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 //
 //  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_ITERATOR_
 #define _BOOST_UBLAS_ITERATOR_
 
 #include <boost/numeric/ublas/exception.hpp>
 #include <iterator>
 
 
 namespace boost { namespace numeric { namespace ublas {
 
   /** \brief Base class of all proxy classes that contain
    *       a (redirectable) reference to an immutable object.
    *
    *       \param C the type of the container referred to
    */
     template<class C>
     class container_const_reference:
         private nonassignable {
     public:
         typedef C container_type;
 
         BOOST_UBLAS_INLINE
         container_const_reference ():
             c_ (0) {}
         BOOST_UBLAS_INLINE
         container_const_reference (const container_type &c):
             c_ (&c) {}
 
         BOOST_UBLAS_INLINE
         const container_type &operator () () const {
             return *c_;
         }
 
         BOOST_UBLAS_INLINE
         container_const_reference &assign (const container_type *c) {
             c_ = c;
             return *this;
         }
         
         // Closure comparison
         BOOST_UBLAS_INLINE
         bool same_closure (const container_const_reference &cr) const {
             return c_ == cr.c_;
         }
 
     private:
         const container_type *c_;
     };
 
   /** \brief Base class of all proxy classes that contain
    *         a (redirectable) reference to a mutable object.
    *
    * \param C the type of the container referred to
    */
     template<class C>
     class container_reference:
         private nonassignable {
     public:
         typedef C container_type;
 
         BOOST_UBLAS_INLINE
         container_reference ():
             c_ (0) {}
         BOOST_UBLAS_INLINE
         container_reference (container_type &c):
             c_ (&c) {}
 
         BOOST_UBLAS_INLINE
         container_type &operator () () const {
            return *c_;
         }
 
         BOOST_UBLAS_INLINE
         container_reference &assign (container_type *c) {
             c_ = c;
             return *this;
         }
 
         // Closure comparison
         BOOST_UBLAS_INLINE
         bool same_closure (const container_reference &cr) const {
             return c_ == cr.c_;
         }
 
     private:
         container_type *c_;
     };
 
   /** \brief Base class of all forward iterators.
    * 
    *  \param IC the iterator category
    *  \param I the derived iterator type
    *  \param T the value type
    * 
    * The forward iterator can only proceed in one direction
    * via the post increment operator.
    */
     template<class IC, class I, class T>
     struct forward_iterator_base {
         typedef IC iterator_category;
         typedef T value_type;
         typedef std::ptrdiff_t difference_type;
         typedef T* pointer;
         typedef T& reference;
         typedef I derived_iterator_type;
         typedef T derived_value_type;
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         derived_iterator_type operator ++ (int) {
             derived_iterator_type &d (*static_cast<const derived_iterator_type *> (this));
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator ++ (derived_iterator_type &d, int) {
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator != (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return ! (*d == it);
         }
     };
 
   /** \brief Base class of all bidirectional iterators.
    *
    * \param IC the iterator category
    * \param I the derived iterator type
    * \param T the value type
    *
    * The bidirectional iterator can proceed in both directions
    * via the post increment and post decrement operator.
    */
     template<class IC, class I, class T>
     struct bidirectional_iterator_base {
         typedef IC iterator_category;
         typedef T value_type;
         typedef std::ptrdiff_t difference_type;
         typedef T* pointer;
         typedef T& reference;
         typedef I derived_iterator_type;
         typedef T derived_value_type;
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         derived_iterator_type operator ++ (int) {
             derived_iterator_type &d (*static_cast<const derived_iterator_type *> (this));
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator ++ (derived_iterator_type &d, int) {
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         derived_iterator_type operator -- (int) {
             derived_iterator_type &d (*static_cast<const derived_iterator_type *> (this));
             derived_iterator_type tmp (d);
             -- d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator -- (derived_iterator_type &d, int) {
             derived_iterator_type tmp (d);
             -- d;
             return tmp;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator != (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return ! (*d == it);
         }
     };
 
