comparison DEPENDENCIES/generic/include/boost/numeric/ublas/traits.hpp @ 16:2665513ce2d3

Add boost headers

+//
+//  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_TRAITS_
+#define _BOOST_UBLAS_TRAITS_
+
+#include <iterator>
+#include <complex>
+#include <boost/config/no_tr1/cmath.hpp>
+
+#include <boost/numeric/ublas/detail/config.hpp>
+#include <boost/numeric/ublas/detail/iterator.hpp>
+#include <boost/numeric/ublas/detail/returntype_deduction.hpp>
+
+#include <boost/type_traits.hpp>
+#include <complex>
+#include <boost/typeof/typeof.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_float.hpp>
+#include <boost/type_traits/is_integral.hpp>
+#include <boost/mpl/and.hpp>
+
+// anonymous namespace to avoid ADL issues
+namespace {
+  template<class T> T boost_numeric_ublas_sqrt (const T& t) {
+    using namespace std;
+    // we'll find either std::sqrt or else another version via ADL:
+    return sqrt (t);
+  }
+  template<class T> T boost_numeric_ublas_abs (const T& t) {
+    using namespace std;
+    // we'll find either std::abs or else another version via ADL:
+    return abs (t);
+  }
+  // unsigned types are always non-negative
+  template<> unsigned int boost_numeric_ublas_abs (const unsigned int& t) {
+    return t;
+  }
+  // unsigned types are always non-negative
+  template<> unsigned long boost_numeric_ublas_abs (const unsigned long& t) {
+    return t;
+  }
+}
+
+namespace boost { namespace numeric { namespace ublas {
+
+    // Use Joel de Guzman's return type deduction
+    // uBLAS assumes a common return type for all binary arithmetic operators
+    template<class X, class Y>
+    struct promote_traits {
+        typedef type_deduction_detail::base_result_of<X, Y> base_type;
+        static typename base_type::x_type x;
+        static typename base_type::y_type y;
+        static const std::size_t size = sizeof (
+                type_deduction_detail::test<
+                    typename base_type::x_type
+                  , typename base_type::y_type
+                >(x + y)     // Use x+y to stand of all the arithmetic actions
+            );
+
+        static const std::size_t index = (size / sizeof (char)) - 1;
+        typedef typename mpl::at_c<
+            typename base_type::types, index>::type id;
+        typedef typename id::type promote_type;
+    };
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator+ (I in1, std::complex<R> const& in2 ) {
+        return R (in1) + in2;
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator+ (std::complex<R> const& in1, I in2) {
+        return in1 + R (in2);
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator- (I in1, std::complex<R> const& in2) {
+        return R (in1) - in2;
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator- (std::complex<R> const& in1, I in2) {
+        return in1 - R (in2);
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator* (I in1, std::complex<R> const& in2) {
+        return R (in1) * in2;
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator* (std::complex<R> const& in1, I in2) {
+        return in1 * R(in2);
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator/ (I in1, std::complex<R> const& in2) {
+        return R(in1) / in2;
+      }
+
+      template<typename R, typename I> 
+      typename boost::enable_if<
+        mpl::and_<
+          boost::is_float<R>,
+          boost::is_integral<I>
+          >,
+        std::complex<R> >::type inline operator/ (std::complex<R> const& in1, I in2) {
+        return in1 / R (in2);
+      }
+
+
+
+    // Type traits - generic numeric properties and functions
+    template<class T>
+    struct type_traits;
+        
+    // Define properties for a generic scalar type
+    template<class T>
+    struct scalar_traits {
+        typedef scalar_traits<T> self_type;
+        typedef T value_type;
+        typedef const T &const_reference;
+        typedef T &reference;
+
+        typedef T real_type;
+        typedef real_type precision_type;       // we do not know what type has more precision then the real_type
+
+        static const unsigned plus_complexity = 1;
+        static const unsigned multiplies_complexity = 1;
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type real (const_reference t) {
+                return t;
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type imag (const_reference /*t*/) {
+                return 0;
+        }
+        static
+        BOOST_UBLAS_INLINE
+        value_type conj (const_reference t) {
+                return t;
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type type_abs (const_reference t) {
