symmetric.hpp

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//
//  Copyright (c) 2000-2002
//  Joerg Walter, Mathias Koch
//
//  Permission to use, copy, modify, distribute and sell this software
//  and its documentation for any purpose is hereby granted without fee,
//  provided that the above copyright notice appear in all copies and
//  that both that copyright notice and this permission notice appear
//  in supporting documentation.  The authors make no representations
//  about the suitability of this software for any purpose.
//  It is provided "as is" without express or implied warranty.
//
//  The authors gratefully acknowledge the support of
//  GeNeSys mbH & Co. KG in producing this work.
//

#ifndef BOOST_UBLAS_SYMMETRIC_H
#define BOOST_UBLAS_SYMMETRIC_H

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

// Iterators based on ideas of Jeremy Siek
// Symmetric matrices are square. Thanks to Peter Schmitteckert for spotting this.

namespace boost { namespace numeric { namespace ublas {

    template<class M>
    bool is_symmetric (const M &m) {
        typedef typename M::size_type size_type;

        if (m.size1 () != m.size2 ())
            return false;
        size_type size = BOOST_UBLAS_SAME (m.size1 (), m.size2 ());
        for (size_type i = 0; i < size; ++ i) {
            for (size_type j = i; j < size; ++ j) {
                if (m (i, j) != m (j, i))
                    return false;
            }
        }
        return true;
    }

    // Array based symmetric matrix class
    template<class T, class F1, class F2, class A>
    class symmetric_matrix:
        public matrix_expression<symmetric_matrix<T, F1, F2, A> > {
    public:
#ifndef BOOST_UBLAS_NO_PROXY_SHORTCUTS
        BOOST_UBLAS_USING matrix_expression<symmetric_matrix<T, F1, F2, A> >::operator ();
#endif
        typedef typename A::size_type size_type;
        typedef typename A::difference_type difference_type;
        typedef T value_type;
        typedef const T &const_reference;
        typedef T &reference;
        typedef A array_type;
    private:
        typedef T *pointer;
        typedef F1 functor1_type;
        typedef F2 functor2_type;
        typedef symmetric_matrix<T, F1, F2, A> self_type;
    public:
#ifndef BOOST_UBLAS_CT_REFERENCE_BASE_TYPEDEFS
        typedef const matrix_const_reference<const self_type> const_closure_type;
#else
        typedef const matrix_reference<const self_type> const_closure_type;
#endif
        typedef matrix_reference<self_type> closure_type;
        typedef vector<T, A> vector_temporary_type;
        typedef matrix<T, F2, A> matrix_temporary_type;  // general sub-matrix
        typedef packed_tag storage_category;
        typedef typename F1::packed_category packed_category;
        typedef typename F2::orientation_category orientation_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        symmetric_matrix ():
            matrix_expression<self_type> (),
            size_ (0), data_ (0) {}
        BOOST_UBLAS_INLINE
        symmetric_matrix (size_type size):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (size, size)), data_ (functor1_type::packed_size (size, size)) {
        }
        BOOST_UBLAS_INLINE
        symmetric_matrix (size_type size1, size_type size2):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (size1, size2)), data_ (functor1_type::packed_size (size1, size2)) {
        }
        BOOST_UBLAS_INLINE
        symmetric_matrix (size_type size, const array_type &data):
            matrix_expression<self_type> (),
            size_ (size), data_ (data) {}
        BOOST_UBLAS_INLINE
        symmetric_matrix (const symmetric_matrix &m):
            matrix_expression<self_type> (),
            size_ (m.size_), data_ (m.data_) {}
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix (const matrix_expression<AE> &ae):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (ae ().size1 (), ae ().size2 ())),
            data_ (functor1_type::packed_size (size_, size_)) {
            matrix_assign (scalar_assign<reference, BOOST_UBLAS_TYPENAME AE::value_type> (), *this, ae);
        }

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size1 () const {
            return size_;
        }
        BOOST_UBLAS_INLINE
        size_type size2 () const {
            return size_;
        }
        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 size, bool preserve = true) {
            size_ = size;
            if (preserve) {
                self_type temporary (size_, size_);
                // FIXME use matrix_resize_preserve on conformant compilers
                // detail::matrix_resize_reserve<functor_type> (*this, temporary, size_, size_);
                assign_temporary (temporary);
            }
            else
                data ().resize (functor1_type::packed_size (size_, size_));
        }
        BOOST_UBLAS_INLINE
        void resize (size_type size1, size_type size2, bool preserve = true) {
            resize (BOOST_UBLAS_SAME (size1, size2), preserve);
        }
        BOOST_UBLAS_INLINE
        void resize_packed_preserve (size_type size) {
            size_ = BOOST_UBLAS_SAME (size, size);
            data ().resize (functor1_type::packed_size (size_, size_), value_type (0));
        }

        // Element access
        BOOST_UBLAS_INLINE
        const_reference operator () (size_type i, size_type j) const {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            BOOST_UBLAS_CHECK (j < size_, bad_index ());
            if (functor1_type::other (i, j))
                return data () [functor1_type::element (functor2_type (), i, size_, j, size_)];
            else
                return data () [functor1_type::element (functor2_type (), j, size_, i, size_)];
        }
        BOOST_UBLAS_INLINE
        reference operator () (size_type i, size_type j) {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            BOOST_UBLAS_CHECK (j < size_, bad_index ());
            if (functor1_type::other (i, j))
                return data () [functor1_type::element (functor2_type (), i, size_, j, size_)];
            else
                return data () [functor1_type::element (functor2_type (), j, size_, i, size_)];
        }