   /** \brief Base class of all random access iterators.
    *
    * \param IC the iterator category
    * \param I the derived iterator type
    * \param T the value type
    * \param D the difference type, default: std::ptrdiff_t
    *
    * The random access iterator can proceed in both directions
    * via the post increment/decrement operator or in larger steps
    * via the +, - and +=, -= operators. The random access iterator
    * is LessThan Comparable.
    */
     template<class IC, class I, class T, class D = std::ptrdiff_t>
     // ISSUE the default for D seems rather dangerous as it can easily be (silently) incorrect
     struct random_access_iterator_base {
         typedef IC iterator_category;
         typedef T value_type;
         typedef D difference_type;
         typedef T* pointer;
         typedef T& reference;
         typedef I derived_iterator_type;
         typedef T derived_value_type;
         typedef D derived_difference_type;
 
         /* FIXME Need to explicitly pass derived_reference_type as otherwise I undefined type or forward declared
         typedef typename derived_iterator_type::reference derived_reference_type;
         // Indexed element
         BOOST_UBLAS_INLINE
         derived_reference_type operator [] (derived_difference_type n) {
             return *(*this + n);
         }
         */
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         derived_iterator_type operator ++ (int) {
             derived_iterator_type &d (*static_cast<derived_iterator_type *> (this));
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator ++ (derived_iterator_type &d, int) {
             derived_iterator_type tmp (d);
             ++ d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         derived_iterator_type operator -- (int) {
             derived_iterator_type &d (*static_cast<derived_iterator_type *> (this));
             derived_iterator_type tmp (d);
             -- d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator -- (derived_iterator_type &d, int) {
             derived_iterator_type tmp (d);
             -- d;
             return tmp;
         }
         BOOST_UBLAS_INLINE
         derived_iterator_type operator + (derived_difference_type n) const {
             derived_iterator_type tmp (*static_cast<const derived_iterator_type *> (this));
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator + (const derived_iterator_type &d, derived_difference_type n) {
             derived_iterator_type tmp (d);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator + (derived_difference_type n, const derived_iterator_type &d) {
             derived_iterator_type tmp (d);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         derived_iterator_type operator - (derived_difference_type n) const {
             derived_iterator_type tmp (*static_cast<const derived_iterator_type *> (this));
             return tmp -= n;
         }
         BOOST_UBLAS_INLINE
         friend derived_iterator_type operator - (const derived_iterator_type &d, derived_difference_type n) {
             derived_iterator_type tmp (d);
             return tmp -= n;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator != (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return ! (*d == it);
         }
         BOOST_UBLAS_INLINE
         bool operator <= (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return ! (it < *d);
         }
         BOOST_UBLAS_INLINE
         bool operator >= (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return ! (*d < it);
         }
         BOOST_UBLAS_INLINE
         bool operator > (const derived_iterator_type &it) const {
             const derived_iterator_type *d = static_cast<const derived_iterator_type *> (this);
             return it < *d;
         }
     };
 
   /** \brief Base class of all reverse iterators. (non-MSVC version)
    *
    * \param I the derived iterator type
    * \param T the value type
    * \param R the reference type
    *
    * The reverse iterator implements a bidirectional iterator
    * reversing the elements of the underlying iterator. It
    * implements most operators of a random access iterator.
    *
    * uBLAS extension: it.index()
    */
 
     // Renamed this class from reverse_iterator to get
     // typedef reverse_iterator<...> reverse_iterator
     // working. Thanks to Gabriel Dos Reis for explaining this.
     template <class I>
     class reverse_iterator_base:
         public std::reverse_iterator<I> {
     public:
         typedef typename I::container_type container_type;
         typedef typename container_type::size_type size_type;
         typedef typename I::difference_type difference_type;
         typedef I iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         reverse_iterator_base ():
             std::reverse_iterator<iterator_type> () {}
         BOOST_UBLAS_INLINE
         reverse_iterator_base (const iterator_type &it):
             std::reverse_iterator<iterator_type> (it) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         reverse_iterator_base &operator ++ () {
             return *this = -- this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base operator ++ (int) {
             reverse_iterator_base tmp (*this);
             *this = -- this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base &operator -- () {
             return *this = ++ this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base operator -- (int) {
             reverse_iterator_base tmp (*this);
             *this = ++ this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base &operator += (difference_type n) {
             return *this = this->base () - n;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base &operator -= (difference_type n) {
             return *this = this->base () + n;
         }
 
