//

//  Copyright (c) 2000-2007

//  Joerg Walter, Mathias Koch, Gunter Winkler

//

//  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_SPARSE_

#define _BOOST_UBLAS_MATRIX_SPARSE_



#include <boost/numeric/ublas/vector_sparse.hpp>

#include <boost/numeric/ublas/matrix_expression.hpp>

#include <boost/numeric/ublas/detail/matrix_assign.hpp>

#if BOOST_UBLAS_TYPE_CHECK

#include <boost/numeric/ublas/matrix.hpp>

#endif



// Iterators based on ideas of Jeremy Siek



namespace boost { namespace numeric { namespace ublas {



#ifdef BOOST_UBLAS_STRICT_MATRIX_SPARSE



    template<class M>

    class sparse_matrix_element:

       public container_reference<M> {

    public:

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::value_type value_type;

        typedef const value_type &const_reference;

        typedef value_type *pointer;

        typedef const value_type *const_pointer;



    private:

        // Proxied element operations

        void get_d () const {

            const_pointer p = (*this) ().find_element (i_, j_);

            if (p)

                d_ = *p;

            else

                d_ = value_type/*zero*/();

        }



        void set (const value_type &s) const {

            pointer p = (*this) ().find_element (i_, j_);

            if (!p)

                (*this) ().insert_element (i_, j_, s);

            else

                *p = s;

        }

        

    public:

        // Construction and destruction

        BOOST_UBLAS_INLINE

        sparse_matrix_element (matrix_type &m, size_type i, size_type j):

            container_reference<matrix_type> (m), i_ (i), j_ (j) {

        }

        BOOST_UBLAS_INLINE

        sparse_matrix_element (const sparse_matrix_element &p):

            container_reference<matrix_type> (p), i_ (p.i_), j_ (p.j_) {}

        BOOST_UBLAS_INLINE

        ~sparse_matrix_element () {

        }



        // Assignment

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator = (const sparse_matrix_element &p) {

            // Overide the implict copy assignment

            p.get_d ();

            set (p.d_);

            return *this;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator = (const D &d) {

            set (d);

            return *this;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator += (const D &d) {

            get_d ();

            d_ += d;

            set (d_);

            return *this;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator -= (const D &d) {

            get_d ();

            d_ -= d;

            set (d_);

            return *this;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator *= (const D &d) {

            get_d ();

            d_ *= d;

            set (d_);

            return *this;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        sparse_matrix_element &operator /= (const D &d) {

            get_d ();

            d_ /= d;

            set (d_);

            return *this;

        }



        // Comparison

        template<class D>

        BOOST_UBLAS_INLINE

        bool operator == (const D &d) const {

            get_d ();

            return d_ == d;

        }

        template<class D>

        BOOST_UBLAS_INLINE

        bool operator != (const D &d) const {

            get_d ();

            return d_ != d;

        }



        // Conversion - weak link in proxy as d_ is not a perfect alias for the element

        BOOST_UBLAS_INLINE

        operator const_reference () const {

            get_d ();

            return d_;

        }



        // Conversion to reference - may be invalidated

        BOOST_UBLAS_INLINE

        value_type& ref () const {

            const pointer p = (*this) ().find_element (i_, j_);

            if (!p)

                return (*this) ().insert_element (i_, j_, value_type/*zero*/());

            else

                return *p;

        }



    private:

        size_type i_;

        size_type j_;

        mutable value_type d_;

    };



    /*

     * Generalise explicit reference access

     */

    namespace detail {

        template <class V>

        struct element_reference<sparse_matrix_element<V> > {

            typedef typename V::value_type& reference;

            static reference get_reference (const sparse_matrix_element<V>& sve)

            {

                return sve.ref ();

            }

        };

    }





    template<class M>

    struct type_traits<sparse_matrix_element<M> > {

        typedef typename M::value_type element_type;

        typedef type_traits<sparse_matrix_element<M> > self_type;

        typedef typename type_traits<element_type>::value_type value_type;

        typedef typename type_traits<element_type>::const_reference const_reference;

        typedef sparse_matrix_element<M> reference;

        typedef typename type_traits<element_type>::real_type real_type;

        typedef typename type_traits<element_type>::precision_type precision_type;



        static const unsigned plus_complexity = type_traits<element_type>::plus_complexity;

        static const unsigned multiplies_complexity = type_traits<element_type>::multiplies_complexity;



        static

        BOOST_UBLAS_INLINE

        real_type real (const_reference t) {

            return type_traits<element_type>::real (t);

        }

        static

        BOOST_UBLAS_INLINE

        real_type imag (const_reference t) {

            return type_traits<element_type>::imag (t);

        }

        static

        BOOST_UBLAS_INLINE

        value_type conj (const_reference t) {

            return type_traits<element_type>::conj (t);

        }



        static

        BOOST_UBLAS_INLINE

        real_type type_abs (const_reference t) {

            return type_traits<element_type>::type_abs (t);

        }

        static

        BOOST_UBLAS_INLINE

        value_type type_sqrt (const_reference t) {

            return type_traits<element_type>::type_sqrt (t);

        }



        static

        BOOST_UBLAS_INLINE

        real_type norm_1 (const_reference t) {

            return type_traits<element_type>::norm_1 (t);

        }

        static

        BOOST_UBLAS_INLINE

        real_type norm_2 (const_reference t) {

            return type_traits<element_type>::norm_2 (t);

        }

        static

        BOOST_UBLAS_INLINE

        real_type norm_inf (const_reference t) {

            return type_traits<element_type>::norm_inf (t);

        }



        static

        BOOST_UBLAS_INLINE

        bool equals (const_reference t1, const_reference t2) {

            return type_traits<element_type>::equals (t1, t2);

        }

    };



    template<class M1, class T2>

    struct promote_traits<sparse_matrix_element<M1>, T2> {

        typedef typename promote_traits<typename sparse_matrix_element<M1>::value_type, T2>::promote_type promote_type;

    };

    template<class T1, class M2>

    struct promote_traits<T1, sparse_matrix_element<M2> > {

        typedef typename promote_traits<T1, typename sparse_matrix_element<M2>::value_type>::promote_type promote_type;

    };

    template<class M1, class M2>

    struct promote_traits<sparse_matrix_element<M1>, sparse_matrix_element<M2> > {

        typedef typename promote_traits<typename sparse_matrix_element<M1>::value_type,

                                        typename sparse_matrix_element<M2>::value_type>::promote_type promote_type;

    };



#endif





    // Index map based sparse matrix class

    template<class T, class L, class A>

    class mapped_matrix:

        public matrix_container<mapped_matrix<T, L, A> > {



        typedef T &true_reference;

        typedef T *pointer;

        typedef const T * const_pointer;

        typedef L layout_type;

        typedef mapped_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 A array_type;

        typedef const T &const_reference;

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

        typedef typename detail::map_traits<A, T>::reference reference;

#else

        typedef sparse_matrix_element<self_type> reference;

#endif

        typedef const matrix_reference<const self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef mapped_vector<T, A> vector_temporary_type;

        typedef self_type matrix_temporary_type;

        typedef sparse_tag storage_category;

        typedef typename L::orientation_category orientation_category;



        // Construction and destruction

        BOOST_UBLAS_INLINE

        mapped_matrix ():

            matrix_container<self_type> (),

            size1_ (0), size2_ (0), data_ () {}

        BOOST_UBLAS_INLINE

        mapped_matrix (size_type size1, size_type size2, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (size1), size2_ (size2), data_ () {

            detail::map_reserve (data (), restrict_capacity (non_zeros));

        }

        BOOST_UBLAS_INLINE

        mapped_matrix (const mapped_matrix &m):

            matrix_container<self_type> (),

            size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), data_ () {

            detail::map_reserve (data (), restrict_capacity (non_zeros));

            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

        size_type nnz_capacity () const {

            return detail::map_capacity (data ());

        }

        BOOST_UBLAS_INLINE

        size_type nnz () const {

            return data (). size ();

        }



        // Storage accessors

        BOOST_UBLAS_INLINE

        const array_type &data () const {

            return data_;

        }

        BOOST_UBLAS_INLINE

        array_type &data () {

            return data_;

        }



        // Resizing

    private:

        BOOST_UBLAS_INLINE

        size_type restrict_capacity (size_type non_zeros) const {

            // Guarding against overflow - thanks to Alexei Novakov for the hint.

            // non_zeros = (std::min) (non_zeros, size1_ * size2_);

            if (size1_ > 0 && non_zeros / size1_ >= size2_)

                non_zeros = size1_ * size2_;

            return non_zeros;

        }

    public:

        BOOST_UBLAS_INLINE

        void resize (size_type size1, size_type size2, bool preserve = true) {

            // FIXME preserve unimplemented

            BOOST_UBLAS_CHECK (!preserve, internal_logic ());

            size1_ = size1;

            size2_ = size2;

            data ().clear ();

        }



        // Reserving

        BOOST_UBLAS_INLINE

        void reserve (size_type non_zeros, bool preserve = true) {

            detail::map_reserve (data (), restrict_capacity (non_zeros));

        }



        // Element support

        BOOST_UBLAS_INLINE

        pointer find_element (size_type i, size_type j) {

            return const_cast<pointer> (const_cast<const self_type&>(*this).find_element (i, j));

        }

        BOOST_UBLAS_INLINE

        const_pointer find_element (size_type i, size_type j) const {

            const size_type element = layout_type::element (i, size1_, j, size2_);

            const_subiterator_type it (data ().find (element));

            if (it == data ().end ())

                return 0;

            BOOST_UBLAS_CHECK ((*it).first == element, internal_logic ());   // broken map

            return &(*it).second;

        }



        // Element access

        BOOST_UBLAS_INLINE

        const_reference operator () (size_type i, size_type j) const {

            const size_type element = layout_type::element (i, size1_, j, size2_);

            const_subiterator_type it (data ().find (element));

            if (it == data ().end ())

                return zero_;

            BOOST_UBLAS_CHECK ((*it).first == element, internal_logic ());   // broken map

            return (*it).second;

        }

        BOOST_UBLAS_INLINE

        reference operator () (size_type i, size_type j) {

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

            const size_type element = layout_type::element (i, size1_, j, size2_);

            std::pair<subiterator_type, bool> ii (data ().insert (typename array_type::value_type (element, value_type/*zero*/())));

            BOOST_UBLAS_CHECK ((ii.first)->first == element, internal_logic ());   // broken map

            return (ii.first)->second;

#else

            return reference (*this, i, j);

#endif

        }



        // Element assingment

        BOOST_UBLAS_INLINE

        true_reference insert_element (size_type i, size_type j, const_reference t) {

            BOOST_UBLAS_CHECK (!find_element (i, j), bad_index ());        // duplicate element

            const size_type element = layout_type::element (i, size1_, j, size2_);

            std::pair<subiterator_type, bool> ii (data ().insert (typename array_type::value_type (element, t)));

            BOOST_UBLAS_CHECK ((ii.first)->first == element, internal_logic ());   // broken map

            if (!ii.second)     // existing element

                (ii.first)->second = t;

            return (ii.first)->second;

        }

        BOOST_UBLAS_INLINE

        void erase_element (size_type i, size_type j) {

            subiterator_type it = data ().find (layout_type::element (i, size1_, j, size2_));

            if (it == data ().end ())

                return;

            data ().erase (it);

        }

        

        // Zeroing

        BOOST_UBLAS_INLINE

        void clear () {

            data ().clear ();

        }



        // Assignment

        BOOST_UBLAS_INLINE

        mapped_matrix &operator = (const mapped_matrix &m) {

            if (this != &m) {

                size1_ = m.size1_;

                size2_ = m.size2_;

                data () = m.data ();

