matrix_expression.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_MATRIX_EXPRESSION_H
#define BOOST_UBLAS_MATRIX_EXPRESSION_H

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

// Expression templates based on ideas of Todd Veldhuizen and Geoffrey Furnish
// Iterators based on ideas of Jeremy Siek

namespace boost { namespace numeric { namespace ublas {

    // Base class Matrix Expressions - see the Barton Nackman trick
    template<class E>
    class matrix_expression:
        public ublas_expression<E> {
    public:
        BOOST_STATIC_CONSTANT (unsigned, complexity = 0);
        typedef E expression_type;
        typedef matrix_tag type_category;
        typedef abstract_tag simd_category;
        // FIXME: Template instantiation order problem
        // typedef typename E::size_type size_type;
        typedef std::size_t size_type;
        typedef noalias_proxy<E> noalias_proxy_type;
        typedef const matrix_row<const E> const_matrix_row_type;
        typedef matrix_row<E> matrix_row_type;
        typedef const matrix_column<const E> const_matrix_column_type;
        typedef matrix_column<E> matrix_column_type;
        typedef const matrix_range<const E> const_matrix_range_type;
        typedef matrix_range<E> matrix_range_type;
        typedef const matrix_slice<const E> const_matrix_slice_type;
        typedef matrix_slice<E> matrix_slice_type;
        typedef const matrix_indirect<const E> const_matrix_indirect_type;
        typedef matrix_indirect<E> matrix_indirect_type;

        // This class could define an common interface for all
        // statically derived expression type classes.
        // Due to a compiler deficiency - one can not reference class typedefs of E
        // on MSVC 6.0 (error C2027) - we only implement the casts.

        BOOST_UBLAS_INLINE
        const expression_type &operator () () const {
            return *static_cast<const expression_type *> (this);
        }
        BOOST_UBLAS_INLINE
        expression_type &operator () () {
            return *static_cast<expression_type *> (this);
        }

        BOOST_UBLAS_INLINE
        noalias_proxy_type noalias () {
            return noalias_proxy_type (operator () ());
        }
        BOOST_UBLAS_INLINE
        const_matrix_row_type operator [] (size_type i) const {
            return const_matrix_row_type (operator () (), i);
        }
        BOOST_UBLAS_INLINE
        matrix_row_type operator [] (size_type i) {
            return matrix_row_type (operator () (), i);
        }
        BOOST_UBLAS_INLINE
        const_matrix_row_type row (size_type i) const {
            return const_matrix_row_type (operator () (), i);
        }
        BOOST_UBLAS_INLINE
        matrix_row_type row (size_type i) {
            return matrix_row_type (operator () (), i);
        }
        BOOST_UBLAS_INLINE
        const_matrix_column_type column (size_type j) const {
            return const_matrix_column_type (operator () (), j);
        }
        BOOST_UBLAS_INLINE
        matrix_column_type column (size_type j) {
            return matrix_column_type (operator () (), j);
        }
#ifndef BOOST_UBLAS_NO_PROXY_SHORTCUTS
        BOOST_UBLAS_INLINE
        const_matrix_range_type operator () (const range &r1, const range &r2) const {
            return const_matrix_range_type (operator () (), r1, r2);
        }
        BOOST_UBLAS_INLINE
        matrix_range_type operator () (const range &r1, const range &r2) {
            return matrix_range_type (operator () (), r1, r2);
        }
        BOOST_UBLAS_INLINE
        const_matrix_slice_type operator () (const slice &s1, const slice &s2) const {
            return const_matrix_slice_type (operator () (), s1, s2);
        }
        BOOST_UBLAS_INLINE
        matrix_slice_type operator () (const slice &s1, const slice &s2) {
            return matrix_slice_type (operator () (), s1, s2);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        const_matrix_indirect_type operator () (const indirect_array<A> &ia1, const indirect_array<A> &ia2) const {
            return const_matrix_indirect_type (operator () (), ia1, ia2);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        matrix_indirect_type operator () (const indirect_array<A> &ia1, const indirect_array<A> &ia2) {
            return matrix_indirect_type (operator () (), ia1, ia2);
        }
#else
        BOOST_UBLAS_INLINE
        const_matrix_range_type project (const range &r1, const range &r2) const {
            return const_matrix_range_type (operator () (), r1, r2);
        }
        BOOST_UBLAS_INLINE
        matrix_range_type project (const range &r1, const range &r2) {
            return matrix_range_type (operator () (), r1, r2);
        }
        BOOST_UBLAS_INLINE
        const_matrix_slice_type project (const slice &s1, const slice &s2) const {
            return const_matrix_slice_type (operator () (), s1, s2);
        }
        BOOST_UBLAS_INLINE
        matrix_slice_type project (const slice &s1, const slice &s2) {
            return matrix_slice_type (operator () (), s1, s2);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        const_matrix_indirect_type project (const indirect_array<A> &ia1, const indirect_array<A> &ia2) const {
            return const_matrix_indirect_type (operator () (), ia1, ia2);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        matrix_indirect_type project (const indirect_array<A> &ia1, const indirect_array<A> &ia2) {
            return matrix_indirect_type (operator () (), ia1, ia2);
        }
#endif
    };