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base operator + (const reverse_iterator_base &it, difference_type n) {
             reverse_iterator_base tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base operator + (difference_type n, const reverse_iterator_base &it) {
             reverse_iterator_base tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base operator - (const reverse_iterator_base &it, difference_type n) {
             reverse_iterator_base tmp (it);
             return tmp -= n;
         }
         BOOST_UBLAS_INLINE
         friend difference_type operator - (const reverse_iterator_base &it1, const reverse_iterator_base &it2) {
             return it2.base () - it1.base ();
         }
 
         BOOST_UBLAS_INLINE
         const container_type &operator () () const {
             return this->base () ();
         }
 
         BOOST_UBLAS_INLINE
         size_type index () const {
             iterator_type tmp (this->base ());
             return (-- tmp).index ();
         }
     };
 
   /** \brief 1st base class of all matrix reverse iterators. (non-MSVC version)
    *
    * \param I the derived iterator type
    *
    * The reverse iterator implements a bidirectional iterator
    * reversing the elements of the underlying iterator. It
    * implements most operators of a random access iterator.
    *
    * uBLAS extension: it.index1(), it.index2() and access to
    * the dual iterator via begin(), end(), rbegin(), rend()
    */
 
     // Renamed this class from reverse_iterator1 to get
     // typedef reverse_iterator1<...> reverse_iterator1
     // working. Thanks to Gabriel Dos Reis for explaining this.
     template <class I>
     class reverse_iterator_base1:
         public std::reverse_iterator<I> {
     public:
         typedef typename I::container_type container_type;
         typedef typename container_type::size_type size_type;
         typedef typename I::difference_type difference_type;
         typedef I iterator_type;
         typedef typename I::dual_iterator_type dual_iterator_type;
         typedef typename I::dual_reverse_iterator_type dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 ():
             std::reverse_iterator<iterator_type> () {}
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 (const iterator_type &it):
             std::reverse_iterator<iterator_type> (it) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 &operator ++ () {
             return *this = -- this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 operator ++ (int) {
             reverse_iterator_base1 tmp (*this);
             *this = -- this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 &operator -- () {
             return *this = ++ this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 operator -- (int) {
             reverse_iterator_base1 tmp (*this);
             *this = ++ this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 &operator += (difference_type n) {
             return *this = this->base () - n;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base1 &operator -= (difference_type n) {
             return *this = this->base () + n;
         }
 
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base1 operator + (const reverse_iterator_base1 &it, difference_type n) {
             reverse_iterator_base1 tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base1 operator + (difference_type n, const reverse_iterator_base1 &it) {
             reverse_iterator_base1 tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base1 operator - (const reverse_iterator_base1 &it, difference_type n) {
             reverse_iterator_base1 tmp (it);
             return tmp -= n;
         }
         BOOST_UBLAS_INLINE
         friend difference_type operator - (const reverse_iterator_base1 &it1, const reverse_iterator_base1 &it2) {
             return it2.base () - it1.base ();
         }
 
         BOOST_UBLAS_INLINE
         const container_type &operator () () const {
             return this->base () ();
         }
 
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             iterator_type tmp (this->base ());
             return (-- tmp).index1 ();
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             iterator_type tmp (this->base ());
             return (-- tmp).index2 ();
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             iterator_type tmp (this->base ());
             return (-- tmp).begin ();
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             iterator_type tmp (this->base ());
             return (-- tmp).end ();
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ());
         }
     };
 
