EIC code displayed by LXR master/​include/​boost/​numeric/​ublas/​banded.hpp	Source navigation Diff markup Identifier search General search
	Version: master test Revert   Change

File indexing completed on 2025-01-18 09:43:04

 //
 //  Copyright (c) 2000-2013
 //  Joerg Walter, Mathias Koch, Athanasios Iliopoulos
 //
 //  Distributed under the Boost Software License, Version 1.0. (See
 //  accompanying file LICENSE_1_0.txt or copy at
 //  http://www.boost.org/LICENSE_1_0.txt)
 //
 //  The authors gratefully acknowledge the support of
 //  GeNeSys mbH & Co. KG in producing this work.
 //
 
 #ifndef _BOOST_UBLAS_BANDED_
 #define _BOOST_UBLAS_BANDED_
 
 #include <boost/numeric/ublas/matrix.hpp>
 #include <boost/numeric/ublas/detail/temporary.hpp>
 
 // Iterators based on ideas of Jeremy Siek
 
 namespace boost { namespace numeric { namespace ublas {
 
 
 namespace hidden {
 
 
 
 /** \brief A helper for band_matrix indexing.
  *
  * The indexing happens as per the netlib description: http://www.netlib.org/lapack/lug/node124.html.
  * In the case of a row_major matrix a different approach is followed;
  */
 template <class LayoutType>
 class banded_indexing { };
 
 /** \brief A helper for indexing column major banded matrices.
  *
  */
 template <>
 class banded_indexing<column_major_tag> {
 public:
 
     template <class T>
     BOOST_UBLAS_INLINE static T size(T /*size1*/, T size2) {
         return size2;
     }
 
 //    template <class T>
 //    BOOST_UBLAS_INLINE static bool valid_index(T size1, T /*size2*/, T lower, T upper, T i, T j) {
 //        return (upper+i >= j) && i <= std::min(size1 - 1, j + lower); // upper + i is used by get_index. Maybe find a way to consolidate the operations to increase performance
 //    }
 
     template <class T>
     BOOST_UBLAS_INLINE static T get_index(T /*size1*/, T size2, T lower, T upper, T i, T j) {
         return column_major::element (upper + i - j, lower + 1 + upper, j, size2);
     }
 };
 
 /** \brief A helper for indexing row major banded matrices.
  *
  */
 template <>
 class banded_indexing<row_major_tag> {
 public:
 
     template <class T>
     BOOST_UBLAS_INLINE static T size(T size1, T /*size2*/) {
         return size1;
     }
 
   //  template <class T>
   //  BOOST_UBLAS_INLINE static bool valid_index(T /*size1*/, T  size2, T lower, T upper, T i, T j) {
   //      return (lower+j >= i) && j <= std::min(size2 - 1, i + upper); // lower + j is used by get_index. Maybe find a way to consolidate the operations to increase performance
   //  }
 
     template <class T>
     BOOST_UBLAS_INLINE static T get_index(T size1, T /*size2*/, T lower, T upper, T i, T j) {
         return row_major::element (i, size1, lower + j - i, lower + 1 + upper);
     }
 };
 
 }
 
     /** \brief A banded matrix of values of type \c T.
      *
      * For a \f$(mxn)\f$-dimensional banded matrix with \f$l\f$ lower and \f$u\f$ upper diagonals and 
      * \f$0 \leq i < m\f$ and \f$0 \leq j < n\f$, if \f$i>j+l\f$ or \f$i<j-u\f$ then \f$b_{i,j}=0\f$. 
      * The default storage for banded matrices is packed. Orientation and storage can also be specified. 
      * Default is \c row_major and and unbounded_array. It is \b not required by the storage to initialize 
      * elements of the matrix.
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
      * \tparam A the type of Storage array. Default is \c unbounded_array
      */
     template<class T, class L, class A>
     class banded_matrix:
         public matrix_container<banded_matrix<T, L, A> > {
 
         typedef T *pointer;
         typedef L layout_type;
         typedef banded_matrix<T, L, A> self_type;
 
 
 
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_container<self_type>::operator ();
 #endif
         typedef typename A::size_type size_type;
         typedef typename A::difference_type difference_type;
         typedef T value_type;
         typedef const T &const_reference;
         typedef T &reference;
         typedef A array_type;
         typedef const matrix_reference<const self_type> const_closure_type;
         typedef matrix_reference<self_type> closure_type;
         typedef vector<T, A> vector_temporary_type;
         typedef matrix<T, L, A> matrix_temporary_type;  // general sub-matrix
         typedef packed_tag storage_category;
         typedef typename L::orientation_category orientation_category;
 
