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 //
 //  Copyright (c) 2000-2010
 //  Joerg Walter, Mathias Koch, Gunter Winkler, David Bellot
 //  Copyright (c) 2014, Athanasios Iliopoulos
 //
 //  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_MATRIX_
 #define _BOOST_UBLAS_MATRIX_
 
 #include <boost/config.hpp>
 #include <boost/numeric/ublas/vector.hpp>
 #include <boost/numeric/ublas/matrix_expression.hpp>
 #include <boost/numeric/ublas/detail/matrix_assign.hpp>
 #include <boost/serialization/collection_size_type.hpp>
 #include <boost/serialization/array.hpp>
 #include <boost/serialization/nvp.hpp>
 
 // Iterators based on ideas of Jeremy Siek
 
 namespace boost { namespace numeric { 
     
     /** \brief main namespace of uBLAS.
      *
      * Use this namespace for all operations with uBLAS. It can also be abbreviated with
      * \code namespace ublas = boost::numeric::ublas; \endcode
      *
      * A common practice is to bring this namespace into the current scope with
      * \code using namespace boost::numeric::ublas; \endcode.
      *
      * However, be warned that using the ublas namespace and the std::vector at the same time can lead to the compiler to confusion. 
      * The solution is simply to prefix each ublas vector like \c boost::numeric::ublas::vector<T>. If you think it's too long to 
      * write, you can define a new namespace like \c namespace ublas = boost::numeric::ublas and then just declare your vectors
      * with \c ublas::vector<T>. STL vectors will be declared as vector<T>. No need to prefix with \c std::
      */
     namespace ublas {
 
     namespace detail {
         using namespace boost::numeric::ublas;
 
         // Matrix resizing algorithm
         template <class L, class M>
         BOOST_UBLAS_INLINE
         void matrix_resize_preserve (M& m, M& temporary) {
             typedef L layout_type;
             typedef typename M::size_type size_type;
             const size_type msize1 (m.size1 ());        // original size
             const size_type msize2 (m.size2 ());
             const size_type size1 (temporary.size1 ());    // new size is specified by temporary
             const size_type size2 (temporary.size2 ());
             // Common elements to preserve
             const size_type size1_min = (std::min) (size1, msize1);
             const size_type size2_min = (std::min) (size2, msize2);
             // Order for major and minor sizes
             const size_type major_size = layout_type::size_M (size1_min, size2_min);
             const size_type minor_size = layout_type::size_m (size1_min, size2_min);
             // Indexing copy over major
             for (size_type major = 0; major != major_size; ++major) {
                 for (size_type minor = 0; minor != minor_size; ++minor) {
                         // find indexes - use invertability of element_ functions
                     const size_type i1 = layout_type::index_M(major, minor);
                     const size_type i2 = layout_type::index_m(major, minor);
                     temporary.data () [layout_type::element (i1, size1, i2, size2)] =
                             m.data() [layout_type::element (i1, msize1, i2, msize2)];
                 }
             }
             m.assign_temporary (temporary);
         }
     }
 
     /** \brief A dense matrix of values of type \c T.
      *
      * For a \f$(m \times n)\f$-dimensional matrix and \f$ 0 \leq i < m, 0 \leq j < n\f$, every element \f$ m_{i,j} \f$ is mapped to 
      * the \f$(i.n + j)\f$-th element of the container for row major orientation or the \f$ (i + j.m) \f$-th element of 
      * the container for column major orientation. In a dense matrix all elements are represented in memory in a 
      * contiguous chunk of memory by definition.
      * 
      * Orientation and storage can also be specified, otherwise a \c row_major and \c unbounded_array are used. It is \b not 
      * required by the storage to initialize elements of the matrix.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
      * \tparam A the type of Storage array. Default is \c unbounded_array
      */
     template<class T, class L, class A>
     class matrix:
         public matrix_container<matrix<T, L, A> > {
 
         typedef T *pointer;
         typedef L layout_type;
         typedef matrix<T, L, A> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename A::size_type size_type;
         typedef typename A::difference_type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef A array_type;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef vector<T, A> vector_temporary_type;
         typedef self_type matrix_temporary_type;
         typedef dense_tag storage_category;
         // This could be better for performance,
         // typedef typename unknown_orientation_tag orientation_category;
         // but others depend on the orientation information...
         typedef typename L::orientation_category orientation_category;
 
         // Construction and destruction
       
       /// Default dense matrix constructor. Make a dense matrix of size (0,0)
         BOOST_UBLAS_INLINE
         matrix ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0), data_ () {}
     
       /** Dense matrix constructor with defined size
        * \param size1 number of rows
        * \param size2 number of columns
        */
         BOOST_UBLAS_INLINE
         matrix (size_type size1, size_type size2):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), data_ (layout_type::storage_size (size1, size2)) {
         }
     
       /** Dense matrix constructor with defined size a initial value for all the matrix elements
        * \param size1 number of rows
        * \param size2 number of columns
        * \param init initial value assigned to all elements
        */
         matrix (size_type size1, size_type size2, const value_type &init):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), data_ (layout_type::storage_size (size1, size2), init) {
         }
 
       /** Dense matrix constructor with defined size and an initial data array
        * \param size1 number of rows
        * \param size2 number of columns
        * \param data array to copy into the matrix. Must have the same dimension as the matrix
        */
         BOOST_UBLAS_INLINE
         matrix (size_type size1, size_type size2, const array_type &data):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), data_ (data) {}
 
       /** Copy-constructor of a dense matrix
        * \param m is a dense matrix
        */
         BOOST_UBLAS_INLINE
         matrix (const matrix &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}
 
       /** Copy-constructor of a dense matrix from a matrix expression
        * \param ae is a matrix expression
        */
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix (const matrix_expression<AE> &ae):
             matrix_container<self_type> (),
             size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), data_ (layout_type::storage_size (size1_, size2_)) {
             matrix_assign<scalar_assign> (*this, ae);
         }
 
         // Accessors
       /** Return the number of rows of the matrix
        * You can also use the free size<>() function in operation/size.hpp as size<1>(m) where m is a matrix
        */
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
 
       /** Return the number of colums of the matrix
        * You can also use the free size<>() function in operation/size.hpp as size<2>(m) where m is a matrix
        */
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
 
         // Storage accessors
       /** Return a constant reference to the internal storage of a dense matrix, i.e. the raw data
        * It's type depends on the type used by the matrix to store its data
        */
         BOOST_UBLAS_INLINE
         const array_type &data () const {
             return data_;
         }
       /** Return a reference to the internal storage of a dense matrix, i.e. the raw data
        * It's type depends on the type used by the matrix to store its data
        */
         BOOST_UBLAS_INLINE
         array_type &data () {
             return data_;
         }
 
         // Resizing
       /** Resize a matrix to new dimensions
        * If data are preserved, then if the size if bigger at least on one dimension, extra values are filled with zeros.
        * If data are not preserved, then nothing has to be assumed regarding the content of the matrix after resizing.
        * \param size1 the new number of rows
        * \param size2 the new number of colums
        * \param preserve a boolean to say if one wants the data to be preserved during the resizing. Default is true.
        */
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool preserve = true) {
             if (preserve) {
                 self_type temporary (size1, size2);
                 detail::matrix_resize_preserve<layout_type> (*this, temporary);
             }
             else {
                 data ().resize (layout_type::storage_size (size1, size2));
                 size1_ = size1;
                 size2_ = size2;
             }
         }
 
         // Element access
     
     /** Access a matrix element. Here we return a const reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a const reference to the element
      */
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             return data () [layout_type::element (i, size1_, j, size2_)];
         }
 
