Chris@16: //
Chris@16: //  Copyright (c) 2000-2002
Chris@16: //  Joerg Walter, Mathias Koch
Chris@16: //
Chris@16: //  Distributed under the Boost Software License, Version 1.0. (See
Chris@16: //  accompanying file LICENSE_1_0.txt or copy at
Chris@16: //  http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //
Chris@16: //  The authors gratefully acknowledge the support of
Chris@16: //  GeNeSys mbH & Co. KG in producing this work.
Chris@16: //
Chris@16: 
Chris@16: #ifndef _BOOST_UBLAS_TRAITS_
Chris@16: #define _BOOST_UBLAS_TRAITS_
Chris@16: 
Chris@16: #include <iterator>
Chris@16: #include <complex>
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/ublas/detail/config.hpp>
Chris@16: #include <boost/numeric/ublas/detail/iterator.hpp>
Chris@16: #include <boost/numeric/ublas/detail/returntype_deduction.hpp>
Chris@101: #ifdef BOOST_UBLAS_USE_INTERVAL
Chris@101: #include <boost/numeric/interval.hpp>
Chris@101: #endif
Chris@16: 
Chris@16: #include <boost/type_traits.hpp>
Chris@16: #include <complex>
Chris@16: #include <boost/typeof/typeof.hpp>
Chris@16: #include <boost/utility/enable_if.hpp>
Chris@16: #include <boost/type_traits/is_float.hpp>
Chris@16: #include <boost/type_traits/is_integral.hpp>
Chris@101: #include <boost/type_traits/is_unsigned.hpp>
Chris@16: #include <boost/mpl/and.hpp>
Chris@16: 
Chris@16: // anonymous namespace to avoid ADL issues
Chris@16: namespace {
Chris@16:   template<class T> T boost_numeric_ublas_sqrt (const T& t) {
Chris@16:     using namespace std;
Chris@16:     // we'll find either std::sqrt or else another version via ADL:
Chris@16:     return sqrt (t);
Chris@16:   }
Chris@101: 
Chris@101: template<typename T>
Chris@101: inline typename boost::disable_if<
Chris@101:     boost::is_unsigned<T>, T >::type
Chris@101:     boost_numeric_ublas_abs (const T &t ) {
Chris@101:         using namespace std;
Chris@101:         return abs( t );
Chris@101:     }
Chris@101: 
Chris@101: template<typename T>
Chris@101: inline typename boost::enable_if<
Chris@101:     boost::is_unsigned<T>, T >::type
Chris@101:     boost_numeric_ublas_abs (const T &t ) {
Chris@101:         return t;
Chris@101:     }
Chris@16: }
Chris@16: 
Chris@16: namespace boost { namespace numeric { namespace ublas {
Chris@16: 
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator+ (I in1, std::complex<R> const& in2 ) {
Chris@101:       return R (in1) + in2;
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator+ (std::complex<R> const& in1, I in2) {
Chris@101:       return in1 + R (in2);
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator- (I in1, std::complex<R> const& in2) {
Chris@101:       return R (in1) - in2;
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator- (std::complex<R> const& in1, I in2) {
Chris@101:       return in1 - R (in2);
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator* (I in1, std::complex<R> const& in2) {
Chris@101:       return R (in1) * in2;
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator* (std::complex<R> const& in1, I in2) {
Chris@101:       return in1 * R(in2);
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator/ (I in1, std::complex<R> const& in2) {
Chris@101:       return R(in1) / in2;
Chris@101:     }
Chris@101: 
Chris@101:     template<typename R, typename I>
Chris@101:     typename boost::enable_if<
Chris@101:       mpl::and_<
Chris@101:         boost::is_float<R>,
Chris@101:         boost::is_integral<I>
Chris@101:         >,
Chris@101:       std::complex<R> >::type inline operator/ (std::complex<R> const& in1, I in2) {
Chris@101:       return in1 / R (in2);
Chris@101:     }
Chris@101: 
Chris@16:     // Use Joel de Guzman's return type deduction
Chris@16:     // uBLAS assumes a common return type for all binary arithmetic operators
Chris@16:     template<class X, class Y>
Chris@16:     struct promote_traits {
Chris@16:         typedef type_deduction_detail::base_result_of<X, Y> base_type;
Chris@16:         static typename base_type::x_type x;
Chris@16:         static typename base_type::y_type y;
Chris@16:         static const std::size_t size = sizeof (
Chris@16:                 type_deduction_detail::test<
Chris@16:                     typename base_type::x_type
Chris@16:                   , typename base_type::y_type
Chris@16:                 >(x + y)     // Use x+y to stand of all the arithmetic actions
Chris@16:             );
Chris@16: 
Chris@16:         static const std::size_t index = (size / sizeof (char)) - 1;
Chris@16:         typedef typename mpl::at_c<
Chris@16:             typename base_type::types, index>::type id;
Chris@16:         typedef typename id::type promote_type;
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:     // Type traits - generic numeric properties and functions
Chris@16:     template<class T>
Chris@16:     struct type_traits;
Chris@16:         
Chris@16:     // Define properties for a generic scalar type
Chris@16:     template<class T>
Chris@16:     struct scalar_traits {
Chris@16:         typedef scalar_traits<T> self_type;
Chris@16:         typedef T value_type;
Chris@16:         typedef const T &const_reference;
Chris@16:         typedef T &reference;
Chris@16: 
Chris@16:         typedef T real_type;
Chris@16:         typedef real_type precision_type;       // we do not know what type has more precision then the real_type
Chris@16: 
Chris@16:         static const unsigned plus_complexity = 1;