#ifdef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
    struct iterator1_tag {};
    struct iterator2_tag {};

    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_iterator_type begin (const I &it, iterator1_tag) {
        return it ().find2 (1, it.index1 (), 0);
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_iterator_type end (const I &it, iterator1_tag) {
        return it ().find2 (1, it.index1 (), it ().size2 ());
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_reverse_iterator_type rbegin (const I &it, iterator1_tag) {
        return typename I::dual_reverse_iterator_type (end (it, iterator1_tag ()));
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_reverse_iterator_type rend (const I &it, iterator1_tag) {
        return typename I::dual_reverse_iterator_type (begin (it, iterator1_tag ()));
    }

    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_iterator_type begin (const I &it, iterator2_tag) {
        return it ().find1 (1, 0, it.index2 ());
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_iterator_type end (const I &it, iterator2_tag) {
        return it ().find1 (1, it ().size1 (), it.index2 ());
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_reverse_iterator_type rbegin (const I &it, iterator2_tag) {
        return typename I::dual_reverse_iterator_type (end (it, iterator2_tag ()));
    }
    template<class I>
    BOOST_UBLAS_INLINE
    typename I::dual_reverse_iterator_type rend (const I &it, iterator2_tag) {
        return typename I::dual_reverse_iterator_type (begin (it, iterator2_tag ()));
    }
#endif


    template<class E>
    class matrix_reference:
        public matrix_expression<matrix_reference<E> > {
    public:
#ifndef BOOST_UBLAS_NO_PROXY_SHORTCUTS
        BOOST_UBLAS_USING matrix_expression<matrix_reference<E> >::operator ();
#endif
        typedef typename E::size_type size_type;
        typedef typename E::difference_type difference_type;
        typedef typename E::value_type value_type;
#ifndef BOOST_UBLAS_CT_REFERENCE_BASE_TYPEDEFS
        typedef typename E::const_reference const_reference;
        typedef typename E::reference reference;
#else
        typedef typename E::const_reference const_reference;
        typedef typename boost::mpl::if_<boost::is_const<E>,
                                          typename E::const_reference,
                                          typename E::reference>::type reference;
#endif
    private:
        typedef matrix_reference<E> self_type;
    public:
        typedef E refered_type;
        typedef const self_type const_closure_type;
        typedef const_closure_type closure_type;
        typedef typename E::orientation_category orientation_category;
        typedef typename E::storage_category storage_category;
        typedef typename E::simd_category simd_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        matrix_reference ():
              e_ (nil_) {}
        BOOST_UBLAS_INLINE
        explicit matrix_reference (refered_type &e):
              e_ (e) {}

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size1 () const {
            return e_.size1 ();
        }
        BOOST_UBLAS_INLINE
        size_type size2 () const {
            return e_.size2 ();
        }

#ifndef BOOST_UBLAS_NESTED_CLASS_DR45
    private:
#endif
        // Expression accessors - const correct
        BOOST_UBLAS_INLINE
        const refered_type &expression () const {
            return e_;
        }
        BOOST_UBLAS_INLINE
        refered_type &expression () {
            return e_;
        }

    public:
        // Element access
#ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER
        BOOST_UBLAS_INLINE
        const_reference operator () (size_type i, size_type j) const {
            return expression () (i, j);
        }
        BOOST_UBLAS_INLINE
        reference operator () (size_type i, size_type j) {
            return expression () (i, j);
        }
#else
        BOOST_UBLAS_INLINE
        reference operator () (size_type i, size_type j) const {
            return expression () (i, j);
        }
#endif

        // Assignment
        BOOST_UBLAS_INLINE
        matrix_reference &operator = (const matrix_reference &m) {
            expression ().operator = (m);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &operator = (const matrix_expression<AE> &ae) {
            expression ().operator = (ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &assign (const matrix_expression<AE> &ae) {
            expression ().assign (ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &operator += (const matrix_expression<AE> &ae) {
            expression ().operator += (ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &plus_assign (const matrix_expression<AE> &ae) {
            expression ().plus_assign (ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &operator -= (const matrix_expression<AE> &ae) {
            expression ().operator -= (ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        matrix_reference &minus_assign (const matrix_expression<AE> &ae) {
            expression ().minus_assign (ae);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        matrix_reference &operator *= (const AT &at) {
            expression ().operator *= (at);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        matrix_reference &operator /= (const AT &at) {
            expression ().operator /= (at);
            return *this;
        }

         // Swapping
        BOOST_UBLAS_INLINE
        void swap (matrix_reference &m) {
            expression ().swap (m.expression ());
        }

        // Closure comparison
        BOOST_UBLAS_INLINE
        bool same_closure (const matrix_reference &mr) const {
            return &(*this).e_ == &mr.e_;
        }

        // Iterator types
#ifndef BOOST_UBLAS_CT_REFERENCE_BASE_TYPEDEFS
        typedef typename E::const_iterator1 const_iterator1;
        typedef typename E::iterator1 iterator1;
        typedef typename E::const_iterator2 const_iterator2;
        typedef typename E::iterator2 iterator2;
#else
        typedef typename E::const_iterator1 const_iterator1;
        typedef typename boost::mpl::if_<boost::is_const<E>,
                                          typename E::const_iterator1,