     /** Access a matrix element. Here we return a reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a reference to the element
      */
         BOOST_UBLAS_INLINE
         reference at_element (size_type i, size_type j) {
             return data () [layout_type::element (i, size1_, j, size2_)];
         }
 
     /** Access a matrix element. Here we return a reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a reference to the element
      */
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             return at_element (i, j);
         }
 
     /** Access a matrix element. Here we return a reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a reference to the element
      */
         BOOST_UBLAS_INLINE
         reference operator () (size_type i) {
             return data()[i];
         }
 
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i) const {
             return data()[i];
         }
 
 //      /** Access a matrix element. Here we return a reference
 //       * \param i the first coordinate of the element. By default it's the row
 //       * \param j the second coordinate of the element. By default it's the column
 //       * \return a reference to the element
 //       */
 //          BOOST_UBLAS_INLINE
 //          const_reference operator () const (size_type i) {
 //              return data()[i];
 //          }
         // Element assignment
 
     /** Change the value of a matrix element. Return back a reference to it
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \param t the new value of the element
      * \return a reference to the newly changed element
      */
         BOOST_UBLAS_INLINE
         reference insert_element (size_type i, size_type j, const_reference t) {
             return (at_element (i, j) = t);
         }
 
     /** Erase the element 
      * For most types (int, double, etc...) it means setting 0 (zero) the element at zero in fact.
      * For user-defined types, it could be another value if you decided it. Your type in that case must
      * contain a default null value.
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      */
         void erase_element (size_type i, size_type j) {
             at_element (i, j) = value_type/*zero*/();
         }
 
         // Zeroing
     /** Erase all elements in the matrix
      * For most types (int, double, etc...) it means writing 0 (zero) everywhere.
      * For user-defined types, it could be another value if you decided it. Your type in that case must
      * contain a default null value.
      */
         BOOST_UBLAS_INLINE
         void clear () {
             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
         }
 
         // Assignment
 #ifdef BOOST_UBLAS_MOVE_SEMANTICS
 
         /*! @note "pass by value" the key idea to enable move semantics */
         BOOST_UBLAS_INLINE
         matrix &operator = (matrix m) {
             assign_temporary(m);
             return *this;
         }
 #else
         BOOST_UBLAS_INLINE
         matrix &operator = (const matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             data () = m.data ();
             return *this;
         }
 #endif
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         matrix &operator = (const matrix_container<C> &m) {
             resize (m ().size1 (), m ().size2 (), false);
             assign (m);
             return *this;
         }
         BOOST_UBLAS_INLINE
         matrix &assign_temporary (matrix &m) {
             swap (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix &operator = (const matrix_expression<AE> &ae) {
             self_type temporary (ae);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix &assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix& operator += (const matrix_expression<AE> &ae) {
             self_type temporary (*this + ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         matrix &operator += (const matrix_container<C> &m) {
             plus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix &plus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_plus_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix& operator -= (const matrix_expression<AE> &ae) {
             self_type temporary (*this - ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         matrix &operator -= (const matrix_container<C> &m) {
             minus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         matrix &minus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_minus_assign> (*this, ae);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         matrix& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         matrix& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (matrix &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 data ().swap (m.data ());
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (matrix &m1, matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use the storage array iterator
         typedef typename A::const_iterator const_subiterator_type;
         typedef typename A::iterator subiterator_type;
 
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, dense_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, dense_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int /* rank */, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator1 (*this, i, j);
 #else
             return const_iterator1 (*this, data ().begin () + layout_type::address (i, size1_, j, size2_));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int /* rank */, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator1 (*this, i, j);
 #else
             return iterator1 (*this, data ().begin () + layout_type::address (i, size1_, j, size2_));
 #endif
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /* rank */, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator2 (*this, i, j);
 #else
             return const_iterator2 (*this, data ().begin () + layout_type::address (i, size1_, j, size2_));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int /* rank */, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator2 (*this, i, j);
 #else
             return iterator2 (*this, data ().begin () + layout_type::address (i, size1_, j, size2_));
 #endif
         }
 
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename matrix::value_type value_type;
             typedef typename matrix::difference_type difference_type;
             typedef typename matrix::const_reference reference;
             typedef const typename matrix::pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 layout_type::increment_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 layout_type::decrement_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 layout_type::increment_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 layout_type::decrement_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_i (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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_iterator2 begin () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1_, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator1, value_type> {
         public:
             typedef typename matrix::value_type value_type;
             typedef typename matrix::difference_type difference_type;
             typedef typename matrix::reference reference;
             typedef typename matrix::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 layout_type::increment_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 layout_type::decrement_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 layout_type::increment_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 layout_type::decrement_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_i (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator2 begin () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, size1_, 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename matrix::value_type value_type;
             typedef typename matrix::difference_type difference_type;
             typedef typename matrix::const_reference reference;
             typedef const typename matrix::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 &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 layout_type::increment_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 layout_type::decrement_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 layout_type::increment_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 layout_type::decrement_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_j (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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 {
                 const self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 const self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator2, value_type> {
         public:
             typedef typename matrix::value_type value_type;
             typedef typename matrix::difference_type difference_type;
             typedef typename matrix::reference reference;
             typedef typename matrix::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 layout_type::increment_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 layout_type::decrement_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 layout_type::increment_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 layout_type::decrement_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_j (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator1 begin () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             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 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
         // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
             }
             ar & serialization::make_nvp("data",data_);
         }
 
     private:
         size_type size1_;
         size_type size2_;
         array_type data_;
     };
 
 
 #ifdef BOOST_UBLAS_CPP_GE_2011
     /** \brief A fixed size dense matrix of values of type \c T. Equivalent to a c-style 2 dimensional array.
      *
      * For a \f$(m \times n)\f$-dimensional fixed_matrix and \f$ 0 \leq i < m, 0 \leq j < n\f$, every element \f$ m_{i,j} \f$ is mapped to
      * the \f$(i.n + j)\f$-th element of the container for row major orientation or the \f$ (i + j.m) \f$-th element of
      * the container for column major orientation. In a dense matrix all elements are represented in memory in a
      * contiguous chunk of memory by definition.
      *
      * Orientation and storage can also be specified, otherwise \c row_major and \c std::array are used. It is \b not
      * required by the storage container to initialize elements of the matrix.
      *
      * \tparam T the type of object stored in the matrix (like double, float, std::complex<double>, etc...)
      * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
      * \tparam A the type of Storage array. Default is \c std::array<T, M*N>
      */
     template<class T, std::size_t M, std::size_t N, class L, class A>
     class fixed_matrix:
         public matrix_container<fixed_matrix<T, M, N, L, A> > {
 
         typedef T *pointer;
         typedef L layout_type;
         typedef fixed_matrix<T, M, N, L, A> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename A::size_type size_type;
         typedef typename A::difference_type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef A array_type;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef vector<T, A> vector_temporary_type;
         typedef self_type matrix_temporary_type;
         typedef dense_tag storage_category;
         // This could be better for performance,
         // typedef typename unknown_orientation_tag orientation_category;
         // but others depend on the orientation information...
         typedef typename L::orientation_category orientation_category;
 
         // Construction and destruction
 
       /// Default dense fixed_matrix constructor. Make a dense fixed_matrix of size M x N
         BOOST_UBLAS_INLINE
         fixed_matrix ():
             matrix_container<self_type> (),
             data_ () {}
 