Chris@16:         static const unsigned multiplies_complexity = 1;
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type real (const_reference t) {
Chris@16:                 return t;
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type imag (const_reference /*t*/) {
Chris@16:                 return 0;
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         value_type conj (const_reference t) {
Chris@16:                 return t;
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type type_abs (const_reference t) {
Chris@16:             return boost_numeric_ublas_abs (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         value_type type_sqrt (const_reference t) {
Chris@16:             // force a type conversion back to value_type for intgral types
Chris@16:             return value_type (boost_numeric_ublas_sqrt (t));
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_1 (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_2 (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_inf (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         bool equals (const_reference t1, const_reference t2) {
Chris@16:             return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
Chris@16:                    (std::max) ((std::max) (self_type::norm_inf (t1),
Chris@16:                                        self_type::norm_inf (t2)),
Chris@16:                              BOOST_UBLAS_TYPE_CHECK_MIN);
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16:     // Define default type traits, assume T is a scalar type
Chris@16:     template<class T>
Chris@16:     struct type_traits : scalar_traits <T> {
Chris@16:         typedef type_traits<T> self_type;
Chris@16:         typedef T value_type;
Chris@16:         typedef const T &const_reference;
Chris@16:         typedef T &reference;
Chris@16: 
Chris@16:         typedef T real_type;
Chris@16:         typedef real_type precision_type;
Chris@16:         static const unsigned multiplies_complexity = 1;
Chris@16: 
Chris@16:     };
Chris@16: 
Chris@16:     // Define real type traits
Chris@16:     template<>
Chris@16:     struct type_traits<float> : scalar_traits<float> {
Chris@16:         typedef type_traits<float> self_type;
Chris@16:         typedef float value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef double precision_type;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<double> : scalar_traits<double> {
Chris@16:         typedef type_traits<double> self_type;
Chris@16:         typedef double value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef long double precision_type;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<long double>  : scalar_traits<long double> {
Chris@16:         typedef type_traits<long double> self_type;
Chris@16:         typedef long double value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef value_type precision_type;
Chris@16:     };
Chris@16: 
Chris@16:     // Define properties for a generic complex type
Chris@16:     template<class T>
Chris@16:     struct complex_traits {
Chris@16:         typedef complex_traits<T> self_type;
Chris@16:         typedef T value_type;
Chris@16:         typedef const T &const_reference;
Chris@16:         typedef T &reference;
Chris@16: 
Chris@16:         typedef typename T::value_type real_type;
Chris@16:         typedef real_type precision_type;       // we do not know what type has more precision then the real_type
Chris@16: 
Chris@16:         static const unsigned plus_complexity = 2;
Chris@16:         static const unsigned multiplies_complexity = 6;
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type real (const_reference t) {
Chris@16:                 return std::real (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type imag (const_reference t) {
Chris@16:                 return std::imag (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         value_type conj (const_reference t) {
Chris@16:                 return std::conj (t);
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type type_abs (const_reference t) {
Chris@16:                 return abs (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         value_type type_sqrt (const_reference t) {
Chris@16:                 return sqrt (t);
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_1 (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:             // original computation has been replaced because a complex number should behave like a scalar type
Chris@16:             // return type_traits<real_type>::type_abs (self_type::real (t)) +
Chris@16:             //       type_traits<real_type>::type_abs (self_type::imag (t));
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_2 (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:         }
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         real_type norm_inf (const_reference t) {
Chris@16:             return self_type::type_abs (t);
Chris@16:             // original computation has been replaced because a complex number should behave like a scalar type
Chris@16:             // return (std::max) (type_traits<real_type>::type_abs (self_type::real (t)),
Chris@16:             //                 type_traits<real_type>::type_abs (self_type::imag (t)));
Chris@16:         }
Chris@16: 
Chris@16:         static
Chris@16:         BOOST_UBLAS_INLINE