            }

            return *this;

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        mapped_matrix &operator = (const matrix_container<C> &m) {

            resize (m ().size1 (), m ().size2 (), false);

            assign (m);

            return *this;

        }

        BOOST_UBLAS_INLINE

        mapped_matrix &assign_temporary (mapped_matrix &m) {

            swap (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix &operator = (const matrix_expression<AE> &ae) {

            self_type temporary (ae, detail::map_capacity (data ()));

            return assign_temporary (temporary);

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix &assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix& operator += (const matrix_expression<AE> &ae) {

            self_type temporary (*this + ae, detail::map_capacity (data ()));

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        mapped_matrix &operator += (const matrix_container<C> &m) {

            plus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix &plus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_plus_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix& operator -= (const matrix_expression<AE> &ae) {

            self_type temporary (*this - ae, detail::map_capacity (data ()));

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        mapped_matrix &operator -= (const matrix_container<C> &m) {

            minus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_matrix &minus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_minus_assign> (*this, ae);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        mapped_matrix& operator *= (const AT &at) {

            matrix_assign_scalar<scalar_multiplies_assign> (*this, at);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        mapped_matrix& operator /= (const AT &at) {

            matrix_assign_scalar<scalar_divides_assign> (*this, at);

            return *this;

        }



        // Swapping

        BOOST_UBLAS_INLINE

        void swap (mapped_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 (mapped_matrix &m1, mapped_matrix &m2) {

            m1.swap (m2);

        }



        // Iterator types

    private:

        // Use storage iterator

        typedef typename A::const_iterator const_subiterator_type;

        typedef typename A::iterator subiterator_type;



        BOOST_UBLAS_INLINE

        true_reference at_element (size_type i, size_type j) {

            const size_type element = layout_type::element (i, size1_, j, size2_);

            subiterator_type it (data ().find (element));

            BOOST_UBLAS_CHECK (it != data ().end(), bad_index ());

            BOOST_UBLAS_CHECK ((*it).first == element, internal_logic ());   // broken map

            return it->second;

        }



    public:

        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        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 This function seems to be big. So we do not let the compiler inline it.    

        const_iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) const {

            const_subiterator_type it (data ().lower_bound (layout_type::address (i, size1_, j, size2_)));

            const_subiterator_type it_end (data ().end ());

            size_type index1 = size_type (-1);

            size_type index2 = size_type (-1);

            while (rank == 1 && it != it_end) {

                index1 = layout_type::index_i ((*it).first, size1_, size2_);

                index2 = layout_type::index_j ((*it).first, size1_, size2_);

                if (direction > 0) {

                    if ((index1 >= i && index2 == j) || (i >= size1_))

                        break;

                    ++ i;

                } else /* if (direction < 0) */ {

                    if ((index1 <= i && index2 == j) || (i == 0))

                        break;

                    -- i;

                }

                it = data ().lower_bound (layout_type::address (i, size1_, j, size2_));

            }

            if (rank == 1 && index2 != j) {

                if (direction > 0)

                    i = size1_;

                else /* if (direction < 0) */

                    i = 0;

                rank = 0;

            }

            return const_iterator1 (*this, rank, i, j, it);

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) {

            subiterator_type it (data ().lower_bound (layout_type::address (i, size1_, j, size2_)));

            subiterator_type it_end (data ().end ());

            size_type index1 = size_type (-1);

            size_type index2 = size_type (-1);

            while (rank == 1 && it != it_end) {

                index1 = layout_type::index_i ((*it).first, size1_, size2_);

                index2 = layout_type::index_j ((*it).first, size1_, size2_);

                if (direction > 0) {

                    if ((index1 >= i && index2 == j) || (i >= size1_))

                        break;

                    ++ i;

                } else /* if (direction < 0) */ {

                    if ((index1 <= i && index2 == j) || (i == 0))

                        break;

                    -- i;

                }

                it = data ().lower_bound (layout_type::address (i, size1_, j, size2_));

            }

            if (rank == 1 && index2 != j) {

                if (direction > 0)

                    i = size1_;

                else /* if (direction < 0) */

                    i = 0;

                rank = 0;

            }

            return iterator1 (*this, rank, i, j, it);

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        const_iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) const {

            const_subiterator_type it (data ().lower_bound (layout_type::address (i, size1_, j, size2_)));

            const_subiterator_type it_end (data ().end ());

            size_type index1 = size_type (-1);

            size_type index2 = size_type (-1);

            while (rank == 1 && it != it_end) {

                index1 = layout_type::index_i ((*it).first, size1_, size2_);

                index2 = layout_type::index_j ((*it).first, size1_, size2_);

                if (direction > 0) {

                    if ((index2 >= j && index1 == i) || (j >= size2_))

                        break;

                    ++ j;

                } else /* if (direction < 0) */ {

                    if ((index2 <= j && index1 == i) || (j == 0))

                        break;

                    -- j;

                }

                it = data ().lower_bound (layout_type::address (i, size1_, j, size2_));

            }

            if (rank == 1 && index1 != i) {

                if (direction > 0)

                    j = size2_;

                else /* if (direction < 0) */

                    j = 0;

                rank = 0;

            }

            return const_iterator2 (*this, rank, i, j, it);

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) {

            subiterator_type it (data ().lower_bound (layout_type::address (i, size1_, j, size2_)));

            subiterator_type it_end (data ().end ());

            size_type index1 = size_type (-1);

            size_type index2 = size_type (-1);

            while (rank == 1 && it != it_end) {

                index1 = layout_type::index_i ((*it).first, size1_, size2_);

                index2 = layout_type::index_j ((*it).first, size1_, size2_);

                if (direction > 0) {

                    if ((index2 >= j && index1 == i) || (j >= size2_))

                        break;

                    ++ j;

                } else /* if (direction < 0) */ {

                    if ((index2 <= j && index1 == i) || (j == 0))

                        break;

                    -- j;

                }

                it = data ().lower_bound (layout_type::address (i, size1_, j, size2_));

            }

            if (rank == 1 && index1 != i) {

                if (direction > 0)

                    j = size2_;

                else /* if (direction < 0) */

                    j = 0;

                rank = 0;

            }

            return iterator2 (*this, rank, i, j, it);

        }





        class const_iterator1:

            public container_const_reference<mapped_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator1, value_type> {

        public:

            typedef typename mapped_matrix::value_type value_type;

            typedef typename mapped_matrix::difference_type difference_type;

            typedef typename mapped_matrix::const_reference reference;

            typedef const typename mapped_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> (), rank_ (), i_ (), j_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const self_type &m, int rank, size_type i, size_type j, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const iterator1 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else

                    *this = (*this) ().find1 (rank_, index1 () + 1, j_, 1);

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else

                    *this = (*this) ().find1 (rank_, index1 () - 1, j_, -1);

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_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 rend () const {

                return const_reverse_iterator2 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_i ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_i ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_j ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_j ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator1 &operator = (const const_iterator1 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator1 begin1 () const {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator1 end1 () const {

            return find1 (0, size1_, 0);

        }



        class iterator1:

            public container_reference<mapped_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator1, value_type> {

        public:

            typedef typename mapped_matrix::value_type value_type;

            typedef typename mapped_matrix::difference_type difference_type;

            typedef typename mapped_matrix::true_reference reference;

            typedef typename mapped_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> (), rank_ (), i_ (), j_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator1 (self_type &m, int rank, size_type i, size_type j, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else

                    *this = (*this) ().find1 (rank_, index1 () + 1, j_, 1);

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else

                    *this = (*this) ().find1 (rank_, index1 () - 1, j_, -1);

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_i ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_i ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_j ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_j ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator1 &operator = (const iterator1 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            subiterator_type it_;



            friend class const_iterator1;

        };



        BOOST_UBLAS_INLINE

        iterator1 begin1 () {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        iterator1 end1 () {

            return find1 (0, size1_, 0);

        }



        class const_iterator2:

            public container_const_reference<mapped_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator2, value_type> {

        public:

            typedef typename mapped_matrix::value_type value_type;

            typedef typename mapped_matrix::difference_type difference_type;

            typedef typename mapped_matrix::const_reference reference;

            typedef const typename mapped_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> (), rank_ (), i_ (), j_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const self_type &m, int rank, size_type i, size_type j, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const iterator2 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else

                    *this = (*this) ().find2 (rank_, i_, index2 () + 1, 1);

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else

                    *this = (*this) ().find2 (rank_, i_, index2 () - 1, -1);

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_reverse_iterator1 rbegin () const {

                return const_reverse_iterator1 (end ());

            }

            BOOST_UBLAS_INLINE

#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION

            typename self_type::

#endif

            const_reverse_iterator1 rend () const {

                return const_reverse_iterator1 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_i ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_i ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_j ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_j ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator2 &operator = (const const_iterator2 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator2 begin2 () const {

            return find2 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator2 end2 () const {

            return find2 (0, 0, size2_);

        }



        class iterator2:

            public container_reference<mapped_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator2, value_type> {

        public:

            typedef typename mapped_matrix::value_type value_type;

            typedef typename mapped_matrix::difference_type difference_type;

            typedef typename mapped_matrix::true_reference reference;

            typedef typename mapped_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> (), rank_ (), i_ (), j_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator2 (self_type &m, int rank, size_type i, size_type j, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else

                    *this = (*this) ().find2 (rank_, i_, index2 () + 1, 1);

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else

                    *this = (*this) ().find2 (rank_, i_, index2 () - 1, -1);

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_i ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_i ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    const self_type &m = (*this) ();

                    BOOST_UBLAS_CHECK (layout_type::index_j ((*it_).first, m.size1 (), m.size2 ()) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_j ((*it_).first, m.size1 (), m.size2 ());

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator2 &operator = (const iterator2 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            subiterator_type it_;



            friend class const_iterator2;

        };



        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 rend1 () const {

            return const_reverse_iterator1 (begin1 ());

        }



        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 rend2 () const {

            return const_reverse_iterator2 (begin2 ());

        }



        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 */){

            serialization::collection_size_type s1 (size1_);

            serialization::collection_size_type s2 (size2_);

            ar & serialization::make_nvp("size1",s1);

            ar & serialization::make_nvp("size2",s2);

            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_;

        static const value_type zero_;

    };



    template<class T, class L, class A>

    const typename mapped_matrix<T, L, A>::value_type mapped_matrix<T, L, A>::zero_ = value_type/*zero*/();





    // Vector index map based sparse matrix class

    template<class T, class L, class A>

    class mapped_vector_of_mapped_vector:

        public matrix_container<mapped_vector_of_mapped_vector<T, L, A> > {



        typedef T &true_reference;

        typedef T *pointer;

        typedef const T *const_pointer;

        typedef A array_type;

        typedef const A const_array_type;

        typedef L layout_type;

        typedef mapped_vector_of_mapped_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;

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

        typedef typename detail::map_traits<typename A::data_value_type, T>::reference reference;

#else

        typedef sparse_matrix_element<self_type> reference;

#endif

        typedef const matrix_reference<const self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef mapped_vector<T, typename A::value_type> vector_temporary_type;

        typedef self_type matrix_temporary_type;

        typedef typename A::value_type::second_type vector_data_value_type;

        typedef sparse_tag storage_category;

        typedef typename L::orientation_category orientation_category;



        // Construction and destruction

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector ():

            matrix_container<self_type> (),

            size1_ (0), size2_ (0), data_ () {

            data_ [layout_type::size_M (size1_, size2_)] = vector_data_value_type ();

        }

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector (size_type size1, size_type size2, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (size1), size2_ (size2), data_ () {

            data_ [layout_type::size_M (size1_, size2_)] = vector_data_value_type ();