     private:
     public:
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         banded_matrix ():
             matrix_container<self_type> (),
             size1_ (0), size2_ (0),
             lower_ (0), upper_ (0), data_ (0) {}
         BOOST_UBLAS_INLINE
         banded_matrix (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2),
             lower_ (lower), upper_ (upper),
 #if defined(BOOST_UBLAS_OWN_BANDED) || (BOOST_UBLAS_LEGACY_BANDED)
             data_ ((std::max) (size1, size2) * (lower + 1 + upper))
 #else
             data_ ( hidden::banded_indexing<orientation_category>::size(size1, size2) * (lower + 1 + upper)) // This is the netlib layout as described here: http://www.netlib.org/lapack/lug/node124.html
 #endif
         {
         }
         BOOST_UBLAS_INLINE
         banded_matrix (size_type size1, size_type size2, size_type lower, size_type upper, const array_type &data):
             matrix_container<self_type> (),
             size1_ (size1), size2_ (size2),
             lower_ (lower), upper_ (upper), data_ (data) {}
         BOOST_UBLAS_INLINE
         banded_matrix (const banded_matrix &m):
             matrix_container<self_type> (),
             size1_ (m.size1_), size2_ (m.size2_),
             lower_ (m.lower_), upper_ (m.upper_), data_ (m.data_) {}
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix (const matrix_expression<AE> &ae, size_type lower = 0, size_type upper = 0):
             matrix_container<self_type> (),
             size1_ (ae ().size1 ()), size2_ (ae ().size2 ()),
             lower_ (lower), upper_ (upper),
 #if defined(BOOST_UBLAS_OWN_BANDED) || (BOOST_UBLAS_LEGACY_BANDED)
             data_ ((std::max) (size1_, size2_) * (lower_ + 1 + upper_))
 #else
             data_ ( hidden::banded_indexing<orientation_category>::size(size1_, size2_) * (lower_ + 1 + upper_)) // This is the netlib layout as described here: http://www.netlib.org/lapack/lug/node124.html
 #endif
         {
             matrix_assign<scalar_assign> (*this, ae);
         }
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return size1_;
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return size2_;
         }
         BOOST_UBLAS_INLINE
         size_type lower () const {
             return lower_;
         }
         BOOST_UBLAS_INLINE
         size_type upper () const {
             return upper_;
         }
 
         // Storage accessors
         BOOST_UBLAS_INLINE
         const array_type &data () const {
             return data_;
         }
         BOOST_UBLAS_INLINE
         array_type &data () {
             return data_;
         }
 
 #if !defined (BOOST_UBLAS_OWN_BANDED)||(BOOST_UBLAS_LEGACY_BANDED)
         BOOST_UBLAS_INLINE
         bool is_element_in_band(size_type i, size_type j) const{
             //return (upper_+i >= j) && i <= std::min(size1() - 1, j + lower_); // We don't need to check if i is outside because it is checked anyway in the accessors.
             return (upper_+i >= j) && i <= ( j + lower_); // Essentially this band has "infinite" positive dimensions
         }
 #endif
         // Resizing
         BOOST_UBLAS_INLINE
         void resize (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0, bool preserve = true) {
             if (preserve) {
                 self_type temporary (size1, size2, lower, upper);
                 detail::matrix_resize_preserve<layout_type> (*this, temporary);
             }
             else {
                 data ().resize ((std::max) (size1, size2) * (lower + 1 + upper));
                 size1_ = size1;
                 size2_ = size2;
                 lower_ = lower;
                 upper_ = upper;
             }
         }
 
         BOOST_UBLAS_INLINE
         void resize_packed_preserve (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0) {
             size1_ = size1;
             size2_ = size2;
             lower_ = lower;
             upper_ = upper;
             data ().resize ((std::max) (size1, size2) * (lower + 1 + upper), value_type ());
         }
 
         // Element access
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             const size_type k = (std::max) (i, j);
             const size_type l = lower_ + j - i;
             if (k < (std::max) (size1_, size2_) && // TODO: probably use BOOST_UBLAS_CHECK here instead of if
                 l < lower_ + 1 + upper_)
                 return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                        l, lower_ + 1 + upper_)];
 #elif BOOST_UBLAS_LEGACY_BANDED // Prior to version: TODO: add version this is actually incorporated in
             const size_type k = j;
             const size_type l = upper_ + i - j;
             if (k < size2_ &&
                 l < lower_ + 1 + upper_)
                 return data () [layout_type::element (k, size2_,
                                                        l, lower_ + 1 + upper_)];
 #else  // New default
             // This is the netlib layout as described here: http://www.netlib.org/lapack/lug/node124.html
             if ( is_element_in_band( i, j) ) {
                 return data () [hidden::banded_indexing<orientation_category>::get_index(size1_, size2_, lower_, upper_, i, j)];
             }
 #endif
             return zero_;
         }
 
         BOOST_UBLAS_INLINE
         reference at_element (size_type i, size_type j) {
             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             const size_type k = (std::max) (i, j);
             const size_type l = lower_ + j - i; // TODO: Don't we need an if or BOOST_UBLAS_CHECK HERE?
             return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                    l, lower_ + 1 + upper_)];
 #elif BOOST_UBLAS_LEGACY_BANDED // Prior to version: TODO: add version this is actually incorporated in
             const size_type k = j;
             const size_type l = upper_ + i - j;
             if (! (k < size2_ &&
                    l < lower_ + 1 + upper_) ) {
                 bad_index ().raise ();
                 // NEVER reached
             }
             return data () [layout_type::element (k, size2_,
                                                        l, lower_ + 1 + upper_)];
 #else
             // This is the netlib layout as described here: http://www.netlib.org/lapack/lug/node124.html
             BOOST_UBLAS_CHECK(is_element_in_band( i, j) , bad_index());
             return data () [hidden::banded_indexing<orientation_category>::get_index(size1_, size2_, lower_, upper_, i, j)];
 #endif
         }
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             BOOST_UBLAS_CHECK (i < size1_, bad_index ());
             BOOST_UBLAS_CHECK (j < size2_, bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             const size_type k = (std::max) (i, j);
             const size_type l = lower_ + j - i;
             if (! (k < (std::max) (size1_, size2_) && // TODO: probably use BOOST_UBLAS_CHECK here instead of if
                   l < lower_ + 1 + upper_) ) {
                 bad_index ().raise ();
                 // NEVER reached
             }
             return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                        l, lower_ + 1 + upper_)];
 #elif BOOST_UBLAS_LEGACY_BANDED // Prior to version: TODO: add version this is actually incorporated in
             const size_type k = j;
             const size_type l = upper_ + i - j;
             if (! (k < size2_ &&
                    l < lower_ + 1 + upper_) ) {
                 bad_index ().raise ();
                 // NEVER reached
             }
             return data () [layout_type::element (k, size2_,
                                                        l, lower_ + 1 + upper_)];
 #else
             // This is the netlib layout as described here: http://www.netlib.org/lapack/lug/node124.html
             BOOST_UBLAS_CHECK( is_element_in_band( i, j) , bad_index());
             return data () [hidden::banded_indexing<orientation_category>::get_index(size1_, size2_, lower_, upper_, i, j)];
 #endif
 