       /** Dense fixed_matrix constructor with defined initial value for all the matrix elements
        * \param init initial value assigned to all elements
        */
         fixed_matrix (const value_type &init):
             matrix_container<self_type> (),
             data_ ( ) {
             data_.fill(init);
         }
 
       /** Dense matrix constructor with defined initial data array
        * \param data array to copy into the matrix. Must have the same dimension as the matrix
        */
         BOOST_UBLAS_INLINE
         fixed_matrix (const array_type &data):
             matrix_container<self_type> (),
             data_ (data) {}
 
       /** Copy-constructor of a dense fixed_matrix
        * \param m is a dense fixed_matrix
        */
         BOOST_UBLAS_INLINE
         fixed_matrix (const fixed_matrix &m):
             matrix_container<self_type> (),
             data_ (m.data_) {}
 
       /** Copy-constructor of a dense matrix from a matrix expression
        * \param ae is a matrix expression
        */
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix (const matrix_expression<AE> &ae):
             matrix_container<self_type> (),
             data_ () {
             matrix_assign<scalar_assign> (*this, ae);
         }
 
         /// \brief Construct a fixed_matrix from a list of values
         /// The list may be included in curly braces. Typical syntax is choices are :
         /// fixed_matrix<double, 2,2> v = { 1, 2, 3, 4 } or fixed_matrix<double,4> v( {1, 2, 3, 4} ) or fixed_matrix<double,2,2> v( 1, 2, 3, 4 )
         template <typename... Types>
         BOOST_UBLAS_INLINE
         fixed_matrix(value_type v0, Types... vrest) :
             matrix_container<self_type> (),
             data_( array_type{ v0, vrest... } ) {}
 
         // Accessors
       /** Return the number of rows of the fixed_matrix
        * You can also use the free size<>() function in operation/size.hpp as size<1>(m) where m is a fixed_matrix
        */
         BOOST_UBLAS_INLINE
         BOOST_CONSTEXPR size_type size1 () const {
             return M;
         }
 
       /** Return the number of colums of the fixed_matrix
        * You can also use the free size<>() function in operation/size.hpp as size<2>(m) where m is a fixed_matrix
        */
         BOOST_UBLAS_INLINE
         BOOST_CONSTEXPR size_type size2 () const {
             return N;
         }
 
         // Storage accessors
       /** Return a constant reference to the internal storage of a dense matrix, i.e. the raw data
        * It's type depends on the type used by the matrix to store its data
        */
         BOOST_UBLAS_INLINE
         const array_type &data () const {
             return data_;
         }
       /** Return a reference to the internal storage of a dense fixed_matrix, i.e. the raw data
        * It's type depends on the type used by the fixed_matrix to store its data
        */
         BOOST_UBLAS_INLINE
         array_type &data () {
             return data_;
         }
 
 
         // Element access
 
     /** Access a fixed_matrix element. Here we return a const reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a const reference to the element
      */
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             return data () [layout_type::element (i, M, j, N)]; // Fixme: add static lookup for element(...) i.e.: element<M, N>(i,j)
         }
 
     /** Access a fixed_matrix element. Here we return a reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a reference to the element
      */
         BOOST_UBLAS_INLINE
         reference at_element (size_type i, size_type j) {
             return data () [layout_type::element (i, M, j, N)];
         }
 
     /** Access a fixed_matrix element. Here we return a reference
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \return a reference to the element
      */
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             return at_element (i, j);
         }
 
         // Element assignment
 
     /** Change the value of a fixed_matrix element. Return back a reference to it
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      * \param t the new value of the element
      * \return a reference to the newly changed element
      */
         BOOST_UBLAS_INLINE
         reference insert_element (size_type i, size_type j, const_reference t) {
             return (at_element (i, j) = t);
         }
 
     /** Erase the element
      * For most types (int, double, etc...) it means setting 0 (zero) the element at zero in fact.
      * For user-defined types, it could be another value if you decided it. Your type in that case must
      * contain a default null value.
      * \param i the first coordinate of the element. By default it's the row
      * \param j the second coordinate of the element. By default it's the column
      */
         void erase_element (size_type i, size_type j) {
             at_element (i, j) = value_type/*zero*/();
         }
 
         // Zeroing
     /** Erase all elements in the fixed_matrix
      * For most types (int, double, etc...) it means writing 0 (zero) everywhere.
      * For user-defined types, it could be another value if you decided it. Your type in that case must
      * contain a default null value.
      */
         BOOST_UBLAS_INLINE
         void clear () {
             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
         }
 
         // Assignment
 #ifdef BOOST_UBLAS_MOVE_SEMANTICS
 
         /*! @note "pass by value" the key idea to enable move semantics */
         BOOST_UBLAS_INLINE
         fixed_matrix &operator = (fixed_matrix m) {
             assign_temporary(m);
             return *this;
         }
 #else
         BOOST_UBLAS_INLINE
         fixed_matrix &operator = (const fixed_matrix &m) {
             data () = m.data ();
             return *this;
         }
 #endif
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         fixed_matrix &operator = (const matrix_container<C> &m) {
             resize (m ().size1 (), m ().size2 (), false);
             assign (m);
             return *this;
         }
         BOOST_UBLAS_INLINE
         fixed_matrix &assign_temporary (fixed_matrix &m) {
             swap (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix &operator = (const matrix_expression<AE> &ae) {
             self_type temporary (ae);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix &assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix& operator += (const matrix_expression<AE> &ae) {
             self_type temporary (*this + ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         fixed_matrix &operator += (const matrix_container<C> &m) {
             plus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix &plus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_plus_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix& operator -= (const matrix_expression<AE> &ae) {
             self_type temporary (*this - ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         fixed_matrix &operator -= (const matrix_container<C> &m) {
             minus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         fixed_matrix &minus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_minus_assign> (*this, ae);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         fixed_matrix& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         fixed_matrix& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (fixed_matrix &m) {
             if (this != &m) {
                 data ().swap (m.data ());
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (fixed_matrix &m1, fixed_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use the storage array iterator
         typedef typename A::const_iterator const_subiterator_type;
         typedef typename A::iterator subiterator_type;
 
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, dense_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, dense_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int /* rank */, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator1 (*this, i, j);
 #else
             return const_iterator1 (*this, data ().begin () + layout_type::address (i, M, j, N));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int /* rank */, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator1 (*this, i, j);
 #else
             return iterator1 (*this, data ().begin () + layout_type::address (i, M, j, N));
 #endif
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /* rank */, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator2 (*this, i, j);
 #else
             return const_iterator2 (*this, data ().begin () + layout_type::address (i, M, j, N));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int /* rank */, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator2 (*this, i, j);
 #else
             return iterator2 (*this, data ().begin () + layout_type::address (i, M, j, N));
 #endif
         }
 