        }

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector (const mapped_vector_of_mapped_vector &m):

            matrix_container<self_type> (),

            size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector (const matrix_expression<AE> &ae, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), data_ () {

            data_ [layout_type::size_M (size1_, size2_)] = vector_data_value_type ();

            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

        size_type nnz_capacity () const {

            size_type non_zeros = 0;

            for (vector_const_subiterator_type itv = data_ ().begin (); itv != data_ ().end (); ++ itv)

                non_zeros += detail::map_capacity (*itv);

            return non_zeros;

        }

        BOOST_UBLAS_INLINE

        size_type nnz () const {

            size_type filled = 0;

            for (vector_const_subiterator_type itv = data_ ().begin (); itv != data_ ().end (); ++ itv)

                filled += (*itv).size ();

            return filled;

        }



        // 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) {

            // FIXME preserve unimplemented

            BOOST_UBLAS_CHECK (!preserve, internal_logic ());

            size1_ = size1;

            size2_ = size2;

            data ().clear ();

            data () [layout_type::size_M (size1_, size2_)] = vector_data_value_type ();

        }



        // Element support

        BOOST_UBLAS_INLINE

        pointer find_element (size_type i, size_type j) {

            return const_cast<pointer> (const_cast<const self_type&>(*this).find_element (i, j));

        }

        BOOST_UBLAS_INLINE

        const_pointer find_element (size_type i, size_type j) const {

            const size_type element1 = layout_type::index_M (i, j);

            const size_type element2 = layout_type::index_m (i, j);

            vector_const_subiterator_type itv (data ().find (element1));

            if (itv == data ().end ())

                return 0;

            BOOST_UBLAS_CHECK ((*itv).first == element1, internal_logic ());   // broken map

            const_subiterator_type it ((*itv).second.find (element2));

            if (it == (*itv).second.end ())

                return 0;

            BOOST_UBLAS_CHECK ((*it).first == element2, internal_logic ());   // broken map

            return &(*it).second;

        }



        // Element access

        BOOST_UBLAS_INLINE

        const_reference operator () (size_type i, size_type j) const {

            const size_type element1 = layout_type::index_M (i, j);

            const size_type element2 = layout_type::index_m (i, j);

            vector_const_subiterator_type itv (data ().find (element1));

            if (itv == data ().end ())

                return zero_;

            BOOST_UBLAS_CHECK ((*itv).first == element1, internal_logic ());   // broken map

            const_subiterator_type it ((*itv).second.find (element2));

            if (it == (*itv).second.end ())

                return zero_;

            BOOST_UBLAS_CHECK ((*itv).first == element1, internal_logic ());   // broken map

            return (*it).second;

        }

        BOOST_UBLAS_INLINE

        reference operator () (size_type i, size_type j) {

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

            const size_type element1 = layout_type::index_M (i, j);

            const size_type element2 = layout_type::index_m (i, j);

            vector_data_value_type& vd (data () [element1]);

            std::pair<subiterator_type, bool> ii (vd.insert (typename array_type::value_type::second_type::value_type (element2, value_type/*zero*/())));

            BOOST_UBLAS_CHECK ((ii.first)->first == element2, internal_logic ());   // broken map

            return (ii.first)->second;

#else

            return reference (*this, i, j);

#endif

        }



        // Element assignment

        BOOST_UBLAS_INLINE

        true_reference insert_element (size_type i, size_type j, const_reference t) {

            BOOST_UBLAS_CHECK (!find_element (i, j), bad_index ());        // duplicate element

            const size_type element1 = layout_type::index_M (i, j);

            const size_type element2 = layout_type::index_m (i, j);



            vector_data_value_type& vd (data () [element1]);

            std::pair<subiterator_type, bool> ii (vd.insert (typename vector_data_value_type::value_type (element2, t)));

            BOOST_UBLAS_CHECK ((ii.first)->first == element2, internal_logic ());   // broken map

            if (!ii.second)     // existing element

                (ii.first)->second = t;

            return (ii.first)->second;

        }

        BOOST_UBLAS_INLINE

        void erase_element (size_type i, size_type j) {

            vector_subiterator_type itv (data ().find (layout_type::index_M (i, j)));

            if (itv == data ().end ())

                return;

            subiterator_type it ((*itv).second.find (layout_type::index_m (i, j)));

            if (it == (*itv).second.end ())

                return;

            (*itv).second.erase (it);

        }

        

        // Zeroing

        BOOST_UBLAS_INLINE

        void clear () {

            data ().clear ();

            data_ [layout_type::size_M (size1_, size2_)] = vector_data_value_type ();

        }



        // Assignment

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &operator = (const mapped_vector_of_mapped_vector &m) {

            if (this != &m) {

                size1_ = m.size1_;

                size2_ = m.size2_;

                data () = m.data ();

            }

            return *this;

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &operator = (const matrix_container<C> &m) {

            resize (m ().size1 (), m ().size2 ());

            assign (m);

            return *this;

        }

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &assign_temporary (mapped_vector_of_mapped_vector &m) {

            swap (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &operator = (const matrix_expression<AE> &ae) {

            self_type temporary (ae);

            return assign_temporary (temporary);

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_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

        mapped_vector_of_mapped_vector &operator += (const matrix_container<C> &m) {

            plus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &plus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_plus_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_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

        mapped_vector_of_mapped_vector &operator -= (const matrix_container<C> &m) {

            minus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector &minus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_minus_assign> (*this, ae);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector& operator *= (const AT &at) {

            matrix_assign_scalar<scalar_multiplies_assign> (*this, at);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        mapped_vector_of_mapped_vector& operator /= (const AT &at) {

            matrix_assign_scalar<scalar_divides_assign> (*this, at);

            return *this;

        }



        // Swapping

        BOOST_UBLAS_INLINE

        void swap (mapped_vector_of_mapped_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 (mapped_vector_of_mapped_vector &m1, mapped_vector_of_mapped_vector &m2) {

            m1.swap (m2);

        }



        // Iterator types

    private:

        // Use storage iterators

        typedef typename A::const_iterator vector_const_subiterator_type;

        typedef typename A::iterator vector_subiterator_type;

        typedef typename A::value_type::second_type::const_iterator const_subiterator_type;

        typedef typename A::value_type::second_type::iterator subiterator_type;



        BOOST_UBLAS_INLINE

        true_reference at_element (size_type i, size_type j) {

            const size_type element1 = layout_type::index_M (i, j);

            const size_type element2 = layout_type::index_m (i, j);

            vector_subiterator_type itv (data ().find (element1));

            BOOST_UBLAS_CHECK (itv != data ().end(), bad_index ());

            BOOST_UBLAS_CHECK ((*itv).first == element1, internal_logic ());   // broken map

            subiterator_type it ((*itv).second.find (element2));

            BOOST_UBLAS_CHECK (it != (*itv).second.end (), bad_index ());

            BOOST_UBLAS_CHECK ((*it).first == element2, internal_logic ());    // broken map

            

            return it->second;

        }



    public:

        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        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 This function seems to be big. So we do not let the compiler inline it.    

        const_iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) const {

            BOOST_UBLAS_CHECK (data ().begin () != data ().end (), internal_logic ());

            for (;;) {

                vector_const_subiterator_type itv (data ().lower_bound (layout_type::index_M (i, j)));

                vector_const_subiterator_type itv_end (data ().end ());

                if (itv == itv_end)

                    return const_iterator1 (*this, rank, i, j, itv_end, (*(-- itv)).second.end ());



                const_subiterator_type it ((*itv).second.lower_bound (layout_type::index_m (i, j)));

                const_subiterator_type it_end ((*itv).second.end ());

                if (rank == 0) {

                    // advance to the first available major index

                    size_type M = itv->first;

                    size_type m;

                    if (it != it_end) { 

                        m = it->first; 

                    } else {

                        m = layout_type::size_m(size1_, size2_);

                    }

                    size_type first_i = layout_type::index_M(M,m);

                    return const_iterator1 (*this, rank, first_i, j, itv, it);

                }

                if (it != it_end && (*it).first == layout_type::index_m (i, j))

                    return const_iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        i = (*it).first;

                    } else {

                        if (i >= size1_)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == (*itv).second.begin ())

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        -- it;

                        i = (*it).first;

                    } else {

                        if (i == 0)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) {

            BOOST_UBLAS_CHECK (data ().begin () != data ().end (), internal_logic ());

            for (;;) {

                vector_subiterator_type itv (data ().lower_bound (layout_type::index_M (i, j)));

                vector_subiterator_type itv_end (data ().end ());

                if (itv == itv_end)

                    return iterator1 (*this, rank, i, j, itv_end, (*(-- itv)).second.end ());



                subiterator_type it ((*itv).second.lower_bound (layout_type::index_m (i, j)));

                subiterator_type it_end ((*itv).second.end ());

                if (rank == 0) {

                    // advance to the first available major index

                    size_type M = itv->first;

                    size_type m;

                    if (it != it_end) { 

                        m = it->first; 

                    } else {

                        m = layout_type::size_m(size1_, size2_);

                    }

                    size_type first_i = layout_type::index_M(M,m);

                    return iterator1 (*this, rank, first_i, j, itv, it);

                }

                if (it != it_end && (*it).first == layout_type::index_m (i, j))

                    return iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return iterator1 (*this, rank, i, j, itv, it);

                        i = (*it).first;

                    } else {

                        if (i >= size1_)

                            return iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == (*itv).second.begin ())

                            return iterator1 (*this, rank, i, j, itv, it);

                        -- it;

                        i = (*it).first;

                    } else {

                        if (i == 0)

                            return iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        const_iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) const {

            BOOST_UBLAS_CHECK (data ().begin () != data ().end (), internal_logic ());

            for (;;) {

                vector_const_subiterator_type itv (data ().lower_bound (layout_type::index_M (i, j)));

                vector_const_subiterator_type itv_end (data ().end ());

                if (itv == itv_end)

                    return const_iterator2 (*this, rank, i, j, itv_end, (*(-- itv)).second.end ());



                const_subiterator_type it ((*itv).second.lower_bound (layout_type::index_m (i, j)));

                const_subiterator_type it_end ((*itv).second.end ());

                if (rank == 0) {

                    // advance to the first available major index

                    size_type M = itv->first;

                    size_type m;

                    if (it != it_end) { 

                        m = it->first; 

                    } else {

                        m = layout_type::size_m(size1_, size2_);

                    }

                    size_type first_j = layout_type::index_m(M,m);

                    return const_iterator2 (*this, rank, i, first_j, itv, it);

                }

                if (it != it_end && (*it).first == layout_type::index_m (i, j))

                    return const_iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        j = (*it).first;

                    } else {

                        if (j >= size2_)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == (*itv).second.begin ())

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        -- it;

                        j = (*it).first;

                    } else {

                        if (j == 0)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) {

            BOOST_UBLAS_CHECK (data ().begin () != data ().end (), internal_logic ());

            for (;;) {

                vector_subiterator_type itv (data ().lower_bound (layout_type::index_M (i, j)));

                vector_subiterator_type itv_end (data ().end ());

                if (itv == itv_end)

                    return iterator2 (*this, rank, i, j, itv_end, (*(-- itv)).second.end ());



                subiterator_type it ((*itv).second.lower_bound (layout_type::index_m (i, j)));

                subiterator_type it_end ((*itv).second.end ());

                if (rank == 0) {

                    // advance to the first available major index

                    size_type M = itv->first;

                    size_type m;

                    if (it != it_end) { 

                        m = it->first; 

                    } else {

                        m = layout_type::size_m(size1_, size2_);

                    }

                    size_type first_j = layout_type::index_m(M,m);

                    return iterator2 (*this, rank, i, first_j, itv, it);