+            return boost_numeric_ublas_abs (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        value_type type_sqrt (const_reference t) {
+            // force a type conversion back to value_type for intgral types
+            return value_type (boost_numeric_ublas_sqrt (t));
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_1 (const_reference t) {
+            return self_type::type_abs (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_2 (const_reference t) {
+            return self_type::type_abs (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_inf (const_reference t) {
+            return self_type::type_abs (t);
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        bool equals (const_reference t1, const_reference t2) {
+            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
+                   (std::max) ((std::max) (self_type::norm_inf (t1),
+                                       self_type::norm_inf (t2)),
+                             BOOST_UBLAS_TYPE_CHECK_MIN);
+        }
+    };
+
+    // Define default type traits, assume T is a scalar type
+    template<class T>
+    struct type_traits : scalar_traits <T> {
+        typedef type_traits<T> self_type;
+        typedef T value_type;
+        typedef const T &const_reference;
+        typedef T &reference;
+
+        typedef T real_type;
+        typedef real_type precision_type;
+        static const unsigned multiplies_complexity = 1;
+
+    };
+
+    // Define real type traits
+    template<>
+    struct type_traits<float> : scalar_traits<float> {
+        typedef type_traits<float> self_type;
+        typedef float value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef double precision_type;
+    };
+    template<>
+    struct type_traits<double> : scalar_traits<double> {
+        typedef type_traits<double> self_type;
+        typedef double value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef long double precision_type;
+    };
+    template<>
+    struct type_traits<long double>  : scalar_traits<long double> {
+        typedef type_traits<long double> self_type;
+        typedef long double value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef value_type precision_type;
+    };
+
+    // Define properties for a generic complex type
+    template<class T>
+    struct complex_traits {
+        typedef complex_traits<T> self_type;
+        typedef T value_type;
+        typedef const T &const_reference;
+        typedef T &reference;
+
+        typedef typename T::value_type real_type;
+        typedef real_type precision_type;       // we do not know what type has more precision then the real_type
+
+        static const unsigned plus_complexity = 2;
+        static const unsigned multiplies_complexity = 6;
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type real (const_reference t) {
+                return std::real (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type imag (const_reference t) {
+                return std::imag (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        value_type conj (const_reference t) {
+                return std::conj (t);
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type type_abs (const_reference t) {
+                return abs (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        value_type type_sqrt (const_reference t) {
+                return sqrt (t);
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_1 (const_reference t) {
+            return self_type::type_abs (t);
+            // original computation has been replaced because a complex number should behave like a scalar type
+            // return type_traits<real_type>::type_abs (self_type::real (t)) +
+            //       type_traits<real_type>::type_abs (self_type::imag (t));
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_2 (const_reference t) {
+            return self_type::type_abs (t);
+        }
+        static
+        BOOST_UBLAS_INLINE
+        real_type norm_inf (const_reference t) {
+            return self_type::type_abs (t);
+            // original computation has been replaced because a complex number should behave like a scalar type
+            // return (std::max) (type_traits<real_type>::type_abs (self_type::real (t)),
+            //                 type_traits<real_type>::type_abs (self_type::imag (t)));
+        }
+
+        static
+        BOOST_UBLAS_INLINE
+        bool equals (const_reference t1, const_reference t2) {
+            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
+                   (std::max) ((std::max) (self_type::norm_inf (t1),
+                                       self_type::norm_inf (t2)),
