matrix_expression.hpp

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                return const_reverse_iterator2 (end ());
            }
            BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
            typename self_type::
#endif
            const_reverse_iterator2 rend () const {
                return const_reverse_iterator2 (begin ());
            }
#endif

            // Indices
            BOOST_UBLAS_INLINE
            size_type index1 () const {
                return it_.index2 ();
            }
            BOOST_UBLAS_INLINE
            size_type index2 () const {
                return it_.index1 ();
            }

            // Assignment 
            BOOST_UBLAS_INLINE
            const_iterator1 &operator = (const const_iterator1 &it) {
                container_const_reference<self_type>::assign (&it ());
                it_ = it.it_;
                return *this;
            }

            // Comparison
            BOOST_UBLAS_INLINE
            bool operator == (const const_iterator1 &it) const {
                BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ());
                return it_ == it.it_;
            }
            BOOST_UBLAS_INLINE
            bool operator < (const const_iterator1 &it) const {
                BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ());
                return it_ < it.it_;
            }

        private:
            const_subiterator1_type it_;
        };
#endif

        BOOST_UBLAS_INLINE
        const_iterator1 begin1 () const {
            return find1 (0, 0, 0);
        }
        BOOST_UBLAS_INLINE
        const_iterator1 end1 () const {
            return find1 (0, size1 (), 0);
        }

#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
        class const_iterator2:
            public container_const_reference<matrix_unary2>,
            public iterator_base_traits<typename E::const_iterator1::iterator_category>::template
                iterator_base<const_iterator2, value_type>::type {
        public:
            typedef typename E::const_iterator1::iterator_category iterator_category;
            typedef typename matrix_unary2::difference_type difference_type;
            typedef typename matrix_unary2::value_type value_type;
            typedef typename matrix_unary2::const_reference reference;
            typedef typename matrix_unary2::const_pointer pointer;

            typedef const_iterator1 dual_iterator_type;
            typedef const_reverse_iterator1 dual_reverse_iterator_type;

            // Construction and destruction
            BOOST_UBLAS_INLINE
            const_iterator2 ():
                container_const_reference<self_type> (), it_ () {}
            BOOST_UBLAS_INLINE
            const_iterator2 (const self_type &mu, const const_subiterator2_type &it):
                container_const_reference<self_type> (mu), it_ (it) {}

            // Arithmetic
            BOOST_UBLAS_INLINE
            const_iterator2 &operator ++ () {
                ++ it_;
                return *this;
            }
            BOOST_UBLAS_INLINE
            const_iterator2 &operator -- () {
                -- it_;
                return *this;
            }
            BOOST_UBLAS_INLINE
            const_iterator2 &operator += (difference_type n) {
                it_ += n;
                return *this;
            }
            BOOST_UBLAS_INLINE
            const_iterator2 &operator -= (difference_type n) {
                it_ -= n;
                return *this;
            }
            BOOST_UBLAS_INLINE
            difference_type operator - (const const_iterator2 &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);
            }

#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
            BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
            typename self_type::
#endif
            const_iterator1 begin () const {
                return (*this) ().find1 (1, 0, index2 ());
            }
            BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
            typename self_type::
#endif
            const_iterator1 end () const {
                return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
            }
            BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
            typename self_type::
#endif
            const_reverse_iterator1 rbegin () const {
                return const_reverse_iterator1 (end ());
            }
            BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
            typename self_type::
#endif
            const_reverse_iterator1 rend () const {
                return const_reverse_iterator1 (begin ());
            }
#endif

            // Indices
            BOOST_UBLAS_INLINE
            size_type index1 () const {
                return it_.index2 ();
            }
            BOOST_UBLAS_INLINE
            size_type index2 () const {
                return it_.index1 ();
            }

            // Assignment
            BOOST_UBLAS_INLINE
            const_iterator2 &operator = (const const_iterator2 &it) {
                container_const_reference<self_type>::assign (&it ());
                it_ = it.it_;
                return *this;
            }

            // Comparison
            BOOST_UBLAS_INLINE
            bool operator == (const const_iterator2 &it) const {
                BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ());
                return it_ == it.it_;
            }
            BOOST_UBLAS_INLINE
            bool operator < (const const_iterator2 &it) const {
                BOOST_UBLAS_CHECK ((*this) ().same_closure (it ()), external_logic ());
                return it_ < it.it_;
            }

        private:
            const_subiterator2_type it_;
        };
#endif

        BOOST_UBLAS_INLINE
        const_iterator2 begin2 () const {
            return find2 (0, 0, 0);
        }
        BOOST_UBLAS_INLINE
        const_iterator2 end2 () const {
            return find2 (0, 0, size2 ());
        }

        // Reverse iterators

        BOOST_UBLAS_INLINE
        const_reverse_iterator1 rbegin1 () const {
            return const_reverse_iterator1 (end1 ());
        }
        BOOST_UBLAS_INLINE
        const_reverse_iterator1 rend1 () const {
            return const_reverse_iterator1 (begin1 ());
        }

