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_TRIANGULAR_
sl@0: #define _BOOST_UBLAS_TRIANGULAR_
sl@0: 
sl@0: #include <boost/numeric/ublas/matrix.hpp>
sl@0: #include <boost/numeric/ublas/detail/temporary.hpp>
sl@0: #include <boost/type_traits/remove_const.hpp>
sl@0: 
sl@0: // Iterators based on ideas of Jeremy Siek
sl@0: 
sl@0: namespace boost { namespace numeric { namespace ublas {
sl@0: 
sl@0:     // Array based triangular matrix class
sl@0:     template<class T, class TRI, class L, class A>
sl@0:     class triangular_matrix:
sl@0:         public matrix_container<triangular_matrix<T, TRI, L, A> > {
sl@0: 
sl@0:         typedef T *pointer;
sl@0:         typedef TRI triangular_type;
sl@0:         typedef L layout_type;
sl@0:         typedef triangular_matrix<T, TRI, L, A> self_type;
sl@0:     public:
sl@0: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
sl@0:         using matrix_container<self_type>::operator ();
sl@0: #endif
sl@0:         typedef typename A::size_type size_type;
sl@0:         typedef typename A::difference_type difference_type;
sl@0:         typedef T value_type;
sl@0:         typedef const T &const_reference;
sl@0:         typedef T &reference;
sl@0:         typedef A array_type;
sl@0: 
sl@0:         typedef const matrix_reference<const self_type> const_closure_type;
sl@0:         typedef matrix_reference<self_type> closure_type;
sl@0:         typedef vector<T, A> vector_temporary_type;
sl@0:         typedef matrix<T, L, A> matrix_temporary_type;  // general sub-matrix
sl@0:         typedef packed_tag storage_category;
sl@0:         typedef typename L::orientation_category orientation_category;
sl@0: 
sl@0:         // Construction and destruction
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix ():
sl@0:             matrix_container<self_type> (),
sl@0:             size1_ (0), size2_ (0), data_ (0) {}
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix (size_type size1, size_type size2):
sl@0:             matrix_container<self_type> (),
sl@0:             size1_ (size1), size2_ (size2), data_ (triangular_type::packed_size (layout_type (), size1, size2)) {
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix (size_type size1, size_type size2, const array_type &data):
sl@0:             matrix_container<self_type> (),
sl@0:             size1_ (size1), size2_ (size2), data_ (data) {}
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix (const triangular_matrix &m):
sl@0:             matrix_container<self_type> (),
sl@0:             size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix (const matrix_expression<AE> &ae):
sl@0:             matrix_container<self_type> (),
sl@0:             size1_ (ae ().size1 ()), size2_ (ae ().size2 ()),
sl@0:             data_ (triangular_type::packed_size (layout_type (), size1_, size2_)) {
sl@0:             matrix_assign<scalar_assign> (*this, ae);
sl@0:         }
sl@0: 
sl@0:         // Accessors
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size1 () const {
sl@0:             return size1_;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size2 () const {
sl@0:             return size2_;
sl@0:         }
sl@0: 
sl@0:         // Storage accessors
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const array_type &data () const {
sl@0:             return data_;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         array_type &data () {
sl@0:             return data_;
sl@0:         }
sl@0: 
sl@0:         // Resizing
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void resize (size_type size1, size_type size2, bool preserve = true) {
sl@0:             if (preserve) {
sl@0:                 self_type temporary (size1, size2);
sl@0:                 detail::matrix_resize_preserve<layout_type> (*this, temporary);
sl@0:             }
sl@0:             else {
sl@0:                 data ().resize (triangular_type::packed_size (layout_type (), size1, size2));
sl@0:                 size1_ = size1;
sl@0:                 size2_ = size2;
sl@0:             }
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void resize_packed_preserve (size_type size1, size_type size2) {
sl@0:             size1_ = size1;
sl@0:             size2_ = size2;
sl@0:             data ().resize (triangular_type::packed_size (layout_type (), size1_, size2_), value_type ());
sl@0:         }
sl@0: 
sl@0:         // Element access
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reference operator () (size_type i, size_type j) const {
sl@0:             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
sl@0:             if (triangular_type::other (i, j))
sl@0:                 return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
sl@0:             else if (triangular_type::one (i, j))
sl@0:                 return one_;
sl@0:             else
sl@0:                 return zero_;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reference at_element (size_type i, size_type j) {
sl@0:             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
sl@0:             return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reference operator () (size_type i, size_type j) {
sl@0:             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
sl@0:             if (triangular_type::other (i, j))
sl@0:                 return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
sl@0:             else {
sl@0:                 bad_index ().raise ();
sl@0:                 // arbitary return value
sl@0:                 return const_cast<reference>(zero_);
sl@0:             }
sl@0:         }
sl@0:         
sl@0:         // Element assignment
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reference insert_element (size_type i, size_type j, const_reference t) {
sl@0:             return (operator () (i, j) = t);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void erase_element (size_type i, size_type j) {
sl@0:             operator () (i, j) = value_type/*zero*/();
sl@0:         }
sl@0:         
sl@0:         // Zeroing
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void clear () {
sl@0:             // data ().clear ();
sl@0:             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
sl@0:         }
sl@0: 
sl@0:         // Assignment
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &operator = (const triangular_matrix &m) {
sl@0:             size1_ = m.size1_;
sl@0:             size2_ = m.size2_;
sl@0:             data () = m.data ();
sl@0:             return *this;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &assign_temporary (triangular_matrix &m) {
sl@0:             swap (m);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &operator = (const matrix_expression<AE> &ae) {
sl@0:             self_type temporary (ae);
sl@0:             return assign_temporary (temporary);
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix& operator += (const matrix_expression<AE> &ae) {
sl@0:             self_type temporary (*this + ae);
sl@0:             return assign_temporary (temporary);
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &plus_assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_plus_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix& operator -= (const matrix_expression<AE> &ae) {
sl@0:             self_type temporary (*this - ae);
sl@0:             return assign_temporary (temporary);
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix &minus_assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_minus_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AT>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix& operator *= (const AT &at) {
sl@0:             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AT>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_matrix& operator /= (const AT &at) {
sl@0:             matrix_assign_scalar<scalar_divides_assign> (*this, at);
sl@0:             return *this;
sl@0:         }
sl@0: 
sl@0:         // Swapping
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void swap (triangular_matrix &m) {
sl@0:             if (this != &m) {
sl@0:                 // BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ());
sl@0:                 std::swap (size1_, m.size1_);
sl@0:                 std::swap (size2_, m.size2_);