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<fixed_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename fixed_matrix::value_type value_type;
             typedef typename fixed_matrix::difference_type difference_type;
             typedef typename fixed_matrix::const_reference reference;
             typedef const typename fixed_matrix::pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 layout_type::increment_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 layout_type::decrement_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 layout_type::increment_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 layout_type::decrement_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_i (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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_iterator2 begin () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, M, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<fixed_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator1, value_type> {
         public:
             typedef typename fixed_matrix::value_type value_type;
             typedef typename fixed_matrix::difference_type difference_type;
             typedef typename fixed_matrix::reference reference;
             typedef typename fixed_matrix::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 layout_type::increment_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 layout_type::decrement_i (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 layout_type::increment_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 layout_type::decrement_i (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_i (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator2 begin () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin1 ().it_, m.size1 (), m.size2 ());
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, M, 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<fixed_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename fixed_matrix::value_type value_type;
             typedef typename fixed_matrix::difference_type difference_type;
             typedef typename fixed_matrix::const_reference reference;
             typedef const typename fixed_matrix::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 &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 layout_type::increment_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 layout_type::decrement_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 layout_type::increment_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 layout_type::decrement_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_j (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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 {
                 const self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 const self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, N);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<fixed_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator2, value_type> {
         public:
             typedef typename fixed_matrix::value_type value_type;
             typedef typename fixed_matrix::difference_type difference_type;
             typedef typename fixed_matrix::reference reference;
             typedef typename fixed_matrix::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 layout_type::increment_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 layout_type::decrement_j (it_, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 layout_type::increment_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 layout_type::decrement_j (it_, n, (*this) ().size1 (), (*this) ().size2 ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return layout_type::distance_j (it_ - it.it_, (*this) ().size1 (), (*this) ().size2 ());
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator1 begin () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_i (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 self_type &m = (*this) ();
                 return layout_type::index_j (it_ - m.begin2 ().it_, m.size1 (), m.size2 ());
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             return find2 (0, 0, N);
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
         // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
             ar & serialization::make_nvp("data",data_);
         }
 
     private:
         array_type data_;
     };
 
 #endif // BOOST_UBLAS_CPP_GE_2011
 
     /** \brief A dense matrix of values of type \c T with a variable size bounded to a maximum of \f$M\f$ by \f$N\f$. 
      *
      * For a \f$(m \times n)\f$-dimensional matrix and \f$ 0 \leq i < m, 0 \leq j < n\f$, every element \f$m_{i,j}\f$ is mapped
      * to the \f$(i.n + j)\f$-th element of the container for row major orientation or the \f$(i + j.m)\f$-th element
      * of the container for column major orientation. Finally in a dense matrix all elements are represented in memory 
      * in a contiguous chunk of memory.
      *
      * Orientation can be specified. Default is \c row_major
      * The default constructor creates the matrix with size \f$M\f$ by \f$N\f$. Elements are constructed by the storage 
      * type \c bounded_array, which need not initialise their value.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam M maximum and default number of rows (if not specified at construction)
      * \tparam N maximum and default number of columns (if not specified at construction)
      * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
      */
     template<class T, std::size_t M, std::size_t N, class L>
     class bounded_matrix:
         public matrix<T, L, bounded_array<T, M * N> > {
 
         typedef matrix<T, L, bounded_array<T, M * N> > matrix_type;
     public:
         typedef typename matrix_type::size_type size_type;
         static const size_type max_size1 = M;
         static const size_type max_size2 = N;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         bounded_matrix ():
             matrix_type (M, N) {}
         BOOST_UBLAS_INLINE
         bounded_matrix (size_type size1, size_type size2):
             matrix_type (size1, size2) {}
         BOOST_UBLAS_INLINE
         bounded_matrix (const bounded_matrix &m):
             matrix_type (m) {}
         template<class A2>              // Allow matrix<T, L, bounded_array<M,N> > construction
         BOOST_UBLAS_INLINE
         bounded_matrix (const matrix<T, L, A2> &m):
             matrix_type (m) {}
         template<class AE>
         BOOST_UBLAS_INLINE
         bounded_matrix (const matrix_expression<AE> &ae):
             matrix_type (ae) {}
         BOOST_UBLAS_INLINE
         ~bounded_matrix () {}
 
         // Assignment
 #ifdef BOOST_UBLAS_MOVE_SEMANTICS
 
         /*! @note "pass by value" the key idea to enable move semantics */
         BOOST_UBLAS_INLINE
         bounded_matrix &operator = (bounded_matrix m) {
             matrix_type::operator = (m);
             return *this;
         }
 #else
         BOOST_UBLAS_INLINE
         bounded_matrix &operator = (const bounded_matrix &m) {
             matrix_type::operator = (m);
             return *this;
         }
 #endif
         template<class L2, class A2>        // Generic matrix assignment
         BOOST_UBLAS_INLINE
         bounded_matrix &operator = (const matrix<T, L2, A2> &m) {
             matrix_type::operator = (m);
             return *this;
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         bounded_matrix &operator = (const matrix_container<C> &m) {
             matrix_type::operator = (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         bounded_matrix &operator = (const matrix_expression<AE> &ae) {
             matrix_type::operator = (ae);
             return *this;
         }
     };
 
 
     /** \brief A dense matrix of values of type \c T stored as a vector of vectors.
     *
     * Rows or columns are not stored into contiguous chunks of memory but data inside rows (or columns) are. 
     * Orientation and storage can also be specified, otherwise a row major and unbounded arrays are used.
     * The data is stored as a vector of vectors, meaning that rows or columns might not be stored into contiguous chunks
     * of memory. Orientation and storage can also be specified, otherwise a row major and unbounded arrays are used. 
     * The storage type defaults to \c unbounded_array<unbounded_array<T>> and orientation is \c row_major. It is \b not 
     * required by the storage to initialize elements of the matrix. For a \f$(m \times n)\f$-dimensional matrix and 
     * \f$ 0 \leq i < m, 0 \leq j < n\f$, every element \f$m_{i,j}\f$ is mapped to the \f$(i.n + j)\f$-th element of the 
     * container for row major orientation or the \f$(i + j.m)\f$-th element of the container for column major orientation.
     *
     * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
     * \tparam L the storage organization. It can be either \c row_major or \c column_major. By default it is \c row_major
     * \tparam A the type of Storage array. By default, it is an \unbounded_array<unbounder_array<T>>
     */
     template<class T, class L, class A>
     class vector_of_vector:
         public matrix_container<vector_of_vector<T, L, A> > {
 
         typedef T *pointer;
         typedef L layout_type;
         typedef vector_of_vector<T, L, A> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename A::size_type size_type;
         typedef typename A::difference_type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef A array_type;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef vector<T, typename A::value_type> vector_temporary_type;
         typedef self_type matrix_temporary_type;
         typedef dense_tag storage_category;
         // This could be better for performance,
         // typedef typename unknown_orientation_tag orientation_category;
         // but others depend on the orientation information...
         typedef typename L::orientation_category orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         vector_of_vector ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0), data_ (1) {}
         BOOST_UBLAS_INLINE
         vector_of_vector (size_type size1, size_type size2):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), data_ (1) {
             resize (size1, size2, true);
         }
         BOOST_UBLAS_INLINE
         vector_of_vector (const vector_of_vector &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector (const matrix_expression<AE> &ae):
             matrix_container<self_type> (),
             size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), data_ (layout_type::size_M (size1_, size2_) + 1) {
             for (size_type k = 0; k < layout_type::size_M (size1_, size2_); ++ k)
                 data ()[k].resize (layout_type::size_m (size1_, size2_));
             matrix_assign<scalar_assign> (*this, ae);
         }
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const { 
             return size2_;
         }
 
         // Storage accessors
         BOOST_UBLAS_INLINE
         const array_type &data () const {
             return data_;
         }
         BOOST_UBLAS_INLINE
         array_type &data () {
             return data_;
         }
 
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool preserve = true) {
             size1_ = size1;
             size2_ = size2;
             if (preserve)
                 data ().resize (layout_type::size_M (size1, size2) + 1, typename array_type::value_type ());
             else
                 data ().resize (layout_type::size_M (size1, size2) + 1);
             for (size_type k = 0; k < layout_type::size_M (size1, size2); ++ k) {
                 if (preserve)
                     data () [k].resize (layout_type::size_m (size1, size2), value_type ());
                 else
                     data () [k].resize (layout_type::size_m (size1, size2));
             }
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             return data () [layout_type::index_M (i, j)] [layout_type::index_m (i, j)];
         }
         BOOST_UBLAS_INLINE
         reference at_element (size_type i, size_type j) {
             return data () [layout_type::index_M (i, j)] [layout_type::index_m (i, j)];
         }
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             return at_element (i, j); 
         }
 
