sl@0: //
sl@0: //  Copyright (c) 2000-2002
sl@0: //  Joerg Walter, Mathias Koch
sl@0: //
sl@0: //  Permission to use, copy, modify, distribute and sell this software
sl@0: //  and its documentation for any purpose is hereby granted without fee,
sl@0: //  provided that the above copyright notice appear in all copies and
sl@0: //  that both that copyright notice and this permission notice appear
sl@0: //  in supporting documentation.  The authors make no representations
sl@0: //  about the suitability of this software for any purpose.
sl@0: //  It is provided "as is" without express or implied warranty.
sl@0: //
sl@0: //  The authors gratefully acknowledge the support of
sl@0: //  GeNeSys mbH & Co. KG in producing this work.
sl@0: //
sl@0: 
sl@0: #ifndef _BOOST_UBLAS_FUNCTIONAL_
sl@0: #define _BOOST_UBLAS_FUNCTIONAL_
sl@0: 
sl@0: #include <functional>
sl@0: 
sl@0: #include <boost/numeric/ublas/traits.hpp>
sl@0: #ifdef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0: #include <boost/numeric/ublas/detail/duff.hpp>
sl@0: #endif
sl@0: #ifdef BOOST_UBLAS_USE_SIMD
sl@0: #include <boost/numeric/ublas/detail/raw.hpp>
sl@0: #else
sl@0: namespace boost { namespace numeric { namespace ublas { namespace raw {
sl@0: }}}}
sl@0: #endif
sl@0: #ifdef BOOST_UBLAS_HAVE_BINDINGS
sl@0: #include <boost/numeric/bindings/traits/std_vector.hpp>
sl@0: #include <boost/numeric/bindings/traits/ublas_vector.hpp>
sl@0: #include <boost/numeric/bindings/traits/ublas_matrix.hpp>
sl@0: #include <boost/numeric/bindings/atlas/cblas.hpp>
sl@0: #endif
sl@0: 
sl@0: #include <boost/numeric/ublas/detail/definitions.hpp>
sl@0: 
sl@0: 
sl@0: 
sl@0: namespace boost { namespace numeric { namespace ublas {
sl@0: 
sl@0:     // Scalar functors
sl@0: 
sl@0:     // Unary
sl@0:     template<class T>
sl@0:     struct scalar_unary_functor {
sl@0:         typedef T value_type;
sl@0:         typedef typename type_traits<T>::const_reference argument_type;
sl@0:         typedef typename type_traits<T>::value_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct scalar_identity:
sl@0:         public scalar_unary_functor<T> {
sl@0:         typedef typename scalar_unary_functor<T>::argument_type argument_type;
sl@0:         typedef typename scalar_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument_type t) {
sl@0:             return t;
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct scalar_negate:
sl@0:         public scalar_unary_functor<T> {
sl@0:         typedef typename scalar_unary_functor<T>::argument_type argument_type;
sl@0:         typedef typename scalar_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument_type t) {
sl@0:             return - t;
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct scalar_conj:
sl@0:         public scalar_unary_functor<T> {
sl@0:         typedef typename scalar_unary_functor<T>::value_type value_type;
sl@0:         typedef typename scalar_unary_functor<T>::argument_type argument_type;
sl@0:         typedef typename scalar_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument_type t) {
sl@0:             return type_traits<value_type>::conj (t);
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Unary returning real
sl@0:     template<class T>
sl@0:     struct scalar_real_unary_functor {
sl@0:         typedef T value_type;
sl@0:         typedef typename type_traits<T>::const_reference argument_type;
sl@0:         typedef typename type_traits<T>::real_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct scalar_real:
sl@0:         public scalar_real_unary_functor<T> {
sl@0:         typedef typename scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename scalar_real_unary_functor<T>::argument_type argument_type;
sl@0:         typedef typename scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument_type t) {
sl@0:             return type_traits<value_type>::real (t);
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct scalar_imag:
sl@0:         public scalar_real_unary_functor<T> {
sl@0:         typedef typename scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename scalar_real_unary_functor<T>::argument_type argument_type;
sl@0:         typedef typename scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument_type t) {
sl@0:             return type_traits<value_type>::imag (t);
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Binary
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_binary_functor {
sl@0:         typedef typename type_traits<T1>::const_reference argument1_type;
sl@0:         typedef typename type_traits<T2>::const_reference argument2_type;
sl@0:         typedef typename promote_traits<T1, T2>::promote_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_plus:
sl@0:         public scalar_binary_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument1_type t1, argument2_type t2) {
sl@0:             return t1 + t2;
sl@0:         }
sl@0:     };
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_minus:
sl@0:         public scalar_binary_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument1_type t1, argument2_type t2) {
sl@0:             return t1 - t2;
sl@0:         }
sl@0:     };
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_multiplies:
sl@0:         public scalar_binary_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument1_type t1, argument2_type t2) {
sl@0:             return t1 * t2;
sl@0:         }
sl@0:     };
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_divides:
sl@0:         public scalar_binary_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type;
sl@0:         typedef typename scalar_binary_functor<T1, T2>::result_type result_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (argument1_type t1, argument2_type t2) {
sl@0:             return t1 / t2;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_binary_assign_functor {
sl@0:         // ISSUE Remove reference to avoid reference to reference problems
sl@0:         typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type;
sl@0:         typedef typename type_traits<T2>::const_reference argument2_type;
sl@0:     };
sl@0: 
sl@0:     struct assign_tag {};
sl@0:     struct computed_assign_tag {};
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_assign:
sl@0:         public scalar_binary_assign_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type;
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:         static const bool computed ;
sl@0: #else
sl@0:         static const bool computed = false ;
sl@0: #endif
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             t1 = t2;
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_assign<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0: 
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:     template<class T1, class T2>
sl@0:     const bool scalar_assign<T1,T2>::computed = false;
sl@0: #endif
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_plus_assign:
sl@0:         public scalar_binary_assign_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type;
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:         static const bool computed ;
sl@0: #else
sl@0:       static const bool computed = true ;
sl@0: #endif
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             t1 += t2;
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_plus_assign<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0: 
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:     template<class T1, class T2>
sl@0:     const bool scalar_plus_assign<T1,T2>::computed = true;
sl@0: #endif
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_minus_assign:
sl@0:         public scalar_binary_assign_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type;
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:         static const bool computed ;
sl@0: #else
sl@0:         static const bool computed = true ;
sl@0: #endif
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             t1 -= t2;
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_minus_assign<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0: 