Chris@16:         bool equals (const_reference t1, const_reference t2) {
Chris@16:             return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
Chris@16:                    (std::max) ((std::max) (self_type::norm_inf (t1),
Chris@16:                                        self_type::norm_inf (t2)),
Chris@16:                              BOOST_UBLAS_TYPE_CHECK_MIN);
Chris@16:         }
Chris@16:     };
Chris@16:     
Chris@16:     // Define complex type traits
Chris@16:     template<>
Chris@16:     struct type_traits<std::complex<float> > : complex_traits<std::complex<float> >{
Chris@16:         typedef type_traits<std::complex<float> > self_type;
Chris@16:         typedef std::complex<float> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef float real_type;
Chris@16:         typedef std::complex<double> precision_type;
Chris@16: 
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<std::complex<double> > : complex_traits<std::complex<double> >{
Chris@16:         typedef type_traits<std::complex<double> > self_type;
Chris@16:         typedef std::complex<double> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef double real_type;
Chris@16:         typedef std::complex<long double> precision_type;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<std::complex<long double> > : complex_traits<std::complex<long double> > {
Chris@16:         typedef type_traits<std::complex<long double> > self_type;
Chris@16:         typedef std::complex<long double> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef long double real_type;
Chris@16:         typedef value_type precision_type;
Chris@16:     };
Chris@16: 
Chris@16: #ifdef BOOST_UBLAS_USE_INTERVAL
Chris@16:     // Define scalar interval type traits
Chris@16:     template<>
Chris@16:     struct type_traits<boost::numeric::interval<float> > : scalar_traits<boost::numeric::interval<float> > {
Chris@16:         typedef type_traits<boost::numeric::interval<float> > self_type;
Chris@16:         typedef boost::numeric::interval<float> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef boost::numeric::interval<double> precision_type;
Chris@16: 
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<boost::numeric::interval<double> > : scalar_traits<boost::numeric::interval<double> > {
Chris@16:         typedef type_traits<boost::numeric::interval<double> > self_type;
Chris@16:         typedef boost::numeric::interval<double> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef boost::numeric::interval<long double> precision_type;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct type_traits<boost::numeric::interval<long double> > : scalar_traits<boost::numeric::interval<long double> > {
Chris@16:         typedef type_traits<boost::numeric::interval<long double> > self_type;
Chris@16:         typedef boost::numeric::interval<long double> value_type;
Chris@16:         typedef const value_type &const_reference;
Chris@16:         typedef value_type &reference;
Chris@16:         typedef value_type real_type;
Chris@16:         typedef value_type precision_type;
Chris@16:     };
Chris@16: #endif
Chris@16: 
Chris@16: 
Chris@16:     // Storage tags -- hierarchical definition of storage characteristics
Chris@16: 
Chris@16:     struct unknown_storage_tag {};
Chris@16:     struct sparse_proxy_tag: public unknown_storage_tag {};
Chris@16:     struct sparse_tag: public sparse_proxy_tag {};
Chris@16:     struct packed_proxy_tag: public sparse_proxy_tag {};
Chris@16:     struct packed_tag: public packed_proxy_tag {};
Chris@16:     struct dense_proxy_tag: public packed_proxy_tag {};
Chris@16:     struct dense_tag: public dense_proxy_tag {};
Chris@16: 
Chris@16:     template<class S1, class S2>
Chris@16:     struct storage_restrict_traits {
Chris@16:         typedef S1 storage_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<sparse_tag, dense_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<sparse_tag, packed_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<sparse_tag, sparse_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<packed_tag, dense_proxy_tag> {
Chris@16:         typedef packed_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<packed_tag, packed_proxy_tag> {
Chris@16:         typedef packed_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<packed_tag, sparse_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<packed_proxy_tag, sparse_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<dense_tag, dense_proxy_tag> {
Chris@16:         typedef dense_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<dense_tag, packed_proxy_tag> {
Chris@16:         typedef packed_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<dense_tag, sparse_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<dense_proxy_tag, packed_proxy_tag> {
Chris@16:         typedef packed_proxy_tag storage_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct storage_restrict_traits<dense_proxy_tag, sparse_proxy_tag> {
Chris@16:         typedef sparse_proxy_tag storage_category;
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16:     // Iterator tags -- hierarchical definition of storage characteristics
Chris@16: 
Chris@16:     struct sparse_bidirectional_iterator_tag : public std::bidirectional_iterator_tag {};
Chris@16:     struct packed_random_access_iterator_tag : public std::random_access_iterator_tag {};