sl@0:                 data ().swap (m.data ());
sl@0:             }
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         friend void swap (triangular_matrix &m1, triangular_matrix &m2) {
sl@0:             m1.swap (m2);
sl@0:         }
sl@0: 
sl@0:         // Iterator types
sl@0: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
sl@0:         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
sl@0:         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
sl@0:         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
sl@0: #else
sl@0:         class const_iterator1;
sl@0:         class iterator1;
sl@0:         class const_iterator2;
sl@0:         class iterator2;
sl@0: #endif
sl@0:         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
sl@0:         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
sl@0:         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
sl@0:         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
sl@0: 
sl@0:         // Element lookup
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 find1 (int rank, size_type i, size_type j) const {
sl@0:             if (rank == 1)
sl@0:                 i = triangular_type::restrict1 (i, j);
sl@0:             return const_iterator1 (*this, i, j);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 find1 (int rank, size_type i, size_type j) {
sl@0:             if (rank == 1)
sl@0:                 i = triangular_type::mutable_restrict1 (i, j);
sl@0:             return iterator1 (*this, i, j);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 find2 (int rank, size_type i, size_type j) const {
sl@0:             if (rank == 1)
sl@0:                 j = triangular_type::restrict2 (i, j);
sl@0:             return const_iterator2 (*this, i, j);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 find2 (int rank, size_type i, size_type j) {
sl@0:             if (rank == 1)
sl@0:                 j = triangular_type::mutable_restrict2 (i, j);
sl@0:             return iterator2 (*this, i, j);
sl@0:         }
sl@0: 
sl@0:         // Iterators simply are indices.
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class const_iterator1:
sl@0:             public container_const_reference<triangular_matrix>,
sl@0:             public random_access_iterator_base<packed_random_access_iterator_tag,
sl@0:                                                const_iterator1, value_type> {
sl@0:         public:
sl@0:             typedef typename triangular_matrix::value_type value_type;
sl@0:             typedef typename triangular_matrix::difference_type difference_type;
sl@0:             typedef typename triangular_matrix::const_reference reference;
sl@0:             typedef const typename triangular_matrix::pointer pointer;
sl@0: 
sl@0:             typedef const_iterator2 dual_iterator_type;
sl@0:             typedef const_reverse_iterator2 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 ():
sl@0:                 container_const_reference<self_type> (), it1_ (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 (const self_type &m, size_type it1, size_type it2):
sl@0:                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 (const iterator1 &it):
sl@0:                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator ++ () {
sl@0:                 ++ it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator -- () {
sl@0:                 -- it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator += (difference_type n) {
sl@0:                 it1_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator -= (difference_type n) {
sl@0:                 it1_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ - it.it1_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator * () const {
sl@0:                 return (*this) () (it1_, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator2 begin () const {
sl@0:                 return (*this) ().find2 (1, it1_, 0);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator2 end () const {
sl@0:                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator2 rbegin () const {
sl@0:                 return const_reverse_iterator2 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator2 rend () const {
sl@0:                 return const_reverse_iterator2 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_;
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator = (const const_iterator1 &it) {
sl@0:                 container_const_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ == it.it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ < it.it1_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             size_type it1_;
sl@0:             size_type it2_;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 begin1 () const {
sl@0:             return find1 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 end1 () const {
sl@0:             return find1 (0, size1_, 0);
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class iterator1:
sl@0:             public container_reference<triangular_matrix>,
sl@0:             public random_access_iterator_base<packed_random_access_iterator_tag,
sl@0:                                                iterator1, value_type> {
sl@0:         public:
sl@0:             typedef typename triangular_matrix::value_type value_type;
sl@0:             typedef typename triangular_matrix::difference_type difference_type;
sl@0:             typedef typename triangular_matrix::reference reference;
sl@0:             typedef typename triangular_matrix::pointer pointer;
sl@0: 
sl@0:             typedef iterator2 dual_iterator_type;
sl@0:             typedef reverse_iterator2 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 ():
sl@0:                 container_reference<self_type> (), it1_ (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 (self_type &m, size_type it1, size_type it2):
sl@0:                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator ++ () {
sl@0:                 ++ it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator -- () {
sl@0:                 -- it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator += (difference_type n) {
sl@0:                 it1_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator -= (difference_type n) {
sl@0:                 it1_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ - it.it1_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator * () const {
sl@0:                 return (*this) () (it1_, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator2 begin () const {
sl@0:                 return (*this) ().find2 (1, it1_, 0);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator2 end () const {
sl@0:                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator2 rbegin () const {
sl@0:                 return reverse_iterator2 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator2 rend () const {
sl@0:                 return reverse_iterator2 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_;
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator = (const iterator1 &it) {
sl@0:                 container_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ == it.it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
sl@0:                 return it1_ < it.it1_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             size_type it1_;
sl@0:             size_type it2_;
sl@0: 
sl@0:             friend class const_iterator1;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 begin1 () {
sl@0:             return find1 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 end1 () {
sl@0:             return find1 (0, size1_, 0);
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class const_iterator2:
sl@0:             public container_const_reference<triangular_matrix>,
sl@0:             public random_access_iterator_base<packed_random_access_iterator_tag,
sl@0:                                                const_iterator2, value_type> {
sl@0:         public:
sl@0:             typedef typename triangular_matrix::value_type value_type;
sl@0:             typedef typename triangular_matrix::difference_type difference_type;
sl@0:             typedef typename triangular_matrix::const_reference reference;