sl@0: #if BOOST_WORKAROUND( __IBMCPP__, <=600 )
sl@0:     template<class T1, class T2>
sl@0:     const bool scalar_minus_assign<T1,T2>::computed = true;
sl@0: #endif
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_multiplies_assign:
sl@0:         public scalar_binary_assign_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type;
sl@0:         static const bool computed = true;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             t1 *= t2;
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_multiplies_assign<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_divides_assign:
sl@0:         public scalar_binary_assign_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type;
sl@0:         static const bool computed ;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             t1 /= t2;
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_divides_assign<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0:     template<class T1, class T2>
sl@0:     const bool scalar_divides_assign<T1,T2>::computed = true;
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_binary_swap_functor {
sl@0:         typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type;
sl@0:         typedef typename type_traits<typename boost::remove_reference<T2>::type>::reference argument2_type;
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2>
sl@0:     struct scalar_swap:
sl@0:         public scalar_binary_swap_functor<T1, T2> {
sl@0:         typedef typename scalar_binary_swap_functor<T1, T2>::argument1_type argument1_type;
sl@0:         typedef typename scalar_binary_swap_functor<T1, T2>::argument2_type argument2_type;
sl@0: 
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         void apply (argument1_type t1, argument2_type t2) {
sl@0:             std::swap (t1, t2);
sl@0:         }
sl@0: 
sl@0:         template<class U1, class U2>
sl@0:         struct rebind {
sl@0:             typedef scalar_swap<U1, U2> other;
sl@0:         };
sl@0:     };
sl@0: 
sl@0:     // Vector functors
sl@0: 
sl@0:     // Unary returning scalar
sl@0:     template<class T>
sl@0:     struct vector_scalar_unary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef T value_type;
sl@0:         typedef T result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct vector_sum: 
sl@0:         public vector_scalar_unary_functor<T> {
sl@0:         typedef typename vector_scalar_unary_functor<T>::size_type size_type;
sl@0:         typedef typename vector_scalar_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_unary_functor<T>::value_type value_type;
sl@0:         typedef typename vector_scalar_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E> &e) { 
sl@0:             result_type t = result_type (0);
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i)
sl@0:                 t += e () (i);
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I it) { 
sl@0:             result_type t = result_type (0);
sl@0:             while (-- size >= 0)
sl@0:                 t += *it, ++ it;
sl@0:             return t; 
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I it, const I &it_end) {
sl@0:             result_type t = result_type (0);
sl@0:             while (it != it_end) 
sl@0:                 t += *it, ++ it;
sl@0:             return t; 
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Unary returning real scalar 
sl@0:     template<class T>
sl@0:     struct vector_scalar_real_unary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef T value_type;
sl@0:         typedef typename type_traits<T>::real_type real_type;
sl@0:         typedef real_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct vector_norm_1:
sl@0:         public vector_scalar_real_unary_functor<T> {
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E> &e) {
sl@0:             real_type t = real_type ();
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i) {
sl@0:                 real_type u (type_traits<value_type>::type_abs (e () (i)));
sl@0:                 t += u;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I it) {
sl@0:             real_type t = real_type ();
sl@0:             while (-- size >= 0) {
sl@0:                 real_type u (type_traits<value_type>::norm_1 (*it));
sl@0:                 t += u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I it, const I &it_end) {
sl@0:             real_type t = real_type ();
sl@0:             while (it != it_end) {
sl@0:                 real_type u (type_traits<value_type>::norm_1 (*it));
sl@0:                 t += u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct vector_norm_2:
sl@0:         public vector_scalar_real_unary_functor<T> {
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E> &e) {
sl@0: #ifndef BOOST_UBLAS_SCALED_NORM
sl@0:             real_type t = real_type ();
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (e () (i)));
sl@0:                 t +=  u * u;
sl@0:             }
sl@0:             return type_traits<real_type>::type_sqrt (t);
sl@0: #else
sl@0:             real_type scale = real_type ();
sl@0:             real_type sum_squares (1);
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (e () (i)));
sl@0:                 if (scale < u) {
sl@0:                     real_type v (scale / u);
sl@0:                     sum_squares = sum_squares * v * v + real_type (1);
sl@0:                     scale = u;
sl@0:                 } else {
sl@0:                     real_type v (u / scale);
sl@0:                     sum_squares += v * v;
sl@0:                 }
sl@0:             }
sl@0:             return scale * type_traits<real_type>::type_sqrt (sum_squares);
sl@0: #endif
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I it) {
sl@0: #ifndef BOOST_UBLAS_SCALED_NORM
sl@0:             real_type t = real_type ();
sl@0:             while (-- size >= 0) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (*it));
sl@0:                 t +=  u * u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return type_traits<real_type>::type_sqrt (t);
sl@0: #else
sl@0:             real_type scale = real_type ();
sl@0:             real_type sum_squares (1);
sl@0:             while (-- size >= 0) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (*it));
sl@0:                 if (scale < u) {
sl@0:                     real_type v (scale / u);
sl@0:                     sum_squares = sum_squares * v * v + real_type (1);
sl@0:                     scale = u;
sl@0:                 } else {
sl@0:                     real_type v (u / scale);
sl@0:                     sum_squares += v * v;
sl@0:                 }
sl@0:                 ++ it;
sl@0:             }
sl@0:             return scale * type_traits<real_type>::type_sqrt (sum_squares);
sl@0: #endif
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I it, const I &it_end) {
sl@0: #ifndef BOOST_UBLAS_SCALED_NORM
sl@0:             real_type t = real_type ();
sl@0:             while (it != it_end) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (*it));
sl@0:                 t +=  u * u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return type_traits<real_type>::type_sqrt (t);
sl@0: #else
sl@0:             real_type scale = real_type ();
sl@0:             real_type sum_squares (1);
sl@0:             while (it != it_end) {
sl@0:                 real_type u (type_traits<value_type>::norm_2 (*it));
sl@0:                 if (scale < u) {
sl@0:                     real_type v (scale / u);
sl@0:                     sum_squares = sum_squares * v * v + real_type (1);
sl@0:                     scale = u;
sl@0:                 } else {
sl@0:                     real_type v (u / scale);
sl@0:                     sum_squares += v * v;
sl@0:                 }
sl@0:                 ++ it;
sl@0:             }
sl@0:             return scale * type_traits<real_type>::type_sqrt (sum_squares);
sl@0: #endif
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct vector_norm_inf:
sl@0:         public vector_scalar_real_unary_functor<T> {