   /** \brief 2nd base class of all matrix reverse iterators. (non-MSVC version)
    *
    * \param I the derived iterator type
    *
    * The reverse iterator implements a bidirectional iterator
    * reversing the elements of the underlying iterator. It
    * implements most operators of a random access iterator.
    *
    * uBLAS extension: it.index1(), it.index2() and access to
    * the dual iterator via begin(), end(), rbegin(), rend()
    *
    * Note: this type is _identical_ to reverse_iterator_base1
    */
 
     // Renamed this class from reverse_iterator2 to get
     // typedef reverse_iterator2<...> reverse_iterator2
     // working. Thanks to Gabriel Dos Reis for explaining this.
     template <class I>
     class reverse_iterator_base2:
         public std::reverse_iterator<I> {
     public:
         typedef typename I::container_type container_type;
         typedef typename container_type::size_type size_type;
         typedef typename I::difference_type difference_type;
         typedef I iterator_type;
         typedef typename I::dual_iterator_type dual_iterator_type;
         typedef typename I::dual_reverse_iterator_type dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 ():
             std::reverse_iterator<iterator_type> () {}
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 (const iterator_type &it):
             std::reverse_iterator<iterator_type> (it) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 &operator ++ () {
             return *this = -- this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 operator ++ (int) {
             reverse_iterator_base2 tmp (*this);
             *this = -- this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 &operator -- () {
             return *this = ++ this->base ();
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 operator -- (int) {
             reverse_iterator_base2 tmp (*this);
             *this = ++ this->base ();
             return tmp;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 &operator += (difference_type n) {
             return *this = this->base () - n;
         }
         BOOST_UBLAS_INLINE
         reverse_iterator_base2 &operator -= (difference_type n) {
             return *this = this->base () + n;
         }
 
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base2 operator + (const reverse_iterator_base2 &it, difference_type n) {
             reverse_iterator_base2 tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base2 operator + (difference_type n, const reverse_iterator_base2 &it) {
             reverse_iterator_base2 tmp (it);
             return tmp += n;
         }
         BOOST_UBLAS_INLINE
         friend reverse_iterator_base2 operator - (const reverse_iterator_base2 &it, difference_type n) {
             reverse_iterator_base2 tmp (it);
             return tmp -= n;
         }
         BOOST_UBLAS_INLINE
         friend difference_type operator - (const reverse_iterator_base2 &it1, const reverse_iterator_base2 &it2) {
             return it2.base () - it1.base ();
         }
 
         BOOST_UBLAS_INLINE
         const container_type &operator () () const {
             return this->base () ();
         }
 
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             iterator_type tmp (this->base ());
             return (-- tmp).index1 ();
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             iterator_type tmp (this->base ());
             return (-- tmp).index2 ();
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             iterator_type tmp (this->base ());
             return (-- tmp).begin ();
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             iterator_type tmp (this->base ());
             return (-- tmp).end ();
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ());
         }
     };
 
   /** \brief A class implementing an indexed random access iterator.
    *
    * \param C the (mutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current 
    * position is stored as the unsigned integer it_ and the
    * values are accessed via operator()(it_) of the container.
    *
    * uBLAS extension: index()
    */
 
     template<class C, class IC>
     class indexed_iterator:
         public container_reference<C>,
         public random_access_iterator_base<IC,
                                            indexed_iterator<C, IC>,
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::reference reference;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_iterator ():
             container_reference<container_type> (), it_ () {}
         BOOST_UBLAS_INLINE
         indexed_iterator (container_type &c, size_type it):
             container_reference<container_type> (c), it_ (it) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_iterator &operator ++ () {
             ++ it_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator &operator -- () {
             -- it_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator &operator += (difference_type n) {
             it_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator &operator -= (difference_type n) {
             it_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ - it.it_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index () < (*this) ().size (), bad_index ());
             return (*this) () (it_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index () const {
             return it_;
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_iterator &operator = (const indexed_iterator &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_reference<C>::assign (&it ());
             it_ = it.it_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ == it.it_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ < it.it_;
         }
 
     private:
         size_type it_;
     };
 
