vector_sparse.hpp

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        typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
        typedef reverse_iterator_base<iterator> reverse_iterator;

        BOOST_UBLAS_INLINE
        const_reverse_iterator rbegin () const {
            return const_reverse_iterator (end ());
        }
        BOOST_UBLAS_INLINE
        const_reverse_iterator rend () const {
            return const_reverse_iterator (begin ());
        }
        BOOST_UBLAS_INLINE
        reverse_iterator rbegin () {
            return reverse_iterator (end ());
        }
        BOOST_UBLAS_INLINE
        reverse_iterator rend () {
            return reverse_iterator (begin ());
        }

         // Serialization
        template<class Archive>
        void serialize(Archive & ar, const unsigned int /* file_version */){
            serialization::collection_size_type s (size_);
            ar & serialization::make_nvp("size",s);
            if (Archive::is_loading::value) {
                size_ = s;
            }
            ar & serialization::make_nvp("data", data_);
        }

    private:
        size_type size_;
        array_type data_;
        static const value_type zero_;
    };

    template<class T, class A>
    const typename mapped_vector<T, A>::value_type mapped_vector<T, A>::zero_ = value_type/*zero*/();


    // Compressed array based sparse vector class
    // Thanks to Kresimir Fresl for extending this to cover different index bases.
    template<class T, std::size_t IB, class IA, class TA>
    class compressed_vector:
        public vector_container<compressed_vector<T, IB, IA, TA> > {

        typedef T &true_reference;
        typedef T *pointer;
        typedef const T *const_pointer;
        typedef compressed_vector<T, IB, IA, TA> self_type;
    public:
#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
        using vector_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;
        typedef typename IA::difference_type difference_type;
        typedef T value_type;
        typedef const T &const_reference;
#ifndef BOOST_UBLAS_STRICT_VECTOR_SPARSE
        typedef T &reference;
#else
        typedef sparse_vector_element<self_type> reference;
#endif
        typedef IA index_array_type;
        typedef TA value_array_type;
        typedef const vector_reference<const self_type> const_closure_type;
        typedef vector_reference<self_type> closure_type;
        typedef self_type vector_temporary_type;
        typedef sparse_tag storage_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        compressed_vector ():
            vector_container<self_type> (),
            size_ (0), capacity_ (restrict_capacity (0)), filled_ (0),
            index_data_ (capacity_), value_data_ (capacity_) {
            storage_invariants ();
        }
        explicit BOOST_UBLAS_INLINE
        compressed_vector (size_type size, size_type non_zeros = 0):
            vector_container<self_type> (),
            size_ (size), capacity_ (restrict_capacity (non_zeros)), filled_ (0),
            index_data_ (capacity_), value_data_ (capacity_) {
        storage_invariants ();
        }
        BOOST_UBLAS_INLINE
        compressed_vector (const compressed_vector &v):
            vector_container<self_type> (),
            size_ (v.size_), capacity_ (v.capacity_), filled_ (v.filled_),
            index_data_ (v.index_data_), value_data_ (v.value_data_) {
            storage_invariants ();
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector (const vector_expression<AE> &ae, size_type non_zeros = 0):
            vector_container<self_type> (),
            size_ (ae ().size ()), capacity_ (restrict_capacity (non_zeros)), filled_ (0),
            index_data_ (capacity_), value_data_ (capacity_) {
            storage_invariants ();
            vector_assign<scalar_assign> (*this, ae);
        }

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size () const {
            return size_;
        }
        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
        typename index_array_type::size_type filled () const {
            return filled_;
        }
        BOOST_UBLAS_INLINE
        const index_array_type &index_data () const {
            return index_data_;
        }
        BOOST_UBLAS_INLINE
        const value_array_type &value_data () const {
            return value_data_;
        }
        BOOST_UBLAS_INLINE
        void set_filled (const typename index_array_type::size_type & filled) {
            filled_ = filled;
            storage_invariants ();
        }
        BOOST_UBLAS_INLINE
        index_array_type &index_data () {
            return index_data_;
        }
        BOOST_UBLAS_INLINE
        value_array_type &value_data () {
            return value_data_;
        }

        // Resizing
    private:
        BOOST_UBLAS_INLINE
        size_type restrict_capacity (size_type non_zeros) const {
            non_zeros = (std::max) (non_zeros, size_type (1));
            non_zeros = (std::min) (non_zeros, size_);
            return non_zeros;
        }
    public:
        BOOST_UBLAS_INLINE
        void resize (size_type size, bool preserve = true) {
            size_ = size;
            capacity_ = restrict_capacity (capacity_);
            if (preserve) {
                index_data_. resize (capacity_, size_type ());
                value_data_. resize (capacity_, value_type ());
                filled_ = (std::min) (capacity_, filled_);
                while ((filled_ > 0) && (zero_based(index_data_[filled_ - 1]) >= size)) {
                    --filled_;
                }
            }
            else {
                index_data_. resize (capacity_);
                value_data_. resize (capacity_);
                filled_ = 0;
            }
            storage_invariants ();
        }

        // Reserving
        BOOST_UBLAS_INLINE
        void reserve (size_type non_zeros, bool preserve = true) {
            capacity_ = restrict_capacity (non_zeros);
            if (preserve) {
                index_data_. resize (capacity_, size_type ());
                value_data_. resize (capacity_, value_type ());
                filled_ = (std::min) (capacity_, filled_);
            }
            else {
                index_data_. resize (capacity_);
                value_data_. resize (capacity_);
                filled_ = 0;
            }
            storage_invariants ();
        }