+                             BOOST_UBLAS_TYPE_CHECK_MIN);
+        }
+    };
+    
+    // Define complex type traits
+    template<>
+    struct type_traits<std::complex<float> > : complex_traits<std::complex<float> >{
+        typedef type_traits<std::complex<float> > self_type;
+        typedef std::complex<float> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef float real_type;
+        typedef std::complex<double> precision_type;
+
+    };
+    template<>
+    struct type_traits<std::complex<double> > : complex_traits<std::complex<double> >{
+        typedef type_traits<std::complex<double> > self_type;
+        typedef std::complex<double> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef double real_type;
+        typedef std::complex<long double> precision_type;
+    };
+    template<>
+    struct type_traits<std::complex<long double> > : complex_traits<std::complex<long double> > {
+        typedef type_traits<std::complex<long double> > self_type;
+        typedef std::complex<long double> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef long double real_type;
+        typedef value_type precision_type;
+    };
+
+#ifdef BOOST_UBLAS_USE_INTERVAL
+    // Define scalar interval type traits
+    template<>
+    struct type_traits<boost::numeric::interval<float> > : scalar_traits<boost::numeric::interval<float> > {
+        typedef type_traits<boost::numeric::interval<float> > self_type;
+        typedef boost::numeric::interval<float> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef boost::numeric::interval<double> precision_type;
+
+    };
+    template<>
+    struct type_traits<boost::numeric::interval<double> > : scalar_traits<boost::numeric::interval<double> > {
+        typedef type_traits<boost::numeric::interval<double> > self_type;
+        typedef boost::numeric::interval<double> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef boost::numeric::interval<long double> precision_type;
+    };
+    template<>
+    struct type_traits<boost::numeric::interval<long double> > : scalar_traits<boost::numeric::interval<long double> > {
+        typedef type_traits<boost::numeric::interval<long double> > self_type;
+        typedef boost::numeric::interval<long double> value_type;
+        typedef const value_type &const_reference;
+        typedef value_type &reference;
+        typedef value_type real_type;
+        typedef value_type precision_type;
+    };
+#endif
+
+
+    // Storage tags -- hierarchical definition of storage characteristics
+
+    struct unknown_storage_tag {};
+    struct sparse_proxy_tag: public unknown_storage_tag {};
+    struct sparse_tag: public sparse_proxy_tag {};
+    struct packed_proxy_tag: public sparse_proxy_tag {};
+    struct packed_tag: public packed_proxy_tag {};
+    struct dense_proxy_tag: public packed_proxy_tag {};
+    struct dense_tag: public dense_proxy_tag {};
+
+    template<class S1, class S2>
+    struct storage_restrict_traits {
+        typedef S1 storage_category;
+    };
+
+    template<>
+    struct storage_restrict_traits<sparse_tag, dense_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<sparse_tag, packed_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<sparse_tag, sparse_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+
+    template<>
+    struct storage_restrict_traits<packed_tag, dense_proxy_tag> {
+        typedef packed_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<packed_tag, packed_proxy_tag> {
+        typedef packed_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<packed_tag, sparse_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+
+    template<>
+    struct storage_restrict_traits<packed_proxy_tag, sparse_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+
+    template<>
+    struct storage_restrict_traits<dense_tag, dense_proxy_tag> {
+        typedef dense_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<dense_tag, packed_proxy_tag> {
+        typedef packed_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<dense_tag, sparse_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+
+    template<>
+    struct storage_restrict_traits<dense_proxy_tag, packed_proxy_tag> {
+        typedef packed_proxy_tag storage_category;
+    };
+    template<>
+    struct storage_restrict_traits<dense_proxy_tag, sparse_proxy_tag> {
+        typedef sparse_proxy_tag storage_category;
+    };
+
+
+    // Iterator tags -- hierarchical definition of storage characteristics
+
+    struct sparse_bidirectional_iterator_tag : public std::bidirectional_iterator_tag {};
+    struct packed_random_access_iterator_tag : public std::random_access_iterator_tag {};