         }
 
         // Element assignment
         BOOST_UBLAS_INLINE
         reference insert_element (size_type i, size_type j, const_reference t) {
             return (operator () (i, j) = t);
         }
         BOOST_UBLAS_INLINE
         void erase_element (size_type i, size_type j) {
             operator () (i, j) = value_type/*zero*/();
         }
 
         // Zeroing
         BOOST_UBLAS_INLINE
         void clear () {
             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
         }
 
         // Assignment
         BOOST_UBLAS_INLINE
         banded_matrix &operator = (const banded_matrix &m) {
             size1_ = m.size1_;
             size2_ = m.size2_;
             lower_ = m.lower_;
             upper_ = m.upper_;
             data () = m.data ();
             return *this;
         }
         BOOST_UBLAS_INLINE
         banded_matrix &assign_temporary (banded_matrix &m) {
             swap (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix &operator = (const matrix_expression<AE> &ae) {
             self_type temporary (ae, lower_, upper_);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix &assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix& operator += (const matrix_expression<AE> &ae) {
             self_type temporary (*this + ae, lower_, upper_);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix &plus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_plus_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix& operator -= (const matrix_expression<AE> &ae) {
             self_type temporary (*this - ae, lower_, upper_);
             return assign_temporary (temporary);
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_matrix &minus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_minus_assign> (*this, ae);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         banded_matrix& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         banded_matrix& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (banded_matrix &m) {
             if (this != &m) {
                 std::swap (size1_, m.size1_);
                 std::swap (size2_, m.size2_);
                 std::swap (lower_, m.lower_);
                 std::swap (upper_, m.upper_);
                 data ().swap (m.data ());
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (banded_matrix &m1, banded_matrix &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int rank, size_type i, size_type j) const {
             if (rank == 1) {
                 size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                 i = (std::max) (i, lower_i);
                 size_type upper_i = (std::min) (j + 1 + lower_, size1_);
                 i = (std::min) (i, upper_i);
             }
             return const_iterator1 (*this, i, j);
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int rank, size_type i, size_type j) {
             if (rank == 1) {
                 size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                 i = (std::max) (i, lower_i);
                 size_type upper_i = (std::min) (j + 1 + lower_, size1_);
                 i = (std::min) (i, upper_i);
             }
             return iterator1 (*this, i, j);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int rank, size_type i, size_type j) const {
             if (rank == 1) {
                 size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                 j = (std::max) (j, lower_j);
                 size_type upper_j = (std::min) (i + 1 + upper_, size2_);
                 j = (std::min) (j, upper_j);
             }
             return const_iterator2 (*this, i, j);
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int rank, size_type i, size_type j) {
             if (rank == 1) {
                 size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                 j = (std::max) (j, lower_j);
                 size_type upper_j = (std::min) (i + 1 + upper_, size2_);
                 j = (std::min) (j, upper_j);
             }
             return iterator2 (*this, i, j);
         }
 
         // Iterators simply are indices.
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<banded_matrix>,
             public random_access_iterator_base<packed_random_access_iterator_tag,
                                                const_iterator1, value_type> {
         public:
             typedef typename banded_matrix::value_type value_type;
             typedef typename banded_matrix::difference_type difference_type;
             typedef typename banded_matrix::const_reference reference;
             typedef const typename banded_matrix::pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, size_type it1, size_type it2):
                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 ++ it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 -- it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 it1_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 it1_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ - it.it1_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 return (*this) () (it1_, it2_);
             }
             BOOST_UBLAS_INLINE
             const_reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 begin () const {
                 return (*this) ().find2 (1, it1_, 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator1 &operator = (const const_iterator1 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ == it.it1_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ < it.it1_;
             }
 
         private:
             size_type it1_;
             size_type it2_;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1_, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<banded_matrix>,
             public random_access_iterator_base<packed_random_access_iterator_tag,
                                                iterator1, value_type> {
         public:
             typedef typename banded_matrix::value_type value_type;
             typedef typename banded_matrix::difference_type difference_type;
             typedef typename banded_matrix::reference reference;
             typedef typename banded_matrix::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, size_type it1, size_type it2):
                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 ++ it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 -- it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 it1_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 it1_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ - it.it1_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 return (*this) ().at_element (it1_, it2_);
             }
             BOOST_UBLAS_INLINE
             reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 begin () const {
                 return (*this) ().find2 (1, it1_, 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
             }
 