sl@0:             typedef const typename triangular_matrix::pointer pointer;
sl@0: 
sl@0:             typedef const_iterator1 dual_iterator_type;
sl@0:             typedef const_reverse_iterator1 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 ():
sl@0:                 container_const_reference<self_type> (), it1_ (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 (const self_type &m, size_type it1, size_type it2):
sl@0:                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 (const iterator2 &it):
sl@0:                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator ++ () {
sl@0:                 ++ it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator -- () {
sl@0:                 -- it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator += (difference_type n) {
sl@0:                 it2_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator -= (difference_type n) {
sl@0:                 it2_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ - it.it2_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator * () const {
sl@0:                 return (*this) () (it1_, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator1 begin () const {
sl@0:                 return (*this) ().find1 (1, 0, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator1 end () const {
sl@0:                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator1 rbegin () const {
sl@0:                 return const_reverse_iterator1 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator1 rend () const {
sl@0:                 return const_reverse_iterator1 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_;
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator = (const const_iterator2 &it) {
sl@0:                 container_const_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ == it.it2_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ < it.it2_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             size_type it1_;
sl@0:             size_type it2_;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 begin2 () const {
sl@0:             return find2 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 end2 () const {
sl@0:             return find2 (0, 0, size2_);
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class iterator2:
sl@0:             public container_reference<triangular_matrix>,
sl@0:             public random_access_iterator_base<packed_random_access_iterator_tag,
sl@0:                                                iterator2, value_type> {
sl@0:         public:
sl@0:             typedef typename triangular_matrix::value_type value_type;
sl@0:             typedef typename triangular_matrix::difference_type difference_type;
sl@0:             typedef typename triangular_matrix::reference reference;
sl@0:             typedef typename triangular_matrix::pointer pointer;
sl@0: 
sl@0:             typedef iterator1 dual_iterator_type;
sl@0:             typedef reverse_iterator1 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 ():
sl@0:                 container_reference<self_type> (), it1_ (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 (self_type &m, size_type it1, size_type it2):
sl@0:                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator ++ () {
sl@0:                 ++ it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator -- () {
sl@0:                 -- it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator += (difference_type n) {
sl@0:                 it2_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator -= (difference_type n) {
sl@0:                 it2_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ - it.it2_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator * () const {
sl@0:                 return (*this) () (it1_, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator1 begin () const {
sl@0:                 return (*this) ().find1 (1, 0, it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator1 end () const {
sl@0:                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator1 rbegin () const {
sl@0:                 return reverse_iterator1 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator1 rend () const {
sl@0:                 return reverse_iterator1 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_;
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator = (const iterator2 &it) {
sl@0:                 container_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ == it.it2_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
sl@0:                 return it2_ < it.it2_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             size_type it1_;
sl@0:             size_type it2_;
sl@0: 
sl@0:             friend class const_iterator2;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 begin2 () {
sl@0:             return find2 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 end2 () {
sl@0:             return find2 (0, 0, size2_);
sl@0:         }
sl@0: 
sl@0:         // Reverse iterators
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator1 rbegin1 () const {
sl@0:             return const_reverse_iterator1 (end1 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator1 rend1 () const {
sl@0:             return const_reverse_iterator1 (begin1 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator1 rbegin1 () {
sl@0:             return reverse_iterator1 (end1 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator1 rend1 () {
sl@0:             return reverse_iterator1 (begin1 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator2 rbegin2 () const {
sl@0:             return const_reverse_iterator2 (end2 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator2 rend2 () const {
sl@0:             return const_reverse_iterator2 (begin2 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator2 rbegin2 () {
sl@0:             return reverse_iterator2 (end2 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator2 rend2 () {
sl@0:             return reverse_iterator2 (begin2 ());
sl@0:         }
sl@0: 
sl@0:     private:
sl@0:         size_type size1_;
sl@0:         size_type size2_;
sl@0:         array_type data_;
sl@0:         static const value_type zero_;
sl@0:         static const value_type one_;
sl@0:     };
sl@0: 
sl@0:     template<class T, class TRI, class L, class A>
sl@0:     const typename triangular_matrix<T, TRI, L, A>::value_type triangular_matrix<T, TRI, L, A>::zero_ = value_type/*zero*/();
sl@0:     template<class T, class TRI, class L, class A>
sl@0:     const typename triangular_matrix<T, TRI, L, A>::value_type triangular_matrix<T, TRI, L, A>::one_ (1);
sl@0: 
sl@0: 
sl@0:     // Triangular matrix adaptor class
sl@0:     template<class M, class TRI>
sl@0:     class triangular_adaptor:
sl@0:         public matrix_expression<triangular_adaptor<M, TRI> > {
sl@0: 
sl@0:         typedef triangular_adaptor<M, TRI> self_type;
sl@0: 
sl@0:     public:
sl@0: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
sl@0:         using matrix_expression<self_type>::operator ();
sl@0: #endif
sl@0:         typedef const M const_matrix_type;
sl@0:         typedef M matrix_type;
sl@0:         typedef TRI triangular_type;
sl@0:         typedef typename M::size_type size_type;
sl@0:         typedef typename M::difference_type difference_type;
sl@0:         typedef typename M::value_type value_type;
sl@0:         typedef typename M::const_reference const_reference;
sl@0:         typedef typename boost::mpl::if_<boost::is_const<M>,
sl@0:                                           typename M::const_reference,
sl@0:                                           typename M::reference>::type reference;
sl@0:         typedef typename boost::mpl::if_<boost::is_const<M>,
sl@0:                                           typename M::const_closure_type,
sl@0:                                           typename M::closure_type>::type matrix_closure_type;
sl@0:         typedef const self_type const_closure_type;
sl@0:         typedef self_type closure_type;
sl@0:         // Replaced by _temporary_traits to avoid type requirements on M
sl@0:         //typedef typename M::vector_temporary_type vector_temporary_type;
