); } size_type index2 = (*this) ().size (); if (it2_ != it2_end_) { if (i_ <= it2_.index ()) -- it2_; if (it2_ != it2_end_) index2 = it2_.index (); } i_ = (std::max) (index1, index2); } BOOST_UBLAS_INLINE void increment (sparse_bidirectional_iterator_tag, difference_type n) { while (n > 0) { increment (sparse_bidirectional_iterator_tag ()); --n; } while (n < 0) { decrement (sparse_bidirectional_iterator_tag ()); ++n; } } BOOST_UBLAS_INLINE void decrement (sparse_bidirectional_iterator_tag, difference_type n) { while (n > 0) { decrement (sparse_bidirectional_iterator_tag ()); --n; } while (n < 0) { increment (sparse_bidirectional_iterator_tag ()); ++n; } } BOOST_UBLAS_INLINE value_type dereference (sparse_bidirectional_iterator_tag) const { value_type t1 = value_type/*zero*/(); if (it1_ != it1_end_) if (it1_.index () == i_) t1 = *it1_; value_type t2 = value_type/*zero*/(); if (it2_ != it2_end_) if (it2_.index () == i_) t2 = *it2_; return functor_type::apply (t1, t2); } public: // Arithmetic BOOST_UBLAS_INLINE const_iterator &operator ++ () { increment (iterator_category ()); return *this; } BOOST_UBLAS_INLINE const_iterator &operator -- () { decrement (iterator_category ()); return *this; } BOOST_UBLAS_INLINE const_iterator &operator += (difference_type n) { increment (iterator_category (), n); return *this; } BOOST_UBLAS_INLINE const_iterator &operator -= (difference_type n) { decrement (iterator_category (), n); return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return index () - it.index (); } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return dereference (iterator_category ()); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } // Index BOOST_UBLAS_INLINE size_type index () const { return i_; } // Assignment BOOST_UBLAS_INLINE const_iterator &operator = (const const_iterator &it) { container_const_reference<self_type>::assign (&it ()); i_ = it.i_; it1_ = it.it1_; it1_end_ = it.it1_end_; it2_ = it.it2_; it2_end_ = it.it2_end_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return index () == it.index (); } BOOST_UBLAS_INLINE bool operator < (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); return index () < it.index (); } private: size_type i_; const_subiterator1_type it1_; const_subiterator1_type it1_end_; const_subiterator2_type it2_; const_subiterator2_type it2_end_; }; #endif BOOST_UBLAS_INLINE const_iterator begin () const { return find (0); } BOOST_UBLAS_INLINE const_iterator end () const { return find (size ()); } // Reverse iterator typedef reverse_iterator_base<const_iterator> const_reverse_iterator; BOOST_UBLAS_INLINE const_reverse_iterator rbegin () const { return const_reverse_iterator (end ()); } BOOST_UBLAS_INLINE const_reverse_iterator rend () const { return const_reverse_iterator (begin ()); } private: expression1_closure_type e1_; expression2_closure_type e2_; }; template<class E1, class E2, class F> struct vector_binary_traits { typedef vector_binary<E1, E2, F> expression_type; #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG typedef expression_type result_type; #else typedef typename E1::vector_temporary_type result_type; #endif }; // (v1 + v2) [i] = v1 [i] + v2 [i] template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type, typename E2::value_type> >::result_type operator + (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type, typename E2::value_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } // (v1 - v2) [i] = v1 [i] - v2 [i] template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type, typename E2::value_type> >::result_type operator - (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type, typename E2::value_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } // (v1 * v2) [i] = v1 [i] * v2 [i] template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type element_prod (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } // (v1 / v2) [i] = v1 [i] / v2 [i] template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_binary_traits<E1, E2, scalar_divides<typename E1::value_type, typename E2::value_type> >::result_type element_div (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_binary_traits<E1, E2, scalar_divides<typename E1::value_type, typename E2::value_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } template<class E1, class E2, class F> class vector_binary_scalar1: public vector_expression<vector_binary_scalar1<E1, E2, F> > { typedef F functor_type; typedef E1 expression1_type; typedef E2 expression2_type; public: typedef const E1& expression1_closure_type; typedef typename E2::const_closure_type expression2_closure_type; private: typedef vector_binary_scalar1<E1, E2, F> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using