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename vector_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E> &e) {
sl@0:             real_type t = real_type ();
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (e () (i)));
sl@0:                 if (u > t)
sl@0:                     t = u;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I it) {
sl@0:             real_type t = real_type ();
sl@0:             while (-- size >= 0) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (*it));
sl@0:                 if (u > t)
sl@0:                     t = u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I it, const I &it_end) { 
sl@0:             real_type t = real_type ();
sl@0:             while (it != it_end) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (*it));
sl@0:                 if (u > t) 
sl@0:                     t = u;
sl@0:                 ++ it;
sl@0:             }
sl@0:             return t; 
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Unary returning index
sl@0:     template<class T>
sl@0:     struct vector_scalar_index_unary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef T value_type;
sl@0:         typedef typename type_traits<T>::real_type real_type;
sl@0:         typedef size_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct vector_index_norm_inf:
sl@0:         public vector_scalar_index_unary_functor<T> {
sl@0:         typedef typename vector_scalar_index_unary_functor<T>::size_type size_type;
sl@0:         typedef typename vector_scalar_index_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_index_unary_functor<T>::value_type value_type;
sl@0:         typedef typename vector_scalar_index_unary_functor<T>::real_type real_type;
sl@0:         typedef typename vector_scalar_index_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E> &e) {
sl@0:             // ISSUE For CBLAS compatibility return 0 index in empty case
sl@0:             result_type i_norm_inf (0);
sl@0:             real_type t = real_type ();
sl@0:             size_type size (e ().size ());
sl@0:             for (size_type i = 0; i < size; ++ i) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (e () (i)));
sl@0:                 if (u > t) {
sl@0:                     i_norm_inf = i;
sl@0:                     t = u;
sl@0:                 }
sl@0:             }
sl@0:             return i_norm_inf;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I it) {
sl@0:             // ISSUE For CBLAS compatibility return 0 index in empty case
sl@0:             result_type i_norm_inf (0);
sl@0:             real_type t = real_type ();
sl@0:             while (-- size >= 0) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (*it));
sl@0:                 if (u > t) {
sl@0:                     i_norm_inf = it.index ();
sl@0:                     t = u;
sl@0:                 }
sl@0:                 ++ it;
sl@0:             }
sl@0:             return i_norm_inf;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I it, const I &it_end) {
sl@0:             // ISSUE For CBLAS compatibility return 0 index in empty case
sl@0:             result_type i_norm_inf (0);
sl@0:             real_type t = real_type ();
sl@0:             while (it != it_end) {
sl@0:                 real_type u (type_traits<value_type>::norm_inf (*it));
sl@0:                 if (u > t) {
sl@0:                     i_norm_inf = it.index ();
sl@0:                     t = u;
sl@0:                 }
sl@0:                 ++ it;
sl@0:             }
sl@0:             return i_norm_inf;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Binary returning scalar
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct vector_scalar_binary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef TR value_type;
sl@0:         typedef TR result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct vector_inner_prod:
sl@0:         public vector_scalar_binary_functor<T1, T2, TR> {
sl@0:         typedef typename vector_scalar_binary_functor<T1, T2, TR>::size_type size_type ;
sl@0:         typedef typename vector_scalar_binary_functor<T1, T2, TR>::difference_type difference_type;
sl@0:         typedef typename vector_scalar_binary_functor<T1, T2, TR>::value_type value_type;
sl@0:         typedef typename vector_scalar_binary_functor<T1, T2, TR>::result_type result_type;
sl@0: 
sl@0:         template<class C1, class C2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_container<C1> &c1,
sl@0:                            const vector_container<C2> &c2) {
sl@0: #ifdef BOOST_UBLAS_USE_SIMD
sl@0:             using namespace raw;
sl@0:             size_type size (BOOST_UBLAS_SAME (c1 ().size (), c2 ().size ()));
sl@0:             const T1 *data1 = data_const (c1 ());
sl@0:             const T2 *data2 = data_const (c2 ());
sl@0:             size_type s1 = stride (c1 ());
sl@0:             size_type s2 = stride (c2 ());
sl@0:             result_type t = result_type (0);
sl@0:             if (s1 == 1 && s2 == 1) {
sl@0:                 for (size_type i = 0; i < size; ++ i)
sl@0:                     t += data1 [i] * data2 [i];
sl@0:             } else if (s2 == 1) {
sl@0:                 for (size_type i = 0, i1 = 0; i < size; ++ i, i1 += s1)
sl@0:                     t += data1 [i1] * data2 [i];
sl@0:             } else if (s1 == 1) {
sl@0:                 for (size_type i = 0, i2 = 0; i < size; ++ i, i2 += s2)
sl@0:                     t += data1 [i] * data2 [i2];
sl@0:             } else {
sl@0:                 for (size_type i = 0, i1 = 0, i2 = 0; i < size; ++ i, i1 += s1, i2 += s2)
sl@0:                     t += data1 [i1] * data2 [i2];
sl@0:             }
sl@0:             return t;
sl@0: #elif defined(BOOST_UBLAS_HAVE_BINDINGS)
sl@0:             return boost::numeric::bindings::atlas::dot (c1 (), c2 ());
sl@0: #else
sl@0:             return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2));
sl@0: #endif
sl@0:         }
sl@0:         template<class E1, class E2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E1> &e1,
sl@0:                            const vector_expression<E2> &e2) {
sl@0:             size_type size (BOOST_UBLAS_SAME (e1 ().size (), e2 ().size ()));
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             for (size_type i = 0; i < size; ++ i)
sl@0:                 t += e1 () (i) * e2 () (i);
sl@0: #else
sl@0:             size_type i (0);
sl@0:             DD (size, 4, r, (t += e1 () (i) * e2 () (i), ++ i));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I1 it1, I2 it2) {
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0: #else
sl@0:             DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) {
sl@0:             result_type t = result_type (0);
sl@0:             difference_type it1_size (it1_end - it1);
sl@0:             difference_type it2_size (it2_end - it2);
sl@0:             difference_type diff (0);
sl@0:             if (it1_size > 0 && it2_size > 0)
sl@0:                 diff = it2.index () - it1.index ();
sl@0:             if (diff != 0) {
sl@0:                 difference_type size = (std::min) (diff, it1_size);
sl@0:                 if (size > 0) {
sl@0:                     it1 += size;
sl@0:                     it1_size -= size;
sl@0:                     diff -= size;
sl@0:                 }
sl@0:                 size = (std::min) (- diff, it2_size);
sl@0:                 if (size > 0) {
sl@0:                     it2 += size;
sl@0:                     it2_size -= size;
sl@0:                     diff += size;
sl@0:                 }
sl@0:             }
sl@0:             difference_type size ((std::min) (it1_size, it2_size));
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             if (it1 != it1_end && it2 != it2_end) {
sl@0:                 size_type it1_index = it1.index (), it2_index = it2.index ();
sl@0:                 while (true) {
sl@0:                     difference_type compare = it1_index - it2_index;
sl@0:                     if (compare == 0) {
sl@0:                         t += *it1 * *it2, ++ it1, ++ it2;
sl@0:                         if (it1 != it1_end && it2 != it2_end) {
