matrix_sparse.hpp

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//
//  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_)