   /** \brief A class implementing an indexed random access iterator.
    *
    * \param C the (immutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current 
    * position is stored as the unsigned integer \c it_ and the
    * values are accessed via \c operator()(it_) of the container.
    *
    * uBLAS extension: \c index()
    *
    * Note: there is an automatic conversion from 
    * \c indexed_iterator to \c indexed_const_iterator
    */
 
     template<class C, class IC>
     class indexed_const_iterator:
         public container_const_reference<C>,
         public random_access_iterator_base<IC,
                                            indexed_const_iterator<C, IC>,
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::const_reference reference;
         typedef indexed_iterator<container_type, iterator_category> iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_const_iterator ():
             container_const_reference<container_type> (), it_ () {}
         BOOST_UBLAS_INLINE
         indexed_const_iterator (const container_type &c, size_type it):
             container_const_reference<container_type> (c), it_ (it) {}
         BOOST_UBLAS_INLINE 
         indexed_const_iterator (const iterator_type &it):
             container_const_reference<container_type> (it ()), it_ (it.index ()) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_const_iterator &operator ++ () {
             ++ it_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator &operator -- () {
             -- it_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator &operator += (difference_type n) {
             it_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator &operator -= (difference_type n) {
             it_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_const_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ - it.it_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index () < (*this) ().size (), bad_index ());
             return (*this) () (it_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index () const {
             return it_;
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_const_iterator &operator = (const indexed_const_iterator &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_const_reference<C>::assign (&it ());
             it_ = it.it_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_const_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ == it.it_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_const_iterator &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             return it_ < it.it_;
         }
 
     private:
         size_type it_;
 
         friend class indexed_iterator<container_type, iterator_category>;
     };
 
     template<class C, class IC>
     class indexed_iterator2;
 
   /** \brief A class implementing an indexed random access iterator 
    * of a matrix.
    *
    * \param C the (mutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current
    * position is stored as two unsigned integers \c it1_ and \c it2_
    * and the values are accessed via \c operator()(it1_, it2_) of the
    * container. The iterator changes the first index.
    *
    * uBLAS extension: \c index1(), \c index2() and access to the
    * dual iterator via \c begin(), \c end(), \c rbegin() and \c rend()
    *
    * Note: The container has to support the \code find2(rank, i, j) \endcode 
    * method
    */
 
     template<class C, class IC>
     class indexed_iterator1:
         public container_reference<C>, 
         public random_access_iterator_base<IC,
                                            indexed_iterator1<C, IC>, 
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::reference reference;
 
         typedef indexed_iterator2<container_type, iterator_category> dual_iterator_type;
         typedef reverse_iterator_base2<dual_iterator_type> dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_iterator1 ():
             container_reference<container_type> (), it1_ (), it2_ () {}
         BOOST_UBLAS_INLINE 
         indexed_iterator1 (container_type &c, size_type it1, size_type it2):
             container_reference<container_type> (c), it1_ (it1), it2_ (it2) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_iterator1 &operator ++ () {
             ++ it1_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator1 &operator -- () {
             -- it1_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator1 &operator += (difference_type n) {
             it1_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator1 &operator -= (difference_type n) {
             it1_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ - it.it1_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
             BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
             return (*this) () (it1_, it2_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             return it1_;
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             return it2_;
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             return (*this) ().find2 (1, index1 (), 0); 
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ());
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_iterator1 &operator = (const indexed_iterator1 &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_reference<C>::assign (&it ());
             it1_ = it.it1_;
             it2_ = it.it2_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ == it.it1_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ < it.it1_;
         }
 
     private:
         size_type it1_;
         size_type it2_;
     };
 
     template<class C, class IC>
     class indexed_const_iterator2;
 