sl@0:                             it1_index = it1.index ();
sl@0:                             it2_index = it2.index ();
sl@0:                         } else
sl@0:                             break;
sl@0:                     } else if (compare < 0) {
sl@0:                         increment (it1, it1_end, - compare);
sl@0:                         if (it1 != it1_end)
sl@0:                             it1_index = it1.index ();
sl@0:                         else
sl@0:                             break;
sl@0:                     } else if (compare > 0) {
sl@0:                         increment (it2, it2_end, compare);
sl@0:                         if (it2 != it2_end)
sl@0:                             it2_index = it2.index ();
sl@0:                         else
sl@0:                             break;
sl@0:                     }
sl@0:                 }
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Matrix functors
sl@0: 
sl@0:     // Binary returning vector
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct matrix_vector_binary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef TR value_type;
sl@0:         typedef TR result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct matrix_vector_prod1:
sl@0:         public matrix_vector_binary_functor<T1, T2, TR> {
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::size_type size_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::difference_type difference_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::value_type value_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::result_type result_type;
sl@0: 
sl@0:         template<class C1, class C2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_container<C1> &c1,
sl@0:                            const vector_container<C2> &c2,
sl@0:                            size_type i) {
sl@0: #ifdef BOOST_UBLAS_USE_SIMD
sl@0:             using namespace raw;
sl@0:             size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().size ());
sl@0:             const T1 *data1 = data_const (c1 ()) + i * stride1 (c1 ());
sl@0:             const T2 *data2 = data_const (c2 ());
sl@0:             size_type s1 = stride2 (c1 ());
sl@0:             size_type s2 = stride (c2 ());
sl@0:             result_type t = result_type (0);
sl@0:             if (s1 == 1 && s2 == 1) {
sl@0:                 for (size_type j = 0; j < size; ++ j)
sl@0:                     t += data1 [j] * data2 [j];
sl@0:             } else if (s2 == 1) {
sl@0:                 for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1)
sl@0:                     t += data1 [j1] * data2 [j];
sl@0:             } else if (s1 == 1) {
sl@0:                 for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2)
sl@0:                     t += data1 [j] * data2 [j2];
sl@0:             } else {
sl@0:                 for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2)
sl@0:                     t += data1 [j1] * data2 [j2];
sl@0:             }
sl@0:             return t;
sl@0: #elif defined(BOOST_UBLAS_HAVE_BINDINGS)
sl@0:             return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ());
sl@0: #else
sl@0:             return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2, i));
sl@0: #endif
sl@0:         }
sl@0:         template<class E1, class E2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_expression<E1> &e1,
sl@0:                                  const vector_expression<E2> &e2,
sl@0:                            size_type i) {
sl@0:             size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size ());
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             for (size_type j = 0; j < size; ++ j)
sl@0:                 t += e1 () (i, j) * e2 () (j);
sl@0: #else
sl@0:             size_type j (0);
sl@0:             DD (size, 4, r, (t += e1 () (i, j) * e2 () (j), ++ j));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I1 it1, I2 it2) {
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0: #else
sl@0:             DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) {
sl@0:             result_type t = result_type (0);
sl@0:             difference_type it1_size (it1_end - it1);
sl@0:             difference_type it2_size (it2_end - it2);
sl@0:             difference_type diff (0);
sl@0:             if (it1_size > 0 && it2_size > 0)
sl@0:                 diff = it2.index () - it1.index2 ();
sl@0:             if (diff != 0) {
sl@0:                 difference_type size = (std::min) (diff, it1_size);
sl@0:                 if (size > 0) {
sl@0:                     it1 += size;
sl@0:                     it1_size -= size;
sl@0:                     diff -= size;
sl@0:                 }
sl@0:                 size = (std::min) (- diff, it2_size);
sl@0:                 if (size > 0) {
sl@0:                     it2 += size;
sl@0:                     it2_size -= size;
sl@0:                     diff += size;
sl@0:                 }
sl@0:             }
sl@0:             difference_type size ((std::min) (it1_size, it2_size));
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end,
sl@0:                                  sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             if (it1 != it1_end && it2 != it2_end) {
sl@0:                 size_type it1_index = it1.index2 (), it2_index = it2.index ();
sl@0:                 while (true) {
sl@0:                     difference_type compare = it1_index - it2_index;
sl@0:                     if (compare == 0) {
sl@0:                         t += *it1 * *it2, ++ it1, ++ it2;
sl@0:                         if (it1 != it1_end && it2 != it2_end) {
sl@0:                             it1_index = it1.index2 ();
sl@0:                             it2_index = it2.index ();
sl@0:                         } else
sl@0:                             break;
sl@0:                     } else if (compare < 0) {
sl@0:                         increment (it1, it1_end, - compare);
sl@0:                         if (it1 != it1_end)
sl@0:                             it1_index = it1.index2 ();
sl@0:                         else
sl@0:                             break;
sl@0:                     } else if (compare > 0) {
sl@0:                         increment (it2, it2_end, compare);
sl@0:                         if (it2 != it2_end)
sl@0:                             it2_index = it2.index ();
sl@0:                         else
sl@0:                             break;
sl@0:                     }
sl@0:                 }
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */,
sl@0:                                  sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             while (it1 != it1_end) {
sl@0:                 t += *it1 * it2 () (it1.index2 ());
sl@0:                 ++ it1;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Packed sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end,
sl@0:                                  packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             while (it2 != it2_end) {
sl@0:                 t += it1 () (it1.index1 (), it2.index ()) * *it2;
sl@0:                 ++ it2;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Another dispatcher
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end,
sl@0:                                  sparse_bidirectional_iterator_tag) {
sl@0:             typedef typename I1::iterator_category iterator1_category;
sl@0:             typedef typename I2::iterator_category iterator2_category;
sl@0:             return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ());
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct matrix_vector_prod2:
sl@0:         public matrix_vector_binary_functor<T1, T2, TR> {
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::size_type size_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::difference_type difference_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::value_type value_type;
sl@0:         typedef typename matrix_vector_binary_functor<T1, T2, TR>::result_type result_type;
sl@0: 
