vector_sparse.hpp

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            vector_assign<scalar_minus_assign> (*this, ae);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        compressed_vector &operator *= (const AT &at) {
            vector_assign_scalar<scalar_multiplies_assign> (*this, at);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        compressed_vector &operator /= (const AT &at) {
            vector_assign_scalar<scalar_divides_assign> (*this, at);
            return *this;
        }

        // Swapping
        BOOST_UBLAS_INLINE
        void swap (compressed_vector &v) {
            if (this != &v) {
                std::swap (size_, v.size_);
                std::swap (capacity_, v.capacity_);
                std::swap (filled_, v.filled_);
                index_data_.swap (v.index_data_);
                value_data_.swap (v.value_data_);
            }
            storage_invariants ();
        }
        BOOST_UBLAS_INLINE
        friend void swap (compressed_vector &v1, compressed_vector &v2) {
            v1.swap (v2);
        }

        // Back element insertion and erasure
        BOOST_UBLAS_INLINE
        void push_back (size_type i, const_reference t) {
            BOOST_UBLAS_CHECK (filled_ == 0 || index_data_ [filled_ - 1] < k_based (i), external_logic ());
            if (filled_ >= capacity_)
                reserve (2 * capacity_, true);
            BOOST_UBLAS_CHECK (filled_ < capacity_, internal_logic ());
            index_data_ [filled_] = k_based (i);
            value_data_ [filled_] = t;
            ++ filled_;
            storage_invariants ();
        }
        BOOST_UBLAS_INLINE
        void pop_back () {
            BOOST_UBLAS_CHECK (filled_ > 0, external_logic ());
            -- filled_;
            storage_invariants ();
        }

        // Iterator types
    private:
        // Use index array iterator
        typedef typename IA::const_iterator const_subiterator_type;
        typedef typename IA::iterator subiterator_type;

        BOOST_UBLAS_INLINE
        true_reference at_element (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> ()));
            BOOST_UBLAS_CHECK (it != index_data_.begin () + filled_ && *it == k_based (i), bad_index ());
            return value_data_ [it - index_data_.begin ()];
        }

    public:
        class const_iterator;
        class iterator;

        // Element lookup
        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    
        const_iterator find (size_type i) const {
            return const_iterator (*this, detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
        }
        // BOOST_UBLAS_INLINE This function seems to be big. So we do not let the compiler inline it.    
        iterator find (size_type i) {
            return iterator (*this, detail::lower_bound (index_data_.begin (), index_data_.begin () + filled_, k_based (i), std::less<size_type> ()));
        }


        class const_iterator:
            public container_const_reference<compressed_vector>,
            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                               const_iterator, value_type> {
        public:
            typedef typename compressed_vector::value_type value_type;
            typedef typename compressed_vector::difference_type difference_type;
            typedef typename compressed_vector::const_reference reference;
            typedef const typename compressed_vector::pointer pointer;

            // Construction and destruction
            BOOST_UBLAS_INLINE
            const_iterator ():
                container_const_reference<self_type> (), it_ () {}
            BOOST_UBLAS_INLINE
            const_iterator (const self_type &v, const const_subiterator_type &it):
                container_const_reference<self_type> (v), it_ (it) {}
            BOOST_UBLAS_INLINE
            const_iterator (const typename self_type::iterator &it):  // ISSUE self_type:: stops VC8 using std::iterator here
                container_const_reference<self_type> (it ()), it_ (it.it_) {}

            // Arithmetic
            BOOST_UBLAS_INLINE
            const_iterator &operator ++ () {
                ++ it_;
                return *this;
            }
            BOOST_UBLAS_INLINE
            const_iterator &operator -- () {
                -- it_;
                return *this;
            }

            // Dereference
            BOOST_UBLAS_INLINE
            const_reference operator * () const {
                BOOST_UBLAS_CHECK (index () < (*this) ().size (), bad_index ());
                return (*this) ().value_data_ [it_ - (*this) ().index_data_.begin ()];
            }

            // Index
            BOOST_UBLAS_INLINE
            size_type index () const {
                BOOST_UBLAS_CHECK (*this != (*this) ().end (), bad_index ());
                BOOST_UBLAS_CHECK ((*this) ().zero_based (*it_) < (*this) ().size (), bad_index ());
                return (*this) ().zero_based (*it_);
            }

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

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

        private:
            const_subiterator_type it_;
        };

