FM / ublas

/usr/include/boost/numeric/ublas

Name	Size	Mode	Actions
detail/	-	0755	rm
experimental/	-	0755	rm
opencl/	-	0755	rm
operation/	-	0755	rm
tensor/	-	0755	rm
traits/	-	0755	rm
assignment.hpp	35756	0644	edit dl rm
banded.hpp	86847	0644	edit dl rm
blas.hpp	18132	0644	edit dl rm
doxydoc.hpp	4087	0644	edit dl rm
exception.hpp	8822	0644	edit dl rm
expression_types.hpp	18467	0644	edit dl rm
functional.hpp	80865	0644	edit dl rm
fwd.hpp	7215	0644	edit dl rm
hermitian.hpp	102000	0644	edit dl rm
io.hpp	13687	0644	edit dl rm
lu.hpp	14044	0644	edit dl rm
matrix.hpp	216096	0644	edit dl rm
matrix_expression.hpp	169092	0644	edit dl rm
matrix_proxy.hpp	201494	0644	edit dl rm
matrix_sparse.hpp	231409	0644	edit dl rm
matrix_vector.hpp	11475	0644	edit dl rm
opencl.hpp	490	0644	edit dl rm
operation.hpp	32110	0644	edit dl rm
operations.hpp	739	0644	edit dl rm
operation_blocked.hpp	13813	0644	edit dl rm
operation_sparse.hpp	8146	0644	edit dl rm
storage.hpp	67562	0644	edit dl rm
storage_sparse.hpp	19762	0644	edit dl rm
symmetric.hpp	88183	0644	edit dl rm
tags.hpp	731	0644	edit dl rm
tensor.hpp	800	0644	edit dl rm
traits.hpp	24952	0644	edit dl rm
triangular.hpp	105304	0644	edit dl rm
vector.hpp	105769	0644	edit dl rm
vector_expression.hpp	65815	0644	edit dl rm
vector_of_vector.hpp	53270	0644	edit dl rm
vector_proxy.hpp	64597	0644	edit dl rm
vector_sparse.hpp	84156	0644	edit dl rm

Edit: /usr/include/boost/numeric/ublas/vector_expression.hpp (65815B)

//
//  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 cbegin () const {
            return begin ();
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return expression ().end ();
        }
        BOOST_UBLAS_INLINE
        const_iterator cend () const {
            return 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 crbegin () const {
            return rbegin ();
        }
        BOOST_UBLAS_INLINE
        const_reverse_iterator rend () const {
            return const_reverse_iterator (begin ());
        }
        BOOST_UBLAS_INLINE
        const_reverse_iterator crend () const {
            return rend ();
        }

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 cbegin () const {
            return begin ();
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return find (size ());
        }
        BOOST_UBLAS_INLINE
        const_iterator cend () const {
            return end ();
        }

// Reverse iterator
        typedef reverse_iterator_base<const_iterator> const_reverse_iterator;

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 {
                typename E1::value_type t1 = typename E1::value_type/*zero*/();
                if (it1_ != it1_end_)
                    if (it1_.index () == i_)
                        t1 = *it1_;
                typename E2::value_type t2 = typename E2::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 {
                typename E1::value_type t1 = typename E1::value_type/*zero*/();
                if (it1_ != it1_end_)
                    if (it1_.index () == i_)
                        t1 = *it1_;
                typename E2::value_type t2 = typename E2::value_type/*zero*/();
                if (it2_ != it2_end_)
                    if (it2_.index () == i_)
                        t2 = *it2_;
                return static_cast<value_type>(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 cbegin () const {
            return begin ();
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return find (size ());
        }
        BOOST_UBLAS_INLINE
        const_iterator cend () const {
            return end ();
        }

// Reverse iterator
        typedef reverse_iterator_base<const_iterator> const_reverse_iterator;

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 cbegin () const {
            return begin ();
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return find (size ()); 
        }
        BOOST_UBLAS_INLINE
        const_iterator cend () const {
            return end ();
        }

// Reverse iterator
        typedef reverse_iterator_base<const_iterator> const_reverse_iterator;

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 boost::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;

// 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;

// 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 cbegin () const {
            return begin ();
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return find (size ());
        }
        BOOST_UBLAS_INLINE
        const_iterator cend () const {
            return end ();
        }

// Reverse iterator
        typedef reverse_iterator_base<const_iterator> const_reverse_iterator;

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 boost::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 boost::enable_if< is_convertible<T2, typename E1::value_type >,
    typename vector_binary_scalar2_traits<E1, const T2, scalar_divides<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_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_2_square v = sum(v [i] * v [i])
    // complex: norm_2_square v = sum(v [i] * conj (v [i]))
    template<class E>
    BOOST_UBLAS_INLINE
    typename vector_scalar_unary_traits<E, vector_norm_2_square<E> >::result_type
    norm_2_square (const vector_expression<E> &e) {
        typedef typename vector_scalar_unary_traits<E, vector_norm_2_square<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) {}

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

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