                }

                if (it != it_end && (*it).first == layout_type::index_m (i, j))

                    return iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return iterator2 (*this, rank, i, j, itv, it);

                        j = (*it).first;

                    } else {

                        if (j >= size2_)

                            return iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == (*itv).second.begin ())

                            return iterator2 (*this, rank, i, j, itv, it);

                        -- it;

                        j = (*it).first;

                    } else {

                        if (j == 0)

                            return iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }



        class const_iterator1:

            public container_const_reference<mapped_vector_of_mapped_vector>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator1, value_type> {

        public:

            typedef typename mapped_vector_of_mapped_vector::value_type value_type;

            typedef typename mapped_vector_of_mapped_vector::difference_type difference_type;

            typedef typename mapped_vector_of_mapped_vector::const_reference reference;

            typedef const typename mapped_vector_of_mapped_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type &itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const iterator1 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    const self_type &m = (*this) ();

                    if (rank_ == 0) {

                        ++ itv_;

                        i_ = itv_->first;

                    } else {

                        i_ = index1 () + 1;

                    }

                    if (rank_ == 1 && ++ itv_ == m.end1 ().itv_)

                        *this = m.find1 (rank_, i_, j_, 1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index2 () != j_)

                            *this = m.find1 (rank_, i_, j_, 1);

                    }

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    const self_type &m = (*this) ();

                    if (rank_ == 0) {

                        -- itv_;

                        i_ = itv_->first;

                    } else {

                        i_ = index1 () - 1;

                    }

                    // FIXME: this expression should never become true!

                    if (rank_ == 1 && -- itv_ == m.end1 ().itv_)

                        *this = m.find1 (rank_, i_, j_, -1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index2 () != j_)

                            *this = m.find1 (rank_, i_, j_, -1);

                    }

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_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 rend () const {

                return const_reverse_iterator2 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*itv_).first, (*it_).first) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*itv_).first, (*it_).first);

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*itv_).first, (*it_).first) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*itv_).first, (*it_).first);

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator1 &operator = (const const_iterator1 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator1 begin1 () const {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator1 end1 () const {

            return find1 (0, size1_, 0);

        }



        class iterator1:

            public container_reference<mapped_vector_of_mapped_vector>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator1, value_type> {

        public:

            typedef typename mapped_vector_of_mapped_vector::value_type value_type;

            typedef typename mapped_vector_of_mapped_vector::difference_type difference_type;

            typedef typename mapped_vector_of_mapped_vector::true_reference reference;

            typedef typename mapped_vector_of_mapped_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator1 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    self_type &m = (*this) ();

                    if (rank_ == 0) {

                        ++ itv_;

                        i_ = itv_->first;

                    } else {

                        i_ = index1 () + 1;

                    }

                    if (rank_ == 1 && ++ itv_ == m.end1 ().itv_)

                        *this = m.find1 (rank_, i_, j_, 1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index2 () != j_)

                            *this = m.find1 (rank_, i_, j_, 1);

                    }

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    self_type &m = (*this) ();

                    if (rank_ == 0) {

                        -- itv_;

                        i_ = itv_->first;

                    } else {

                        i_ = index1 () - 1;

                    }

                    // FIXME: this expression should never become true!

                    if (rank_ == 1 && -- itv_ == m.end1 ().itv_)

                        *this = m.find1 (rank_, i_, j_, -1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index2 () != j_)

                            *this = m.find1 (rank_, i_, j_, -1);

                    }

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*itv_).first, (*it_).first) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*itv_).first, (*it_).first);

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*itv_).first, (*it_).first) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*itv_).first, (*it_).first);

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator1 &operator = (const iterator1 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator1;

        };



        BOOST_UBLAS_INLINE

        iterator1 begin1 () {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        iterator1 end1 () {

            return find1 (0, size1_, 0);

        }



        class const_iterator2:

            public container_const_reference<mapped_vector_of_mapped_vector>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator2, value_type> {

        public:

            typedef typename mapped_vector_of_mapped_vector::value_type value_type;

            typedef typename mapped_vector_of_mapped_vector::difference_type difference_type;

            typedef typename mapped_vector_of_mapped_vector::const_reference reference;

            typedef const typename mapped_vector_of_mapped_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type &itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const iterator2 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    const self_type &m = (*this) ();

                    if (rank_ == 0) {

                        ++ itv_;

                        j_ = itv_->first;

                    } else {

                        j_ = index2 () + 1;

                    }

                    if (rank_ == 1 && ++ itv_ == m.end2 ().itv_)

                        *this = m.find2 (rank_, i_, j_, 1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index1 () != i_)

                            *this = m.find2 (rank_, i_, j_, 1);

                    }

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    const self_type &m = (*this) ();

                    if (rank_ == 0) {

                        -- itv_;

                        j_ = itv_->first;

                    } else {

                        j_ = index2 () - 1;

                    }

                    // FIXME: this expression should never become true!

                    if (rank_ == 1 && -- itv_ == m.end2 ().itv_)

                        *this = m.find2 (rank_, i_, j_, -1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index1 () != i_)

                            *this = m.find2 (rank_, i_, j_, -1);

                    }

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_reverse_iterator1 rbegin () const {

                return const_reverse_iterator1 (end ());

            }

            BOOST_UBLAS_INLINE

#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION

            typename self_type::

#endif

            const_reverse_iterator1 rend () const {

                return const_reverse_iterator1 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*itv_).first, (*it_).first) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*itv_).first, (*it_).first);

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*itv_).first, (*it_).first) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*itv_).first, (*it_).first);

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator2 &operator = (const const_iterator2 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator2 begin2 () const {

            return find2 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator2 end2 () const {

            return find2 (0, 0, size2_);

        }



        class iterator2:

            public container_reference<mapped_vector_of_mapped_vector>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator2, value_type> {

        public:

            typedef typename mapped_vector_of_mapped_vector::value_type value_type;

            typedef typename mapped_vector_of_mapped_vector::difference_type difference_type;

            typedef typename mapped_vector_of_mapped_vector::true_reference reference;

            typedef typename mapped_vector_of_mapped_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator2 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    self_type &m = (*this) ();

                    if (rank_ == 0) {

                        ++ itv_;

                        j_ = itv_->first;

                    } else {

                        j_ = index2 () + 1;

                    }

                    if (rank_ == 1 && ++ itv_ == m.end2 ().itv_)

                        *this = m.find2 (rank_, i_, j_, 1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index1 () != i_)

                            *this = m.find2 (rank_, i_, j_, 1);

                    }

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    self_type &m = (*this) ();

                    if (rank_ == 0) {

                        -- itv_;

                        j_ = itv_->first;

                    } else {

                        j_ = index2 () - 1;

                    }

                    // FIXME: this expression should never become true!

                    if (rank_ == 1 && -- itv_ == m.end2 ().itv_)

                        *this = m.find2 (rank_, i_, j_, -1);

                    else if (rank_ == 1) {

                        it_ = (*itv_).second.begin ();

                        if (it_ == (*itv_).second.end () || index1 () != i_)

                            *this = m.find2 (rank_, i_, j_, -1);

                    }

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*it_).second;

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*itv_).first, (*it_).first) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*itv_).first, (*it_).first);

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*itv_).first, (*it_).first) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*itv_).first, (*it_).first);

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator2 &operator = (const iterator2 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator2;

        };



        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 rend1 () const {

            return const_reverse_iterator1 (begin1 ());

        }



        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 rend2 () const {

            return const_reverse_iterator2 (begin2 ());

        }



        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 */){

            serialization::collection_size_type s1 (size1_);

            serialization::collection_size_type s2 (size2_);

            ar & serialization::make_nvp("size1",s1);

            ar & serialization::make_nvp("size2",s2);

            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_;

        static const value_type zero_;

    };



    template<class T, class L, class A>

    const typename mapped_vector_of_mapped_vector<T, L, A>::value_type mapped_vector_of_mapped_vector<T, L, A>::zero_ = value_type/*zero*/();





    // Comperssed array based sparse matrix class

    // Thanks to Kresimir Fresl for extending this to cover different index bases.

    template<class T, class L, std::size_t IB, class IA, class TA>

    class compressed_matrix:

        public matrix_container<compressed_matrix<T, L, IB, IA, TA> > {



        typedef T &true_reference;

        typedef T *pointer;

        typedef const T *const_pointer;

        typedef L layout_type;

        typedef compressed_matrix<T, L, IB, IA, TA> self_type;

    public:

#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS

        using matrix_container<self_type>::operator ();

#endif

        // ISSUE require type consistency check

        // is_convertable (IA::size_type, TA::size_type)

        typedef typename IA::value_type size_type;

        // size_type for the data arrays.

        typedef typename IA::size_type array_size_type;

        // FIXME difference type for sparse storage iterators should it be in the container?

        typedef typename IA::difference_type difference_type;

        typedef T value_type;

        typedef const T &const_reference;

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

        typedef T &reference;

#else

        typedef sparse_matrix_element<self_type> reference;

#endif

        typedef IA index_array_type;

        typedef TA value_array_type;

        typedef const matrix_reference<const self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef compressed_vector<T, IB, IA, TA> vector_temporary_type;

        typedef self_type matrix_temporary_type;

        typedef sparse_tag storage_category;

        typedef typename L::orientation_category orientation_category;



        // Construction and destruction

        BOOST_UBLAS_INLINE

        compressed_matrix ():

            matrix_container<self_type> (),

            size1_ (0), size2_ (0), capacity_ (restrict_capacity (0)),

            filled1_ (1), filled2_ (0),

            index1_data_ (layout_type::size_M (size1_, size2_) + 1), index2_data_ (capacity_), value_data_ (capacity_) {

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        compressed_matrix (size_type size1, size_type size2, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (size1), size2_ (size2), capacity_ (restrict_capacity (non_zeros)),

            filled1_ (1), filled2_ (0),

            index1_data_ (layout_type::size_M (size1_, size2_) + 1), index2_data_ (capacity_), value_data_ (capacity_) {

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        compressed_matrix (const compressed_matrix &m):

            matrix_container<self_type> (),

            size1_ (m.size1_), size2_ (m.size2_), capacity_ (m.capacity_),

            filled1_ (m.filled1_), filled2_ (m.filled2_),

            index1_data_ (m.index1_data_), index2_data_ (m.index2_data_), value_data_ (m.value_data_) {

            storage_invariants ();

        }

         

        BOOST_UBLAS_INLINE

        compressed_matrix (const coordinate_matrix<T, L, IB, IA, TA> &m):

            matrix_container<self_type> (),

            size1_ (m.size1()), size2_ (m.size2()),

            index1_data_ (layout_type::size_M (size1_, size2_) + 1)

        {

            m.sort();

            reserve(m.nnz(), false);

            filled2_ = m.nnz();

            const_subiterator_type  i_start = m.index1_data().begin();

            const_subiterator_type  i_end   = (i_start + filled2_);

            const_subiterator_type  i = i_start;

            size_type r = 1;

            for (; (r < layout_type::size_M (size1_, size2_)) && (i != i_end); ++r) {

                i = std::lower_bound(i, i_end, r);

                index1_data_[r] = k_based( i - i_start );

            }

            filled1_ = r + 1;

            std::copy( m.index2_data().begin(), m.index2_data().begin() + filled2_, index2_data_.begin());

            std::copy( m.value_data().begin(), m.value_data().begin() + filled2_, value_data_.begin());

            index1_data_ [filled1_ - 1] = k_based(filled2_);

            storage_invariants ();

        }



       template<class AE>

       BOOST_UBLAS_INLINE

       compressed_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), capacity_ (restrict_capacity (non_zeros)),

            filled1_ (1), filled2_ (0),

            index1_data_ (layout_type::size_M (ae ().size1 (), ae ().size2 ()) + 1),

            index2_data_ (capacity_), value_data_ (capacity_) {

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            storage_invariants ();