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ == it.it1_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
                 return it1_ < it.it1_;
             }
 
         private:
             size_type it1_;
             size_type it2_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, size1_, 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<banded_matrix>,
             public random_access_iterator_base<packed_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename banded_matrix::value_type value_type;
             typedef typename banded_matrix::difference_type difference_type;
             typedef typename banded_matrix::const_reference reference;
             typedef const typename banded_matrix::pointer pointer;
 
             typedef const_iterator1 dual_iterator_type;
             typedef const_reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator2 ():
                 container_const_reference<self_type> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const self_type &m, size_type it1, size_type it2):
                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 ++ it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 -- it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 it2_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 it2_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ - it.it2_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 return (*this) () (it1_, it2_);
             }
             BOOST_UBLAS_INLINE
             const_reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 begin () const {
                 return (*this) ().find1 (1, 0, it2_);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end();
             }
 
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rbegin () const {
                 return const_reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator2 &operator = (const const_iterator2 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ == it.it2_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ < it.it2_;
             }
 
         private:
             size_type it1_;
             size_type it2_;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2_);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<banded_matrix>,
             public random_access_iterator_base<packed_random_access_iterator_tag,
                                                iterator2, value_type> {
         public:
             typedef typename banded_matrix::value_type value_type;
             typedef typename banded_matrix::difference_type difference_type;
             typedef typename banded_matrix::reference reference;
             typedef typename banded_matrix::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), it1_ (), it2_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, size_type it1, size_type it2):
                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 ++ it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 -- it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 it2_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 it2_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ - it.it2_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 return (*this) ().at_element (it1_, it2_);
             }
             BOOST_UBLAS_INLINE
             reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 begin () const {
                 return (*this) ().find1 (1, 0, it2_);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_;
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_;
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ == it.it2_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
                 return it2_ < it.it2_;
             }
 
         private:
             size_type it1_;
             size_type it2_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             return find2 (0, 0, size2_);
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
     private:
         size_type size1_;
         size_type size2_;
         size_type lower_;
         size_type upper_;
         array_type data_;
         typedef const value_type const_value_type;
         static const_value_type zero_;
     };
 
     template<class T, class L, class A>
     typename banded_matrix<T, L, A>::const_value_type banded_matrix<T, L, A>::zero_ = value_type/*zero*/();
 
 
     /** \brief A diagonal matrix of values of type \c T, which is a specialization of a banded matrix
      *
      * For a \f$(m\times m)\f$-dimensional diagonal matrix, \f$0 \leq i < m\f$ and \f$0 \leq j < m\f$, 
      * if \f$i\neq j\f$ then \f$b_{i,j}=0\f$. The default storage for diagonal matrices is packed. 
      * Orientation and storage can also be specified. Default is \c row major \c unbounded_array. 
      *
      * As a specialization of a banded matrix, the constructor of the diagonal matrix creates 
      * a banded matrix with 0 upper and lower diagonals around the main diagonal and the matrix is 
      * obviously a square matrix. Operations are optimized based on these 2 assumptions. It is 
      * \b not required by the storage to initialize elements of the matrix.  
      *
      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
      * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
      * \tparam A the type of Storage array. Default is \c unbounded_array
      */
     template<class T, class L, class A>
     class diagonal_matrix:
         public banded_matrix<T, L, A> {
     public:
         typedef typename A::size_type size_type;
         typedef banded_matrix<T, L, A> matrix_type;
         typedef A array_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         diagonal_matrix ():
             matrix_type () {}
         BOOST_UBLAS_INLINE
         diagonal_matrix (size_type size):
             matrix_type (size, size) {}
         BOOST_UBLAS_INLINE
         diagonal_matrix (size_type size, const array_type& data):
             matrix_type (size, size, 0, 0, data) {}
         BOOST_UBLAS_INLINE
         diagonal_matrix (size_type size1, size_type size2):
             matrix_type (size1, size2) {}
         template<class AE>
         BOOST_UBLAS_INLINE
         diagonal_matrix (const matrix_expression<AE> &ae):
             matrix_type (ae) {}
         BOOST_UBLAS_INLINE
         ~diagonal_matrix () {}
 
         // Assignment
         BOOST_UBLAS_INLINE
         diagonal_matrix &operator = (const diagonal_matrix &m) {
             matrix_type::operator = (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         diagonal_matrix &operator = (const matrix_expression<AE> &ae) {
             matrix_type::operator = (ae);
             return *this;
         }
     };
 
     /** \brief A banded matrix adaptator: convert a any matrix into a banded matrix expression
      *
      * For a \f$(m\times n)\f$-dimensional matrix, the \c banded_adaptor will provide a banded matrix
      * with \f$l\f$ lower and \f$u\f$ upper diagonals and \f$0 \leq i < m\f$ and \f$0 \leq j < n\f$,
      * if \f$i>j+l\f$ or \f$i<j-u\f$ then \f$b_{i,j}=0\f$. 
      *
      * Storage and location are based on those of the underlying matrix. This is important because
      * a \c banded_adaptor does not copy the matrix data to a new place. Therefore, modifying values
      * in a \c banded_adaptor matrix will also modify the underlying matrix too.
      *
      * \tparam M the type of matrix used to generate a banded matrix
      */
     template<class M>
     class banded_adaptor:
         public matrix_expression<banded_adaptor<M> > {
 
         typedef banded_adaptor<M> self_type;
 