sl@0:         template<class C1, class C2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_container<C1> &c1,
sl@0:                            const matrix_container<C2> &c2,
sl@0:                            size_type i) {
sl@0: #ifdef BOOST_UBLAS_USE_SIMD
sl@0:             using namespace raw;
sl@0:             size_type size = BOOST_UBLAS_SAME (c1 ().size (), c2 ().size1 ());
sl@0:             const T1 *data1 = data_const (c1 ());
sl@0:             const T2 *data2 = data_const (c2 ()) + i * stride2 (c2 ());
sl@0:             size_type s1 = stride (c1 ());
sl@0:             size_type s2 = stride1 (c2 ());
sl@0:             result_type t = result_type (0);
sl@0:             if (s1 == 1 && s2 == 1) {
sl@0:                 for (size_type j = 0; j < size; ++ j)
sl@0:                     t += data1 [j] * data2 [j];
sl@0:             } else if (s2 == 1) {
sl@0:                 for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1)
sl@0:                     t += data1 [j1] * data2 [j];
sl@0:             } else if (s1 == 1) {
sl@0:                 for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2)
sl@0:                     t += data1 [j] * data2 [j2];
sl@0:             } else {
sl@0:                 for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2)
sl@0:                     t += data1 [j1] * data2 [j2];
sl@0:             }
sl@0:             return t;
sl@0: #elif defined(BOOST_UBLAS_HAVE_BINDINGS)
sl@0:             return boost::numeric::bindings::atlas::dot (c1 (), c2 ().column (i));
sl@0: #else
sl@0:             return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i));
sl@0: #endif
sl@0:         }
sl@0:         template<class E1, class E2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const vector_expression<E1> &e1,
sl@0:                                  const matrix_expression<E2> &e2,
sl@0:                            size_type i) {
sl@0:             size_type size = BOOST_UBLAS_SAME (e1 ().size (), e2 ().size1 ());
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             for (size_type j = 0; j < size; ++ j)
sl@0:                 t += e1 () (j) * e2 () (j, i);
sl@0: #else
sl@0:             size_type j (0);
sl@0:             DD (size, 4, r, (t += e1 () (j) * e2 () (j, i), ++ j));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I1 it1, I2 it2) {
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0: #else
sl@0:             DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) {
sl@0:             result_type t = result_type (0);
sl@0:             difference_type it1_size (it1_end - it1);
sl@0:             difference_type it2_size (it2_end - it2);
sl@0:             difference_type diff (0);
sl@0:             if (it1_size > 0 && it2_size > 0)
sl@0:                 diff = it2.index1 () - it1.index ();
sl@0:             if (diff != 0) {
sl@0:                 difference_type size = (std::min) (diff, it1_size);
sl@0:                 if (size > 0) {
sl@0:                     it1 += size;
sl@0:                     it1_size -= size;
sl@0:                     diff -= size;
sl@0:                 }
sl@0:                 size = (std::min) (- diff, it2_size);
sl@0:                 if (size > 0) {
sl@0:                     it2 += size;
sl@0:                     it2_size -= size;
sl@0:                     diff += size;
sl@0:                 }
sl@0:             }
sl@0:             difference_type size ((std::min) (it1_size, it2_size));
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end,
sl@0:                                  sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             if (it1 != it1_end && it2 != it2_end) {
sl@0:                 size_type it1_index = it1.index (), it2_index = it2.index1 ();
sl@0:                 while (true) {
sl@0:                     difference_type compare = it1_index - it2_index;
sl@0:                     if (compare == 0) {
sl@0:                         t += *it1 * *it2, ++ it1, ++ it2;
sl@0:                         if (it1 != it1_end && it2 != it2_end) {
sl@0:                             it1_index = it1.index ();
sl@0:                             it2_index = it2.index1 ();
sl@0:                         } else
sl@0:                             break;
sl@0:                     } else if (compare < 0) {
sl@0:                         increment (it1, it1_end, - compare);
sl@0:                         if (it1 != it1_end)
sl@0:                             it1_index = it1.index ();
sl@0:                         else
sl@0:                             break;
sl@0:                     } else if (compare > 0) {
sl@0:                         increment (it2, it2_end, compare);
sl@0:                         if (it2 != it2_end)
sl@0:                             it2_index = it2.index1 ();
sl@0:                         else
sl@0:                             break;
sl@0:                     }
sl@0:                 }
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Packed sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end,
sl@0:                                  packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             while (it2 != it2_end) {
sl@0:                 t += it1 () (it2.index1 ()) * *it2;
sl@0:                 ++ it2;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */,
sl@0:                                  sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             while (it1 != it1_end) {
sl@0:                 t += *it1 * it2 () (it1.index (), it2.index2 ());
sl@0:                 ++ it1;
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:         // Another dispatcher
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end,
sl@0:                                  sparse_bidirectional_iterator_tag) {
sl@0:             typedef typename I1::iterator_category iterator1_category;
sl@0:             typedef typename I2::iterator_category iterator2_category;
sl@0:             return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ());
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Binary returning matrix
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct matrix_matrix_binary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef TR value_type;
sl@0:         typedef TR result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T1, class T2, class TR>
sl@0:     struct matrix_matrix_prod:
sl@0:         public matrix_matrix_binary_functor<T1, T2, TR> {
sl@0:         typedef typename matrix_matrix_binary_functor<T1, T2, TR>::size_type size_type;
sl@0:         typedef typename matrix_matrix_binary_functor<T1, T2, TR>::difference_type difference_type;
sl@0:         typedef typename matrix_matrix_binary_functor<T1, T2, TR>::value_type value_type;
sl@0:         typedef typename matrix_matrix_binary_functor<T1, T2, TR>::result_type result_type;
sl@0: 
sl@0:         template<class C1, class C2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_container<C1> &c1,
sl@0:                            const matrix_container<C2> &c2,
sl@0:                            size_type i, size_type j) {
sl@0: #ifdef BOOST_UBLAS_USE_SIMD
sl@0:             using namespace raw;
sl@0:             size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().sizc1 ());
sl@0:             const T1 *data1 = data_const (c1 ()) + i * stride1 (c1 ());
sl@0:             const T2 *data2 = data_const (c2 ()) + j * stride2 (c2 ());
sl@0:             size_type s1 = stride2 (c1 ());
sl@0:             size_type s2 = stride1 (c2 ());
sl@0:             result_type t = result_type (0);
sl@0:             if (s1 == 1 && s2 == 1) {
sl@0:                 for (size_type k = 0; k < size; ++ k)
sl@0:                     t += data1 [k] * data2 [k];
sl@0:             } else if (s2 == 1) {
sl@0:                 for (size_type k = 0, k1 = 0; k < size; ++ k, k1 += s1)
sl@0:                     t += data1 [k1] * data2 [k];
sl@0:             } else if (s1 == 1) {
sl@0:                 for (size_type k = 0, k2 = 0; k < size; ++ k, k2 += s2)
sl@0:                     t += data1 [k] * data2 [k2];
sl@0:             } else {
sl@0:                 for (size_type k = 0, k1 = 0, k2 = 0; k < size; ++ k, k1 += s1, k2 += s2)