            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

        size_type nnz_capacity () const {

            return capacity_;

        }

        BOOST_UBLAS_INLINE

        size_type nnz () const {

            return filled2_;

        }

        

        // Storage accessors

        BOOST_UBLAS_INLINE

        static size_type index_base () {

            return IB;

        }

        BOOST_UBLAS_INLINE

        array_size_type filled1 () const {

            return filled1_;

        }

        BOOST_UBLAS_INLINE

        array_size_type filled2 () const {

            return filled2_;

        }

        BOOST_UBLAS_INLINE

        const index_array_type &index1_data () const {

            return index1_data_;

        }

        BOOST_UBLAS_INLINE

        const index_array_type &index2_data () const {

            return index2_data_;

        }

        BOOST_UBLAS_INLINE

        const value_array_type &value_data () const {

            return value_data_;

        }

        BOOST_UBLAS_INLINE

        void set_filled (const array_size_type& filled1, const array_size_type& filled2) {

            filled1_ = filled1;

            filled2_ = filled2;

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        index_array_type &index1_data () {

            return index1_data_;

        }

        BOOST_UBLAS_INLINE

        index_array_type &index2_data () {

            return index2_data_;

        }

        BOOST_UBLAS_INLINE

        value_array_type &value_data () {

            return value_data_;

        }

        BOOST_UBLAS_INLINE

        void complete_index1_data () {

            while (filled1_ <= layout_type::size_M (size1_, size2_)) {

                this->index1_data_ [filled1_] = k_based (filled2_);

                ++ this->filled1_;

            }

        }



        // Resizing

    private:

        BOOST_UBLAS_INLINE

        size_type restrict_capacity (size_type non_zeros) const {

            non_zeros = (std::max) (non_zeros, (std::min) (size1_, size2_));

            // Guarding against overflow - Thanks to Alexei Novakov for the hint.

            // non_zeros = (std::min) (non_zeros, size1_ * size2_);

            if (size1_ > 0 && non_zeros / size1_ >= size2_)

                non_zeros = size1_ * size2_;

            return non_zeros;

        }

    public:

        BOOST_UBLAS_INLINE

        void resize (size_type size1, size_type size2, bool preserve = true) {

            // FIXME preserve unimplemented

            BOOST_UBLAS_CHECK (!preserve, internal_logic ());

            size1_ = size1;

            size2_ = size2;

            capacity_ = restrict_capacity (capacity_);

            filled1_ = 1;

            filled2_ = 0;

            index1_data_.resize (layout_type::size_M (size1_, size2_) + 1);

            index2_data_.resize (capacity_);

            value_data_.resize (capacity_);

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            storage_invariants ();

        }



        // Reserving

        BOOST_UBLAS_INLINE

        void reserve (size_type non_zeros, bool preserve = true) {

            capacity_ = restrict_capacity (non_zeros);

            if (preserve) {

                index2_data_.resize (capacity_, size_type ());

                value_data_.resize (capacity_, value_type ());

                filled2_ = (std::min) (capacity_, filled2_);

            }

            else {

                index2_data_.resize (capacity_);

                value_data_.resize (capacity_);

                filled1_ = 1;

                filled2_ = 0;

                index1_data_ [filled1_ - 1] = k_based (filled2_);

            }

            storage_invariants ();

       }



        // Element support

        BOOST_UBLAS_INLINE

        pointer find_element (size_type i, size_type j) {

            return const_cast<pointer> (const_cast<const self_type&>(*this).find_element (i, j));

        }

        BOOST_UBLAS_INLINE

        const_pointer find_element (size_type i, size_type j) const {

            size_type element1 (layout_type::index_M (i, j));

            size_type element2 (layout_type::index_m (i, j));

            if (filled1_ <= element1 + 1)

                return 0;

            vector_const_subiterator_type itv (index1_data_.begin () + element1);

            const_subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

            const_subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));

            const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (element2), std::less<size_type> ()));

            if (it == it_end || *it != k_based (element2))

                return 0;

            return &value_data_ [it - index2_data_.begin ()];

        }



        // Element access

        BOOST_UBLAS_INLINE

        const_reference operator () (size_type i, size_type j) const {

            const_pointer p = find_element (i, j);

            if (p)

                return *p;

            else

                return zero_;

        }

        BOOST_UBLAS_INLINE

        reference operator () (size_type i, size_type j) {

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

            size_type element1 (layout_type::index_M (i, j));

            size_type element2 (layout_type::index_m (i, j));

            if (filled1_ <= element1 + 1)

                return insert_element (i, j, value_type/*zero*/());

            pointer p = find_element (i, j);

            if (p)

                return *p;

            else

                return insert_element (i, j, value_type/*zero*/());

#else

            return reference (*this, i, j);

#endif

        }



        // Element assignment

        BOOST_UBLAS_INLINE

        true_reference insert_element (size_type i, size_type j, const_reference t) {

            BOOST_UBLAS_CHECK (!find_element (i, j), bad_index ());        // duplicate element

            if (filled2_ >= capacity_)

                reserve (2 * filled2_, true);

            BOOST_UBLAS_CHECK (filled2_ < capacity_, internal_logic ());

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            while (filled1_ <= element1 + 1) {

                index1_data_ [filled1_] = k_based (filled2_);

                ++ filled1_;

            }

            vector_subiterator_type itv (index1_data_.begin () + element1);

            subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

            subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));

            subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (element2), std::less<size_type> ()));

            typename std::iterator_traits<subiterator_type>::difference_type n = it - index2_data_.begin ();

            BOOST_UBLAS_CHECK (it == it_end || *it != k_based (element2), internal_logic ());   // duplicate bound by lower_bound

            ++ filled2_;

            it = index2_data_.begin () + n;

            std::copy_backward (it, index2_data_.begin () + filled2_ - 1, index2_data_.begin () + filled2_);

            *it = k_based (element2);

            typename value_array_type::iterator itt (value_data_.begin () + n);

            std::copy_backward (itt, value_data_.begin () + filled2_ - 1, value_data_.begin () + filled2_);

            *itt = t;

            while (element1 + 1 < filled1_) {

                ++ index1_data_ [element1 + 1];

                ++ element1;

            }

            storage_invariants ();

            return *itt;

        }

        BOOST_UBLAS_INLINE

        void erase_element (size_type i, size_type j) {

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            if (element1 + 1 > filled1_)

                return;

            vector_subiterator_type itv (index1_data_.begin () + element1);

            subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

            subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));

            subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (element2), std::less<size_type> ()));

            if (it != it_end && *it == k_based (element2)) {

                typename std::iterator_traits<subiterator_type>::difference_type n = it - index2_data_.begin ();

                std::copy (it + 1, index2_data_.begin () + filled2_, it);

                typename value_array_type::iterator itt (value_data_.begin () + n);

                std::copy (itt + 1, value_data_.begin () + filled2_, itt);

                -- filled2_;

                while (index1_data_ [filled1_ - 2] > k_based (filled2_)) {

                    index1_data_ [filled1_ - 1] = 0;

                    -- filled1_;

                }

                while (element1 + 1 < filled1_) {

                    -- index1_data_ [element1 + 1];

                    ++ element1;

                }

            }

            storage_invariants ();

        }

        

        // Zeroing

        BOOST_UBLAS_INLINE

        void clear () {

            filled1_ = 1;

            filled2_ = 0;

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            storage_invariants ();

        }



        // Assignment

        BOOST_UBLAS_INLINE

        compressed_matrix &operator = (const compressed_matrix &m) {

            if (this != &m) {

                size1_ = m.size1_;

                size2_ = m.size2_;

                capacity_ = m.capacity_;

                filled1_ = m.filled1_;

                filled2_ = m.filled2_;

                index1_data_ = m.index1_data_;

                index2_data_ = m.index2_data_;

                value_data_ = m.value_data_;

            }

            storage_invariants ();

            return *this;

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        compressed_matrix &operator = (const matrix_container<C> &m) {

            resize (m ().size1 (), m ().size2 (), false);

            assign (m);

            return *this;

        }

        BOOST_UBLAS_INLINE

        compressed_matrix &assign_temporary (compressed_matrix &m) {

            swap (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix &operator = (const matrix_expression<AE> &ae) {

            self_type temporary (ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix &assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix& operator += (const matrix_expression<AE> &ae) {

            self_type temporary (*this + ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        compressed_matrix &operator += (const matrix_container<C> &m) {

            plus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix &plus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_plus_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix& operator -= (const matrix_expression<AE> &ae) {

            self_type temporary (*this - ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        compressed_matrix &operator -= (const matrix_container<C> &m) {

            minus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        compressed_matrix &minus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_minus_assign> (*this, ae);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        compressed_matrix& operator *= (const AT &at) {

            matrix_assign_scalar<scalar_multiplies_assign> (*this, at);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        compressed_matrix& operator /= (const AT &at) {

            matrix_assign_scalar<scalar_divides_assign> (*this, at);

            return *this;

        }



        // Swapping

        BOOST_UBLAS_INLINE

        void swap (compressed_matrix &m) {

            if (this != &m) {

                std::swap (size1_, m.size1_);

                std::swap (size2_, m.size2_);

                std::swap (capacity_, m.capacity_);

                std::swap (filled1_, m.filled1_);

                std::swap (filled2_, m.filled2_);

                index1_data_.swap (m.index1_data_);

                index2_data_.swap (m.index2_data_);

                value_data_.swap (m.value_data_);

            }

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        friend void swap (compressed_matrix &m1, compressed_matrix &m2) {

            m1.swap (m2);

        }



        // Back element insertion and erasure

        BOOST_UBLAS_INLINE

        void push_back (size_type i, size_type j, const_reference t) {

            if (filled2_ >= capacity_)

                reserve (2 * filled2_, true);

            BOOST_UBLAS_CHECK (filled2_ < capacity_, internal_logic ());

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            while (filled1_ < element1 + 2) {

                index1_data_ [filled1_] = k_based (filled2_);

                ++ filled1_;

            }

            // must maintain sort order

            BOOST_UBLAS_CHECK ((filled1_ == element1 + 2 &&

                                (filled2_ == zero_based (index1_data_ [filled1_ - 2]) ||

                                index2_data_ [filled2_ - 1] < k_based (element2))), external_logic ());

            ++ filled2_;

            index1_data_ [filled1_ - 1] = k_based (filled2_);

            index2_data_ [filled2_ - 1] = k_based (element2);

            value_data_ [filled2_ - 1] = t;

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        void pop_back () {

            BOOST_UBLAS_CHECK (filled1_ > 0 && filled2_ > 0, external_logic ());

            -- filled2_;

            while (index1_data_ [filled1_ - 2] > k_based (filled2_)) {

                index1_data_ [filled1_ - 1] = 0;

                -- filled1_;

            }

            -- index1_data_ [filled1_ - 1];

            storage_invariants ();

        }



        // Iterator types

    private:

        // Use index array iterator

        typedef typename IA::const_iterator vector_const_subiterator_type;

        typedef typename IA::iterator vector_subiterator_type;

        typedef typename IA::const_iterator const_subiterator_type;

        typedef typename IA::iterator subiterator_type;



        BOOST_UBLAS_INLINE

        true_reference at_element (size_type i, size_type j) {

            pointer p = find_element (i, j);

            BOOST_UBLAS_CHECK (p, bad_index ());

            return *p;

        }



    public:

        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        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 This function seems to be big. So we do not let the compiler inline it.    

