Squashed 'third_party/boostorg/ublas/' content from commit e8607b3

Change-Id: Ia06afd642157a24e17fa9ddea28fb8601810b78e
git-subtree-dir: third_party/boostorg/ublas
git-subtree-split: e8607b3eea238e590eca93bfe498c21f470155c1
diff --git a/include/boost/numeric/ublas/banded.hpp b/include/boost/numeric/ublas/banded.hpp
new file mode 100644
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--- /dev/null
+++ b/include/boost/numeric/ublas/banded.hpp
@@ -0,0 +1,2372 @@
+//
+//  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