   /** \brief A class implementing an indexed random access iterator 
    * of a matrix.
    *
    * \param C the (immutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current
    * position is stored as two unsigned integers \c it1_ and \c it2_
    * and the values are accessed via \c operator()(it1_, it2_) of the
    * container. The iterator changes the first index.
    *
    * uBLAS extension: \c index1(), \c index2() and access to the
    * dual iterator via \c begin(), \c end(), \c rbegin() and \c rend()
    *
    * Note 1: The container has to support the find2(rank, i, j) method
    *
    * Note 2: there is an automatic conversion from 
    * \c indexed_iterator1 to \c indexed_const_iterator1
    */
 
     template<class C, class IC>
     class indexed_const_iterator1:
         public container_const_reference<C>, 
         public random_access_iterator_base<IC,
                                            indexed_const_iterator1<C, IC>, 
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::const_reference reference;
 
         typedef indexed_iterator1<container_type, iterator_category> iterator_type;
         typedef indexed_const_iterator2<container_type, iterator_category> dual_iterator_type;
         typedef reverse_iterator_base2<dual_iterator_type> dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 ():
             container_const_reference<container_type> (), it1_ (), it2_ () {}
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 (const container_type &c, size_type it1, size_type it2):
             container_const_reference<container_type> (c), it1_ (it1), it2_ (it2) {}
         BOOST_UBLAS_INLINE 
         indexed_const_iterator1 (const iterator_type &it):
             container_const_reference<container_type> (it ()), it1_ (it.index1 ()), it2_ (it.index2 ()) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 &operator ++ () {
             ++ it1_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 &operator -- () {
             -- it1_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 &operator += (difference_type n) {
             it1_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 &operator -= (difference_type n) {
             it1_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_const_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ - it.it1_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
             BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
             return (*this) () (it1_, it2_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             return it1_;
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             return it2_;
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             return (*this) ().find2 (1, index1 (), 0); 
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             return (*this) ().find2 (1, index1 (), (*this) ().size2 ()); 
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ()); 
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ()); 
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_const_iterator1 &operator = (const indexed_const_iterator1 &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_const_reference<C>::assign (&it ());
             it1_ = it.it1_;
             it2_ = it.it2_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_const_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ == it.it1_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_const_iterator1 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
             return it1_ < it.it1_;
         }
 
     private:
         size_type it1_;
         size_type it2_;
 
         friend class indexed_iterator1<container_type, iterator_category>;
     };
 
   /** \brief A class implementing an indexed random access iterator 
    * of a matrix.
    *
    * \param C the (mutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current
    * position is stored as two unsigned integers \c it1_ and \c it2_
    * and the values are accessed via \c operator()(it1_, it2_) of the
    * container. The iterator changes the second index.
    *
    * uBLAS extension: \c index1(), \c index2() and access to the
    * dual iterator via \c begin(), \c end(), \c rbegin() and \c rend()
    *
    * Note: The container has to support the find1(rank, i, j) method
    */
     template<class C, class IC>
     class indexed_iterator2:
         public container_reference<C>, 
         public random_access_iterator_base<IC,
                                            indexed_iterator2<C, IC>, 
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::reference reference;
 
         typedef indexed_iterator1<container_type, iterator_category> dual_iterator_type;
         typedef reverse_iterator_base1<dual_iterator_type> dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_iterator2 ():
             container_reference<container_type> (), it1_ (), it2_ () {}
         BOOST_UBLAS_INLINE
         indexed_iterator2 (container_type &c, size_type it1, size_type it2):
             container_reference<container_type> (c), it1_ (it1), it2_ (it2) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_iterator2 &operator ++ () {
             ++ it2_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator2 &operator -- () {
             -- it2_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator2 &operator += (difference_type n) {
             it2_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_iterator2 &operator -= (difference_type n) {
             it2_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ - it.it2_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
             BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
             return (*this) () (it1_, it2_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             return it1_;
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             return it2_;
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             return (*this) ().find1 (1, 0, index2 ());
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ());
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_iterator2 &operator = (const indexed_iterator2 &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_reference<C>::assign (&it ());
             it1_ = it.it1_;
             it2_ = it.it2_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ == it.it2_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ < it.it2_;
         }
 
     private:
         size_type it1_;
         size_type it2_;
     };
 