+    struct dense_random_access_iterator_tag : public packed_random_access_iterator_tag {};
+
+    // Thanks to Kresimir Fresl for convincing Comeau with iterator_base_traits ;-)
+    template<class IC>
+    struct iterator_base_traits {};
+
+    template<>
+    struct iterator_base_traits<std::forward_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef forward_iterator_base<std::forward_iterator_tag, I, T> type;
+        };
+    };
+
+    template<>
+    struct iterator_base_traits<std::bidirectional_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef bidirectional_iterator_base<std::bidirectional_iterator_tag, I, T> type;
+        };
+    };
+    template<>
+    struct iterator_base_traits<sparse_bidirectional_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef bidirectional_iterator_base<sparse_bidirectional_iterator_tag, I, T> type;
+        };
+    };
+
+    template<>
+    struct iterator_base_traits<std::random_access_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef random_access_iterator_base<std::random_access_iterator_tag, I, T> type;
+        };
+    };
+    template<>
+    struct iterator_base_traits<packed_random_access_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef random_access_iterator_base<packed_random_access_iterator_tag, I, T> type;
+        };
+    };
+    template<>
+    struct iterator_base_traits<dense_random_access_iterator_tag> {
+        template<class I, class T>
+        struct iterator_base {
+            typedef random_access_iterator_base<dense_random_access_iterator_tag, I, T> type;
+        };
+    };
+
+    template<class I1, class I2>
+    struct iterator_restrict_traits {
+        typedef I1 iterator_category;
+    };
+
+    template<>
+    struct iterator_restrict_traits<packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag> {
+        typedef sparse_bidirectional_iterator_tag iterator_category;
+    };
+    template<>
+    struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag> {
+        typedef sparse_bidirectional_iterator_tag iterator_category;
+    };
+
+    template<>
+    struct iterator_restrict_traits<dense_random_access_iterator_tag, sparse_bidirectional_iterator_tag> {
+        typedef sparse_bidirectional_iterator_tag iterator_category;
+    };
+    template<>
+    struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, dense_random_access_iterator_tag> {
+        typedef sparse_bidirectional_iterator_tag iterator_category;
+    };
+
+    template<>
+    struct iterator_restrict_traits<dense_random_access_iterator_tag, packed_random_access_iterator_tag> {
+        typedef packed_random_access_iterator_tag iterator_category;
+    };
+    template<>
+    struct iterator_restrict_traits<packed_random_access_iterator_tag, dense_random_access_iterator_tag> {
+        typedef packed_random_access_iterator_tag iterator_category;
+    };
+
+    template<class I>
+    BOOST_UBLAS_INLINE
+    void increment (I &it, const I &it_end, typename I::difference_type compare, packed_random_access_iterator_tag) {
+        it += (std::min) (compare, it_end - it);
+    }
+    template<class I>
+    BOOST_UBLAS_INLINE
+    void increment (I &it, const I &/* it_end */, typename I::difference_type /* compare */, sparse_bidirectional_iterator_tag) {
+        ++ it;
+    }
+    template<class I>
+    BOOST_UBLAS_INLINE
+    void increment (I &it, const I &it_end, typename I::difference_type compare) {
+        increment (it, it_end, compare, typename I::iterator_category ());
+    }
+
+    template<class I>
+    BOOST_UBLAS_INLINE
+    void increment (I &it, const I &it_end) {
+#if BOOST_UBLAS_TYPE_CHECK
+        I cit (it);
+        while (cit != it_end) {
+            BOOST_UBLAS_CHECK (*cit == typename I::value_type/*zero*/(), internal_logic ());
+            ++ cit;
+        }
+#endif
+        it = it_end;
+    }
+
+    namespace detail {
+
+        // specialisation which define whether a type has a trivial constructor
+        // or not. This is used by array types.
+        template<typename T>
+        struct has_trivial_constructor : public boost::has_trivial_constructor<T> {};
+
+        template<typename T>
+        struct has_trivial_destructor : public boost::has_trivial_destructor<T> {};
+
+        template<typename FLT>
+        struct has_trivial_constructor<std::complex<FLT> > : public has_trivial_constructor<FLT> {};
+        
+        template<typename FLT>
+        struct has_trivial_destructor<std::complex<FLT> > : public has_trivial_destructor<FLT> {};
+
+    }
+
+
+    /**  \brief Traits class to extract type information from a constant matrix or vector CONTAINER.