sl@0:         //typedef typename M::matrix_temporary_type matrix_temporary_type;
sl@0:         typedef typename storage_restrict_traits<typename M::storage_category,
sl@0:                                                  packed_proxy_tag>::storage_category storage_category;
sl@0:         typedef typename M::orientation_category orientation_category;
sl@0: 
sl@0:         // Construction and destruction
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor (matrix_type &data):
sl@0:             matrix_expression<self_type> (),
sl@0:             data_ (data) {}
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor (const triangular_adaptor &m):
sl@0:             matrix_expression<self_type> (),
sl@0:             data_ (m.data_) {}
sl@0: 
sl@0:         // Accessors
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size1 () const {
sl@0:             return data_.size1 ();
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         size_type size2 () const {
sl@0:             return data_.size2 ();
sl@0:         }
sl@0: 
sl@0:         // Storage accessors
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const matrix_closure_type &data () const {
sl@0:             return data_;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         matrix_closure_type &data () {
sl@0:             return data_;
sl@0:         }
sl@0: 
sl@0:         // Element access
sl@0: #ifndef BOOST_UBLAS_PROXY_CONST_MEMBER
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reference operator () (size_type i, size_type j) const {
sl@0:             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
sl@0:             if (triangular_type::other (i, j))
sl@0:                 return data () (i, j);
sl@0:             else if (triangular_type::one (i, j))
sl@0:                 return one_;
sl@0:             else
sl@0:                 return zero_;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reference operator () (size_type i, size_type j) {
sl@0:             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
sl@0:             if (triangular_type::other (i, j))
sl@0:                 return data () (i, j);
sl@0:             else if (triangular_type::one (i, j)) {
sl@0:                 bad_index ().raise ();
sl@0:                 // arbitary return value
sl@0:                 return const_cast<reference>(one_);
sl@0:             } else {
sl@0:                 bad_index ().raise ();
sl@0:                 // arbitary return value
sl@0:                 return const_cast<reference>(zero_);
sl@0:             }
sl@0:         }
sl@0: #else
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reference operator () (size_type i, size_type j) const {
sl@0:             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
sl@0:             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
sl@0:             if (triangular_type::other (i, j))
sl@0:                 return data () (i, j);
sl@0:             else if (triangular_type::one (i, j)) {
sl@0:                 bad_index ().raise ();
sl@0:                 // arbitary return value
sl@0:                 return const_cast<reference>(one_);
sl@0:             } else {
sl@0:                 bad_index ().raise ();
sl@0:                 // arbitary return value
sl@0:                 return const_cast<reference>(zero_);
sl@0:             }
sl@0:         }
sl@0: #endif
sl@0: 
sl@0:         // Assignment
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &operator = (const triangular_adaptor &m) {
sl@0:             matrix_assign<scalar_assign> (*this, m);
sl@0:             return *this;
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &assign_temporary (triangular_adaptor &m) {
sl@0:             *this = m;
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &operator = (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_assign> (*this, matrix<value_type> (ae));
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor& operator += (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_assign> (*this, matrix<value_type> (*this + ae));
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &plus_assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_plus_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor& operator -= (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_assign> (*this, matrix<value_type> (*this - ae));
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AE>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor &minus_assign (const matrix_expression<AE> &ae) {
sl@0:             matrix_assign<scalar_minus_assign> (*this, ae);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AT>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor& operator *= (const AT &at) {
sl@0:             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
sl@0:             return *this;
sl@0:         }
sl@0:         template<class AT>
sl@0:         BOOST_UBLAS_INLINE
sl@0:         triangular_adaptor& operator /= (const AT &at) {
sl@0:             matrix_assign_scalar<scalar_divides_assign> (*this, at);
sl@0:             return *this;
sl@0:         }
sl@0: 
sl@0:         // Closure comparison
sl@0:         BOOST_UBLAS_INLINE
sl@0:         bool same_closure (const triangular_adaptor &ta) const {
sl@0:             return (*this).data ().same_closure (ta.data ());
sl@0:         }
sl@0: 
sl@0:         // Swapping
sl@0:         BOOST_UBLAS_INLINE
sl@0:         void swap (triangular_adaptor &m) {
sl@0:             if (this != &m)
sl@0:                 matrix_swap<scalar_swap> (*this, m);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         friend void swap (triangular_adaptor &m1, triangular_adaptor &m2) {
sl@0:             m1.swap (m2);
sl@0:         }
sl@0: 
sl@0:         // Iterator types
sl@0:    private:
sl@0:         typedef typename M::const_iterator1 const_subiterator1_type;
sl@0:         typedef typename boost::mpl::if_<boost::is_const<M>,
sl@0:                                           typename M::const_iterator1,
sl@0:                                           typename M::iterator1>::type subiterator1_type;
sl@0:         typedef typename M::const_iterator2 const_subiterator2_type;
sl@0:         typedef typename boost::mpl::if_<boost::is_const<M>,
sl@0:                                           typename M::const_iterator2,
sl@0:                                           typename M::iterator2>::type subiterator2_type;
sl@0: 
sl@0:     public:
sl@0: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
sl@0:         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
sl@0:         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
sl@0:         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
sl@0: #else
sl@0:         class const_iterator1;
sl@0:         class iterator1;
sl@0:         class const_iterator2;
sl@0:         class iterator2;
sl@0: #endif
sl@0:         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
sl@0:         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
sl@0:         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
sl@0:         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
sl@0: 
sl@0:         // Element lookup
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 find1 (int rank, size_type i, size_type j) const {
sl@0:             if (rank == 1)
sl@0:                 i = triangular_type::restrict1 (i, j);
sl@0:             return const_iterator1 (*this, data ().find1 (rank, i, j));
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 find1 (int rank, size_type i, size_type j) {
sl@0:             if (rank == 1)
sl@0:                 i = triangular_type::mutable_restrict1 (i, j);
sl@0:             return iterator1 (*this, data ().find1 (rank, i, j));
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 find2 (int rank, size_type i, size_type j) const {
sl@0:             if (rank == 1)
sl@0:                 j = triangular_type::restrict2 (i, j);
sl@0:             return const_iterator2 (*this, data ().find2 (rank, i, j));
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 find2 (int rank, size_type i, size_type j) {
sl@0:             if (rank == 1)
sl@0:                 j = triangular_type::mutable_restrict2 (i, j);
sl@0:             return iterator2 (*this, data ().find2 (rank, i, j));
sl@0:         }
sl@0: 
sl@0:         // Iterators simply are indices.