     public:
 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
         using matrix_expression<self_type>::operator ();
 #endif
         typedef const M const_matrix_type;
         typedef M matrix_type;
         typedef typename M::size_type size_type;
         typedef typename M::difference_type difference_type;
         typedef typename M::value_type value_type;
         typedef typename M::const_reference const_reference;
         typedef typename boost::mpl::if_<boost::is_const<M>,
                                           typename M::const_reference,
                                           typename M::reference>::type reference;
         typedef typename boost::mpl::if_<boost::is_const<M>,
                                           typename M::const_closure_type,
                                           typename M::closure_type>::type matrix_closure_type;
         typedef const self_type const_closure_type;
         typedef self_type closure_type;
         // Replaced by _temporary_traits to avoid type requirements on M
         //typedef typename M::vector_temporary_type vector_temporary_type;
         //typedef typename M::matrix_temporary_type matrix_temporary_type;
         typedef typename storage_restrict_traits<typename M::storage_category,
                                                  packed_proxy_tag>::storage_category storage_category;
         typedef typename M::orientation_category orientation_category;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         banded_adaptor (matrix_type &data, size_type lower = 0, size_type upper = 0):
             matrix_expression<self_type> (),
             data_ (data), lower_ (lower), upper_ (upper) {}
         BOOST_UBLAS_INLINE
         banded_adaptor (const banded_adaptor &m):
             matrix_expression<self_type> (),
             data_ (m.data_), lower_ (m.lower_), upper_ (m.upper_) {}
 
         // Accessors
         BOOST_UBLAS_INLINE
         size_type size1 () const {
             return data_.size1 ();
         }
         BOOST_UBLAS_INLINE
         size_type size2 () const {
             return data_.size2 ();
         }
         BOOST_UBLAS_INLINE
         size_type lower () const {
             return lower_;
         }
         BOOST_UBLAS_INLINE
         size_type upper () const {
             return upper_;
         }
 
         // Storage accessors
         BOOST_UBLAS_INLINE
         const matrix_closure_type &data () const {
             return data_;
         }
         BOOST_UBLAS_INLINE
         matrix_closure_type &data () {
             return data_;
         }
 
 #if !defined (BOOST_UBLAS_OWN_BANDED)||(BOOST_UBLAS_LEGACY_BANDED)
         BOOST_UBLAS_INLINE
         bool is_element_in_band(size_type i, size_type j) const{
             //return (upper_+i >= j) && i <= std::min(size1() - 1, j + lower_); // We don't need to check if i is outside because it is checked anyway in the accessors.
             return (upper_+i >= j) && i <= ( j + lower_); // Essentially this band has "infinite" positive dimensions
         }
 #endif
 
         // Element access
 #ifndef BOOST_UBLAS_PROXY_CONST_MEMBER
         BOOST_UBLAS_INLINE
         const_reference operator () (size_type i, size_type j) const {
             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             size_type k = (std::max) (i, j);
             size_type l = lower_ + j - i;
             if (k < (std::max) (size1 (), size2 ()) &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #elif BOOST_UBLAS_LEGACY_BANDED
             size_type k = j;
             size_type l = upper_ + i - j;
             if (k < size2 () &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #else
             if (is_element_in_band( i, j))
                 return data () (i, j);
 #endif
             return zero_;
         }
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) {
             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             size_type k = (std::max) (i, j);
             size_type l = lower_ + j - i;
             if (k < (std::max) (size1 (), size2 ()) &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #elif BOOST_UBLAS_LEGACY_BANDED
             size_type k = j;
             size_type l = upper_ + i - j;
             if (k < size2 () &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #else
             if (is_element_in_band( i, j))
                 return data () (i, j);
 #endif
 #ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER
             bad_index ().raise ();
 #endif
             return const_cast<reference>(zero_);
         }
 #else
         BOOST_UBLAS_INLINE
         reference operator () (size_type i, size_type j) const {
             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
             size_type k = (std::max) (i, j);
             size_type l = lower_ + j - i;
             if (k < (std::max) (size1 (), size2 ()) &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #elif BOOST_UBLAS_LEGACY_BANDED
             size_type k = j;
             size_type l = upper_ + i - j;
             if (k < size2 () &&
                 l < lower_ + 1 + upper_)
                 return data () (i, j);
 #else
             if (is_element_in_band( i, j))
                 return data () (i, j);
 #endif
 #ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER
             bad_index ().raise ();
 #endif
             return const_cast<reference>(zero_);
         }
 #endif
 
         // Assignment
         BOOST_UBLAS_INLINE
         banded_adaptor &operator = (const banded_adaptor &m) {
             matrix_assign<scalar_assign> (*this, m);
             return *this;
         }
         BOOST_UBLAS_INLINE
         banded_adaptor &assign_temporary (banded_adaptor &m) {
             *this = m;
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor &operator = (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, matrix<value_type> (ae));
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor &assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor& operator += (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, matrix<value_type> (*this + ae));
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor &plus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_plus_assign> (*this, ae);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor& operator -= (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_assign> (*this, matrix<value_type> (*this - ae));
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         banded_adaptor &minus_assign (const matrix_expression<AE> &ae) {
             matrix_assign<scalar_minus_assign> (*this, ae);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         banded_adaptor& operator *= (const AT &at) {
             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
             return *this;
         }
         template<class AT>
         BOOST_UBLAS_INLINE
         banded_adaptor& operator /= (const AT &at) {
             matrix_assign_scalar<scalar_divides_assign> (*this, at);
             return *this;
         }
 
         // Closure comparison
         BOOST_UBLAS_INLINE
         bool same_closure (const banded_adaptor &ba) const {
             return (*this).data ().same_closure (ba.data ());
         }
 
         // Swapping
         BOOST_UBLAS_INLINE
         void swap (banded_adaptor &m) {
             if (this != &m) {
                 BOOST_UBLAS_CHECK (lower_ == m.lower_, bad_size ());
                 BOOST_UBLAS_CHECK (upper_ == m.upper_, bad_size ());
                 matrix_swap<scalar_swap> (*this, m);
             }
         }
         BOOST_UBLAS_INLINE
         friend void swap (banded_adaptor &m1, banded_adaptor &m2) {
             m1.swap (m2);
         }
 