vector_expression<vector_binary_scalar1<E1, E2, F> >::operator (); #endif typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename F::result_type value_type; typedef value_type const_reference; typedef const_reference reference; typedef const self_type const_closure_type; typedef const_closure_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE vector_binary_scalar1 (const expression1_type &e1, const expression2_type &e2): e1_ (e1), e2_ (e2) {} // Accessors BOOST_UBLAS_INLINE size_type size () const { return e2_.size (); } public: // Element access BOOST_UBLAS_INLINE const_reference operator () (size_type i) const { return functor_type::apply (e1_, e2_ (i)); } BOOST_UBLAS_INLINE const_reference operator [] (size_type i) const { return functor_type::apply (e1_, e2_ [i]); } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const vector_binary_scalar1 &vbs1) const { return &e1_ == &(vbs1.e1_) && (*this).e2_.same_closure (vbs1.e2_); } // Iterator types private: typedef expression1_type const_subiterator1_type; typedef typename expression2_type::const_iterator const_subiterator2_type; typedef const value_type *const_pointer; public: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef indexed_const_iterator<const_closure_type, typename const_subiterator2_type::iterator_category> const_iterator; typedef const_iterator iterator; #else class const_iterator; typedef const_iterator iterator; #endif // Element lookup BOOST_UBLAS_INLINE const_iterator find (size_type i) const { #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR const_subiterator2_type it (e2_.find (i)); return const_iterator (*this, it.index ()); #else return const_iterator (*this, const_subiterator1_type (e1_), e2_.find (i)); #endif } // Iterator enhances the iterator of the referenced vector expression // with the binary functor. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator: public container_const_reference<vector_binary_scalar1>, public iterator_base_traits<typename E2::const_iterator::iterator_category>::template iterator_base<const_iterator, value_type>::type { public: typedef typename E2::const_iterator::iterator_category iterator_category; typedef typename vector_binary_scalar1::difference_type difference_type; typedef typename vector_binary_scalar1::value_type value_type; typedef typename vector_binary_scalar1::const_reference reference; typedef typename vector_binary_scalar1::const_pointer pointer; // Construction and destruction BOOST_UBLAS_INLINE const_iterator (): container_const_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE const_iterator (const self_type &vbs, const const_subiterator1_type &it1, const const_subiterator2_type &it2): container_const_reference<self_type> (vbs), it1_ (it1), it2_ (it2) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator &operator ++ () { ++ it2_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -- () { -- it2_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator += (difference_type n) { it2_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -= (difference_type n) { it2_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ - it.it2_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return functor_type::apply (it1_, *it2_); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } // Index BOOST_UBLAS_INLINE size_type index () const { return it2_.index (); } // Assignment BOOST_UBLAS_INLINE const_iterator &operator = (const const_iterator &it) { container_const_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ == it.it2_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ < it.it2_; } private: const_subiterator1_type it1_; const_subiterator2_type it2_; }; #endif BOOST_UBLAS_INLINE const_iterator begin () const { return find (0); } BOOST_UBLAS_INLINE const_iterator end () const { return find (size ()); } // Reverse iterator typedef reverse_iterator_base<const_iterator> const_reverse_iterator; BOOST_UBLAS_INLINE const_reverse_iterator rbegin () const { return const_reverse_iterator (end ()); } BOOST_UBLAS_INLINE const_reverse_iterator rend () const { return const_reverse_iterator (begin ()); } private: expression1_closure_type e1_; expression2_closure_type e2_; }; template<class E1, class E2, class F> struct vector_binary_scalar1_traits { typedef vector_binary_scalar1<E1, E2, F> expression_type; // allow E1 to be builtin type #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG typedef expression_type result_type; #else typedef typename E2::vector_temporary_type result_type; #endif }; // (t * v) [i] = t * v [i] template<class T1, class E2> BOOST_UBLAS_INLINE typename enable_if< is_convertible<T1, typename E2::value_type >, typename vector_binary_scalar1_traits<const T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type >::type operator * (const T1 &e1, const vector_expression<E2> &e2) { typedef typename vector_binary_scalar1_traits<const T1, E2, scalar_multiplies<T1, typename E2::value_type> >::expression_type expression_type; return expression_type (e1, e2 ()); } template<class E1, class E2, class F> class vector_binary_scalar2: public vector_expression<vector_binary_scalar2<E1, E2, F> > { typedef F functor_type; typedef E1 expression1_type; typedef E2 expression2_type; typedef typename E1::const_closure_type expression1_closure_type; typedef const E2& expression2_closure_type; typedef vector_binary_scalar2<E1, E2, F> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using vector_expression<vector_binary_scalar2<E1, E2, F> >::operator (); #endif typedef typename E1::size_type size_type; typedef typename E1::difference_type difference_type; typedef typename F::result_type value_type; typedef value_type const_reference; typedef const_reference reference; typedef const self_type const_closure_type; typedef const_closure_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE vector_binary_scalar2 (const expression1_type &e1, const expression2_type &e2): e1_ (e1), e2_ (e2) {} // Accessors BOOST_UBLAS_INLINE size_type size () const { return e1_.size (); } public: // Element access BOOST_UBLAS_INLINE const_reference operator () (size_type i) const { return functor_type::apply (e1_ (i), e2_); } BOOST_UBLAS_INLINE const_reference operator [] (size_type i) const { return functor_type::apply (e1_ [i], e2_); } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const vector_binary_scalar2 &vbs2) const { return (*this).e1_.same_closure (vbs2.e1_) && &e2_ == &(vbs2.e2_); } // Iterator types private: typedef typename expression1_type::const_iterator const_subiterator1_type; typedef expression2_type const_subiterator2_type; typedef const value_type *const_pointer; public: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef indexed_const_iterator<const_closure_type, typename const_subiterator2_type::iterator_category> const_iterator; typedef const_iterator iterator; #else class const_iterator; typedef const_iterator iterator; #endif // Element lookup BOOST_UBLAS_INLINE const_iterator find (size_type i) const { #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR const_subiterator1_type it (e1_.find (i)); return const_iterator (*this, it.index ()); #else return const_iterator (*this, e1_.find (i), const_subiterator2_type (e2_)); #endif } // Iterator enhances the iterator of the referenced vector expression // with the binary functor. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator: public container_const_reference<vector_binary_scalar2>, public iterator_base_traits<typename E1::const_iterator::iterator_category>::template iterator_base<const_iterator, value_type>::type { public: typedef typename E1::const_iterator::iterator_category iterator_category; typedef typename vector_binary_scalar2::difference_type difference_type; typedef typename vector_binary_scalar2::value_type value_type; typedef typename vector_binary_scalar2::const_reference reference; typedef typename vector_binary_scalar2::const_pointer pointer; // Construction and destruction BOOST_UBLAS_INLINE const_iterator (): container_const_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE const_iterator (const self_type &vbs, const const_subiterator1_type &it1, const const_subiterator2_type &it2): container_const_reference<self_type> (vbs), it1_ (it1), it2_ (it2) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator &operator ++ () { ++ it1_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -- () { -- it1_; return *this; } BOOST_UBLAS_INLINE const_iterator &operator += (difference_type n) { it1_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator &operator -= (difference_type n) { it1_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ - it.it1_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return functor_type::apply (*it1_, it2_); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } // Index BOOST_UBLAS_INLINE size_type index () const { return it1_.index (); } // Assignment BOOST_UBLAS_INLINE const_iterator &operator = (const const_iterator &it) { container_const_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ == it.it1_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator &it) const { BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ()); // FIXME we shouldn't compare floats // BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ < it.it1_; } private: const_subiterator1_type it1_; const_subiterator2_type it2_; }; #endif BOOST_UBLAS_INLINE const_iterator begin () const { return find (0); } BOOST_UBLAS_INLINE const_iterator end () const { return find (size ()); } // Reverse iterator typedef