numeric/ublas/hermitian.hpp

0001 //
0002 //  Copyright (c) 2000-2010
0003 //  Joerg Walter, Mathias Koch, David Bellot
0004 //
0005 //  Distributed under the Boost Software License, Version 1.0. (See
0006 //  accompanying file LICENSE_1_0.txt or copy at
0007 //  http://www.boost.org/LICENSE_1_0.txt)
0008 //
0009 //  The authors gratefully acknowledge the support of
0010 //  GeNeSys mbH & Co. KG in producing this work.
0011 //
0012
0013 #ifndef BOOST_UBLAS_HERMITIAN_H
0014 #define BOOST_UBLAS_HERMITIAN_H
0015
0016 #include <boost/numeric/ublas/matrix.hpp>
0017 #include <boost/numeric/ublas/triangular.hpp>  // for resize_preserve
0018 #include <boost/numeric/ublas/detail/temporary.hpp>
0019
0020 // Iterators based on ideas of Jeremy Siek
0021 // Hermitian matrices are square. Thanks to Peter Schmitteckert for spotting this.
0022
0023 namespace boost { namespace numeric { namespace ublas {
0024
0025     template<class M>
0026     bool is_hermitian (const M &m) {
0027         typedef typename M::size_type size_type;
0028
0029         if (m.size1 () != m.size2 ())
0030             return false;
0031         size_type size = BOOST_UBLAS_SAME (m.size1 (), m.size2 ());
0032         for (size_type i = 0; i < size; ++ i) {
0033             for (size_type j = i; j < size; ++ j) {
0034                 if (m (i, j) != conj (m (j, i)))
0035                     return false;
0036             }
0037         }
0038         return true;
0039     }
0040
0041 #ifdef BOOST_UBLAS_STRICT_HERMITIAN
0042
0043     template<class M>
0044     class hermitian_matrix_element:
0045        public container_reference<M> {
0046     public:
0047         typedef M matrix_type;
0048         typedef typename M::size_type size_type;
0049         typedef typename M::value_type value_type;
0050         typedef const value_type &const_reference;
0051         typedef value_type &reference;
0052         typedef value_type *pointer;
0053
0054         // Construction and destruction
0055         BOOST_UBLAS_INLINE
0056         hermitian_matrix_element (matrix_type &m, size_type i, size_type j, value_type d):
0057             container_reference<matrix_type> (m), i_ (i), j_ (j), d_ (d), dirty_ (false) {}
0058         BOOST_UBLAS_INLINE
0059         ~hermitian_matrix_element () {
0060             if (dirty_)
0061                 (*this) ().insert_element (i_, j_, d_);
0062         }
0063
0064         // Assignment
0065         BOOST_UBLAS_INLINE
0066         hermitian_matrix_element &operator = (const hermitian_matrix_element &p) {
0067             // Overide the implict copy assignment
0068             d_ = p.d_;
0069             dirty_ = true;
0070             return *this;
0071         }
0072         template<class D>
0073         BOOST_UBLAS_INLINE
0074         hermitian_matrix_element &operator = (const D &d) {
0075             d_ = d;
0076             dirty_ = true;
0077             return *this;
0078         }
0079         template<class D>
0080         BOOST_UBLAS_INLINE
0081         hermitian_matrix_element &operator += (const D &d) {
0082             d_ += d;
0083             dirty_ = true;
0084             return *this;
0085         }
0086         template<class D>
0087         BOOST_UBLAS_INLINE
0088         hermitian_matrix_element &operator -= (const D &d) {
0089             d_ -= d;
0090             dirty_ = true;
0091             return *this;
0092         }
0093         template<class D>
0094         BOOST_UBLAS_INLINE
0095         hermitian_matrix_element &operator *= (const D &d) {
0096             d_ *= d;
0097             dirty_ = true;
0098             return *this;
0099         }
0100         template<class D>
0101         BOOST_UBLAS_INLINE
0102         hermitian_matrix_element &operator /= (const D &d) {
0103             d_ /= d;
0104             dirty_ = true;
0105             return *this;
0106         }
0107
0108         // Comparison
0109         template<class D>
0110         BOOST_UBLAS_INLINE
0111         bool operator == (const D &d) const {
0112             return d_ == d;
0113         }
0114         template<class D>
0115         BOOST_UBLAS_INLINE
0116         bool operator != (const D &d) const {
0117             return d_ != d;
0118         }
0119
0120         // Conversion
0121         BOOST_UBLAS_INLINE
0122         operator const_reference () const {
0123             return d_;
0124         }
0125
0126         // Swapping
0127         BOOST_UBLAS_INLINE
0128         void swap (hermitian_matrix_element p) {