         // Element assignment
         BOOST_UBLAS_INLINE
         reference insert_element (size_type i, size_type j, const_reference t) {
             return (at_element (i, j) = t); 
         }
         BOOST_UBLAS_INLINE
         void erase_element (size_type i, size_type j) {
             at_element (i, j) = value_type/*zero*/(); 
         }
         
         // Zeroing
         BOOST_UBLAS_INLINE
         void clear () {
             for (size_type k = 0; k < layout_type::size_M (size1_, size2_); ++ k)
                 std::fill (data () [k].begin (), data () [k].end (), value_type/*zero*/());
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         vector_of_vector &operator = (const vector_of_vector &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             data () = m.data ();
             return *this;
         }
         BOOST_UBLAS_INLINE
         vector_of_vector &assign_temporary (vector_of_vector &m) { 
             swap (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector &operator = (const matrix_expression<AE> &ae) { 
             self_type temporary (ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         vector_of_vector &operator = (const matrix_container<C> &m) {
             resize (m ().size1 (), m ().size2 (), false);
             assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector &assign (const matrix_expression<AE> &ae) { 
             matrix_assign<scalar_assign> (*this, ae); 
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector& operator += (const matrix_expression<AE> &ae) {
             self_type temporary (*this + ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         vector_of_vector &operator += (const matrix_container<C> &m) {
             plus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector &plus_assign (const matrix_expression<AE> &ae) { 
             matrix_assign<scalar_plus_assign> (*this, ae); 
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector& operator -= (const matrix_expression<AE> &ae) {
             self_type temporary (*this - ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         vector_of_vector &operator -= (const matrix_container<C> &m) {
             minus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         vector_of_vector &minus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_minus_assign> (*this, ae); 
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         vector_of_vector& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         vector_of_vector& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (vector_of_vector &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 data ().swap (m.data ());
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (vector_of_vector &m1, vector_of_vector &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use the vector iterator
         typedef typename A::value_type::const_iterator const_subiterator_type;
         typedef typename A::value_type::iterator subiterator_type;
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, dense_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, dense_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int /*rank*/, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator1 (*this, i, j);
 #else
             return const_iterator1 (*this, i, j, data () [layout_type::index_M (i, j)].begin ()  + layout_type::index_m (i, j));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int /*rank*/, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator1 (*this, i, j);
 #else
             return iterator1 (*this, i, j, data () [layout_type::index_M (i, j)].begin ()  + layout_type::index_m (i, j));
 #endif
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /*rank*/, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator2 (*this, i, j);
 #else
             return const_iterator2 (*this, i, j, data () [layout_type::index_M (i, j)].begin ()  + layout_type::index_m (i, j));
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int /*rank*/, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator2 (*this, i, j);
 #else
             return iterator2 (*this, i, j, data () [layout_type::index_M (i, j)].begin () + layout_type::index_m (i, j));
 #endif
         }
 
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<vector_of_vector>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename vector_of_vector::value_type value_type;
             typedef typename vector_of_vector::difference_type difference_type;
             typedef typename vector_of_vector::const_reference reference;
             typedef const typename vector_of_vector::pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), i_ (), j_ (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, size_type i, size_type j, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), i_ (i), j_ (j), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), i_ (it.i_), j_ (it.j_), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 ++ i_;
                 const self_type &m = (*this) ();
                 if (layout_type::fast_i ())
                     ++ it_;
                 else 
                     it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 -- i_;
                 const self_type &m = (*this) ();
                 if (layout_type::fast_i ())
                     -- it_;
                 else
                     it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 i_ += n;
                 const self_type &m = (*this) ();
                 it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 i_ -= n;
                 const self_type &m = (*this) ();
                 it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return index1 () - it.index1 ();
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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_iterator2 begin () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return i_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return j_;
             }
 
             // 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) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return it_ < it.it_;
             }
 
         private:
             size_type i_;
             size_type j_;
             const_subiterator_type it_;
 
             friend class iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1_, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<vector_of_vector>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator1, value_type> {
         public:
             typedef typename vector_of_vector::value_type value_type;
             typedef typename vector_of_vector::difference_type difference_type;
             typedef typename vector_of_vector::reference reference;
             typedef typename vector_of_vector::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), i_ (), j_ (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, size_type i, size_type j, const subiterator_type &it):
                 container_reference<self_type> (m), i_ (i), j_ (j), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 ++ i_;
                 self_type &m = (*this) ();
                 if (layout_type::fast_i ())
                     ++ it_;
                 else
                     it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 -- i_;
                 self_type &m = (*this) ();
                 if (layout_type::fast_i ())
                     -- it_;
                 else
                     it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 i_ += n;
                 self_type &m = (*this) ();
                 it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 i_ -= n;
                 self_type &m = (*this) ();
                 it_ = m.find1 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return index1 () - it.index1 ();
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator2 begin () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return i_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return j_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index2 () == it.index2 (), bad_index ());
                 return it_ < it.it_;
             }
 
         private:
             size_type i_;
             size_type j_;
             subiterator_type it_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, size1_, 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<vector_of_vector>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename vector_of_vector::value_type value_type;
             typedef typename vector_of_vector::difference_type difference_type;
             typedef typename vector_of_vector::const_reference reference;
             typedef const typename vector_of_vector::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> (), i_ (), j_ (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const self_type &m, size_type i, size_type j, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), i_ (i), j_ (j), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), i_ (it.i_), j_ (it.j_), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 ++ j_;
                 const self_type &m = (*this) ();
                 if (layout_type::fast_j ())
                     ++ it_;
                 else
                     it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 -- j_;
                 const self_type &m = (*this) ();
                 if (layout_type::fast_j ())
                     -- it_;
                 else
                     it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 j_ += n;
                 const self_type &m = (*this) ();
                 it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 j_ -= n;
                 const self_type &m = (*this) ();
                 it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return index2 () - it.index2 ();
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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 {
                 const self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 const self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return i_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return j_;
             }
 
             // 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) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return it_ < it.it_;
             }
 
         private:
             size_type i_;
             size_type j_;
             const_subiterator_type it_;
 
             friend class iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<vector_of_vector>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator2, value_type> {
         public:
             typedef typename vector_of_vector::value_type value_type;
             typedef typename vector_of_vector::difference_type difference_type;
             typedef typename vector_of_vector::reference reference;
             typedef typename vector_of_vector::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), i_ (), j_ (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, size_type i, size_type j, const subiterator_type &it):
                 container_reference<self_type> (m), i_ (i), j_ (j), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 ++ j_;
                 self_type &m = (*this) ();
                 if (layout_type::fast_j ())
                     ++ it_;
                 else
                     it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 -- j_;
                 self_type &m = (*this) ();
                 if (layout_type::fast_j ())
                     -- it_;
                 else
                     it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 j_ += n;
                 self_type &m = (*this) ();
                 it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 j_ -= n;
                 self_type &m = (*this) ();
                 it_ = m.find2 (1, i_, j_).it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return index2 () - it.index2 ();
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator1 begin () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return i_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return j_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (index1 () == it.index1 (), bad_index ());
                 return it_ < it.it_;
             }
 
         private:
             size_type i_;
             size_type j_;
             subiterator_type it_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             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 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
         // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
             }
             ar & serialization::make_nvp("data",data_);
         }
 
     private:
         size_type size1_;
         size_type size2_;
         array_type data_;
     };
 