sl@0:                     t += data1 [k1] * data2 [k2];
sl@0:             }
sl@0:             return t;
sl@0: #elif defined(BOOST_UBLAS_HAVE_BINDINGS)
sl@0:             return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ().column (j));
sl@0: #else
sl@0:             return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i));
sl@0: #endif
sl@0:         }
sl@0:         template<class E1, class E2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_expression<E1> &e1,
sl@0:                                  const matrix_expression<E2> &e2,
sl@0:                            size_type i, size_type j) {
sl@0:             size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ());
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             for (size_type k = 0; k < size; ++ k)
sl@0:                 t += e1 () (i, k) * e2 () (k, j);
sl@0: #else
sl@0:             size_type k (0);
sl@0:             DD (size, 4, r, (t += e1 () (i, k) * e2 () (k, j), ++ k));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Dense case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (difference_type size, I1 it1, I2 it2) {
sl@0:             result_type t = result_type (0);
sl@0: #ifndef BOOST_UBLAS_USE_DUFF_DEVICE
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0: #else
sl@0:             DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2));
sl@0: #endif
sl@0:             return t;
sl@0:         }
sl@0:         // Packed case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, packed_random_access_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             difference_type it1_size (it1_end - it1);
sl@0:             difference_type it2_size (it2_end - it2);
sl@0:             difference_type diff (0);
sl@0:             if (it1_size > 0 && it2_size > 0)
sl@0:                 diff = it2.index1 () - it1.index2 ();
sl@0:             if (diff != 0) {
sl@0:                 difference_type size = (std::min) (diff, it1_size);
sl@0:                 if (size > 0) {
sl@0:                     it1 += size;
sl@0:                     it1_size -= size;
sl@0:                     diff -= size;
sl@0:                 }
sl@0:                 size = (std::min) (- diff, it2_size);
sl@0:                 if (size > 0) {
sl@0:                     it2 += size;
sl@0:                     it2_size -= size;
sl@0:                     diff += size;
sl@0:                 }
sl@0:             }
sl@0:             difference_type size ((std::min) (it1_size, it2_size));
sl@0:             while (-- size >= 0)
sl@0:                 t += *it1 * *it2, ++ it1, ++ it2;
sl@0:             return t;
sl@0:         }
sl@0:         // Sparse case
sl@0:         template<class I1, class I2>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) {
sl@0:             result_type t = result_type (0);
sl@0:             if (it1 != it1_end && it2 != it2_end) {
sl@0:                 size_type it1_index = it1.index2 (), it2_index = it2.index1 ();
sl@0:                 while (true) {
sl@0:                     difference_type compare = it1_index - it2_index;
sl@0:                     if (compare == 0) {
sl@0:                         t += *it1 * *it2, ++ it1, ++ it2;
sl@0:                         if (it1 != it1_end && it2 != it2_end) {
sl@0:                             it1_index = it1.index2 ();
sl@0:                             it2_index = it2.index1 ();
sl@0:                         } else
sl@0:                             break;
sl@0:                     } else if (compare < 0) {
sl@0:                         increment (it1, it1_end, - compare);
sl@0:                         if (it1 != it1_end)
sl@0:                             it1_index = it1.index2 ();
sl@0:                         else
sl@0:                             break;
sl@0:                     } else if (compare > 0) {
sl@0:                         increment (it2, it2_end, compare);
sl@0:                         if (it2 != it2_end)
sl@0:                             it2_index = it2.index1 ();
sl@0:                         else
sl@0:                             break;
sl@0:                     }
sl@0:                 }
sl@0:             }
sl@0:             return t;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // Unary returning scalar norm
sl@0:     template<class T>
sl@0:     struct matrix_scalar_real_unary_functor {
sl@0:         typedef std::size_t size_type;
sl@0:         typedef std::ptrdiff_t difference_type;
sl@0:         typedef T value_type;
sl@0:         typedef typename type_traits<T>::real_type real_type;
sl@0:         typedef real_type result_type;
sl@0:     };
sl@0: 
sl@0:     template<class T>
sl@0:     struct matrix_norm_1:
sl@0:         public matrix_scalar_real_unary_functor<T> {
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_expression<E> &e) {
sl@0:             real_type t = real_type ();
sl@0:             size_type size2 (e ().size2 ());
sl@0:             for (size_type j = 0; j < size2; ++ j) {
sl@0:                 real_type u = real_type ();
sl@0:                 size_type size1 (e ().size1 ());
sl@0:                 for (size_type i = 0; i < size1; ++ i) {
sl@0:                     real_type v (type_traits<value_type>::norm_1 (e () (i, j)));
sl@0:                     u += v;
sl@0:                 }
sl@0:                 if (u > t)
sl@0:                     t = u;
sl@0:             }
sl@0:             return t; 
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct matrix_norm_frobenius:
sl@0:         public matrix_scalar_real_unary_functor<T> {
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_expression<E> &e) { 
sl@0:             real_type t = real_type ();
sl@0:             size_type size1 (e ().size1 ());
sl@0:             for (size_type i = 0; i < size1; ++ i) {
sl@0:                 size_type size2 (e ().size2 ());
sl@0:                 for (size_type j = 0; j < size2; ++ j) {
sl@0:                     real_type u (type_traits<value_type>::norm_2 (e () (i, j)));
sl@0:                     t +=  u * u;
sl@0:                 }
sl@0:             }
sl@0:             return type_traits<real_type>::type_sqrt (t); 
sl@0:         }
sl@0:     };
sl@0:     template<class T>
sl@0:     struct matrix_norm_inf: 
sl@0:         public matrix_scalar_real_unary_functor<T> {
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
sl@0:         typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
sl@0: 
sl@0:         template<class E>
sl@0:         static BOOST_UBLAS_INLINE
sl@0:         result_type apply (const matrix_expression<E> &e) {
sl@0:             real_type t = real_type ();
sl@0:             size_type size1 (e ().size1 ());
sl@0:             for (size_type i = 0; i < size1; ++ i) {
sl@0:                 real_type u = real_type ();
sl@0:                 size_type size2 (e ().size2 ());
sl@0:                 for (size_type j = 0; j < size2; ++ j) {
sl@0:                     real_type v (type_traits<value_type>::norm_inf (e () (i, j)));
sl@0:                     u += v;
sl@0:                 }
sl@0:                 if (u > t) 
sl@0:                     t = u;  
sl@0:             }
sl@0:             return t; 
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // This functor computes the address translation
sl@0:     // matrix [i] [j] -> storage [i * size2 + j]
sl@0:     template <class Z, class D>
sl@0:     struct basic_row_major {
sl@0:         typedef Z size_type;
sl@0:         typedef D difference_type;
sl@0:         typedef row_major_tag orientation_category;
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type storage_size (size_type size1, size_type size2) {
sl@0:             // Guard against size_type overflow
sl@0:             BOOST_UBLAS_CHECK (size2 == 0 || size1 <= (std::numeric_limits<size_type>::max) () / size2, bad_size ());
sl@0:             return size1 * size2;
sl@0:         }
sl@0: 
sl@0:         // Indexing
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             // Guard against size_type overflow
sl@0:             BOOST_UBLAS_CHECK (i <= ((std::numeric_limits<size_type>::max) () - j) / size2, bad_index ());