        const_iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) const {

            for (;;) {

                array_size_type address1 (layout_type::index_M (i, j));

                array_size_type address2 (layout_type::index_m (i, j));

                vector_const_subiterator_type itv (index1_data_.begin () + (std::min) (filled1_ - 1, address1));

                if (filled1_ <= address1 + 1)

                    return const_iterator1 (*this, rank, i, j, itv, index2_data_.begin () + filled2_);



                const_subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

                const_subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));



                const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                if (rank == 0)

                    return const_iterator1 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return const_iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*it);

                    } else {

                        if (i >= size1_)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == index2_data_.begin () + zero_based (*itv))

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*(it - 1));

                    } else {

                        if (i == 0)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) {

            for (;;) {

                array_size_type address1 (layout_type::index_M (i, j));

                array_size_type address2 (layout_type::index_m (i, j));

                vector_subiterator_type itv (index1_data_.begin () + (std::min) (filled1_ - 1, address1));

                if (filled1_ <= address1 + 1)

                    return iterator1 (*this, rank, i, j, itv, index2_data_.begin () + filled2_);



                subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

                subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));



                subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                if (rank == 0)

                    return iterator1 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*it);

                    } else {

                        if (i >= size1_)

                            return iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == index2_data_.begin () + zero_based (*itv))

                            return iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*(it - 1));

                    } else {

                        if (i == 0)

                            return iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        const_iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) const {

            for (;;) {

                array_size_type address1 (layout_type::index_M (i, j));

                array_size_type address2 (layout_type::index_m (i, j));

                vector_const_subiterator_type itv (index1_data_.begin () + (std::min) (filled1_ - 1, address1));

                if (filled1_ <= address1 + 1)

                    return const_iterator2 (*this, rank, i, j, itv, index2_data_.begin () + filled2_);



                const_subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

                const_subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));



                const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                if (rank == 0)

                    return const_iterator2 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return const_iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*it);

                    } else {

                        if (j >= size2_)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == index2_data_.begin () + zero_based (*itv))

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*(it - 1));

                    } else {

                        if (j == 0)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) {

            for (;;) {

                array_size_type address1 (layout_type::index_M (i, j));

                array_size_type address2 (layout_type::index_m (i, j));

                vector_subiterator_type itv (index1_data_.begin () + (std::min) (filled1_ - 1, address1));

                if (filled1_ <= address1 + 1)

                    return iterator2 (*this, rank, i, j, itv, index2_data_.begin () + filled2_);



                subiterator_type it_begin (index2_data_.begin () + zero_based (*itv));

                subiterator_type it_end (index2_data_.begin () + zero_based (*(itv + 1)));



                subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                if (rank == 0)

                    return iterator2 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*it);

                    } else {

                        if (j >= size2_)

                            return iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == index2_data_.begin () + zero_based (*itv))

                            return iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*(it - 1));

                    } else {

                        if (j == 0)

                            return iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }





        class const_iterator1:

            public container_const_reference<compressed_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator1, value_type> {

        public:

            typedef typename compressed_matrix::value_type value_type;

            typedef typename compressed_matrix::difference_type difference_type;

            typedef typename compressed_matrix::const_reference reference;

            typedef const typename compressed_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type &itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const iterator1 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    i_ = index1 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    --i_;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_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 rend () const {

                return const_reverse_iterator2 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator1 &operator = (const const_iterator1 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator1 begin1 () const {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator1 end1 () const {

            return find1 (0, size1_, 0);

        }



        class iterator1:

            public container_reference<compressed_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator1, value_type> {

        public:

            typedef typename compressed_matrix::value_type value_type;

            typedef typename compressed_matrix::difference_type difference_type;

            typedef typename compressed_matrix::true_reference reference;

            typedef typename compressed_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator1 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    i_ = index1 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    --i_;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator1 &operator = (const iterator1 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator1;

        };



        BOOST_UBLAS_INLINE

        iterator1 begin1 () {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        iterator1 end1 () {

            return find1 (0, size1_, 0);

        }



        class const_iterator2:

            public container_const_reference<compressed_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator2, value_type> {

        public:

            typedef typename compressed_matrix::value_type value_type;

            typedef typename compressed_matrix::difference_type difference_type;

            typedef typename compressed_matrix::const_reference reference;

            typedef const typename compressed_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const iterator2 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    j_ = index2 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    --j_;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_reverse_iterator1 rbegin () const {

                return const_reverse_iterator1 (end ());

            }

            BOOST_UBLAS_INLINE

#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION

            typename self_type::

#endif

            const_reverse_iterator1 rend () const {

                return const_reverse_iterator1 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator2 &operator = (const const_iterator2 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator2 begin2 () const {

            return find2 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator2 end2 () const {

            return find2 (0, 0, size2_);

        }



        class iterator2:

            public container_reference<compressed_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator2, value_type> {

        public:

            typedef typename compressed_matrix::value_type value_type;

            typedef typename compressed_matrix::difference_type difference_type;

            typedef typename compressed_matrix::true_reference reference;

            typedef typename compressed_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator2 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    j_ = index2 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    --j_;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m (itv_ - (*this) ().index1_data_.begin (), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator2 &operator = (const iterator2 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator2;

        };



        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 rend1 () const {

            return const_reverse_iterator1 (begin1 ());

        }



        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 rend2 () const {

            return const_reverse_iterator2 (begin2 ());

        }



        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 */){

            serialization::collection_size_type s1 (size1_);

            serialization::collection_size_type s2 (size2_);

            ar & serialization::make_nvp("size1",s1);

            ar & serialization::make_nvp("size2",s2);

            if (Archive::is_loading::value) {

                size1_ = s1;

                size2_ = s2;

            }

            ar & serialization::make_nvp("capacity", capacity_);

            ar & serialization::make_nvp("filled1", filled1_);

            ar & serialization::make_nvp("filled2", filled2_);

            ar & serialization::make_nvp("index1_data", index1_data_);

            ar & serialization::make_nvp("index2_data", index2_data_);

            ar & serialization::make_nvp("value_data", value_data_);

            storage_invariants();

        }



    private:

        void storage_invariants () const {

            BOOST_UBLAS_CHECK (layout_type::size_M (size1_, size2_) + 1 == index1_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (capacity_ == index2_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (capacity_ == value_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (filled1_ > 0 && filled1_ <= layout_type::size_M (size1_, size2_) + 1, internal_logic ());

            BOOST_UBLAS_CHECK (filled2_ <= capacity_, internal_logic ());

            BOOST_UBLAS_CHECK (index1_data_ [filled1_ - 1] == k_based (filled2_), internal_logic ());

        }

        

        size_type size1_;

        size_type size2_;

        array_size_type capacity_;

        array_size_type filled1_;

        array_size_type filled2_;

        index_array_type index1_data_;

        index_array_type index2_data_;

        value_array_type value_data_;

        static const value_type zero_;



        BOOST_UBLAS_INLINE

        static size_type zero_based (size_type k_based_index) {

            return k_based_index - IB;

        }

        BOOST_UBLAS_INLINE

        static size_type k_based (size_type zero_based_index) {

            return zero_based_index + IB;

        }



        friend class iterator1;

        friend class iterator2;

        friend class const_iterator1;

        friend class const_iterator2;

    };



    template<class T, class L, std::size_t IB, class IA, class TA>

    const typename compressed_matrix<T, L, IB, IA, TA>::value_type compressed_matrix<T, L, IB, IA, TA>::zero_ = value_type/*zero*/();





    // Coordinate array based sparse matrix class

    // Thanks to Kresimir Fresl for extending this to cover different index bases.

    template<class T, class L, std::size_t IB, class IA, class TA>

    class coordinate_matrix:

        public matrix_container<coordinate_matrix<T, L, IB, IA, TA> > {



        typedef T &true_reference;

        typedef T *pointer;

        typedef const T *const_pointer;

        typedef L layout_type;

        typedef coordinate_matrix<T, L, IB, IA, TA> self_type;

    public:

#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS

        using matrix_container<self_type>::operator ();

#endif

        // ISSUE require type consistency check, is_convertable (IA::size_type, TA::size_type)

        typedef typename IA::value_type size_type;

        // ISSUE difference_type cannot be deduced for sparse indices, we only know the value_type

        typedef std::ptrdiff_t difference_type;

        // size_type for the data arrays.

        typedef typename IA::size_type array_size_type;

        typedef T value_type;

        typedef const T &const_reference;

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

        typedef T &reference;

#else

        typedef sparse_matrix_element<self_type> reference;

#endif

        typedef IA index_array_type;

        typedef TA value_array_type;

        typedef const matrix_reference<const self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef coordinate_vector<T, IB, IA, TA> vector_temporary_type;

        typedef self_type matrix_temporary_type;

        typedef sparse_tag storage_category;

        typedef typename L::orientation_category orientation_category;



        // Construction and destruction

        BOOST_UBLAS_INLINE

        coordinate_matrix ():

            matrix_container<self_type> (),

            size1_ (0), size2_ (0), capacity_ (restrict_capacity (0)),

            filled_ (0), sorted_filled_ (filled_), sorted_ (true),

            index1_data_ (capacity_), index2_data_ (capacity_), value_data_ (capacity_) {

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        coordinate_matrix (size_type size1, size_type size2, array_size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (size1), size2_ (size2), capacity_ (restrict_capacity (non_zeros)),

            filled_ (0), sorted_filled_ (filled_), sorted_ (true),

            index1_data_ (capacity_), index2_data_ (capacity_), value_data_ (capacity_) {

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        coordinate_matrix (const coordinate_matrix &m):

            matrix_container<self_type> (),

            size1_ (m.size1_), size2_ (m.size2_), capacity_ (m.capacity_),

            filled_ (m.filled_), sorted_filled_ (m.sorted_filled_), sorted_ (m.sorted_),

            index1_data_ (m.index1_data_), index2_data_ (m.index2_data_), value_data_ (m.value_data_) {

            storage_invariants ();

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix (const matrix_expression<AE> &ae, array_size_type non_zeros = 0):

            matrix_container<self_type> (),

            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), capacity_ (restrict_capacity (non_zeros)),

            filled_ (0), sorted_filled_ (filled_), sorted_ (true),

            index1_data_ (capacity_), index2_data_ (capacity_), value_data_ (capacity_) {

            storage_invariants ();

            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

        size_type nnz_capacity () const {

            return capacity_;

        }

        BOOST_UBLAS_INLINE

        size_type nnz () const {

            return filled_;

        }



        // Storage accessors

        BOOST_UBLAS_INLINE

        static size_type index_base () {

            return IB;

        }

        BOOST_UBLAS_INLINE

        array_size_type filled () const {

            return filled_;

        }

        BOOST_UBLAS_INLINE

        const index_array_type &index1_data () const {

            return index1_data_;

        }

        BOOST_UBLAS_INLINE

        const index_array_type &index2_data () const {

            return index2_data_;

        }

        BOOST_UBLAS_INLINE

        const value_array_type &value_data () const {

            return value_data_;

        }

        BOOST_UBLAS_INLINE

        void set_filled (const array_size_type &filled) {

            // Make sure that storage_invariants() succeeds

            if (sorted_ && filled < filled_)

                sorted_filled_ = filled;

            else

                sorted_ = (sorted_filled_ == filled);

            filled_ = filled;

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        index_array_type &index1_data () {

            return index1_data_;

        }

        BOOST_UBLAS_INLINE

        index_array_type &index2_data () {

            return index2_data_;

        }

        BOOST_UBLAS_INLINE

        value_array_type &value_data () {

            return value_data_;

        }



        // Resizing

    private:

        BOOST_UBLAS_INLINE

        array_size_type restrict_capacity (array_size_type non_zeros) const {

            // minimum non_zeros

            non_zeros = (std::max) (non_zeros, array_size_type((std::min) (size1_, size2_)));