0129             if (this != &p) {
0130                 dirty_ = true;
0131                 p.dirty_ = true;
0132                 std::swap (d_, p.d_);
0133             }
0134         }
0135         BOOST_UBLAS_INLINE
0136         friend void swap (hermitian_matrix_element p1, hermitian_matrix_element p2) {
0137             p1.swap (p2);
0138         }
0139
0140     private:
0141         size_type i_;
0142         size_type j_;
0143         value_type d_;
0144         bool dirty_;
0145     };
0146
0147     template<class M>
0148     struct type_traits<hermitian_matrix_element<M> > {
0149         typedef typename M::value_type element_type;
0150         typedef type_traits<hermitian_matrix_element<M> > self_type;
0151         typedef typename type_traits<element_type>::value_type value_type;
0152         typedef typename type_traits<element_type>::const_reference const_reference;
0153         typedef hermitian_matrix_element<M> reference;
0154         typedef typename type_traits<element_type>::real_type real_type;
0155         typedef typename type_traits<element_type>::precision_type precision_type;
0156
0157         static const unsigned plus_complexity = type_traits<element_type>::plus_complexity;
0158         static const unsigned multiplies_complexity = type_traits<element_type>::multiplies_complexity;
0159
0160         static
0161         BOOST_UBLAS_INLINE
0162         real_type real (const_reference t) {
0163             return type_traits<element_type>::real (t);
0164         }
0165         static
0166         BOOST_UBLAS_INLINE
0167         real_type imag (const_reference t) {
0168             return type_traits<element_type>::imag (t);
0169         }
0170         static
0171         BOOST_UBLAS_INLINE
0172         value_type conj (const_reference t) {
0173             return type_traits<element_type>::conj (t);
0174         }
0175
0176         static
0177         BOOST_UBLAS_INLINE
0178         real_type type_abs (const_reference t) {
0179             return type_traits<element_type>::type_abs (t);
0180         }
0181         static
0182         BOOST_UBLAS_INLINE
0183         value_type type_sqrt (const_reference t) {
0184             return type_traits<element_type>::type_sqrt (t);
0185         }
0186
0187         static
0188         BOOST_UBLAS_INLINE
0189         real_type norm_1 (const_reference t) {
0190             return type_traits<element_type>::norm_1 (t);
0191         }
0192         static
0193         BOOST_UBLAS_INLINE
0194         real_type norm_2 (const_reference t) {
0195             return type_traits<element_type>::norm_2 (t);
0196         }
0197         static
0198         BOOST_UBLAS_INLINE
0199         real_type norm_inf (const_reference t) {
0200             return type_traits<element_type>::norm_inf (t);
0201         }
0202
0203         static
0204         BOOST_UBLAS_INLINE
0205         bool equals (const_reference t1, const_reference t2) {
0206             return type_traits<element_type>::equals (t1, t2);
0207         }
0208     };
0209
0210     template<class M1, class T2>
0211     struct promote_traits<hermitian_matrix_element<M1>, T2> {
0212         typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type, T2>::promote_type promote_type;
0213     };
0214     template<class T1, class M2>
0215     struct promote_traits<T1, hermitian_matrix_element<M2> > {
0216         typedef typename promote_traits<T1, typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
0217     };
0218     template<class M1, class M2>
0219     struct promote_traits<hermitian_matrix_element<M1>, hermitian_matrix_element<M2> > {
0220         typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type,
0221                                         typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
0222     };
0223
0224 #endif
0225     /** \brief A hermitian matrix of values of type \c T
0226      *
0227      * For a \f$(n \times n)\f$-dimensional matrix and \f$ 0 \leq i < n, 0 \leq j < n\f$, every element
0228      * \f$m_{i,j}\f$ is mapped to the \f$(i.n + j)\f$-th element of the container for row major orientation
0229      * or the \f$(i + j.m)\f$-th element of the container for column major orientation. And
0230      * \f$\forall i,j\f$, \f$m_{i,j} = \overline{m_{i,j}}\f$.
0231      *
0232      * Orientation and storage can also be specified, otherwise a row major and unbounded array are used.
0233      * It is \b not required by the storage to initialize elements of the matrix.