sl@0:             return i * size2 + j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i <= size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j <= size2, bad_index ());
sl@0:             // Guard against size_type overflow - address may be size2 past end of storage
sl@0:             BOOST_UBLAS_CHECK (size2 == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             return i * size2 + j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         difference_type distance1 (difference_type k, size_type /* size1 */, size_type size2) {
sl@0:             return size2 != 0 ? k / size2 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         difference_type distance2 (difference_type k, size_type /* size1 */, size_type /* size2 */) {
sl@0:             return k;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index1 (difference_type k, size_type /* size1 */, size_type size2) {
sl@0:             return size2 != 0 ? k / size2 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index2 (difference_type k, size_type /* size1 */, size_type size2) {
sl@0:             return size2 != 0 ? k % size2 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool fast1 () {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type one1 (size_type /* size1 */, size_type size2) {
sl@0:             return size2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool fast2 () {
sl@0:             return true;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type one2 (size_type /* size1 */, size_type /* size2 */) {
sl@0:             return 1;
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type triangular_size (size_type size1, size_type size2) {
sl@0:             size_type size = (std::max) (size1, size2);
sl@0:             // Guard against size_type overflow - simplified
sl@0:             BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ());
sl@0:             return ((size + 1) * size) / 2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type lower_element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (i >= j, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             // FIXME size_type overflow
sl@0:             // sigma_i (i + 1) = (i + 1) * i / 2
sl@0:             // i = 0 1 2 3, sigma = 0 1 3 6
sl@0:             return ((i + 1) * i) / 2 + j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type upper_element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (i <= j, bad_index ());
sl@0:             // FIXME size_type overflow
sl@0:             // sigma_i (size - i) = size * i - i * (i - 1) / 2
sl@0:             // i = 0 1 2 3, sigma = 0 4 7 9
sl@0:             return (i * (2 * (std::max) (size1, size2) - i + 1)) / 2 + j - i;
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element1 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             return i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element2 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             return j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address1 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
sl@0:             BOOST_UBLAS_CHECK (i <= size1, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             return i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address2 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (j <= size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             return j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index1 (size_type index1, size_type /* index2 */) {
sl@0:             return index1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index2 (size_type /* index1 */, size_type index2) {
sl@0:             return index2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size1 (size_type size1, size_type /* size2 */) {
sl@0:             return size1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size2 (size_type /* size1 */, size_type size2) {
sl@0:             return size2;
sl@0:         }
sl@0: 
sl@0:         // Iterating
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void increment1 (I &it, size_type /* size1 */, size_type size2) {
sl@0:             it += size2;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void decrement1 (I &it, size_type /* size1 */, size_type size2) {
sl@0:             it -= size2;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void increment2 (I &it, size_type /* size1 */, size_type /* size2 */) {
sl@0:             ++ it;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void decrement2 (I &it, size_type /* size1 */, size_type /* size2 */) {
sl@0:             -- it;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     // This functor computes the address translation
sl@0:     // matrix [i] [j] -> storage [i + j * size1]
sl@0:     template <class Z, class D>
sl@0:     struct basic_column_major {
sl@0:         typedef Z size_type;
sl@0:         typedef D difference_type;
sl@0:         typedef column_major_tag orientation_category;
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type storage_size (size_type size1, size_type size2) {
sl@0:             // Guard against size_type overflow
sl@0:             BOOST_UBLAS_CHECK (size1 == 0 || size2 <= (std::numeric_limits<size_type>::max) () / size1, bad_size ());
sl@0:             return size1 * size2;
sl@0:         }
sl@0: 
sl@0:         // Indexing
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             // Guard against size_type overflow
sl@0:             BOOST_UBLAS_CHECK (j <= ((std::numeric_limits<size_type>::max) () - i) / size1, bad_index ());
sl@0:             return i + j * size1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i <= size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j <= size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             // Guard against size_type overflow - address may be size1 past end of storage
sl@0:             BOOST_UBLAS_CHECK (size1 == 0 || j <= ((std::numeric_limits<size_type>::max) () - i) / size1, bad_index ());
sl@0:             return i + j * size1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         difference_type distance1 (difference_type k, size_type /* size1 */, size_type /* size2 */) {
sl@0:             return k;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         difference_type distance2 (difference_type k, size_type size1, size_type /* size2 */) {
sl@0:             return size1 != 0 ? k / size1 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index1 (difference_type k, size_type size1, size_type /* size2 */) {
sl@0:             return size1 != 0 ? k % size1 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index2 (difference_type k, size_type size1, size_type /* size2 */) {
sl@0:             return size1 != 0 ? k / size1 : 0;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool fast1 () {
sl@0:             return true;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type one1 (size_type /* size1 */, size_type /* size2 */) {
sl@0:             return 1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool fast2 () {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type one2 (size_type size1, size_type /* size2 */) {
sl@0:             return size1;
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type triangular_size (size_type size1, size_type size2) {
sl@0:             size_type size = (std::max) (size1, size2);
sl@0:             // Guard against size_type overflow - simplified
sl@0:             BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ());
sl@0:             return ((size + 1) * size) / 2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type lower_element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (i >= j, bad_index ());
sl@0:             // FIXME size_type overflow
sl@0:             // sigma_j (size - j) = size * j - j * (j - 1) / 2
sl@0:             // j = 0 1 2 3, sigma = 0 4 7 9
sl@0:             return i - j + (j * (2 * (std::max) (size1, size2) - j + 1)) / 2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type upper_element (size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (i <= j, bad_index ());