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class const_iterator1:
sl@0:             public container_const_reference<triangular_adaptor>,
sl@0:             public random_access_iterator_base<typename iterator_restrict_traits<
sl@0:                                                    typename const_subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
sl@0:                                                const_iterator1, value_type> {
sl@0:         public:
sl@0:             typedef typename const_subiterator1_type::value_type value_type;
sl@0:             typedef typename const_subiterator1_type::difference_type difference_type;
sl@0:             typedef typename const_subiterator1_type::reference reference;
sl@0:             typedef typename const_subiterator1_type::pointer pointer;
sl@0: 
sl@0:             typedef const_iterator2 dual_iterator_type;
sl@0:             typedef const_reverse_iterator2 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 ():
sl@0:                 container_const_reference<self_type> (), it1_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 (const self_type &m, const const_subiterator1_type &it1):
sl@0:                 container_const_reference<self_type> (m), it1_ (it1) {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 (const iterator1 &it):
sl@0:                 container_const_reference<self_type> (it ()), it1_ (it.it1_) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator ++ () {
sl@0:                 ++ it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator -- () {
sl@0:                 -- it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator += (difference_type n) {
sl@0:                 it1_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator -= (difference_type n) {
sl@0:                 it1_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ - it.it1_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator * () const {
sl@0:                 size_type i = index1 ();
sl@0:                 size_type j = index2 ();
sl@0:                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
sl@0:                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
sl@0:                 if (triangular_type::other (i, j))
sl@0:                     return *it1_;
sl@0:                 else
sl@0:                     return (*this) () (i, j);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator2 begin () const {
sl@0:                 return (*this) ().find2 (1, index1 (), 0);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator2 end () const {
sl@0:                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator2 rbegin () const {
sl@0:                 return const_reverse_iterator2 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator2 rend () const {
sl@0:                 return const_reverse_iterator2 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_.index1 ();
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it1_.index2 ();
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator1 &operator = (const const_iterator1 &it) {
sl@0:                 container_const_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ == it.it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const const_iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ < it.it1_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             const_subiterator1_type it1_;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 begin1 () const {
sl@0:             return find1 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator1 end1 () const {
sl@0:             return find1 (0, size1 (), 0);
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class iterator1:
sl@0:             public container_reference<triangular_adaptor>,
sl@0:             public random_access_iterator_base<typename iterator_restrict_traits<
sl@0:                                                    typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
sl@0:                                                iterator1, value_type> {
sl@0:         public:
sl@0:             typedef typename subiterator1_type::value_type value_type;
sl@0:             typedef typename subiterator1_type::difference_type difference_type;
sl@0:             typedef typename subiterator1_type::reference reference;
sl@0:             typedef typename subiterator1_type::pointer pointer;
sl@0: 
sl@0:             typedef iterator2 dual_iterator_type;
sl@0:             typedef reverse_iterator2 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 ():
sl@0:                 container_reference<self_type> (), it1_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 (self_type &m, const subiterator1_type &it1):
sl@0:                 container_reference<self_type> (m), it1_ (it1) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator ++ () {
sl@0:                 ++ it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator -- () {
sl@0:                 -- it1_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator += (difference_type n) {
sl@0:                 it1_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator -= (difference_type n) {
sl@0:                 it1_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ - it.it1_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator * () const {
sl@0:                 size_type i = index1 ();
sl@0:                 size_type j = index2 ();
sl@0:                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
sl@0:                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
sl@0:                 if (triangular_type::other (i, j))
sl@0:                     return *it1_;
sl@0:                 else
sl@0:                     return (*this) () (i, j);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator2 begin () const {
sl@0:                 return (*this) ().find2 (1, index1 (), 0);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator2 end () const {
sl@0:                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator2 rbegin () const {
sl@0:                 return reverse_iterator2 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator2 rend () const {
sl@0:                 return reverse_iterator2 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it1_.index1 ();
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it1_.index2 ();
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator1 &operator = (const iterator1 &it) {
sl@0:                 container_reference<self_type>::assign (&it ());
sl@0:                 it1_ = it.it1_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ == it.it1_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const iterator1 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it1_ < it.it1_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             subiterator1_type it1_;
sl@0: 
sl@0:             friend class const_iterator1;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 begin1 () {
sl@0:             return find1 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator1 end1 () {
sl@0:             return find1 (0, size1 (), 0);
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class const_iterator2:
sl@0:             public container_const_reference<triangular_adaptor>,
sl@0:             public random_access_iterator_base<typename iterator_restrict_traits<
sl@0:                                                    typename const_subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
sl@0:                                                const_iterator2, value_type> {
sl@0:         public:
sl@0:             typedef typename const_subiterator2_type::value_type value_type;
sl@0:             typedef typename const_subiterator2_type::difference_type difference_type;
sl@0:             typedef typename const_subiterator2_type::reference reference;
sl@0:             typedef typename const_subiterator2_type::pointer pointer;
sl@0: 
sl@0:             typedef const_iterator1 dual_iterator_type;
sl@0:             typedef const_reverse_iterator1 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 ():
sl@0:                 container_const_reference<self_type> (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 (const self_type &m, const const_subiterator2_type &it2):
sl@0:                 container_const_reference<self_type> (m), it2_ (it2) {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 (const iterator2 &it):