Chris@16:     struct dense_random_access_iterator_tag : public packed_random_access_iterator_tag {};
Chris@16: 
Chris@16:     // Thanks to Kresimir Fresl for convincing Comeau with iterator_base_traits ;-)
Chris@16:     template<class IC>
Chris@16:     struct iterator_base_traits {};
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<std::forward_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef forward_iterator_base<std::forward_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<std::bidirectional_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef bidirectional_iterator_base<std::bidirectional_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<sparse_bidirectional_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef bidirectional_iterator_base<sparse_bidirectional_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<std::random_access_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef random_access_iterator_base<std::random_access_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<packed_random_access_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef random_access_iterator_base<packed_random_access_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_base_traits<dense_random_access_iterator_tag> {
Chris@16:         template<class I, class T>
Chris@16:         struct iterator_base {
Chris@16:             typedef random_access_iterator_base<dense_random_access_iterator_tag, I, T> type;
Chris@16:         };
Chris@16:     };
Chris@16: 
Chris@16:     template<class I1, class I2>
Chris@16:     struct iterator_restrict_traits {
Chris@16:         typedef I1 iterator_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag> {
Chris@16:         typedef sparse_bidirectional_iterator_tag iterator_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag> {
Chris@16:         typedef sparse_bidirectional_iterator_tag iterator_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<dense_random_access_iterator_tag, sparse_bidirectional_iterator_tag> {
Chris@16:         typedef sparse_bidirectional_iterator_tag iterator_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, dense_random_access_iterator_tag> {
Chris@16:         typedef sparse_bidirectional_iterator_tag iterator_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<dense_random_access_iterator_tag, packed_random_access_iterator_tag> {
Chris@16:         typedef packed_random_access_iterator_tag iterator_category;
Chris@16:     };
Chris@16:     template<>
Chris@16:     struct iterator_restrict_traits<packed_random_access_iterator_tag, dense_random_access_iterator_tag> {
Chris@16:         typedef packed_random_access_iterator_tag iterator_category;
Chris@16:     };
Chris@16: 
Chris@16:     template<class I>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     void increment (I &it, const I &it_end, typename I::difference_type compare, packed_random_access_iterator_tag) {
Chris@16:         it += (std::min) (compare, it_end - it);
Chris@16:     }
Chris@16:     template<class I>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     void increment (I &it, const I &/* it_end */, typename I::difference_type /* compare */, sparse_bidirectional_iterator_tag) {
Chris@16:         ++ it;
Chris@16:     }
Chris@16:     template<class I>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     void increment (I &it, const I &it_end, typename I::difference_type compare) {
Chris@16:         increment (it, it_end, compare, typename I::iterator_category ());
Chris@16:     }
Chris@16: 
Chris@16:     template<class I>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     void increment (I &it, const I &it_end) {
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         I cit (it);
Chris@16:         while (cit != it_end) {
Chris@16:             BOOST_UBLAS_CHECK (*cit == typename I::value_type/*zero*/(), internal_logic ());
Chris@16:             ++ cit;
Chris@16:         }
Chris@16: #endif
Chris@16:         it = it_end;
Chris@16:     }
Chris@16: 
Chris@16:     namespace detail {
Chris@16: 
Chris@16:         // specialisation which define whether a type has a trivial constructor
Chris@16:         // or not. This is used by array types.
Chris@16:         template<typename T>
Chris@16:         struct has_trivial_constructor : public boost::has_trivial_constructor<T> {};
Chris@16: 
Chris@16:         template<typename T>
Chris@16:         struct has_trivial_destructor : public boost::has_trivial_destructor<T> {};
Chris@16: 
Chris@16:         template<typename FLT>
Chris@16:         struct has_trivial_constructor<std::complex<FLT> > : public has_trivial_constructor<FLT> {};
Chris@16:         
Chris@16:         template<typename FLT>
Chris@16:         struct has_trivial_destructor<std::complex<FLT> > : public has_trivial_destructor<FLT> {};
Chris@16: 
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a constant matrix or vector CONTAINER.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class E >
Chris@16:     struct container_view_traits {
Chris@16:         /// type of indices
Chris@16:         typedef typename E::size_type             size_type;
Chris@16:         /// type of differences of indices
Chris@16:         typedef typename E::difference_type       difference_type;
Chris@16: 
Chris@16:         /// storage category: \c unknown_storage_tag, \c dense_tag, \c packed_tag, ...