 
     /** \brief A matrix with all values of type \c T equal to zero
      *
      * Changing values does not affect the matrix, however assigning it to a normal matrix will put zero 
      * everywhere in the target matrix. All accesses are constant time, due to the trivial value.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam ALLOC an allocator for storing the zero element. By default, a standar allocator is used.
      */
     template<class T, class ALLOC>
     class zero_matrix:
         public matrix_container<zero_matrix<T, ALLOC> > {
 
         typedef const T *const_pointer;
         typedef zero_matrix<T, ALLOC> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename boost::allocator_size_type<ALLOC>::type size_type;
         typedef typename boost::allocator_difference_type<ALLOC>::type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef sparse_tag storage_category;
         typedef unknown_orientation_tag orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         zero_matrix ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0) {}
         BOOST_UBLAS_INLINE
         zero_matrix (size_type size):
             matrix_container<self_type> (),
             size1_ (size), size2_ (size) {}
         BOOST_UBLAS_INLINE
         zero_matrix (size_type size1, size_type size2):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2) {}
         BOOST_UBLAS_INLINE
         zero_matrix (const zero_matrix &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_) {}
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
 
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size, bool /*preserve*/ = true) {
             size1_ = size;
             size2_ = size;
         }
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool /*preserve*/ = true) {
             size1_ = size1;
             size2_ = size2;
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type /* i */, size_type /* j */) const {
             return zero_;
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         zero_matrix &operator = (const zero_matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         zero_matrix &assign_temporary (zero_matrix &m) {
             swap (m);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (zero_matrix &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (zero_matrix &m1, zero_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     public:
         class const_iterator1;
         class const_iterator2;
         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 {
             return const_iterator1 (*this);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /*rank*/, size_type /*i*/, size_type /*j*/) const {
             return const_iterator2 (*this);
         }
 
         class const_iterator1:
             public container_const_reference<zero_matrix>,
             public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename zero_matrix::value_type value_type;
             typedef typename zero_matrix::difference_type difference_type;
             typedef typename zero_matrix::const_reference reference;
             typedef typename zero_matrix::const_pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m):
                 container_const_reference<self_type> (m) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return *this;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return zero_;   // arbitary return value
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 begin () const {
                 return const_iterator2 ((*this) ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 return const_iterator2 ((*this) ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return 0;   // arbitary return value
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return 0;   // arbitary return value
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator1 &operator = (const const_iterator1 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 detail::ignore_unused_variable_warning(it);
                 return true;
             }
         };
 
         typedef const_iterator1 iterator1;
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return const_iterator1 (*this);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return const_iterator1 (*this);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
         class const_iterator2:
             public container_const_reference<zero_matrix>,
             public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename zero_matrix::value_type value_type;
             typedef typename zero_matrix::difference_type difference_type;
             typedef typename zero_matrix::const_reference reference;
             typedef typename zero_matrix::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> () {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const self_type &m):
                 container_const_reference<self_type> (m) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return *this;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return zero_;   // arbitary return value
             }
 
 #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 const_iterator1 ((*this) ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 return const_iterator1 ((*this) ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return 0;   // arbitary return value
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 BOOST_UBLAS_CHECK_FALSE (bad_index ());
                 return 0;   // arbitary return value
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator2 &operator = (const const_iterator2 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 detail::ignore_unused_variable_warning(it);
                 return true;
             }
         };
 
         typedef const_iterator2 iterator2;
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
          // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
             }
         }
 
     private:
         size_type size1_;
         size_type size2_;
         static const value_type zero_;
     };
 
     template<class T, class ALLOC>
     const typename zero_matrix<T, ALLOC>::value_type zero_matrix<T, ALLOC>::zero_ = T(/*zero*/);
 
     /** \brief An identity matrix with values of type \c T
      *
      * Elements or cordinates \f$(i,i)\f$ are equal to 1 (one) and all others to 0 (zero). 
      * Changing values does not affect the matrix, however assigning it to a normal matrix will
      * make the matrix equal to an identity matrix. All accesses are constant du to the trivial values.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam ALLOC an allocator for storing the zeros and one elements. By default, a standar allocator is used.
      */ 
     template<class T, class ALLOC>
     class identity_matrix:
         public matrix_container<identity_matrix<T, ALLOC> > {
 
         typedef const T *const_pointer;
         typedef identity_matrix<T, ALLOC> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename boost::allocator_size_type<ALLOC>::type size_type;
         typedef typename boost::allocator_difference_type<ALLOC>::type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef sparse_tag storage_category;
         typedef unknown_orientation_tag orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         identity_matrix ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0), size_common_ (0) {}
         BOOST_UBLAS_INLINE
         identity_matrix (size_type size):
             matrix_container<self_type> (),
             size1_ (size), size2_ (size), size_common_ ((std::min) (size1_, size2_)) {}
         BOOST_UBLAS_INLINE
         identity_matrix (size_type size1, size_type size2):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), size_common_ ((std::min) (size1_, size2_)) {}
         BOOST_UBLAS_INLINE
         identity_matrix (const identity_matrix &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_), size_common_ ((std::min) (size1_, size2_)) {}
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
 
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size, bool /*preserve*/ = true) {
             size1_ = size;
             size2_ = size;
             size_common_ = ((std::min)(size1_, size2_));
         }
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool /*preserve*/ = true) {
             size1_ = size1;
             size2_ = size2;
             size_common_ = ((std::min)(size1_, size2_));
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             if (i == j)
                 return one_;
             else
                 return zero_;
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         identity_matrix &operator = (const identity_matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             size_common_ = m.size_common_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         identity_matrix &assign_temporary (identity_matrix &m) { 
             swap (m);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (identity_matrix &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 std::swap (size_common_, m.size_common_);
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (identity_matrix &m1, identity_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use an index
         typedef size_type const_subiterator_type;
 
     public:
         class const_iterator1;
         class const_iterator2;
         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 {
             if (rank == 1) {
                 i = (std::max) (i, j);
                 i = (std::min) (i, j + 1);
             }
             return const_iterator1 (*this, i);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int rank, size_type i, size_type j) const {
             if (rank == 1) {
                 j = (std::max) (j, i);
                 j = (std::min) (j, i + 1);
             }
             return const_iterator2 (*this, j);
         }
 
 
         class const_iterator1:
             public container_const_reference<identity_matrix>,
             public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename identity_matrix::value_type value_type;
             typedef typename identity_matrix::difference_type difference_type;
             typedef typename identity_matrix::const_reference reference;
             typedef typename identity_matrix::const_pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 BOOST_UBLAS_CHECK (it_ < (*this) ().size1 (), bad_index ());
                 ++it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 BOOST_UBLAS_CHECK (it_ > 0, bad_index ());
                 --it_;
                 return *this;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 return one_;
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 begin () const {
                 return const_iterator2 ((*this) (), it_); 
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 return const_iterator2 ((*this) (), it_ + 1); 
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it_;
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
 
         private:
             const_subiterator_type it_;
         };
 
         typedef const_iterator1 iterator1;
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return const_iterator1 (*this, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return const_iterator1 (*this, size_common_);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
         class const_iterator2:
             public container_const_reference<identity_matrix>,
             public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename identity_matrix::value_type value_type;
             typedef typename identity_matrix::difference_type difference_type;
             typedef typename identity_matrix::const_reference reference;
             typedef typename identity_matrix::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 &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 BOOST_UBLAS_CHECK (it_ < (*this) ().size_common_, bad_index ());
                 ++it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 BOOST_UBLAS_CHECK (it_ > 0, bad_index ());
                 --it_;
                 return *this;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 return one_;
             }
 