reverse_iterator_base<const_iterator> const_reverse_iterator; BOOST_UBLAS_INLINE const_reverse_iterator rbegin () const { return const_reverse_iterator (end ()); } BOOST_UBLAS_INLINE const_reverse_iterator rend () const { return const_reverse_iterator (begin ()); } private: expression1_closure_type e1_; expression2_closure_type e2_; }; template<class E1, class E2, class F> struct vector_binary_scalar2_traits { typedef vector_binary_scalar2<E1, E2, F> expression_type; // allow E2 to be builtin type #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG typedef expression_type result_type; #else typedef typename E1::vector_temporary_type result_type; #endif }; // (v * t) [i] = v [i] * t template<class E1, class T2> BOOST_UBLAS_INLINE typename enable_if< is_convertible<T2, typename E1::value_type >, typename vector_binary_scalar2_traits<E1, const T2, scalar_multiplies<typename E1::value_type, T2> >::result_type >::type operator * (const vector_expression<E1> &e1, const T2 &e2) { typedef typename vector_binary_scalar2_traits<E1, const T2, scalar_multiplies<typename E1::value_type, T2> >::expression_type expression_type; return expression_type (e1 (), e2); } // (v / t) [i] = v [i] / t template<class E1, class T2> BOOST_UBLAS_INLINE typename vector_binary_scalar2_traits<E1, const T2, scalar_divides<typename E1::value_type, T2> >::result_type operator / (const vector_expression<E1> &e1, const T2 &e2) { typedef typename vector_binary_scalar2_traits<E1, const T2, scalar_divides<typename E1::value_type, T2> >::expression_type expression_type; return expression_type (e1 (), e2); } template<class E, class F> class vector_scalar_unary: public scalar_expression<vector_scalar_unary<E, F> > { typedef E expression_type; typedef F functor_type; typedef typename E::const_closure_type expression_closure_type; typedef typename E::const_iterator::iterator_category iterator_category; typedef vector_scalar_unary<E, F> self_type; public: typedef typename F::result_type value_type; typedef typename E::difference_type difference_type; typedef const self_type const_closure_type; typedef const_closure_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE explicit vector_scalar_unary (const expression_type &e): e_ (e) {} private: // Expression accessors BOOST_UBLAS_INLINE const expression_closure_type &expression () const { return e_; } public: BOOST_UBLAS_INLINE operator value_type () const { return evaluate (iterator_category ()); } private: // Dense random access specialization BOOST_UBLAS_INLINE value_type evaluate (dense_random_access_iterator_tag) const { #ifdef BOOST_UBLAS_USE_INDEXING return functor_type::apply (e_); #elif BOOST_UBLAS_USE_ITERATING difference_type size = e_.size (); return functor_type::apply (size, e_.begin ()); #else difference_type size = e_.size (); if (size >= BOOST_UBLAS_ITERATOR_THRESHOLD) return functor_type::apply (size, e_.begin ()); else return functor_type::apply (e_); #endif } // Packed bidirectional specialization BOOST_UBLAS_INLINE value_type evaluate (packed_random_access_iterator_tag) const { return functor_type::apply (e_.begin (), e_.end ()); } // Sparse bidirectional specialization BOOST_UBLAS_INLINE value_type evaluate (sparse_bidirectional_iterator_tag) const { return functor_type::apply (e_.begin (), e_.end ()); } private: expression_closure_type e_; }; template<class E, class F> struct vector_scalar_unary_traits { typedef vector_scalar_unary<E, F> expression_type; #if !defined (BOOST_UBLAS_SIMPLE_ET_DEBUG) && defined (BOOST_UBLAS_USE_SCALAR_ET) // FIXME don't define USE_SCALAR_ET other then for testing // They do not work for complex types typedef expression_type result_type; #else typedef typename F::result_type result_type; #endif }; // sum v = sum (v [i]) template<class E> BOOST_UBLAS_INLINE typename vector_scalar_unary_traits<E, vector_sum<E> >::result_type sum (const vector_expression<E> &e) { typedef typename vector_scalar_unary_traits<E, vector_sum<E> >::expression_type expression_type; return expression_type (e ()); } // real: norm_1 v = sum (abs (v [i])) // complex: norm_1 v = sum (abs (real (v [i])) + abs (imag (v [i]))) template<class E> BOOST_UBLAS_INLINE typename vector_scalar_unary_traits<E, vector_norm_1<E> >::result_type norm_1 (const vector_expression<E> &e) { typedef typename vector_scalar_unary_traits<E, vector_norm_1<E> >::expression_type expression_type; return expression_type (e ()); } // real: norm_2 v = sqrt (sum (v [i] * v [i])) // complex: norm_2 v = sqrt (sum (v [i] * conj (v [i]))) template<class E> BOOST_UBLAS_INLINE typename vector_scalar_unary_traits<E, vector_norm_2<E> >::result_type norm_2 (const vector_expression<E> &e) { typedef typename vector_scalar_unary_traits<E, vector_norm_2<E> >::expression_type expression_type; return