0234      * Moreover, only the given triangular matrix is stored and the storage of hermitian matrices is packed.
0235      *
0236      * See http://en.wikipedia.org/wiki/Hermitian_matrix for more details on hermitian matrices.
0237      *
0238      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
0239      * \tparam TRI the type of triangular matrix is either \c lower or \c upper. Default is \c lower
0240      * \tparam L the storage organization. It is either \c row_major or \c column_major. Default is \c row_major
0241      * \tparam A the type of Storage array. Default is \unbounded_array.
0242      */
0243     template<class T, class TRI, class L, class A>
0244     class hermitian_matrix:
0245         public matrix_container<hermitian_matrix<T, TRI, L, A> > {
0246
0247         typedef T &true_reference;
0248         typedef T *pointer;
0249         typedef TRI triangular_type;
0250         typedef L layout_type;
0251         typedef hermitian_matrix<T, TRI, L, A> self_type;
0252     public:
0253 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
0254         using matrix_container<self_type>::operator ();
0255 #endif
0256         typedef typename A::size_type size_type;
0257         typedef typename A::difference_type difference_type;
0258         typedef T value_type;
0259         // FIXME no better way to not return the address of a temporary?
0260         // typedef const T &const_reference;
0261         typedef const T const_reference;
0262 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
0263         typedef T &reference;
0264 #else
0265         typedef hermitian_matrix_element<self_type> reference;
0266 #endif
0267         typedef A array_type;
0268
0269         typedef const matrix_reference<const self_type> const_closure_type;
0270         typedef matrix_reference<self_type> closure_type;
0271         typedef vector<T, A> vector_temporary_type;
0272         typedef matrix<T, L, A> matrix_temporary_type;  // general sub-matrix
0273         typedef packed_tag storage_category;
0274         typedef typename L::orientation_category orientation_category;
0275
0276         // Construction and destruction
0277         BOOST_UBLAS_INLINE
0278         hermitian_matrix ():
0279             matrix_container<self_type> (),
0280             size_ (0), data_ (0) {}
0281         BOOST_UBLAS_INLINE
0282         hermitian_matrix (size_type size):
0283             matrix_container<self_type> (),
0284             size_ (BOOST_UBLAS_SAME (size, size)), data_ (triangular_type::packed_size (layout_type (), size, size)) {
0285         }
0286         BOOST_UBLAS_INLINE
0287         hermitian_matrix (size_type size1, size_type size2):
0288             matrix_container<self_type> (),
0289             size_ (BOOST_UBLAS_SAME (size1, size2)), data_ (triangular_type::packed_size (layout_type (), size1, size2)) {
0290         }
0291         BOOST_UBLAS_INLINE
0292         hermitian_matrix (size_type size, const array_type &data):
0293             matrix_container<self_type> (),
0294             size_ (size), data_ (data) {}
0295         BOOST_UBLAS_INLINE
0296         hermitian_matrix (const hermitian_matrix &m):
0297             matrix_container<self_type> (),
0298             size_ (m.size_), data_ (m.data_) {}
0299         template<class AE>
0300         BOOST_UBLAS_INLINE
0301         hermitian_matrix (const matrix_expression<AE> &ae):
0302             matrix_container<self_type> (),
0303             size_ (BOOST_UBLAS_SAME (ae ().size1 (), ae ().size2 ())),
0304             data_ (triangular_type::packed_size (layout_type (), size_, size_)) {
0305             matrix_assign<scalar_assign> (*this, ae);
0306         }
0307
0308         // Accessors
0309         BOOST_UBLAS_INLINE
0310         size_type size1 () const {
0311             return size_;
0312         }
0313         BOOST_UBLAS_INLINE
0314         size_type size2 () const {
0315             return size_;
0316         }
0317
0318         // Storage accessors
0319         BOOST_UBLAS_INLINE
0320         const array_type &data () const {
0321             return data_;
0322         }
0323         BOOST_UBLAS_INLINE
0324         array_type &data () {
0325             return data_;
0326         }
0327
0328         // Resizing
0329         BOOST_UBLAS_INLINE
0330         void resize (size_type size, bool preserve = true) {
0331             if (preserve) {
0332                 self_type temporary (size, size);
0333                 detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary);
0334             }
0335             else {
0336                 data ().resize (triangular_type::packed_size (layout_type (), size, size));