   /** \brief A class implementing an indexed random access iterator 
    * of a matrix.
    *
    * \param C the (immutable) container type
    * \param IC the iterator category
    *
    * This class implements a random access iterator. The current
    * position is stored as two unsigned integers \c it1_ and \c it2_
    * and the values are accessed via \c operator()(it1_, it2_) of the
    * container. The iterator changes the second index.
    *
    * uBLAS extension: \c index1(), \c index2() and access to the
    * dual iterator via \c begin(), \c end(), \c rbegin() and \c rend()
    *
    * Note 1: The container has to support the \c find2(rank, i, j) method
    *
    * Note 2: there is an automatic conversion from 
    * \c indexed_iterator2 to \c indexed_const_iterator2
    */
 
     template<class C, class IC>
     class indexed_const_iterator2:
         public container_const_reference<C>,
         public random_access_iterator_base<IC,
                                            indexed_const_iterator2<C, IC>,
                                            typename C::value_type,
                                            typename C::difference_type> {
     public:
         typedef C container_type;
         typedef IC iterator_category;
         typedef typename container_type::size_type size_type;
         typedef typename container_type::difference_type difference_type;
         typedef typename container_type::value_type value_type;
         typedef typename container_type::const_reference reference;
 
         typedef indexed_iterator2<container_type, iterator_category> iterator_type;
         typedef indexed_const_iterator1<container_type, iterator_category> dual_iterator_type;
         typedef reverse_iterator_base1<dual_iterator_type> dual_reverse_iterator_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 ():
             container_const_reference<container_type> (), it1_ (), it2_ () {}
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 (const container_type &c, size_type it1, size_type it2):
             container_const_reference<container_type> (c), it1_ (it1), it2_ (it2) {}
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 (const iterator_type &it):
             container_const_reference<container_type> (it ()), it1_ (it.index1 ()), it2_ (it.index2 ()) {}
 
         // Arithmetic
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 &operator ++ () {
             ++ it2_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 &operator -- () {
             -- it2_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 &operator += (difference_type n) {
             it2_ += n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 &operator -= (difference_type n) {
             it2_ -= n;
             return *this;
         }
         BOOST_UBLAS_INLINE
         difference_type operator - (const indexed_const_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ - it.it2_;
         }
 
         // Dereference
         BOOST_UBLAS_INLINE
         reference operator * () const {
             BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
             BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
             return (*this) () (it1_, it2_);
         }
         BOOST_UBLAS_INLINE
         reference operator [] (difference_type n) const {
             return *((*this) + n);
         }
 
         // Index
         BOOST_UBLAS_INLINE
         size_type index1 () const {
             return it1_;
         }
         BOOST_UBLAS_INLINE
         size_type index2 () const {
             return it2_;
         }
 
         BOOST_UBLAS_INLINE
         dual_iterator_type begin () const {
             return (*this) ().find1 (1, 0, index2 ());
         }
         BOOST_UBLAS_INLINE
         dual_iterator_type end () const {
             return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rbegin () const {
             return dual_reverse_iterator_type (end ());
         }
         BOOST_UBLAS_INLINE
         dual_reverse_iterator_type rend () const {
             return dual_reverse_iterator_type (begin ());
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         indexed_const_iterator2 &operator = (const indexed_const_iterator2 &it) {
             // FIX: ICC needs full qualification?!
             // assign (&it ());
             container_const_reference<C>::assign (&it ());
             it1_ = it.it1_;
             it2_ = it.it2_;
             return *this;
         }
 
         // Comparison
         BOOST_UBLAS_INLINE
         bool operator == (const indexed_const_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ == it.it2_;
         }
         BOOST_UBLAS_INLINE
         bool operator < (const indexed_const_iterator2 &it) const {
             BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
             BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
             return it2_ < it.it2_;
         }
 
     private:
         size_type it1_;
         size_type it2_;
 
         friend class indexed_iterator2<container_type, iterator_category>;
     };
 
 }}}
 
 #endif

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