sl@0:                 container_const_reference<self_type> (it ()), it2_ (it.it2_) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator ++ () {
sl@0:                 ++ it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator -- () {
sl@0:                 -- it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator += (difference_type n) {
sl@0:                 it2_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator -= (difference_type n) {
sl@0:                 it2_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ - it.it2_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator * () const {
sl@0:                 size_type i = index1 ();
sl@0:                 size_type j = index2 ();
sl@0:                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
sl@0:                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
sl@0:                 if (triangular_type::other (i, j))
sl@0:                     return *it2_;
sl@0:                 else
sl@0:                     return (*this) () (i, j);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator1 begin () const {
sl@0:                 return (*this) ().find1 (1, 0, index2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_iterator1 end () const {
sl@0:                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator1 rbegin () const {
sl@0:                 return const_reverse_iterator1 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             const_reverse_iterator1 rend () const {
sl@0:                 return const_reverse_iterator1 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it2_.index1 ();
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_.index2 ();
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             const_iterator2 &operator = (const const_iterator2 &it) {
sl@0:                 container_const_reference<self_type>::assign (&it ());
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ == it.it2_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const const_iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ < it.it2_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             const_subiterator2_type it2_;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 begin2 () const {
sl@0:             return find2 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_iterator2 end2 () const {
sl@0:             return find2 (0, 0, size2 ());
sl@0:         }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
sl@0:         class iterator2:
sl@0:             public container_reference<triangular_adaptor>,
sl@0:             public random_access_iterator_base<typename iterator_restrict_traits<
sl@0:                                                    typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
sl@0:                                                iterator2, value_type> {
sl@0:         public:
sl@0:             typedef typename subiterator2_type::value_type value_type;
sl@0:             typedef typename subiterator2_type::difference_type difference_type;
sl@0:             typedef typename subiterator2_type::reference reference;
sl@0:             typedef typename subiterator2_type::pointer pointer;
sl@0: 
sl@0:             typedef iterator1 dual_iterator_type;
sl@0:             typedef reverse_iterator1 dual_reverse_iterator_type;
sl@0: 
sl@0:             // Construction and destruction
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 ():
sl@0:                 container_reference<self_type> (), it2_ () {}
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 (self_type &m, const subiterator2_type &it2):
sl@0:                 container_reference<self_type> (m), it2_ (it2) {}
sl@0: 
sl@0:             // Arithmetic
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator ++ () {
sl@0:                 ++ it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator -- () {
sl@0:                 -- it2_;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator += (difference_type n) {
sl@0:                 it2_ += n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator -= (difference_type n) {
sl@0:                 it2_ -= n;
sl@0:                 return *this;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             difference_type operator - (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ - it.it2_;
sl@0:             }
sl@0: 
sl@0:             // Dereference
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator * () const {
sl@0:                 size_type i = index1 ();
sl@0:                 size_type j = index2 ();
sl@0:                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
sl@0:                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
sl@0:                 if (triangular_type::other (i, j))
sl@0:                     return *it2_;
sl@0:                 else
sl@0:                     return (*this) () (i, j);
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             reference operator [] (difference_type n) const {
sl@0:                 return *(*this + n);
sl@0:             }
sl@0: 
sl@0: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator1 begin () const {
sl@0:                 return (*this) ().find1 (1, 0, index2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             iterator1 end () const {
sl@0:                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator1 rbegin () const {
sl@0:                 return reverse_iterator1 (end ());
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0: #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
sl@0:             typename self_type::
sl@0: #endif
sl@0:             reverse_iterator1 rend () const {
sl@0:                 return reverse_iterator1 (begin ());
sl@0:             }
sl@0: #endif
sl@0: 
sl@0:             // Indices
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index1 () const {
sl@0:                 return it2_.index1 ();
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             size_type index2 () const {
sl@0:                 return it2_.index2 ();
sl@0:             }
sl@0: 
sl@0:             // Assignment
sl@0:             BOOST_UBLAS_INLINE
sl@0:             iterator2 &operator = (const iterator2 &it) {
sl@0:                 container_reference<self_type>::assign (&it ());
sl@0:                 it2_ = it.it2_;
sl@0:                 return *this;
sl@0:             }
sl@0: 
sl@0:             // Comparison
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator == (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ == it.it2_;
sl@0:             }
sl@0:             BOOST_UBLAS_INLINE
sl@0:             bool operator < (const iterator2 &it) const {
sl@0:                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
sl@0:                 return it2_ < it.it2_;
sl@0:             }
sl@0: 
sl@0:         private:
sl@0:             subiterator2_type it2_;
sl@0: 
sl@0:             friend class const_iterator2;
sl@0:         };
sl@0: #endif
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 begin2 () {
sl@0:             return find2 (0, 0, 0);
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         iterator2 end2 () {
sl@0:             return find2 (0, 0, size2 ());
sl@0:         }
sl@0: 
sl@0:         // Reverse iterators
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator1 rbegin1 () const {
sl@0:             return const_reverse_iterator1 (end1 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator1 rend1 () const {
sl@0:             return const_reverse_iterator1 (begin1 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator1 rbegin1 () {
sl@0:             return reverse_iterator1 (end1 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator1 rend1 () {
sl@0:             return reverse_iterator1 (begin1 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator2 rbegin2 () const {
sl@0:             return const_reverse_iterator2 (end2 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         const_reverse_iterator2 rend2 () const {
sl@0:             return const_reverse_iterator2 (begin2 ());
sl@0:         }
sl@0: 
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator2 rbegin2 () {
sl@0:             return reverse_iterator2 (end2 ());
sl@0:         }
sl@0:         BOOST_UBLAS_INLINE
sl@0:         reverse_iterator2 rend2 () {
sl@0:             return reverse_iterator2 (begin2 ());
sl@0:         }
sl@0: 
sl@0:     private:
sl@0:         matrix_closure_type data_;
sl@0:         static const value_type zero_;
sl@0:         static const value_type one_;