         // Iterator types
     private:
         // Use the matrix iterator
         typedef typename M::const_iterator1 const_subiterator1_type;
         typedef typename boost::mpl::if_<boost::is_const<M>,
                                           typename M::const_iterator1,
                                           typename M::iterator1>::type subiterator1_type;
         typedef typename M::const_iterator2 const_subiterator2_type;
         typedef typename boost::mpl::if_<boost::is_const<M>,
                                           typename M::const_iterator2,
                                           typename M::iterator2>::type subiterator2_type;
 
     public:
 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
 #else
         class const_iterator1;
         class iterator1;
         class const_iterator2;
         class iterator2;
 #endif
         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
 
         // Element lookup
         BOOST_UBLAS_INLINE
         const_iterator1 find1 (int rank, size_type i, size_type j) const {
             if (rank == 1) {
                 size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                 i = (std::max) (i, lower_i);
                 size_type upper_i = (std::min) (j + 1 + lower_, size1 ());
                 i = (std::min) (i, upper_i);
             }
             return const_iterator1 (*this, data ().find1 (rank, i, j));
         }
         BOOST_UBLAS_INLINE
         iterator1 find1 (int rank, size_type i, size_type j) {
             if (rank == 1) {
                 size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                 i = (std::max) (i, lower_i);
                 size_type upper_i = (std::min) (j + 1 + lower_, size1 ());
                 i = (std::min) (i, upper_i);
             }
             return iterator1 (*this, data ().find1 (rank, i, j));
         }
         BOOST_UBLAS_INLINE
         const_iterator2 find2 (int rank, size_type i, size_type j) const {
             if (rank == 1) {
                 size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                 j = (std::max) (j, lower_j);
                 size_type upper_j = (std::min) (i + 1 + upper_, size2 ());
                 j = (std::min) (j, upper_j);
             }
             return const_iterator2 (*this, data ().find2 (rank, i, j));
         }
         BOOST_UBLAS_INLINE
         iterator2 find2 (int rank, size_type i, size_type j) {
             if (rank == 1) {
                 size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                 j = (std::max) (j, lower_j);
                 size_type upper_j = (std::min) (i + 1 + upper_, size2 ());
                 j = (std::min) (j, upper_j);
             }
             return iterator2 (*this, data ().find2 (rank, i, j));
         }
 
         // Iterators simply are indices.
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator1:
             public container_const_reference<banded_adaptor>,
             public random_access_iterator_base<typename iterator_restrict_traits<
                                                    typename const_subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
                                                const_iterator1, value_type> {
         public:
             typedef typename const_subiterator1_type::value_type value_type;
             typedef typename const_subiterator1_type::difference_type difference_type;
             typedef typename const_subiterator1_type::reference reference;
             typedef typename const_subiterator1_type::pointer pointer;
 
             typedef const_iterator2 dual_iterator_type;
             typedef const_reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator1 ():
                 container_const_reference<self_type> (), it1_ () {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const self_type &m, const const_subiterator1_type &it1):
                 container_const_reference<self_type> (m), it1_ (it1) {}
             BOOST_UBLAS_INLINE
             const_iterator1 (const iterator1 &it):
                 container_const_reference<self_type> (it ()), it1_ (it.it1_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator1 &operator ++ () {
                 ++ it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -- () {
                 -- it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator += (difference_type n) {
                 it1_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator1 &operator -= (difference_type n) {
                 it1_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ - it.it1_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 size_type i = index1 ();
                 size_type j = index2 ();
                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
                 size_type k = (std::max) (i, j);
                 size_type l = (*this) ().lower () + j - i;
                 if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it1_;
 #else
                 size_type k = j;
                 size_type l = (*this) ().upper () + i - j;
                 if (k < (*this) ().size2 () &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it1_;
 #endif
                 return (*this) () (i, j);
             }
             BOOST_UBLAS_INLINE
             const_reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 begin () const {
                 return (*this) ().find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 end () const {
                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator2 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rbegin () const {
                 return const_reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 rend () const {
                 return const_reverse_iterator2 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator2 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_.index1 ();
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it1_.index2 ();
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator1 &operator = (const const_iterator1 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ == it.it1_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ < it.it1_;
             }
 
         private:
             const_subiterator1_type it1_;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator1 begin1 () const {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cbegin1 () const {
             return begin1 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator1 end1 () const {
             return find1 (0, size1 (), 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator1 cend1 () const {
             return end1 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator1:
             public container_reference<banded_adaptor>,
             public random_access_iterator_base<typename iterator_restrict_traits<
                                                    typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
                                                iterator1, value_type> {
         public:
             typedef typename subiterator1_type::value_type value_type;
             typedef typename subiterator1_type::difference_type difference_type;
             typedef typename subiterator1_type::reference reference;
             typedef typename subiterator1_type::pointer pointer;
 