 #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 const_iterator1 ((*this) (), it_); 
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 return const_iterator1 ((*this) (), it_ + 1); 
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it_;
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
 
         private:
             const_subiterator_type it_;
         };
 
         typedef const_iterator2 iterator2;
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return const_iterator2 (*this, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return const_iterator2 (*this, size_common_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
          // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
                 size_common_ = ((std::min)(size1_, size2_));
             }
         }
 
     private:
         size_type size1_;
         size_type size2_;
         size_type size_common_;
         static const value_type zero_;
         static const value_type one_;
     };
 
     template<class T, class ALLOC>
     const typename identity_matrix<T, ALLOC>::value_type identity_matrix<T, ALLOC>::zero_ = T(/*zero*/);
     template<class T, class ALLOC>
     const typename identity_matrix<T, ALLOC>::value_type identity_matrix<T, ALLOC>::one_ (1); // ISSUE: need 'one'-traits here
 
 
     /** \brief A matrix with all values of type \c T equal to the same value
      *
      * Changing one value has the effect of changing all the values. Assigning it to a normal matrix will copy
      * the same value everywhere in this matrix. All accesses are constant time, due to the trivial value.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam ALLOC an allocator for storing the unique value. By default, a standar allocator is used.
      */
     template<class T, class ALLOC>
     class scalar_matrix:
         public matrix_container<scalar_matrix<T, ALLOC> > {
 
         typedef const T *const_pointer;
         typedef scalar_matrix<T, ALLOC> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef std::size_t size_type;
         typedef std::ptrdiff_t difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef dense_tag storage_category;
         typedef unknown_orientation_tag orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         scalar_matrix ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0), value_ () {}
         BOOST_UBLAS_INLINE
         scalar_matrix (size_type size1, size_type size2, const value_type &value = value_type(1)):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2), value_ (value) {}
         BOOST_UBLAS_INLINE
         scalar_matrix (const scalar_matrix &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_), value_ (m.value_) {}
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
 
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool /*preserve*/ = true) {
             size1_ = size1;
             size2_ = size2;
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type /*i*/, size_type /*j*/) const {
             return value_; 
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         scalar_matrix &operator = (const scalar_matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             value_ = m.value_;
             return *this;
         }
         BOOST_UBLAS_INLINE
         scalar_matrix &assign_temporary (scalar_matrix &m) { 
             swap (m);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (scalar_matrix &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 std::swap (value_, m.value_);
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (scalar_matrix &m1, scalar_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use an index
         typedef size_type const_subiterator_type;
 
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class const_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 {
             return const_iterator1 (*this, i, j);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /*rank*/, size_type i, size_type j) const {
             return const_iterator2 (*this, i, j);
         }   
 
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<scalar_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename scalar_matrix::value_type value_type;
             typedef typename scalar_matrix::difference_type difference_type;
             typedef typename scalar_matrix::const_reference reference;
             typedef typename scalar_matrix::const_pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<scalar_matrix> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const scalar_matrix &m, const const_subiterator_type &it1, const const_subiterator_type &it2):
                 container_const_reference<scalar_matrix> (m), it1_ (it1), it2_ (it2) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 ++ it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 -- it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 it1_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 it1_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const 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
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return (*this) () (index1 (), index2 ());
             }
             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_iterator2 begin () const {
                 const scalar_matrix &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 const scalar_matrix &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator1 &operator = (const const_iterator1 &it) {
                 container_const_reference<scalar_matrix>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const 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 const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ < it.it1_;
             }
 
         private:
             const_subiterator_type it1_;
             const_subiterator_type it2_;
         };
 
         typedef const_iterator1 iterator1;
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1_, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<scalar_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename scalar_matrix::value_type value_type;
             typedef typename scalar_matrix::difference_type difference_type;
             typedef typename scalar_matrix::const_reference reference;
             typedef typename scalar_matrix::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<scalar_matrix> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const scalar_matrix &m, const const_subiterator_type &it1, const const_subiterator_type &it2):
                 container_const_reference<scalar_matrix> (m), it1_ (it1), it2_ (it2) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 ++ it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 -- it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 it2_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 it2_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const 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
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return (*this) () (index1 (), index2 ());
             }
             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 {
                 const scalar_matrix &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 const scalar_matrix &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator2 &operator = (const const_iterator2 &it) {
                 container_const_reference<scalar_matrix>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const 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 const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ < it.it2_;
             }
 
         private:
             const_subiterator_type it1_;
             const_subiterator_type it2_;
         };
 
         typedef const_iterator2 iterator2;
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
          // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
             }
 
             ar & serialization::make_nvp("value", value_);
         }
 
     private:
         size_type size1_;
         size_type size2_;
         value_type value_;
     };
 
 
     /** \brief An array based matrix class which size is defined at type specification or object instanciation
      *
      * This matrix is directly based on a predefined C-style arry of data, thus providing the fastest
      * implementation possible. The constraint is that dimensions of the matrix must be specified at 
      * the instanciation or the type specification. 
      *
      * For instance, \code typedef c_matrix<double,4,4> my_4by4_matrix \endcode 
      * defines a 4 by 4 double-precision matrix.  You can also instantiate it directly with 
      * \code c_matrix<int,8,5> my_fast_matrix \endcode. This will make a 8 by 5 integer matrix. The 
      * price to pay for this speed is that you cannot resize it to a size larger than the one defined 
      * in the template parameters. In the previous example, a size of 4 by 5 or 3 by 2 is acceptable, 
      * but a new size of 9 by 5 or even 10 by 10 will raise a bad_size() exception.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam N the default maximum number of rows
      * \tparam M the default maximum number of columns
      */
     template<class T, std::size_t N, std::size_t M>
     class c_matrix:
         public matrix_container<c_matrix<T, N, M> > {
 
         typedef c_matrix<T, N, M> self_type;
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef std::size_t size_type;
         typedef std::ptrdiff_t difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef const T *const_pointer;
         typedef T *pointer;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef c_vector<T, N * M> vector_temporary_type;     // vector able to store all elements of c_matrix
         typedef self_type matrix_temporary_type;
         typedef dense_tag storage_category;
         // This could be better for performance,
         // typedef typename unknown_orientation_tag orientation_category;
         // but others depend on the orientation information...
         typedef row_major_tag orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         c_matrix ():
             size1_ (N), size2_ (M) /* , data_ () */ {
         }
         BOOST_UBLAS_INLINE
         c_matrix (size_type size1, size_type size2):
             size1_ (size1), size2_ (size2) /* , data_ () */ {
             if (size1_ > N || size2_ > M)
                 bad_size ().raise ();
         }
         BOOST_UBLAS_INLINE
         c_matrix (const c_matrix &m):
             size1_ (m.size1_), size2_ (m.size2_) /* , data_ () */ {
             if (size1_ > N || size2_ > M)
                 bad_size ().raise ();
             assign(m);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix (const matrix_expression<AE> &ae):
             size1_ (ae ().size1 ()), size2_ (ae ().size2 ()) /* , data_ () */ {
             if (size1_ > N || size2_ > M)
                 bad_size ().raise ();
             matrix_assign<scalar_assign> (*this, ae);
         }
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
         BOOST_UBLAS_INLINE
         const_pointer data () const {
             return reinterpret_cast<const_pointer> (data_);
         }
         BOOST_UBLAS_INLINE
         pointer data () {
             return reinterpret_cast<pointer> (data_);
         }
 