+     *
+     */
+    template < class E >
+    struct container_view_traits {
+        /// type of indices
+        typedef typename E::size_type             size_type;
+        /// type of differences of indices
+        typedef typename E::difference_type       difference_type;
+
+        /// storage category: \c unknown_storage_tag, \c dense_tag, \c packed_tag, ...
+        typedef typename E::storage_category      storage_category;
+
+        /// type of elements
+        typedef typename E::value_type            value_type;
+        /// const reference to an element
+        typedef typename E::const_reference       const_reference;
+  
+        /// type used in expressions to mark a reference to this class (usually a const container_reference<const E> or the class itself)
+        typedef typename E::const_closure_type    const_closure_type;
+    };
+
+    /**  \brief Traits class to extract additional type information from a mutable matrix or vector CONTAINER.
+     *
+     */
+    template < class E >
+    struct mutable_container_traits {
+        /// reference to an element
+        typedef typename E::reference             reference;
+  
+        /// type used in expressions to mark a reference to this class (usually a container_reference<E> or the class itself)
+        typedef typename E::closure_type          closure_type;
+    };
+
+    /**  \brief Traits class to extract type information from a matrix or vector CONTAINER.
+     *
+     */
+    template < class E >
+    struct container_traits 
+        : container_view_traits<E>, mutable_container_traits<E> {
+
+    };
+
+
+    /**  \brief Traits class to extract type information from a constant MATRIX.
+     *
+     */
+    template < class MATRIX >
+    struct matrix_view_traits : container_view_traits <MATRIX> {
+
+        /// orientation of the matrix, either \c row_major_tag, \c column_major_tag or \c unknown_orientation_tag
+        typedef typename MATRIX::orientation_category  orientation_category;
+  
+        /// row iterator for the matrix
+        typedef typename MATRIX::const_iterator1  const_iterator1;
+
+        /// column iterator for the matrix
+        typedef typename MATRIX::const_iterator2  const_iterator2;
+    };
+
+    /**  \brief Traits class to extract additional type information from a mutable MATRIX.
+     *
+     */
+    template < class MATRIX >
+    struct mutable_matrix_traits 
+        : mutable_container_traits <MATRIX> {
+
+        /// row iterator for the matrix
+        typedef typename MATRIX::iterator1  iterator1;
+
+        /// column iterator for the matrix
+        typedef typename MATRIX::iterator2  iterator2;
+    };
+
+
+    /**  \brief Traits class to extract type information from a MATRIX.
+     *
+     */
+    template < class MATRIX >
+    struct matrix_traits 
+        : matrix_view_traits <MATRIX>, mutable_matrix_traits <MATRIX> {
+    };
+
+    /**  \brief Traits class to extract type information from a VECTOR.
+     *
+     */
+    template < class VECTOR >
+    struct vector_view_traits : container_view_traits <VECTOR> {
+
+        /// iterator for the VECTOR
+        typedef typename VECTOR::const_iterator  const_iterator;
+
+        /// iterator pointing to the first element
+        static
+        const_iterator begin(const VECTOR & v) {
+            return v.begin();
+        }
+        /// iterator pointing behind the last element
+        static
+        const_iterator end(const VECTOR & v) {
+            return v.end();
+        }
+
+    };
+
+    /**  \brief Traits class to extract type information from a VECTOR.
+     *
+     */
+    template < class VECTOR >
+    struct mutable_vector_traits : mutable_container_traits <VECTOR> {
+        /// iterator for the VECTOR
+        typedef typename VECTOR::iterator  iterator;
+
+        /// iterator pointing to the first element
+        static
+        iterator begin(VECTOR & v) {
+            return v.begin();
+        }
+
+        /// iterator pointing behind the last element
+        static
+        iterator end(VECTOR & v) {
+            return v.end();
+        }
+    };
+
+    /**  \brief Traits class to extract type information from a VECTOR.
+     *
+     */
+    template < class VECTOR >
+    struct vector_traits 
+        : vector_view_traits <VECTOR>, mutable_vector_traits <VECTOR> {
+    };
+
+
+    // Note: specializations for T[N] and T[M][N] have been moved to traits/c_array.hpp
+
+}}}
+
+#endif