expression_types.hpp

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//
//  Copyright (c) 2000-2002
//  Joerg Walter, Mathias Koch
//
//  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_EXPRESSION_TYPE_
#define _BOOST_UBLAS_EXPRESSION_TYPE_

#include <boost/numeric/ublas/exception.hpp>
#include <boost/numeric/ublas/traits.hpp>
#include <boost/numeric/ublas/functional.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 for uBLAS staticaly derived expressions - see the Barton Nackman trick
    //  Provides numeric properties for linear algebra
    template<class E>
    class ublas_expression {
    public:
        typedef E expression_type;
        /* E can be an incomplete type - to define the following we would need more template arguments
        typedef typename E::type_category type_category;
        typedef typename E::value_type value_type;
        */
        
        // Directly implement nonassignable - simplifes debugging call trace!
    protected:
        ublas_expression () {}
        ~ublas_expression () {}
    private:
        const ublas_expression& operator= (const ublas_expression &);
    };


    // Base class for Scalar Expression models -
    //  it does not model the Scalar Expression concept but all derived types should.
    // The class defines a common base type and some common interface for all
    // statically derived Scalar Expression classes
    // We implement the casts to the statically derived type.
    template<class E>
    class scalar_expression:
        public ublas_expression<E> {
    public:
        typedef E expression_type;
        typedef scalar_tag type_category;

        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);
        }
    };

    template<class T>
    class scalar_reference:
        public scalar_expression<scalar_reference<T> > {

        typedef scalar_reference<T> self_type;
    public:
        typedef T value_type;
        typedef const value_type &const_reference;
        typedef typename boost::mpl::if_<boost::is_const<T>,
                                          const_reference,
                                          value_type &>::type reference;
        typedef const self_type const_closure_type;
        typedef const_closure_type closure_type;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        explicit scalar_reference (reference t):
            t_ (t) {}

        // Conversion
        BOOST_UBLAS_INLINE
        operator value_type () const {
            return t_;
        }

        // Assignment
        BOOST_UBLAS_INLINE
        scalar_reference &operator = (const scalar_reference &s) {
            t_ = s.t_;
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        scalar_reference &operator = (const scalar_expression<AE> &ae) {
            t_ = ae;
            return *this;
        }

        // Closure comparison
        BOOST_UBLAS_INLINE
        bool same_closure (const scalar_reference &sr) const {
            return &t_ == &sr.t_;
        }

    private:
        reference t_;
    };

    template<class T>
    class scalar_value:
        public scalar_expression<scalar_value<T> > {

        typedef scalar_value<T> self_type;
    public:
        typedef T value_type;
        typedef const value_type &const_reference;
        typedef typename boost::mpl::if_<boost::is_const<T>,
                                          const_reference,
                                          value_type &>::type reference;
        typedef const scalar_reference<const self_type> const_closure_type;
        typedef scalar_reference<self_type> closure_type;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        scalar_value ():
            t_ () {}
        BOOST_UBLAS_INLINE
        scalar_value (const value_type &t):
            t_ (t) {}

        BOOST_UBLAS_INLINE
        operator value_type () const {
            return t_;
        }

        // Assignment
        BOOST_UBLAS_INLINE
        scalar_value &operator = (const scalar_value &s) {
            t_ = s.t_;
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        scalar_value &operator = (const scalar_expression<AE> &ae) {
            t_ = ae;
            return *this;
        }

        // Closure comparison
        BOOST_UBLAS_INLINE
        bool same_closure (const scalar_value &sv) const {
            return this == &sv;    // self closing on instances value
        }

    private:
        value_type t_;
    };


    // Base class for Vector Expression models -
    //  it does not model the Vector Expression concept but all derived types should.
    // The class defines a common base type and some common interface for all
    // statically derived Vector Expression classes
    // We implement the casts to the statically derived type.
    template<class E>
    class vector_expression:
        public ublas_expression<E> {
    public:
        static const unsigned complexity = 0;
        typedef E expression_type;
        typedef vector_tag type_category;
        /* E can be an incomplete type - to define the following we would need more template arguments
        typedef typename E::size_type size_type;
        */
 
        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);
        }

#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
    private:
        // projection types
        typedef vector_range<E> vector_range_type;
        typedef vector_range<const E> const_vector_range_type;
        typedef vector_slice<E> vector_slice_type;
        typedef vector_slice<const E> const_vector_slice_type;
        // vector_indirect_type will depend on the A template parameter 
        typedef basic_range<> default_range;    // required to avoid range/slice name confusion
        typedef basic_slice<> default_slice;
   public:
        BOOST_UBLAS_INLINE
        const_vector_range_type operator () (const default_range &r) const {
            return const_vector_range_type (operator () (), r);
        }
        BOOST_UBLAS_INLINE
        vector_range_type operator () (const default_range &r) {
            return vector_range_type (operator () (), r);
        }
        BOOST_UBLAS_INLINE
        const_vector_slice_type operator () (const default_slice &s) const {
            return const_vector_slice_type (operator () (), s);
        }
        BOOST_UBLAS_INLINE
        vector_slice_type operator () (const default_slice &s) {
            return vector_slice_type (operator () (), s);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        const vector_indirect<const E, indirect_array<A> > operator () (const indirect_array<A> &ia) const {
            return vector_indirect<const E, indirect_array<A> >  (operator () (), ia);
        }
        template<class A>
        BOOST_UBLAS_INLINE
        vector_indirect<E, indirect_array<A> > operator () (const indirect_array<A> &ia) {
            return vector_indirect<E, indirect_array<A> > (operator () (), ia);
        }

        BOOST_UBLAS_INLINE
        const_vector_range_type project (const default_range &r) const {
            return const_vector_range_type (operator () (), r);
        }
        BOOST_UBLAS_INLINE
        vector_range_type project (const default_range &r) {
            return vector_range_type (operator () (), r);
        }
        BOOST_UBLAS_INLINE
        const_vector_slice_type project (const default_slice &s) const {
            return const_vector_slice_type (operator () (), s);
        }
        BOOST_UBLAS_INLINE
        vector_slice_type project (const default_slice &s) {
            return vector_slice_type (operator () (), s);
        }
        template<class A>