             typedef iterator2 dual_iterator_type;
             typedef reverse_iterator2 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator1 ():
                 container_reference<self_type> (), it1_ () {}
             BOOST_UBLAS_INLINE
             iterator1 (self_type &m, const subiterator1_type &it1):
                 container_reference<self_type> (m), it1_ (it1) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator1 &operator ++ () {
                 ++ it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -- () {
                 -- it1_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator += (difference_type n) {
                 it1_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator1 &operator -= (difference_type n) {
                 it1_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ - it.it1_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 size_type i = index1 ();
                 size_type j = index2 ();
                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
                 size_type k = (std::max) (i, j);
                 size_type l = (*this) ().lower () + j - i;
                 if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it1_;
 #else
                 size_type k = j;
                 size_type l = (*this) ().upper () + i - j;
                 if (k < (*this) ().size2 () &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it1_;
 #endif
                 return (*this) () (i, j);
             }
             BOOST_UBLAS_INLINE
             reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 begin () const {
                 return (*this) ().find2 (1, index1 (), 0);
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator2 end () const {
                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rbegin () const {
                 return reverse_iterator2 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator2 rend () const {
                 return reverse_iterator2 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it1_.index1 ();
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it1_.index2 ();
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator1 &operator = (const iterator1 &it) {
                 container_reference<self_type>::assign (&it ());
                 it1_ = it.it1_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ == it.it1_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator1 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it1_ < it.it1_;
             }
 
         private:
             subiterator1_type it1_;
 
             friend class const_iterator1;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator1 begin1 () {
             return find1 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator1 end1 () {
             return find1 (0, size1 (), 0);
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class const_iterator2:
             public container_const_reference<banded_adaptor>,
             public random_access_iterator_base<packed_random_access_iterator_tag,
                                                const_iterator2, value_type> {
         public:
             typedef typename iterator_restrict_traits<typename const_subiterator2_type::iterator_category,
                                                       packed_random_access_iterator_tag>::iterator_category iterator_category;
             typedef typename const_subiterator2_type::value_type value_type;
             typedef typename const_subiterator2_type::difference_type difference_type;
             typedef typename const_subiterator2_type::reference reference;
             typedef typename const_subiterator2_type::pointer pointer;
 
             typedef const_iterator1 dual_iterator_type;
             typedef const_reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             const_iterator2 ():
                 container_const_reference<self_type> (), it2_ () {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const self_type &m, const const_subiterator2_type &it2):
                 container_const_reference<self_type> (m), it2_ (it2) {}
             BOOST_UBLAS_INLINE
             const_iterator2 (const iterator2 &it):
                 container_const_reference<self_type> (it ()), it2_ (it.it2_) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             const_iterator2 &operator ++ () {
                 ++ it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -- () {
                 -- it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator += (difference_type n) {
                 it2_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             const_iterator2 &operator -= (difference_type n) {
                 it2_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ - it.it2_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             const_reference operator * () const {
                 size_type i = index1 ();
                 size_type j = index2 ();
                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
                 size_type k = (std::max) (i, j);
                 size_type l = (*this) ().lower () + j - i;
                 if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it2_;
 #else
                 size_type k = j;
                 size_type l = (*this) ().upper () + i - j;
                 if (k < (*this) ().size2 () &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it2_;
 #endif
                 return (*this) () (i, j);
             }
             BOOST_UBLAS_INLINE
             const_reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 begin () const {
                 return (*this) ().find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cbegin () const {
                 return begin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 end () const {
                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_iterator1 cend () const {
                 return end ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rbegin () const {
                 return const_reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crbegin () const {
                 return rbegin ();
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 rend () const {
                 return const_reverse_iterator1 (begin ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             const_reverse_iterator1 crend () const {
                 return rend ();
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it2_.index1 ();
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_.index2 ();
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             const_iterator2 &operator = (const const_iterator2 &it) {
                 container_const_reference<self_type>::assign (&it ());
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ == it.it2_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const const_iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ < it.it2_;
             }
 
         private:
             const_subiterator2_type it2_;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         const_iterator2 begin2 () const {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cbegin2 () const {
             return begin2 ();
         }
         BOOST_UBLAS_INLINE
         const_iterator2 end2 () const {
             return find2 (0, 0, size2 ());
         }
         BOOST_UBLAS_INLINE
         const_iterator2 cend2 () const {
             return end2 ();
         }
 
 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
         class iterator2:
             public container_reference<banded_adaptor>,
             public random_access_iterator_base<typename iterator_restrict_traits<
                                                    typename subiterator2_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
                                                iterator2, value_type> {
         public:
             typedef typename subiterator2_type::value_type value_type;
             typedef typename subiterator2_type::difference_type difference_type;
             typedef typename subiterator2_type::reference reference;
             typedef typename subiterator2_type::pointer pointer;
 
             typedef iterator1 dual_iterator_type;
             typedef reverse_iterator1 dual_reverse_iterator_type;
 
             // Construction and destruction
             BOOST_UBLAS_INLINE
             iterator2 ():
                 container_reference<self_type> (), it2_ () {}
             BOOST_UBLAS_INLINE
             iterator2 (self_type &m, const subiterator2_type &it2):
                 container_reference<self_type> (m), it2_ (it2) {}
 
             // Arithmetic
             BOOST_UBLAS_INLINE
             iterator2 &operator ++ () {
                 ++ it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -- () {
                 -- it2_;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator += (difference_type n) {
                 it2_ += n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             iterator2 &operator -= (difference_type n) {
                 it2_ -= n;
                 return *this;
             }
             BOOST_UBLAS_INLINE
             difference_type operator - (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ - it.it2_;
             }
 