        BOOST_UBLAS_INLINE
        const_iterator begin () const {
            return find (0);
        }
        BOOST_UBLAS_INLINE
        const_iterator end () const {
            return find (size_);
        }

        class iterator:
            public container_reference<compressed_vector>,
            public bidirectional_iterator_base<sparse_bidirectional_iterator_tag,
                                               iterator, value_type> {
        public:
            typedef typename compressed_vector::value_type value_type;
            typedef typename compressed_vector::difference_type difference_type;
            typedef typename compressed_vector::true_reference reference;
            typedef typename compressed_vector::pointer pointer;

            // Construction and destruction
            BOOST_UBLAS_INLINE
            iterator ():
                container_reference<self_type> (), it_ () {}
            BOOST_UBLAS_INLINE
            iterator (self_type &v, const subiterator_type &it):
                container_reference<self_type> (v), it_ (it) {}

            // Arithmetic
            BOOST_UBLAS_INLINE
            iterator &operator ++ () {
                ++ it_;
                return *this;
            }
            BOOST_UBLAS_INLINE
            iterator &operator -- () {
                -- it_;
                return *this;
            }

            // Dereference
            BOOST_UBLAS_INLINE
            reference operator * () const {
                BOOST_UBLAS_CHECK (index () < (*this) ().size (), bad_index ());
                return (*this) ().value_data_ [it_ - (*this) ().index_data_.begin ()];
            }

            // Index
            BOOST_UBLAS_INLINE
            size_type index () const {
                BOOST_UBLAS_CHECK (*this != (*this) ().end (), bad_index ());
                BOOST_UBLAS_CHECK ((*this) ().zero_based (*it_) < (*this) ().size (), bad_index ());
                return (*this) ().zero_based (*it_);
            }

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

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

        private:
            subiterator_type it_;

            friend class const_iterator;
        };

        BOOST_UBLAS_INLINE
        iterator begin () {
            return find (0);
        }
        BOOST_UBLAS_INLINE
        iterator end () {
            return find (size_);
        }

        // Reverse iterator
        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;
            }
            // ISSUE: filled may be much less than capacity
            // ISSUE: index_data_ and value_data_ are undefined between filled and capacity (trouble with 'nan'-values)
            ar & serialization::make_nvp("capacity", capacity_);
            ar & serialization::make_nvp("filled", filled_);
            ar & serialization::make_nvp("index_data", index_data_);
            ar & serialization::make_nvp("value_data", value_data_);
            storage_invariants();
        }

    private:
        void storage_invariants () const
        {
            BOOST_UBLAS_CHECK (capacity_ == index_data_.size (), internal_logic ());
            BOOST_UBLAS_CHECK (capacity_ == value_data_.size (), internal_logic ());
            BOOST_UBLAS_CHECK (filled_ <= capacity_, internal_logic ());
            BOOST_UBLAS_CHECK ((0 == filled_) || (zero_based(index_data_[filled_ - 1]) < size_), internal_logic ());
        }

        size_type size_;
        typename index_array_type::size_type capacity_;
        typename index_array_type::size_type filled_;
        index_array_type index_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 iterator;
        friend class const_iterator;
    };

    template<class T, std::size_t IB, class IA, class TA>
    const typename compressed_vector<T, IB, IA, TA>::value_type compressed_vector<T, IB, IA, TA>::zero_ = value_type/*zero*/();


    // Coordimate 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 coordinate_vector:
        public vector_container<coordinate_vector<T, IB, IA, TA> > {

        typedef T &true_reference;
        typedef T *pointer;
        typedef const T *const_pointer;
        typedef coordinate_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
        coordinate_vector ():
            vector_container<self_type> (),
            size_ (0), capacity_ (restrict_capacity (0)),
            filled_ (0), sorted_filled_ (filled_), sorted_ (true),
            index_data_ (capacity_), value_data_ (capacity_) {
            storage_invariants ();
        }
        explicit BOOST_UBLAS_INLINE
        coordinate_vector (size_type size, size_type non_zeros = 0):
            vector_container<self_type> (),
            size_ (size), capacity_ (restrict_capacity (non_zeros)),
            filled_ (0), sorted_filled_ (filled_), sorted_ (true),
            index_data_ (capacity_), value_data_ (capacity_) {
            storage_invariants ();
        }
        BOOST_UBLAS_INLINE
        coordinate_vector (const coordinate_vector &v):
            vector_container<self_type> (),
            size_ (v.size_), capacity_ (v.capacity_),
            filled_ (v.filled_), sorted_filled_ (v.sorted_filled_), sorted_ (v.sorted_),
            index_data_ (v.index_data_), value_data_ (v.value_data_) {