        // Element support
        BOOST_UBLAS_INLINE
        pointer find_element (size_type i) {
            return const_cast<pointer> (const_cast<const self_type&>(*this).find_element (i));
        }
        BOOST_UBLAS_INLINE
        const_pointer find_element (size_type i) const {
            const_subiterator_type it (detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
            if (it == index_data_.begin () + filled_ || *it != k_based (i))
                return 0;
            return &value_data_ [it - index_data_.begin ()];
        }

        // Element access
        BOOST_UBLAS_INLINE
        const_reference operator () (size_type i) const {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            const_subiterator_type it (detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
            if (it == index_data_.begin () + filled_ || *it != k_based (i))
                return zero_;
            return value_data_ [it - index_data_.begin ()];
        }
        BOOST_UBLAS_INLINE
        true_reference ref (size_type i) {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            subiterator_type it (detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
            if (it == index_data_.begin () + filled_ || *it != k_based (i))
                return insert_element (i, value_type/*zero*/());
            else
                return value_data_ [it - index_data_.begin ()];
        }
        BOOST_UBLAS_INLINE
        reference operator () (size_type i) {
#ifndef BOOST_UBLAS_STRICT_VECTOR_SPARSE
            return ref (i) ;
#else
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            return reference (*this, i);
#endif
        }

        BOOST_UBLAS_INLINE
        const_reference operator [] (size_type i) const {
            return (*this) (i);
        }
        BOOST_UBLAS_INLINE
        reference operator [] (size_type i) {
            return (*this) (i);
        }

        // Element assignment
        BOOST_UBLAS_INLINE
        true_reference insert_element (size_type i, const_reference t) {
            BOOST_UBLAS_CHECK (!find_element (i), bad_index ());        // duplicate element
            if (filled_ >= capacity_)
                reserve (2 * capacity_, true);
            subiterator_type it (detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
            // ISSUE max_capacity limit due to difference_type
            typename std::iterator_traits<subiterator_type>::difference_type n = it - index_data_.begin ();
            BOOST_UBLAS_CHECK (filled_ == 0 || filled_ == typename index_array_type::size_type (n) || *it != k_based (i), internal_logic ());   // duplicate found by lower_bound
            ++ filled_;
            it = index_data_.begin () + n;
            std::copy_backward (it, index_data_.begin () + filled_ - 1, index_data_.begin () + filled_);
            *it = k_based (i);
            typename value_array_type::iterator itt (value_data_.begin () + n);
            std::copy_backward (itt, value_data_.begin () + filled_ - 1, value_data_.begin () + filled_);
            *itt = t;
            storage_invariants ();
            return *itt;
        }
        BOOST_UBLAS_INLINE
        void erase_element (size_type i) {
            subiterator_type it (detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
            typename std::iterator_traits<subiterator_type>::difference_type  n = it - index_data_.begin ();
            if (filled_ > typename index_array_type::size_type (n) && *it == k_based (i)) {
                std::copy (it + 1, index_data_.begin () + filled_, it);
                typename value_array_type::iterator itt (value_data_.begin () + n);
                std::copy (itt + 1, value_data_.begin () + filled_, itt);
                -- filled_;
            }
            storage_invariants ();
        }
        
        // Zeroing
        BOOST_UBLAS_INLINE
        void clear () {
            filled_ = 0;
            storage_invariants ();
        }

        // Assignment
        BOOST_UBLAS_INLINE
        compressed_vector &operator = (const compressed_vector &v) {
            if (this != &v) {
                size_ = v.size_;
                capacity_ = v.capacity_;
                filled_ = v.filled_;
                index_data_ = v.index_data_;
                value_data_ = v.value_data_;
            }
            storage_invariants ();
            return *this;
        }
        template<class C>          // Container assignment without temporary
        BOOST_UBLAS_INLINE
        compressed_vector &operator = (const vector_container<C> &v) {
            resize (v ().size (), false);
            assign (v);
            return *this;
        }
        BOOST_UBLAS_INLINE
        compressed_vector &assign_temporary (compressed_vector &v) {
            swap (v);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &operator = (const vector_expression<AE> &ae) {
            self_type temporary (ae, capacity_);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &assign (const vector_expression<AE> &ae) {
            vector_assign<scalar_assign> (*this, ae);
            return *this;
        }

        // Computed assignment
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &operator += (const vector_expression<AE> &ae) {
            self_type temporary (*this + ae, capacity_);
            return assign_temporary (temporary);
        }
        template<class C>          // Container assignment without temporary
        BOOST_UBLAS_INLINE
        compressed_vector &operator += (const vector_container<C> &v) {
            plus_assign (v);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &plus_assign (const vector_expression<AE> &ae) {
            vector_assign<scalar_plus_assign> (*this, ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &operator -= (const vector_expression<AE> &ae) {
            self_type temporary (*this - ae, capacity_);
            return assign_temporary (temporary);
        }
        template<class C>          // Container assignment without temporary
        BOOST_UBLAS_INLINE
        compressed_vector &operator -= (const vector_container<C> &v) {
            minus_assign (v);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        compressed_vector &minus_assign (const vector_expression<AE> &ae) {