             // Dereference
             BOOST_UBLAS_INLINE
             reference operator * () const {
                 size_type i = index1 ();
                 size_type j = index2 ();
                 BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ());
                 BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ());
 #ifdef BOOST_UBLAS_OWN_BANDED
                 size_type k = (std::max) (i, j);
                 size_type l = (*this) ().lower () + j - i;
                 if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it2_;
 #else
                 size_type k = j;
                 size_type l = (*this) ().upper () + i - j;
                 if (k < (*this) ().size2 () &&
                     l < (*this) ().lower () + 1 + (*this) ().upper ())
                     return *it2_;
 #endif
                 return (*this) () (i, j);
             }
             BOOST_UBLAS_INLINE
             reference operator [] (difference_type n) const {
                 return *(*this + n);
             }
 
 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 begin () const {
                 return (*this) ().find1 (1, 0, index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             iterator1 end () const {
                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rbegin () const {
                 return reverse_iterator1 (end ());
             }
             BOOST_UBLAS_INLINE
 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
             typename self_type::
 #endif
             reverse_iterator1 rend () const {
                 return reverse_iterator1 (begin ());
             }
 #endif
 
             // Indices
             BOOST_UBLAS_INLINE
             size_type index1 () const {
                 return it2_.index1 ();
             }
             BOOST_UBLAS_INLINE
             size_type index2 () const {
                 return it2_.index2 ();
             }
 
             // Assignment
             BOOST_UBLAS_INLINE
             iterator2 &operator = (const iterator2 &it) {
                 container_reference<self_type>::assign (&it ());
                 it2_ = it.it2_;
                 return *this;
             }
 
             // Comparison
             BOOST_UBLAS_INLINE
             bool operator == (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ == it.it2_;
             }
             BOOST_UBLAS_INLINE
             bool operator < (const iterator2 &it) const {
                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
                 return it2_ < it.it2_;
             }
 
         private:
             subiterator2_type it2_;
 
             friend class const_iterator2;
         };
 #endif
 
         BOOST_UBLAS_INLINE
         iterator2 begin2 () {
             return find2 (0, 0, 0);
         }
         BOOST_UBLAS_INLINE
         iterator2 end2 () {
             return find2 (0, 0, size2 ());
         }
 
         // Reverse iterators
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rbegin1 () const {
             return const_reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crbegin1 () const {
             return rbegin1 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 rend1 () const {
             return const_reverse_iterator1 (begin1 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator1 crend1 () const {
             return rend1 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator1 rbegin1 () {
             return reverse_iterator1 (end1 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator1 rend1 () {
             return reverse_iterator1 (begin1 ());
         }
 
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rbegin2 () const {
             return const_reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crbegin2 () const {
             return rbegin2 ();
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 rend2 () const {
             return const_reverse_iterator2 (begin2 ());
         }
         BOOST_UBLAS_INLINE
         const_reverse_iterator2 crend2 () const {
             return rend2 ();
         }
 
         BOOST_UBLAS_INLINE
         reverse_iterator2 rbegin2 () {
             return reverse_iterator2 (end2 ());
         }
         BOOST_UBLAS_INLINE
         reverse_iterator2 rend2 () {
             return reverse_iterator2 (begin2 ());
         }
 
     private:
         matrix_closure_type data_;
         size_type lower_;
         size_type upper_;
         typedef const value_type const_value_type;
         static const_value_type zero_;
     };
 
     // Specialization for temporary_traits
     template <class M>
     struct vector_temporary_traits< banded_adaptor<M> >
     : vector_temporary_traits< M > {} ;
     template <class M>
     struct vector_temporary_traits< const banded_adaptor<M> >
     : vector_temporary_traits< M > {} ;
 
     template <class M>
     struct matrix_temporary_traits< banded_adaptor<M> >
     : matrix_temporary_traits< M > {} ;
     template <class M>
     struct matrix_temporary_traits< const banded_adaptor<M> >
     : matrix_temporary_traits< M > {} ;
 
 
     template<class M>
     typename banded_adaptor<M>::const_value_type banded_adaptor<M>::zero_ = value_type/*zero*/();
 
     /** \brief A diagonal matrix adaptator: convert a any matrix into a diagonal matrix expression
      *
      * For a \f$(m\times m)\f$-dimensional matrix, the \c diagonal_adaptor will provide a diagonal matrix
      * with \f$0 \leq i < m\f$ and \f$0 \leq j < m\f$, if \f$i\neq j\f$ then \f$b_{i,j}=0\f$. 
      *
      * Storage and location are based on those of the underlying matrix. This is important because
      * a \c diagonal_adaptor does not copy the matrix data to a new place. Therefore, modifying values
      * in a \c diagonal_adaptor matrix will also modify the underlying matrix too.
      *
      * \tparam M the type of matrix used to generate the diagonal matrix
      */
 
     template<class M>
     class diagonal_adaptor:
         public banded_adaptor<M> {
     public:
         typedef M matrix_type;
         typedef banded_adaptor<M> adaptor_type;
 
         // Construction and destruction
         BOOST_UBLAS_INLINE
         diagonal_adaptor ():
             adaptor_type () {}
         BOOST_UBLAS_INLINE
         diagonal_adaptor (matrix_type &data):
             adaptor_type (data) {}
         BOOST_UBLAS_INLINE
         ~diagonal_adaptor () {}
 
         // Assignment
         BOOST_UBLAS_INLINE
         diagonal_adaptor &operator = (const diagonal_adaptor &m) {
             adaptor_type::operator = (m);
             return *this;
         }
         template<class AE>
         BOOST_UBLAS_INLINE
         diagonal_adaptor &operator = (const matrix_expression<AE> &ae) {
             adaptor_type::operator = (ae);
             return *this;
         }
     };
 
 }}}
 
 #endif

This page was automatically generated by the 2.3.7 LXR engine. The LXR team