        BOOST_UBLAS_INLINE
        const_reverse_iterator2 rbegin2 () const {
            return const_reverse_iterator2 (end2 ());
        }
        BOOST_UBLAS_INLINE
        const_reverse_iterator2 rend2 () const {
            return const_reverse_iterator2 (begin2 ());
        }

    private:
        expression_closure_type e_;
    };

    template<class E, class F>
    struct matrix_unary2_traits {
        typedef matrix_unary2<E, F> expression_type;
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
        typedef expression_type result_type; 
#else
        typedef typename E::matrix_temporary_type result_type;
#endif
    };

    // (trans m) [i] [j] = m [j] [i]
    template<class E>
    BOOST_UBLAS_INLINE
    typename matrix_unary2_traits<const E, scalar_identity<typename E::value_type> >::result_type
    trans (const matrix_expression<E> &e) {
        typedef typename matrix_unary2_traits<const E, scalar_identity<typename E::value_type> >::expression_type expression_type;
        return expression_type (e ());
    }
    template<class E>
    BOOST_UBLAS_INLINE
    typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type
    trans (matrix_expression<E> &e) {
        typedef typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::expression_type expression_type;
        return expression_type (e ());
    }

    // (herm m) [i] [j] = conj (m [j] [i])
    template<class E>
    BOOST_UBLAS_INLINE
    typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type
    herm (const matrix_expression<E> &e) {
        typedef typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::expression_type expression_type;
        return expression_type (e ());
    }

    template<class E1, class E2, class F>
    class matrix_binary:
        public matrix_expression<matrix_binary<E1, E2, F> > {

        typedef E1 expression1_type;
        typedef E2 expression2_type;
        typedef F functor_type;
    public:
        typedef typename E1::const_closure_type expression1_closure_type;
        typedef typename E2::const_closure_type expression2_closure_type;
    private:
        typedef matrix_binary<E1, E2, F> self_type;
    public:
#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
        using matrix_expression<self_type>::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_orientation_tag orientation_category;
        typedef unknown_storage_tag storage_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        matrix_binary (const E1 &e1, const E2 &e2): 
            e1_ (e1), e2_ (e2) {}

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size1 () const { 
            return BOOST_UBLAS_SAME (e1_.size1 (), e2_.size1 ());
        }
        BOOST_UBLAS_INLINE
        size_type size2 () const {
            return BOOST_UBLAS_SAME (e1_.size2 (), e2_.size2 ());
        }

    public:
        // Expression 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, size_type j) const {
            return functor_type::apply (e1_ (i, j), e2_ (i, j));
        }

        // Closure comparison
        BOOST_UBLAS_INLINE
        bool same_closure (const matrix_binary &mb) const {
            return (*this).expression1 ().same_closure (mb.expression1 ()) &&
                   (*this).expression2 ().same_closure (mb.expression2 ());
        }

        // Iterator types
    private:
        typedef typename E1::const_iterator1 const_iterator11_type;
        typedef typename E1::const_iterator2 const_iterator12_type;
        typedef typename E2::const_iterator1 const_iterator21_type;
        typedef typename E2::const_iterator2 const_iterator22_type;
        typedef const value_type *const_pointer;

    public:
#ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
        typedef typename iterator_restrict_traits<typename const_iterator11_type::iterator_category,
                                                  typename const_iterator21_type::iterator_category>::iterator_category iterator_category1;
        typedef indexed_const_iterator1<const_closure_type, iterator_category1> const_iterator1;
        typedef const_iterator1 iterator1;
        typedef typename iterator_restrict_traits<typename const_iterator12_type::iterator_category,
                                                  typename const_iterator22_type::iterator_category>::iterator_category iterator_category2;
        typedef indexed_const_iterator2<const_closure_type, iterator_category2> const_iterator2;
        typedef const_iterator2 iterator2;
#else
        class const_iterator1;
        typedef const_iterator1 iterator1;
        class const_iterator2;
        typedef const_iterator2 iterator2;
#endif
        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

        // Element lookup
        BOOST_UBLAS_INLINE
        const_iterator1 find1 (int rank, size_type i, size_type j) const {
            const_iterator11_type it11 (e1_.find1 (rank, i, j));
            const_iterator11_type it11_end (e1_.find1 (rank, size1 (), j));
            const_iterator21_type it21 (e2_.find1 (rank, i, j));
            const_iterator21_type it21_end (e2_.find1 (rank, size1 (), j));
            BOOST_UBLAS_CHECK (rank == 0 || it11 == it11_end || it11.index2 () == j, internal_logic ())
            BOOST_UBLAS_CHECK (rank == 0 || it21 == it21_end || it21.index2 () == j, internal_logic ())
            i = (std::min) (it11 != it11_end ? it11.index1 () : size1 (),
                          it21 != it21_end ? it21.index