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, bool preserve = true) {
             if (size1 > N || size2 > M)
                 bad_size ().raise ();
             if (preserve) {
                 self_type temporary (size1, size2);
                 // Common elements to preserve
                 const size_type size1_min = (std::min) (size1, size1_);
                 const size_type size2_min = (std::min) (size2, size2_);
                 for (size_type i = 0; i != size1_min; ++i) {    // indexing copy over major
                     for (size_type j = 0; j != size2_min; ++j) {
                         temporary.data_[i][j] = data_[i][j];
                     }
                 }
                 assign_temporary (temporary);
             }
             else {
                 size1_ = size1;
                 size2_ = size2;
             }
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
             return data_ [i] [j];
         }
         BOOST_UBLAS_INLINE
         reference at_element (size_type i, size_type j) {
             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
             return data_ [i] [j];
         }
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             return at_element (i, j);
         }
 
         // Element assignment
         BOOST_UBLAS_INLINE
         reference insert_element (size_type i, size_type j, const_reference t) {
             return (at_element (i, j) = t);
         }
         
         // Zeroing
         BOOST_UBLAS_INLINE
         void clear () {
             for (size_type i = 0; i < size1_; ++ i)
                 std::fill (data_ [i], data_ [i] + size2_, value_type/*zero*/());
         }
 
         // Assignment
 #ifdef BOOST_UBLAS_MOVE_SEMANTICS
 
         /*! @note "pass by value" the key idea to enable move semantics */
         BOOST_UBLAS_INLINE
         c_matrix &operator = (c_matrix m) {
             assign_temporary(m);
             return *this;
         }
 #else
         BOOST_UBLAS_INLINE
         c_matrix &operator = (const c_matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             for (size_type i = 0; i < m.size1_; ++ i)
                 std::copy (m.data_ [i], m.data_ [i] + m.size2_, data_ [i]);
             return *this;
         }
 #endif
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         c_matrix &operator = (const matrix_container<C> &m) {
             resize (m ().size1 (), m ().size2 (), false);
             assign (m);
             return *this;
         }
         BOOST_UBLAS_INLINE
         c_matrix &assign_temporary (c_matrix &m) {
             swap (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix &operator = (const matrix_expression<AE> &ae) { 
             self_type temporary (ae);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix &assign (const matrix_expression<AE> &ae) { 
             matrix_assign<scalar_assign> (*this, ae); 
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix& operator += (const matrix_expression<AE> &ae) {
             self_type temporary (*this + ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         c_matrix &operator += (const matrix_container<C> &m) {
             plus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix &plus_assign (const matrix_expression<AE> &ae) { 
             matrix_assign<scalar_plus_assign> (*this, ae); 
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix& operator -= (const matrix_expression<AE> &ae) {
             self_type temporary (*this - ae);
             return assign_temporary (temporary);
         }
         template<class C>          // Container assignment without temporary
         BOOST_UBLAS_INLINE
         c_matrix &operator -= (const matrix_container<C> &m) {
             minus_assign (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         c_matrix &minus_assign (const matrix_expression<AE> &ae) { 
             matrix_assign<scalar_minus_assign> (*this, ae); 
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         c_matrix& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         c_matrix& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (c_matrix &m) {
             if (this != &m) {
                 BOOST_UBLAS_CHECK (size1_ == m.size1_, bad_size ());
                 BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ());
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 for (size_type i = 0; i < size1_; ++ i)
                     std::swap_ranges (data_ [i], data_ [i] + size2_, m.data_ [i]);
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (c_matrix &m1, c_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use pointers for iterator
         typedef const_pointer const_subiterator_type;
         typedef pointer subiterator_type;
 
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, dense_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, dense_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int /*rank*/, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator1 (*this, i, j);
 #else
             return const_iterator1 (*this, &data_ [i] [j]);
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int /*rank*/, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator1 (*this, i, j);
 #else
             return iterator1 (*this, &data_ [i] [j]);
 #endif
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int /*rank*/, size_type i, size_type j) const {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return const_iterator2 (*this, i, j);
 #else
             return const_iterator2 (*this, &data_ [i] [j]);
 #endif
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int /*rank*/, size_type i, size_type j) {
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
             return iterator2 (*this, i, j);
 #else
             return iterator2 (*this, &data_ [i] [j]);
 #endif
         }
 
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<c_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename c_matrix::difference_type difference_type;
             typedef typename c_matrix::value_type value_type;
             typedef typename c_matrix::const_reference reference;
             typedef typename c_matrix::const_pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), it_ (it.it_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 it_ += M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 it_ -= M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 it_ += n * M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 it_ -= n * M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return (it_ - it.it_) / M;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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_iterator2 begin () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 const self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin1 ().it_) / M;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin1 ().it_) % M;
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1_, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<c_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator1, value_type> {
         public:
 
             typedef typename c_matrix::difference_type difference_type;
             typedef typename c_matrix::value_type value_type;
             typedef typename c_matrix::reference reference;
             typedef typename c_matrix::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 it_ += M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 it_ -= M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 it_ += n * M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 it_ -= n * M;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return (it_ - it.it_) / M;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator2 begin () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 self_type &m = (*this) ();
                 return m.find2 (1, index1 (), m.size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin1 ().it_) / M;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin1 ().it_) % M;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, size1_, 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<c_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename c_matrix::difference_type difference_type;
             typedef typename c_matrix::value_type value_type;
             typedef typename c_matrix::const_reference reference;
             typedef typename c_matrix::const_reference 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 &m, const const_subiterator_type &it):
                 container_const_reference<self_type> (m), it_ (it) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), it_ (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) () == &it (), external_logic ());
                 return it_ - it.it_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *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 {
                 const self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 const self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             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 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin2 ().it_) / M;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin2 ().it_) % M;
             }
 
             // 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) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             const_subiterator_type it_;
 
             friend class iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<c_matrix>,
             public random_access_iterator_base<dense_random_access_iterator_tag,
                                                iterator2, value_type> {
         public:
             typedef typename c_matrix::difference_type difference_type;
             typedef typename c_matrix::value_type value_type;
             typedef typename c_matrix::reference reference;
             typedef typename c_matrix::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), it_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, const subiterator_type &it):
                 container_reference<self_type> (m), it_ (it) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 ++ it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 -- it_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 it_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 it_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ - it.it_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());
                 return *it_;
             }
             BOOST_UBLAS_INLINE
             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
             iterator1 begin () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 self_type &m = (*this) ();
                 return m.find1 (1, m.size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin2 ().it_) / M;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 const self_type &m = (*this) ();
                 return (it_ - m.begin2 ().it_) % M;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it_ = it.it_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ == it.it_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it_ < it.it_;
             }
 
         private:
             subiterator_type it_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             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 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
          // Serialization
         template<class Archive>
         void serialize(Archive & ar, const unsigned int /* file_version */){
         
             // we need to copy to a collection_size_type to get a portable
             // and efficient serialization
             serialization::collection_size_type s1 (size1_);
             serialization::collection_size_type s2 (size2_);
           
             // serialize the sizes
             ar & serialization::make_nvp("size1",s1)
                & serialization::make_nvp("size2",s2);
 
             // copy the values back if loading
             if (Archive::is_loading::value) {
                 size1_ = s1;
                 size2_ = s2;
             }
             // could probably use make_array( &(data[0][0]), N*M ) 
             ar & serialization::make_array(data_, N);
         }
 
     private:
         size_type size1_;
         size_type size2_;
         value_type data_ [N] [M];
     };
 
 }}}
 
 #endif