            // ISSUE no maximum as coordinate may contain inserted duplicates

            return non_zeros;

        }

    public:

        BOOST_UBLAS_INLINE

        void resize (size_type size1, size_type size2, bool preserve = true) {

            // FIXME preserve unimplemented

            BOOST_UBLAS_CHECK (!preserve, internal_logic ());

            size1_ = size1;

            size2_ = size2;

            capacity_ = restrict_capacity (capacity_);

            index1_data_.resize (capacity_);

            index2_data_.resize (capacity_);

            value_data_.resize (capacity_);

            filled_ = 0;

            sorted_filled_ = filled_;

            sorted_ = true;

            storage_invariants ();

        }



        // Reserving

        BOOST_UBLAS_INLINE

        void reserve (array_size_type non_zeros, bool preserve = true) {

            sort ();    // remove duplicate elements

            capacity_ = restrict_capacity (non_zeros);

            if (preserve) {

                index1_data_.resize (capacity_, size_type ());

                index2_data_.resize (capacity_, size_type ());

                value_data_.resize (capacity_, value_type ());

                filled_ = (std::min) (capacity_, filled_);

            }

            else {

                index1_data_.resize (capacity_);

                index2_data_.resize (capacity_);

                value_data_.resize (capacity_);

                filled_ = 0;

            }

            sorted_filled_ = filled_;

            storage_invariants ();

        }



        // Element support

        BOOST_UBLAS_INLINE

        pointer find_element (size_type i, size_type j) {

            return const_cast<pointer> (const_cast<const self_type&>(*this).find_element (i, j));

        }

        BOOST_UBLAS_INLINE

        const_pointer find_element (size_type i, size_type j) const {

            sort ();

            size_type element1 (layout_type::index_M (i, j));

            size_type element2 (layout_type::index_m (i, j));

            vector_const_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (element1), std::less<size_type> ()));

            vector_const_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (element1), std::less<size_type> ()));

            if (itv_begin == itv_end)

                return 0;

            const_subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

            const_subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));

            const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (element2), std::less<size_type> ()));

            if (it == it_end || *it != k_based (element2))

                return 0;

            return &value_data_ [it - index2_data_.begin ()];

        }



        // Element access

        BOOST_UBLAS_INLINE

        const_reference operator () (size_type i, size_type j) const {

            const_pointer p = find_element (i, j);

            if (p)

                return *p;

            else 

                return zero_;

        }

        BOOST_UBLAS_INLINE

        reference operator () (size_type i, size_type j) {

#ifndef BOOST_UBLAS_STRICT_MATRIX_SPARSE

            pointer p = find_element (i, j);

            if (p)

                return *p;

            else

                return insert_element (i, j, value_type/*zero*/());

#else

            return reference (*this, i, j);

#endif

        }



        // Element assignment

        BOOST_UBLAS_INLINE

        void append_element (size_type i, size_type j, const_reference t) {

            if (filled_ >= capacity_)

                reserve (2 * filled_, true);

            BOOST_UBLAS_CHECK (filled_ < capacity_, internal_logic ());

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            index1_data_ [filled_] = k_based (element1);

            index2_data_ [filled_] = k_based (element2);

            value_data_ [filled_] = t;

            ++ filled_;

            sorted_ = false;

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        true_reference insert_element (size_type i, size_type j, const_reference t) {

            BOOST_UBLAS_CHECK (!find_element (i, j), bad_index ());        // duplicate element

            append_element (i, j, t);

            return value_data_ [filled_ - 1];

        }

        BOOST_UBLAS_INLINE

        void erase_element (size_type i, size_type j) {

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            sort ();

            vector_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (element1), std::less<size_type> ()));

            vector_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (element1), std::less<size_type> ()));

            subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

            subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));

            subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (element2), std::less<size_type> ()));

            if (it != it_end && *it == k_based (element2)) {

                typename std::iterator_traits<subiterator_type>::difference_type n = it - index2_data_.begin ();

                vector_subiterator_type itv (index1_data_.begin () + n);

                std::copy (itv + 1, index1_data_.begin () + filled_, itv);

                std::copy (it + 1, index2_data_.begin () + filled_, it);

                typename value_array_type::iterator itt (value_data_.begin () + n);

                std::copy (itt + 1, value_data_.begin () + filled_, itt);

                -- filled_;

                sorted_filled_ = filled_;

            }

            storage_invariants ();

        }

        

        // Zeroing

        BOOST_UBLAS_INLINE

        void clear () {

            filled_ = 0;

            sorted_filled_ = filled_;

            sorted_ = true;

            storage_invariants ();

        }



        // Assignment

        BOOST_UBLAS_INLINE

        coordinate_matrix &operator = (const coordinate_matrix &m) {

            if (this != &m) {

                size1_ = m.size1_;

                size2_ = m.size2_;

                capacity_ = m.capacity_;

                filled_ = m.filled_;

                sorted_filled_ = m.sorted_filled_;

                sorted_ = m.sorted_;

                index1_data_ = m.index1_data_;

                index2_data_ = m.index2_data_;

                value_data_ = m.value_data_;

                BOOST_UBLAS_CHECK (capacity_ == index1_data_.size (), internal_logic ());

                BOOST_UBLAS_CHECK (capacity_ == index2_data_.size (), internal_logic ());

                BOOST_UBLAS_CHECK (capacity_ == value_data_.size (), internal_logic ());

            }

            storage_invariants ();

            return *this;

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        coordinate_matrix &operator = (const matrix_container<C> &m) {

            resize (m ().size1 (), m ().size2 (), false);

            assign (m);

            return *this;

        }

        BOOST_UBLAS_INLINE

        coordinate_matrix &assign_temporary (coordinate_matrix &m) {

            swap (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix &operator = (const matrix_expression<AE> &ae) {

            self_type temporary (ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix &assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix& operator += (const matrix_expression<AE> &ae) {

            self_type temporary (*this + ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        coordinate_matrix &operator += (const matrix_container<C> &m) {

            plus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix &plus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_plus_assign> (*this, ae);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix& operator -= (const matrix_expression<AE> &ae) {

            self_type temporary (*this - ae, capacity_);

            return assign_temporary (temporary);

        }

        template<class C>          // Container assignment without temporary

        BOOST_UBLAS_INLINE

        coordinate_matrix &operator -= (const matrix_container<C> &m) {

            minus_assign (m);

            return *this;

        }

        template<class AE>

        BOOST_UBLAS_INLINE

        coordinate_matrix &minus_assign (const matrix_expression<AE> &ae) {

            matrix_assign<scalar_minus_assign> (*this, ae);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        coordinate_matrix& operator *= (const AT &at) {

            matrix_assign_scalar<scalar_multiplies_assign> (*this, at);

            return *this;

        }

        template<class AT>

        BOOST_UBLAS_INLINE

        coordinate_matrix& operator /= (const AT &at) {

            matrix_assign_scalar<scalar_divides_assign> (*this, at);

            return *this;

        }



        // Swapping

        BOOST_UBLAS_INLINE

        void swap (coordinate_matrix &m) {

            if (this != &m) {

                std::swap (size1_, m.size1_);

                std::swap (size2_, m.size2_);

                std::swap (capacity_, m.capacity_);

                std::swap (filled_, m.filled_);

                std::swap (sorted_filled_, m.sorted_filled_);

                std::swap (sorted_, m.sorted_);

                index1_data_.swap (m.index1_data_);

                index2_data_.swap (m.index2_data_);

                value_data_.swap (m.value_data_);

            }

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        friend void swap (coordinate_matrix &m1, coordinate_matrix &m2) {

            m1.swap (m2);

        }



        // Sorting and summation of duplicates

        BOOST_UBLAS_INLINE

        void sort () const {

            if (! sorted_ && filled_ > 0) {

                typedef index_triple_array<index_array_type, index_array_type, value_array_type> array_triple;

                array_triple ita (filled_, index1_data_, index2_data_, value_data_);

                const typename array_triple::iterator iunsorted = ita.begin () + sorted_filled_;

                // sort new elements and merge

                std::sort (iunsorted, ita.end ());

                std::inplace_merge (ita.begin (), iunsorted, ita.end ());

                

                // sum duplicates with += and remove

                array_size_type filled = 0;

                for (array_size_type i = 1; i < filled_; ++ i) {

                    if (index1_data_ [filled] != index1_data_ [i] ||

                        index2_data_ [filled] != index2_data_ [i]) {

                        ++ filled;

                        if (filled != i) {

                            index1_data_ [filled] = index1_data_ [i];

                            index2_data_ [filled] = index2_data_ [i];

                            value_data_ [filled] = value_data_ [i];

                        }

                    } else {

                        value_data_ [filled] += value_data_ [i];

                    }

                }

                filled_ = filled + 1;

                sorted_filled_ = filled_;

                sorted_ = true;

                storage_invariants ();

            }

        }



        // Back element insertion and erasure

        BOOST_UBLAS_INLINE

        void push_back (size_type i, size_type j, const_reference t) {

            size_type element1 = layout_type::index_M (i, j);

            size_type element2 = layout_type::index_m (i, j);

            // must maintain sort order

            BOOST_UBLAS_CHECK (sorted_ && 

                    (filled_ == 0 ||

                    index1_data_ [filled_ - 1] < k_based (element1) ||

                    (index1_data_ [filled_ - 1] == k_based (element1) && index2_data_ [filled_ - 1] < k_based (element2)))

                    , external_logic ());

            if (filled_ >= capacity_)

                reserve (2 * filled_, true);

            BOOST_UBLAS_CHECK (filled_ < capacity_, internal_logic ());

            index1_data_ [filled_] = k_based (element1);

            index2_data_ [filled_] = k_based (element2);

            value_data_ [filled_] = t;

            ++ filled_;

            sorted_filled_ = filled_;

            storage_invariants ();

        }

        BOOST_UBLAS_INLINE

        void pop_back () {

            // ISSUE invariants could be simpilfied if sorted required as precondition

            BOOST_UBLAS_CHECK (filled_ > 0, external_logic ());

            -- filled_;

            sorted_filled_ = (std::min) (sorted_filled_, filled_);

            sorted_ = sorted_filled_ = filled_;

            storage_invariants ();

        }



        // Iterator types

    private:

        // Use index array iterator

        typedef typename IA::const_iterator vector_const_subiterator_type;

        typedef typename IA::iterator vector_subiterator_type;

        typedef typename IA::const_iterator const_subiterator_type;

        typedef typename IA::iterator subiterator_type;



        BOOST_UBLAS_INLINE

        true_reference at_element (size_type i, size_type j) {

            pointer p = find_element (i, j);

            BOOST_UBLAS_CHECK (p, bad_index ());

            return *p;

        }



    public:

        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        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 This function seems to be big. So we do not let the compiler inline it.    

        const_iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) const {

            sort ();

            for (;;) {

                size_type address1 (layout_type::index_M (i, j));

                size_type address2 (layout_type::index_m (i, j));

                vector_const_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));

                vector_const_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));



                const_subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

                const_subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));



                const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                vector_const_subiterator_type itv (index1_data_.begin () + (it - index2_data_.begin ()));

                if (rank == 0)

                    return const_iterator1 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return const_iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*it);

                    } else {

                        if (i >= size1_)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == index2_data_.begin () + array_size_type (zero_based (*itv)))

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*(it - 1));

                    } else {

                        if (i == 0)

                            return const_iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator1 find1 (int rank, size_type i, size_type j, int direction = 1) {

            sort ();

            for (;;) {

                size_type address1 (layout_type::index_M (i, j));

                size_type address2 (layout_type::index_m (i, j));

                vector_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));

                vector_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));



                subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

                subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));



                subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                vector_subiterator_type itv (index1_data_.begin () + (it - index2_data_.begin ()));

                if (rank == 0)

                    return iterator1 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return iterator1 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_i ()) {