sl@0:     };
sl@0: 
sl@0:     template<class M, class TRI>
sl@0:     const typename triangular_adaptor<M, TRI>::value_type triangular_adaptor<M, TRI>::zero_ = value_type/*zero*/();
sl@0:     template<class M, class TRI>
sl@0:     const typename triangular_adaptor<M, TRI>::value_type triangular_adaptor<M, TRI>::one_ (1);
sl@0: 
sl@0:     template <class M, class TRI>
sl@0:     struct vector_temporary_traits< triangular_adaptor<M, TRI> >
sl@0:     : vector_temporary_traits< typename boost::remove_const<M>::type > {} ;
sl@0:     template <class M, class TRI>
sl@0:     struct vector_temporary_traits< const triangular_adaptor<M, TRI> >
sl@0:     : vector_temporary_traits< typename boost::remove_const<M>::type > {} ;
sl@0: 
sl@0:     template <class M, class TRI>
sl@0:     struct matrix_temporary_traits< triangular_adaptor<M, TRI> >
sl@0:     : matrix_temporary_traits< typename boost::remove_const<M>::type > {};
sl@0:     template <class M, class TRI>
sl@0:     struct matrix_temporary_traits< const triangular_adaptor<M, TRI> >
sl@0:     : matrix_temporary_traits< typename boost::remove_const<M>::type > {};
sl@0: 
sl@0: 
sl@0:     template<class E1, class E2>
sl@0:     struct matrix_vector_solve_traits {
sl@0:         typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
sl@0:         typedef vector<promote_type> result_type;
sl@0:     };
sl@0: 
sl@0:     // Operations:
sl@0:     //  n * (n - 1) / 2 + n = n * (n + 1) / 2 multiplications,
sl@0:     //  n * (n - 1) / 2 additions
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag, column_major_tag, dense_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 for (size_type m = n + 1; m < size; ++ m)
sl@0:                     e2 () (m) -= e1 () (m, n) * t;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag, column_major_tag, packed_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n));
sl@0:                 typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n));
sl@0:                 difference_type m (it1e1_end - it1e1);
sl@0:                 while (-- m >= 0)
sl@0:                     e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag, column_major_tag, unknown_storage_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n));
sl@0:                 typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n));
sl@0:                 while (it1e1 != it1e1_end)
sl@0:                     e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Redirectors :-)
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag, column_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        lower_tag (), column_major_tag (), storage_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag, row_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e2, trans (e1),
sl@0:                        upper_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         lower_tag) {
sl@0:         typedef typename E1::orientation_category orientation_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        lower_tag (), orientation_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         unit_lower_tag) {
sl@0:         typedef typename E1::orientation_category orientation_category;
sl@0:         inplace_solve (triangular_adaptor<const E1, unit_lower> (e1 ()), e2,
sl@0:                        unit_lower_tag (), orientation_category ());
sl@0:     }
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag, column_major_tag, dense_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 for (difference_type m = n - 1; m >= 0; -- m)
sl@0:                     e2 () (m) -= e1 () (m, n) * t;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag, column_major_tag, packed_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
sl@0:                 typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
sl@0:                 difference_type m (it1e1_rend - it1e1);
sl@0:                 while (-- m >= 0)
sl@0:                     e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag, column_major_tag, unknown_storage_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
sl@0:         size_type size = e2 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e2 () (n) /= e1 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
sl@0:                 typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
sl@0:                 while (it1e1 != it1e1_rend)
sl@0:                     e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Redirectors :-)
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag, column_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        upper_tag (), column_major_tag (), storage_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag, row_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e2, trans (e1),
sl@0:                        lower_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         upper_tag) {
sl@0:         typedef typename E1::orientation_category orientation_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        upper_tag (), orientation_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
sl@0:                         unit_upper_tag) {
sl@0:         typedef typename E1::orientation_category orientation_category;
sl@0:         inplace_solve (triangular_adaptor<const E1, unit_upper> (e1 ()), e2,
sl@0:                        unit_upper_tag (), orientation_category ());
sl@0:     }
sl@0: 
sl@0:     template<class E1, class E2, class C>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     typename matrix_vector_solve_traits<E1, E2>::result_type
sl@0:     solve (const matrix_expression<E1> &e1,
sl@0:            const vector_expression<E2> &e2,
sl@0:            C) {
sl@0:         typename matrix_vector_solve_traits<E1, E2>::result_type r (e2);
sl@0:         inplace_solve (e1, r, C ());
sl@0:         return r;
sl@0:     }
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag, row_major_tag, dense_proxy_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 for (difference_type m = n - 1; m >= 0; -- m)
sl@0:                     e1 () (m) -= t * e2 () (n, m);
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag, row_major_tag, packed_proxy_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E2::const_reverse_iterator2 it2e2 (e2 ().find2 (1, n, n));
sl@0:                 typename E2::const_reverse_iterator2 it2e2_rend (e2 ().find2 (1, n, 0));
sl@0:                 difference_type m (it2e2_rend - it2e2);
sl@0:                 while (-- m >= 0)
sl@0:                     e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag, row_major_tag, unknown_storage_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (difference_type n = size - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E2::const_reverse_iterator2 it2e2 (e2 ().find2 (1, n, n));
sl@0:                 typename E2::const_reverse_iterator2 it2e2_rend (e2 ().find2 (1, n, 0));
sl@0:                 while (it2e2 != it2e2_rend)
sl@0:                     e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Redirectors :-)
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag, row_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        lower_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag, column_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (trans (e2), e1,
sl@0:                        upper_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         lower_tag) {
sl@0:         typedef typename E2::orientation_category orientation_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        lower_tag (), orientation_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         unit_lower_tag) {
sl@0:         typedef typename E2::orientation_category orientation_category;
sl@0:         inplace_solve (e1, triangular_adaptor<const E2, unit_lower> (e2 ()),
sl@0:                        unit_lower_tag (), orientation_category ());
sl@0:     }
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag, row_major_tag, dense_proxy_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 for (size_type m = n + 1; m < size; ++ m)
sl@0:                     e1 () (m) -= t * e2 () (n, m);
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag, row_major_tag, packed_proxy_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E2::const_iterator2 it2e2 (e2 ().find2 (1, n, n + 1));
sl@0:                 typename E2::const_iterator2 it2e2_end (e2 ().find2 (1, n, e2 ().size2 ()));
sl@0:                 difference_type m (it2e2_end - it2e2);
sl@0:                 while (-- m >= 0)