sl@0:             // FIXME size_type overflow
sl@0:             // sigma_j (j + 1) = (j + 1) * j / 2
sl@0:             // j = 0 1 2 3, sigma = 0 1 3 6
sl@0:             return i + ((j + 1) * j) / 2;
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element1 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (j < size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             return j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element2 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
sl@0:             BOOST_UBLAS_CHECK (i < size1, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             return i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address1 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
sl@0:             BOOST_UBLAS_CHECK (j <= size2, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size2);
sl@0:             return j;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type address2 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
sl@0:             BOOST_UBLAS_CHECK (i <= size1, bad_index ());
sl@0:             detail::ignore_unused_variable_warning(size1);
sl@0:             return i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index1 (size_type /* index1 */, size_type index2) {
sl@0:             return index2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type index2 (size_type index1, size_type /* index2 */) {
sl@0:             return index1;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size1 (size_type /* size1 */, size_type size2) {
sl@0:             return size2;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size2 (size_type size1, size_type /* size2 */) {
sl@0:             return size1;
sl@0:         }
sl@0: 
sl@0:         // Iterating
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void increment1 (I &it, size_type /* size1 */, size_type /* size2 */) {
sl@0:             ++ it;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void decrement1 (I &it, size_type /* size1 */, size_type /* size2 */) {
sl@0:             -- it;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void increment2 (I &it, size_type size1, size_type /* size2 */) {
sl@0:             it += size1;
sl@0:         }
sl@0:         template<class I>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void decrement2 (I &it, size_type size1, size_type /* size2 */) {
sl@0:             it -= size1;
sl@0:         }
sl@0:     };
sl@0: 
sl@0: 
sl@0:     template <class Z>
sl@0:     struct basic_full {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (size_type size1, size_type size2) {
sl@0:             return L::storage_size (size1, size2);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool zero (size_type /* i */, size_type /* j */) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type /* i */, size_type /* j */) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type /* i */, size_type /* j */) {
sl@0:             return true;
sl@0:         }
sl@0:     };
sl@0: 
sl@0:     template <class Z>
sl@0:     struct basic_lower {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             return L::triangular_size (size1, size2);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool zero (size_type i, size_type j) {
sl@0:             return j > i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type /* i */, size_type /* j */) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j <= i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             return L::lower_element (i, size1, j, size2);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict1 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict2 (size_type i, size_type j) {
sl@0:             return (std::min) (i + 1, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::min) (i + 1, j);
sl@0:         }
sl@0:     };
sl@0:     template <class Z>
sl@0:     struct basic_upper {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             return L::triangular_size (size1, size2);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool zero (size_type i, size_type j) {
sl@0:             return j < i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type /* i */, size_type /* j */) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j >= i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             return L::upper_element (i, size1, j, size2);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict1 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j + 1);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict2 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j + 1);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:     };
sl@0:     template <class Z>
sl@0:     struct basic_unit_lower : public basic_lower<Z> {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::triangular_size (size1 - 1, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type i, size_type j) {
sl@0:             return j == i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j < i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::lower_element (i, size1 - 1, j, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:     };
sl@0:     template <class Z>
sl@0:     struct basic_unit_upper : public basic_upper<Z> {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::triangular_size (size1 - 1, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type i, size_type j) {
sl@0:             return j == i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j > i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::upper_element (i, size1 - 1, j, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:     };
sl@0:     template <class Z>
sl@0:     struct basic_strict_lower : public basic_lower<Z> {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::triangular_size (size1 - 1, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool zero (size_type i, size_type j) {
sl@0:             return j >= i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type /*i*/, size_type /*j*/) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j < i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::lower_element (i, size1 - 1, j, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict1 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict2 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:     };
sl@0:     template <class Z>
sl@0:     struct basic_strict_upper : public basic_upper<Z> {
sl@0:         typedef Z size_type;
sl@0: 
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type packed_size (L, size_type size1, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::triangular_size (size1 - 1, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool zero (size_type i, size_type j) {
sl@0:             return j <= i;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool one (size_type /*i*/, size_type /*j*/) {
sl@0:             return false;
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool other (size_type i, size_type j) {
sl@0:             return j > i;
sl@0:         }
sl@0:         template<class L>
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type element (L, size_type i, size_type size1, size_type j, size_type size2) {
sl@0:             // Zero size strict triangles are bad at this point
sl@0:             BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
sl@0:             return L::upper_element (i, size1 - 1, j, size2 - 1);
sl@0:         }
sl@0: 
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict1 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type restrict2 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict1 (size_type i, size_type j) {
sl@0:             return (std::min) (i, j);
sl@0:         }
sl@0:         static
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type mutable_restrict2 (size_type i, size_type j) {
sl@0:             return (std::max) (i, j);
sl@0:         }
sl@0:     };
sl@0: 
sl@0: }}}
sl@0: 
sl@0: #endif