                        if (it == it_end)

                            return iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*it);

                    } else {

                        if (i >= size1_)

                            return iterator1 (*this, rank, i, j, itv, it);

                        ++ i;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_i ()) {

                        if (it == index2_data_.begin () + array_size_type (zero_based (*itv)))

                            return iterator1 (*this, rank, i, j, itv, it);

                        i = zero_based (*(it - 1));

                    } else {

                        if (i == 0)

                            return iterator1 (*this, rank, i, j, itv, it);

                        -- i;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        const_iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) const {

            sort ();

            for (;;) {

                size_type address1 (layout_type::index_M (i, j));

                size_type address2 (layout_type::index_m (i, j));

                vector_const_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));

                vector_const_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));



                const_subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

                const_subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));



                const_subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                vector_const_subiterator_type itv (index1_data_.begin () + (it - index2_data_.begin ()));

                if (rank == 0)

                    return const_iterator2 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return const_iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*it);

                    } else {

                        if (j >= size2_)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == index2_data_.begin () + array_size_type (zero_based (*itv)))

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*(it - 1));

                    } else {

                        if (j == 0)

                            return const_iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }

        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    

        iterator2 find2 (int rank, size_type i, size_type j, int direction = 1) {

            sort ();

            for (;;) {

                size_type address1 (layout_type::index_M (i, j));

                size_type address2 (layout_type::index_m (i, j));

                vector_subiterator_type itv_begin (detail::lower_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));

                vector_subiterator_type itv_end (detail::upper_bound (index1_data_.begin (), index1_data_.begin () + filled_, k_based (address1), std::less<size_type> ()));



                subiterator_type it_begin (index2_data_.begin () + (itv_begin - index1_data_.begin ()));

                subiterator_type it_end (index2_data_.begin () + (itv_end - index1_data_.begin ()));



                subiterator_type it (detail::lower_bound (it_begin, it_end, k_based (address2), std::less<size_type> ()));

                vector_subiterator_type itv (index1_data_.begin () + (it - index2_data_.begin ()));

                if (rank == 0)

                    return iterator2 (*this, rank, i, j, itv, it);

                if (it != it_end && zero_based (*it) == address2)

                    return iterator2 (*this, rank, i, j, itv, it);

                if (direction > 0) {

                    if (layout_type::fast_j ()) {

                        if (it == it_end)

                            return iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*it);

                    } else {

                        if (j >= size2_)

                            return iterator2 (*this, rank, i, j, itv, it);

                        ++ j;

                    }

                } else /* if (direction < 0)  */ {

                    if (layout_type::fast_j ()) {

                        if (it == index2_data_.begin () + array_size_type (zero_based (*itv)))

                            return iterator2 (*this, rank, i, j, itv, it);

                        j = zero_based (*(it - 1));

                    } else {

                        if (j == 0)

                            return iterator2 (*this, rank, i, j, itv, it);

                        -- j;

                    }

                }

            }

        }





        class const_iterator1:

            public container_const_reference<coordinate_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator1, value_type> {

        public:

            typedef typename coordinate_matrix::value_type value_type;

            typedef typename coordinate_matrix::difference_type difference_type;

            typedef typename coordinate_matrix::const_reference reference;

            typedef const typename coordinate_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type &itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator1 (const iterator1 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    i_ = index1 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    i_ = index1 () - 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_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 rend () const {

                return const_reverse_iterator2 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator1 &operator = (const const_iterator1 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator1 begin1 () const {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator1 end1 () const {

            return find1 (0, size1_, 0);

        }



        class iterator1:

            public container_reference<coordinate_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator1, value_type> {

        public:

            typedef typename coordinate_matrix::value_type value_type;

            typedef typename coordinate_matrix::difference_type difference_type;

            typedef typename coordinate_matrix::true_reference reference;

            typedef typename coordinate_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator1 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator1 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_i ())

                    ++ it_;

                else {

                    i_ = index1 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator1 &operator -- () {

                if (rank_ == 1 && layout_type::fast_i ())

                    -- it_;

                else {

                    i_ = index1 () - 1;

                    if (rank_ == 1)

                        *this = (*this) ().find1 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                BOOST_UBLAS_CHECK (*this != (*this) ().find1 (0, (*this) ().size1 (), j_), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator1 &operator = (const iterator1 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator1;

        };



        BOOST_UBLAS_INLINE

        iterator1 begin1 () {

            return find1 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        iterator1 end1 () {

            return find1 (0, size1_, 0);

        }



        class const_iterator2:

            public container_const_reference<coordinate_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               const_iterator2, value_type> {

        public:

            typedef typename coordinate_matrix::value_type value_type;

            typedef typename coordinate_matrix::difference_type difference_type;

            typedef typename coordinate_matrix::const_reference reference;

            typedef const typename coordinate_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const self_type &m, int rank, size_type i, size_type j, const vector_const_subiterator_type itv, const const_subiterator_type &it):

                container_const_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}

            BOOST_UBLAS_INLINE

            const_iterator2 (const iterator2 &it):

                container_const_reference<self_type> (it ()), rank_ (it.rank_), i_ (it.i_), j_ (it.j_), itv_ (it.itv_), it_ (it.it_) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            const_iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    j_ = index2 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            const_iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    j_ = index2 () - 1;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            const_reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) () (i_, j_);

                }

            }



#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 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_reverse_iterator1 rbegin () const {

                return const_reverse_iterator1 (end ());

            }

            BOOST_UBLAS_INLINE

#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION

            typename self_type::

#endif

            const_reverse_iterator1 rend () const {

                return const_reverse_iterator1 (begin ());

            }

#endif



            // Indices

            BOOST_UBLAS_INLINE

            size_type index1 () const {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            const_iterator2 &operator = (const const_iterator2 &it) {

                container_const_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_const_subiterator_type itv_;

            const_subiterator_type it_;

        };



        BOOST_UBLAS_INLINE

        const_iterator2 begin2 () const {

            return find2 (0, 0, 0);

        }

        BOOST_UBLAS_INLINE

        const_iterator2 end2 () const {

            return find2 (0, 0, size2_);

        }



        class iterator2:

            public container_reference<coordinate_matrix>,

            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,

                                               iterator2, value_type> {

        public:

            typedef typename coordinate_matrix::value_type value_type;

            typedef typename coordinate_matrix::difference_type difference_type;

            typedef typename coordinate_matrix::true_reference reference;

            typedef typename coordinate_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> (), rank_ (), i_ (), j_ (), itv_ (), it_ () {}

            BOOST_UBLAS_INLINE

            iterator2 (self_type &m, int rank, size_type i, size_type j, const vector_subiterator_type &itv, const subiterator_type &it):

                container_reference<self_type> (m), rank_ (rank), i_ (i), j_ (j), itv_ (itv), it_ (it) {}



            // Arithmetic

            BOOST_UBLAS_INLINE

            iterator2 &operator ++ () {

                if (rank_ == 1 && layout_type::fast_j ())

                    ++ it_;

                else {

                    j_ = index2 () + 1;

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, 1);

                }

                return *this;

            }

            BOOST_UBLAS_INLINE

            iterator2 &operator -- () {

                if (rank_ == 1 && layout_type::fast_j ())

                    -- it_;

                else {

                    j_ = index2 ();

                    if (rank_ == 1)

                        *this = (*this) ().find2 (rank_, i_, j_, -1);

                }

                return *this;

            }



            // Dereference

            BOOST_UBLAS_INLINE

            reference operator * () const {

                BOOST_UBLAS_CHECK (index1 () < (*this) ().size1 (), bad_index ());

                BOOST_UBLAS_CHECK (index2 () < (*this) ().size2 (), bad_index ());

                if (rank_ == 1) {

                    return (*this) ().value_data_ [it_ - (*this) ().index2_data_.begin ()];

                } else {

                    return (*this) ().at_element (i_, j_);

                }

            }



#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 {

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size1 (), bad_index ());

                    return layout_type::index_M ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return i_;

                }

            }

            BOOST_UBLAS_INLINE

            size_type index2 () const {

                BOOST_UBLAS_CHECK (*this != (*this) ().find2 (0, i_, (*this) ().size2 ()), bad_index ());

                if (rank_ == 1) {

                    BOOST_UBLAS_CHECK (layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_)) < (*this) ().size2 (), bad_index ());

                    return layout_type::index_m ((*this) ().zero_based (*itv_), (*this) ().zero_based (*it_));

                } else {

                    return j_;

                }

            }



            // Assignment

            BOOST_UBLAS_INLINE

            iterator2 &operator = (const iterator2 &it) {

                container_reference<self_type>::assign (&it ());

                rank_ = it.rank_;

                i_ = it.i_;

                j_ = it.j_;

                itv_ = it.itv_;

                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 (rank_ == it.rank_, internal_logic ());

                if (rank_ == 1 || it.rank_ == 1) {

                    return it_ == it.it_;

                } else {

                    return i_ == it.i_ && j_ == it.j_;

                }

            }



        private:

            int rank_;

            size_type i_;

            size_type j_;

            vector_subiterator_type itv_;

            subiterator_type it_;



            friend class const_iterator2;

        };



        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 rend1 () const {

            return const_reverse_iterator1 (begin1 ());

        }



        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 rend2 () const {

            return const_reverse_iterator2 (begin2 ());

        }



        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 */){

            serialization::collection_size_type s1 (size1_);

            serialization::collection_size_type s2 (size2_);

            ar & serialization::make_nvp("size1",s1);

            ar & serialization::make_nvp("size2",s2);

            if (Archive::is_loading::value) {

                size1_ = s1;

                size2_ = s2;

            }

            ar & serialization::make_nvp("capacity", capacity_);

            ar & serialization::make_nvp("filled", filled_);

            ar & serialization::make_nvp("sorted_filled", sorted_filled_);

            ar & serialization::make_nvp("sorted", sorted_);

            ar & serialization::make_nvp("index1_data", index1_data_);

            ar & serialization::make_nvp("index2_data", index2_data_);

            ar & serialization::make_nvp("value_data", value_data_);

            storage_invariants();

        }



    private:

        void storage_invariants () const

        {

            BOOST_UBLAS_CHECK (capacity_ == index1_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (capacity_ == index2_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (capacity_ == value_data_.size (), internal_logic ());

            BOOST_UBLAS_CHECK (filled_ <= capacity_, internal_logic ());

            BOOST_UBLAS_CHECK (sorted_filled_ <= filled_, internal_logic ());

            BOOST_UBLAS_CHECK (sorted_ == (sorted_filled_ == filled_), internal_logic ());

        }



        size_type size1_;

        size_type size2_;

        array_size_type capacity_;

        mutable array_size_type filled_;

        mutable array_size_type sorted_filled_;

        mutable bool sorted_;

        mutable index_array_type index1_data_;

        mutable index_array_type index2_data_;

        mutable value_array_type value_data_;

        static const value_type zero_;



        BOOST_UBLAS_INLINE

        static size_type zero_based (size_type k_based_index) {

            return k_based_index - IB;

        }

        BOOST_UBLAS_INLINE

        static size_type k_based (size_type zero_based_index) {

            return zero_based_index + IB;

        }



        friend class iterator1;

        friend class iterator2;

        friend class const_iterator1;

        friend class const_iterator2;

    };



    template<class T, class L, std::size_t IB, class IA, class TA>

    const typename coordinate_matrix<T, L, IB, IA, TA>::value_type coordinate_matrix<T, L, IB, IA, TA>::zero_ = value_type/*zero*/();



}}}



#endif