expression_type (e ()); } // real: norm_inf v = maximum (abs (v [i])) // complex: norm_inf v = maximum (maximum (abs (real (v [i])), abs (imag (v [i])))) template<class E> BOOST_UBLAS_INLINE typename vector_scalar_unary_traits<E, vector_norm_inf<E> >::result_type norm_inf (const vector_expression<E> &e) { typedef typename vector_scalar_unary_traits<E, vector_norm_inf<E> >::expression_type expression_type; return expression_type (e ()); } // real: index_norm_inf v = minimum (i: abs (v [i]) == maximum (abs (v [i]))) template<class E> BOOST_UBLAS_INLINE typename vector_scalar_unary_traits<E, vector_index_norm_inf<E> >::result_type index_norm_inf (const vector_expression<E> &e) { typedef typename vector_scalar_unary_traits<E, vector_index_norm_inf<E> >::expression_type expression_type; return expression_type (e ()); } template<class E1, class E2, class F> class vector_scalar_binary: public scalar_expression<vector_scalar_binary<E1, E2, F> > { typedef E1 expression1_type; typedef E2 expression2_type; typedef F functor_type; typedef typename E1::const_closure_type expression1_closure_type; typedef typename E2::const_closure_type expression2_closure_type; typedef typename iterator_restrict_traits<typename E1::const_iterator::iterator_category, typename E2::const_iterator::iterator_category>::iterator_category iterator_category; typedef vector_scalar_binary<E1, E2, F> self_type; public: static const unsigned complexity = 1; typedef typename F::result_type value_type; typedef typename E1::difference_type difference_type; typedef const self_type const_closure_type; typedef const_closure_type closure_type; typedef unknown_storage_tag storage_category; // Construction and destruction BOOST_UBLAS_INLINE vector_scalar_binary (const expression1_type &e1, const expression2_type &e2): e1_ (e1), e2_ (e2) {} private: // Accessors BOOST_UBLAS_INLINE const expression1_closure_type &expression1 () const { return e1_; } BOOST_UBLAS_INLINE const expression2_closure_type &expression2 () const { return e2_; } public: BOOST_UBLAS_INLINE operator value_type () const { return evaluate (iterator_category ()); } private: // Dense random access specialization BOOST_UBLAS_INLINE value_type evaluate (dense_random_access_iterator_tag) const { BOOST_UBLAS_CHECK (e1_.size () == e2_.size (), external_logic()); #ifdef BOOST_UBLAS_USE_INDEXING return functor_type::apply (e1_, e2_); #elif BOOST_UBLAS_USE_ITERATING difference_type size = BOOST_UBLAS_SAME (e1_.size (), e2_.size ()); return functor_type::apply (size, e1_.begin (), e2_.begin ()); #else difference_type size = BOOST_UBLAS_SAME (e1_.size (), e2_.size ()); if (size >= BOOST_UBLAS_ITERATOR_THRESHOLD) return functor_type::apply (size, e1_.begin (), e2_.begin ()); else return functor_type::apply (e1_, e2_); #endif } // Packed bidirectional specialization BOOST_UBLAS_INLINE value_type evaluate (packed_random_access_iterator_tag) const { BOOST_UBLAS_CHECK (e1_.size () == e2_.size (), external_logic()); return functor_type::apply (e1_.begin (), e1_.end (), e2_.begin (), e2_.end ()); } // Sparse bidirectional specialization BOOST_UBLAS_INLINE value_type evaluate (sparse_bidirectional_iterator_tag) const { BOOST_UBLAS_CHECK (e1_.size () == e2_.size (), external_logic()); return functor_type::apply (e1_.begin (), e1_.end (), e2_.begin (), e2_.end (), sparse_bidirectional_iterator_tag ()); } private: expression1_closure_type e1_; expression2_closure_type e2_; }; template<class E1, class E2, class F> struct vector_scalar_binary_traits { typedef vector_scalar_binary<E1, E2, F> expression_type; #if !defined (BOOST_UBLAS_SIMPLE_ET_DEBUG) && defined (BOOST_UBLAS_USE_SCALAR_ET) // FIXME don't define USE_SCALAR_ET other then for testing // They do not work for complex types typedef expression_type result_type; #else typedef typename F::result_type result_type; #endif }; // inner_prod (v1, v2) = sum (v1 [i] * v2 [i]) template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<E1, E2, typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type> >::result_type inner_prod (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<E1, E2, typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } template<class E1, class E2> BOOST_UBLAS_INLINE typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<E1, E2, typename type_traits<typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type>::precision_type> >::result_type prec_inner_prod (const vector_expression<E1> &e1, const vector_expression<E2> &e2) { typedef typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<E1, E2, typename type_traits<typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type>::precision_type> >::expression_type expression_type; return expression_type (e1 (), e2 ()); } }}} #endif