Chris@16:         typedef typename E::storage_category      storage_category;
Chris@16: 
Chris@16:         /// type of elements
Chris@16:         typedef typename E::value_type            value_type;
Chris@16:         /// const reference to an element
Chris@16:         typedef typename E::const_reference       const_reference;
Chris@16:   
Chris@16:         /// type used in expressions to mark a reference to this class (usually a const container_reference<const E> or the class itself)
Chris@16:         typedef typename E::const_closure_type    const_closure_type;
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract additional type information from a mutable matrix or vector CONTAINER.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class E >
Chris@16:     struct mutable_container_traits {
Chris@16:         /// reference to an element
Chris@16:         typedef typename E::reference             reference;
Chris@16:   
Chris@16:         /// type used in expressions to mark a reference to this class (usually a container_reference<E> or the class itself)
Chris@16:         typedef typename E::closure_type          closure_type;
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a matrix or vector CONTAINER.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class E >
Chris@16:     struct container_traits 
Chris@16:         : container_view_traits<E>, mutable_container_traits<E> {
Chris@16: 
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a constant MATRIX.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class MATRIX >
Chris@16:     struct matrix_view_traits : container_view_traits <MATRIX> {
Chris@16: 
Chris@16:         /// orientation of the matrix, either \c row_major_tag, \c column_major_tag or \c unknown_orientation_tag
Chris@16:         typedef typename MATRIX::orientation_category  orientation_category;
Chris@16:   
Chris@16:         /// row iterator for the matrix
Chris@16:         typedef typename MATRIX::const_iterator1  const_iterator1;
Chris@16: 
Chris@16:         /// column iterator for the matrix
Chris@16:         typedef typename MATRIX::const_iterator2  const_iterator2;
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract additional type information from a mutable MATRIX.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class MATRIX >
Chris@16:     struct mutable_matrix_traits 
Chris@16:         : mutable_container_traits <MATRIX> {
Chris@16: 
Chris@16:         /// row iterator for the matrix
Chris@16:         typedef typename MATRIX::iterator1  iterator1;
Chris@16: 
Chris@16:         /// column iterator for the matrix
Chris@16:         typedef typename MATRIX::iterator2  iterator2;
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a MATRIX.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class MATRIX >
Chris@16:     struct matrix_traits 
Chris@16:         : matrix_view_traits <MATRIX>, mutable_matrix_traits <MATRIX> {
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a VECTOR.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class VECTOR >
Chris@16:     struct vector_view_traits : container_view_traits <VECTOR> {
Chris@16: 
Chris@16:         /// iterator for the VECTOR
Chris@16:         typedef typename VECTOR::const_iterator  const_iterator;
Chris@16: 
Chris@16:         /// iterator pointing to the first element
Chris@16:         static
Chris@16:         const_iterator begin(const VECTOR & v) {
Chris@16:             return v.begin();
Chris@16:         }
Chris@16:         /// iterator pointing behind the last element
Chris@16:         static
Chris@16:         const_iterator end(const VECTOR & v) {
Chris@16:             return v.end();
Chris@16:         }
Chris@16: 
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a VECTOR.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class VECTOR >
Chris@16:     struct mutable_vector_traits : mutable_container_traits <VECTOR> {
Chris@16:         /// iterator for the VECTOR
Chris@16:         typedef typename VECTOR::iterator  iterator;
Chris@16: 
Chris@16:         /// iterator pointing to the first element
Chris@16:         static
Chris@16:         iterator begin(VECTOR & v) {
Chris@16:             return v.begin();
Chris@16:         }
Chris@16: 
Chris@16:         /// iterator pointing behind the last element
Chris@16:         static
Chris@16:         iterator end(VECTOR & v) {
Chris@16:             return v.end();
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16:     /**  \brief Traits class to extract type information from a VECTOR.
Chris@16:      *
Chris@16:      */
Chris@16:     template < class VECTOR >
Chris@16:     struct vector_traits 
Chris@16:         : vector_view_traits <VECTOR>, mutable_vector_traits <VECTOR> {
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16:     // Note: specializations for T[N] and T[M][N] have been moved to traits/c_array.hpp
Chris@16: 
Chris@16: }}}
Chris@16: 
Chris@16: #endif