sl@0:                     e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag, row_major_tag, unknown_storage_tag) {
sl@0:         typedef typename E1::size_type size_type;
sl@0:         typedef typename E1::difference_type difference_type;
sl@0:         typedef typename E1::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ());
sl@0:         size_type size = e1 ().size ();
sl@0:         for (size_type n = 0; n < size; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e2 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             value_type t = e1 () (n) /= e2 () (n, n);
sl@0:             if (t != value_type/*zero*/()) {
sl@0:                 typename E2::const_iterator2 it2e2 (e2 ().find2 (1, n, n + 1));
sl@0:                 typename E2::const_iterator2 it2e2_end (e2 ().find2 (1, n, e2 ().size2 ()));
sl@0:                 while (it2e2 != it2e2_end)
sl@0:                     e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2;
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Redirectors :-)
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag, row_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        upper_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag, column_major_tag) {
sl@0:         typedef typename E1::storage_category storage_category;
sl@0:         inplace_solve (trans (e2), e1,
sl@0:                        lower_tag (), row_major_tag (), storage_category ());
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         upper_tag) {
sl@0:         typedef typename E2::orientation_category orientation_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        upper_tag (), orientation_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
sl@0:                         unit_upper_tag) {
sl@0:         typedef typename E2::orientation_category orientation_category;
sl@0:         inplace_solve (e1, triangular_adaptor<const E2, unit_upper> (e2 ()),
sl@0:                        unit_upper_tag (), orientation_category ());
sl@0:     }
sl@0: 
sl@0:     template<class E1, class E2, class C>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     typename matrix_vector_solve_traits<E1, E2>::result_type
sl@0:     solve (const vector_expression<E1> &e1,
sl@0:            const matrix_expression<E2> &e2,
sl@0:            C) {
sl@0:         typename matrix_vector_solve_traits<E1, E2>::result_type r (e1);
sl@0:         inplace_solve (r, e2, C ());
sl@0:         return r;
sl@0:     }
sl@0: 
sl@0:     template<class E1, class E2>
sl@0:     struct matrix_matrix_solve_traits {
sl@0:         typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
sl@0:         typedef matrix<promote_type> result_type;
sl@0:     };
sl@0: 
sl@0:     // Operations:
sl@0:     //  k * n * (n - 1) / 2 + k * n = k * n * (n + 1) / 2 multiplications,
sl@0:     //  k * n * (n - 1) / 2 additions
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         lower_tag, dense_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (size_type n = 0; n < size1; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (size_type l = 0; l < size2; ++ l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     for (size_type m = n + 1; m < size1; ++ m)
sl@0:                         e2 () (m, l) -= e1 () (m, n) * t;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         lower_tag, packed_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (size_type n = 0; n < size1; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (size_type l = 0; l < size2; ++ l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n));
sl@0:                     typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n));
sl@0:                     difference_type m (it1e1_end - it1e1);
sl@0:                     while (-- m >= 0)
sl@0:                         e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         lower_tag, unknown_storage_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (size_type n = 0; n < size1; ++ n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (size_type l = 0; l < size2; ++ l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n));
sl@0:                     typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n));
sl@0:                     while (it1e1 != it1e1_end)
sl@0:                         e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         lower_tag) {
sl@0:         typedef typename E1::storage_category dispatch_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        lower_tag (), dispatch_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         unit_lower_tag) {
sl@0:         typedef typename E1::storage_category dispatch_category;
sl@0:         inplace_solve (triangular_adaptor<const E1, unit_lower> (e1 ()), e2,
sl@0:                        unit_lower_tag (), dispatch_category ());
sl@0:     }
sl@0: 
sl@0:     // Dense (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         upper_tag, dense_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (difference_type n = size1 - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (difference_type l = size2 - 1; l >= 0; -- l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     for (difference_type m = n - 1; m >= 0; -- m)
sl@0:                         e2 () (m, l) -= e1 () (m, n) * t;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Packed (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         upper_tag, packed_proxy_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (difference_type n = size1 - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (difference_type l = size2 - 1; l >= 0; -- l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
sl@0:                     typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
sl@0:                     difference_type m (it1e1_rend - it1e1);
sl@0:                     while (-- m >= 0)
sl@0:                         e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Sparse (proxy) case
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         upper_tag, unknown_storage_tag) {
sl@0:         typedef typename E2::size_type size_type;
sl@0:         typedef typename E2::difference_type difference_type;
sl@0:         typedef typename E2::value_type value_type;
sl@0: 
sl@0:         BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
sl@0:         BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ());
sl@0:         size_type size1 = e2 ().size1 ();
sl@0:         size_type size2 = e2 ().size2 ();
sl@0:         for (difference_type n = size1 - 1; n >= 0; -- n) {
sl@0: #ifndef BOOST_UBLAS_SINGULAR_CHECK
sl@0:             BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
sl@0: #else
sl@0:             if (e1 () (n, n) == value_type/*zero*/())
sl@0:                 singular ().raise ();
sl@0: #endif
sl@0:             for (difference_type l = size2 - 1; l >= 0; -- l) {
sl@0:                 value_type t = e2 () (n, l) /= e1 () (n, n);
sl@0:                 if (t != value_type/*zero*/()) {
sl@0:                     typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
sl@0:                     typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
sl@0:                     while (it1e1 != it1e1_rend)
sl@0:                         e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1;
sl@0:                 }
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:     // Dispatcher
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         upper_tag) {
sl@0:         typedef typename E1::storage_category dispatch_category;
sl@0:         inplace_solve (e1, e2,
sl@0:                        upper_tag (), dispatch_category ());
sl@0:     }
sl@0:     template<class E1, class E2>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
sl@0:                         unit_upper_tag) {
sl@0:         typedef typename E1::storage_category dispatch_category;
sl@0:         inplace_solve (triangular_adaptor<const E1, unit_upper> (e1 ()), e2,
sl@0:                        unit_upper_tag (), dispatch_category ());
sl@0:     }
sl@0: 
sl@0:     template<class E1, class E2, class C>
sl@0:     BOOST_UBLAS_INLINE
sl@0:     typename matrix_matrix_solve_traits<E1, E2>::result_type
sl@0:     solve (const matrix_expression<E1> &e1,
sl@0:            const matrix_expression<E2> &e2,
sl@0:            C) {
sl@0:         typename matrix_matrix_solve_traits<E1, E2>::result_type r (e2);
sl@0:         inplace_solve (e1, r, C ());
sl@0:         return r;
sl@0:     }
sl@0: 
sl@0: }}}
sl@0: 
sl@0: #endif