        // Assignment
        BOOST_UBLAS_INLINE
        symmetric_matrix &operator = (const symmetric_matrix &m) {
            size_ = m.size_;
            data () = m.data ();
            return *this;
        }
        BOOST_UBLAS_INLINE
        symmetric_matrix &assign_temporary (symmetric_matrix &m) {
            swap (m);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix &operator = (const matrix_expression<AE> &ae) {
            // return assign (self_type (ae));
            self_type temporary (ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix &assign (const matrix_expression<AE> &ae) {
            matrix_assign (scalar_assign<reference, BOOST_UBLAS_TYPENAME AE::value_type> (), *this, ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix& operator += (const matrix_expression<AE> &ae) {
            // return assign (self_type (*this + ae));
            self_type temporary (*this + ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix &plus_assign (const matrix_expression<AE> &ae) {
            matrix_assign (scalar_plus_assign<reference, BOOST_UBLAS_TYPENAME AE::value_type> (), *this, ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix& operator -= (const matrix_expression<AE> &ae) {
            // return assign (self_type (*this - ae));
            self_type temporary (*this - ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        symmetric_matrix &minus_assign (const matrix_expression<AE> &ae) {
            matrix_assign (scalar_minus_assign<reference, BOOST_UBLAS_TYPENAME AE::value_type> (), *this, ae);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        symmetric_matrix& operator *= (const AT &at) {
            matrix_assign_scalar (scalar_multiplies_assign<reference, AT> (), *this, at);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        symmetric_matrix& operator /= (const AT &at) {
            matrix_assign_scalar (scalar_divides_assign<reference, AT> (), *this, at);
            return *this;
        }

        // Swapping
        BOOST_UBLAS_INLINE
        void swap (symmetric_matrix &m) {
            if (this != &m) {
                std::swap (size_, m.size_);
                data ().swap (m.data ());
            }
        }
#ifndef BOOST_UBLAS_NO_MEMBER_FRIENDS
        BOOST_UBLAS_INLINE
        friend void swap (symmetric_matrix &m1, symmetric_matrix &m2) {
            m1.swap (m2);
        }
#endif

        // Element insertion and erasure
        // These functions should work with std::vector.
        // Thanks to Kresimir Fresl for spotting this.
        BOOST_UBLAS_INLINE
        void insert (size_type i, size_type j, const_reference t) {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            BOOST_UBLAS_CHECK (j < size_, bad_index ());
            if (functor1_type::other (i, j)) {
                size_type k = functor1_type::element (functor2_type (), i, size_, j, size_);
                BOOST_UBLAS_CHECK (type_traits<value_type>::equals (data () [k], value_type (0)) ||
                                   type_traits<value_type>::equals (data () [k], t), bad_index ());
                // data ().insert (data ().begin () + k, t);
                data () [k] = t;
            } else {
                size_type k = functor1_type::element (functor2_type (), j, size_, i, size_);
                BOOST_UBLAS_CHECK (type_traits<value_type>::equals (data () [k], value_type (0)) ||
                                   type_traits<value_type>::equals (data () [k], t), bad_index ());
                // data ().insert (data ().begin () + k, t);
                data () [k] = t;
            }
        }
        BOOST_UBLAS_INLINE
        void erase (size_type i, size_type j) {
            BOOST_UBLAS_CHECK (i < size_, bad_index ());
            BOOST_UBLAS_CHECK (j < size_, bad_index ());
            if (functor1_type::other (i, j)) {
                // size_type k = functor1_type::element (functor2_type (), i, size_, j, size_);
                // data ().erase (data ().begin () + k));
                data () [functor1_type::element (functor2_type (), i, size_, j, size_)] = value_type (0);
            } else {
                // data ().erase (data ().begin () + k);
                data () [functor1_type::element (functor2_type (), j, size_, i, size_)] = value_type (0);
            }
        }
        BOOST_UBLAS_INLINE
        void clear () {
            // data ().clear ();
            std::fill (data ().begin (), data ().end (), value_type (0));
        }

        // Iterator types
#ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
        typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
        typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
        typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
        typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
#else
        class const_iterator1;
        class iterator1;
        class const_iterator2;
        class iterator2;
#endif
#ifdef BOOST_MSVC_STD_ITERATOR
        typedef reverse_iterator_base1<const_iterator1, value_type, const_reference> const_reverse_iterator1;
        typedef reverse_iterator_base1<iterator1, value_type, reference> reverse_iterator1;
        typedef reverse_iterator_base2<const_iterator2, value_type, const_reference> const_reverse_iterator2;
        typedef reverse_iterator_base2<iterator2, value_type, reference> reverse_iterator2;
#else
        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;
#endif

        // Element lookup
        BOOST_UBLAS_INLINE
        const_iterator1 find1 (int /* rank */, size_type i, size_type j) const {
            return const_iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        iterator1 find1 (int rank, size_type i, size_type j) {
            if (rank == 1)
                i = functor1_type::restrict1 (i, j);
            return iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        const_iterator2 find2 (int /* rank */, size_type i, size_type j) const {
            return const_iterator2 (*this, i, j);