0337                 size_ = size;
0338             }
0339         }
0340         BOOST_UBLAS_INLINE
0341         void resize (size_type size1, size_type size2, bool preserve = true) {
0342             resize (BOOST_UBLAS_SAME (size1, size2), preserve);
0343         }
0344         BOOST_UBLAS_INLINE
0345         void resize_packed_preserve (size_type size) {
0346             size_ = BOOST_UBLAS_SAME (size, size);
0347             data ().resize (triangular_type::packed_size (layout_type (), size_, size_), value_type ());
0348         }
0349
0350         // Element access
0351         BOOST_UBLAS_INLINE
0352         const_reference operator () (size_type i, size_type j) const {
0353             BOOST_UBLAS_CHECK (i < size_, bad_index ());
0354             BOOST_UBLAS_CHECK (j < size_, bad_index ());
0355             // if (i == j)
0356             //    return type_traits<value_type>::real (data () [triangular_type::element (layout_type (), i, size_, i, size_)]);
0357             // else
0358             if (triangular_type::other (i, j))
0359                 return data () [triangular_type::element (layout_type (), i, size_, j, size_)];
0360             else
0361                 return type_traits<value_type>::conj (data () [triangular_type::element (layout_type (), j, size_, i, size_)]);
0362         }
0363         BOOST_UBLAS_INLINE
0364         true_reference at_element (size_type i, size_type j) {
0365             BOOST_UBLAS_CHECK (i < size_, bad_index ());
0366             BOOST_UBLAS_CHECK (j < size_, bad_index ());
0367             BOOST_UBLAS_CHECK (triangular_type::other (i, j), bad_index ());
0368             return data () [triangular_type::element (layout_type (), i, size_, j, size_)];
0369         }
0370         BOOST_UBLAS_INLINE
0371         reference operator () (size_type i, size_type j) {
0372 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
0373             if (!triangular_type::other (i, j)) {
0374                 bad_index ().raise ();
0375                 // NEVER reached
0376             }
0377             return at_element (i, j);
0378 #else
0379         if (triangular_type::other (i, j))
0380             return reference (*this, i, j, data () [triangular_type::element (layout_type (), i, size_, j, size_)]);
0381         else
0382             return reference (*this, i, j, type_traits<value_type>::conj (data () [triangular_type::element (layout_type (), j, size_, i, size_)]));
0383 #endif
0384         }
0385
0386         // Element assignemnt
0387         BOOST_UBLAS_INLINE
0388         true_reference insert_element (size_type i, size_type j, const_reference t) {
0389             BOOST_UBLAS_CHECK (i < size_, bad_index ());
0390             BOOST_UBLAS_CHECK (j < size_, bad_index ());
0391             if (triangular_type::other (i, j)) {
0392                 return (data () [triangular_type::element (layout_type (), i, size_, j, size_)] = t);
0393             } else {
0394                 return (data () [triangular_type::element (layout_type (), j, size_, i, size_)] = type_traits<value_type>::conj (t));
0395             }
0396         }
0397         BOOST_UBLAS_INLINE
0398         void erase_element (size_type i, size_type j) {
0399             BOOST_UBLAS_CHECK (i < size_, bad_index ());
0400             BOOST_UBLAS_CHECK (j < size_, bad_index ());
0401             data () [triangular_type::element (layout_type (), i, size_, j, size_)] = value_type/*zero*/();
0402         }
0403
0404         // Zeroing
0405         BOOST_UBLAS_INLINE
0406         void clear () {
0407             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
0408         }
0409
0410         // Assignment
0411         BOOST_UBLAS_INLINE
0412         hermitian_matrix &operator = (const hermitian_matrix &m) {
0413             size_ = m.size_;
0414             data () = m.data ();
0415             return *this;
0416         }
0417         BOOST_UBLAS_INLINE
0418         hermitian_matrix &assign_temporary (hermitian_matrix &m) {
0419             swap (m);
0420             return *this;
0421         }
0422         template<class AE>
0423         BOOST_UBLAS_INLINE
0424         hermitian_matrix &operator = (const matrix_expression<AE> &ae) {
0425             self_type temporary (ae);
0426             return assign_temporary (temporary);
0427         }
0428         template<class AE>
0429         BOOST_UBLAS_INLINE
0430         hermitian_matrix &assign (const matrix_expression<AE> &ae) {
0431             matrix_assign<scalar_assign> (*this, ae);
0432             return *this;
0433         }
0434         template<class AE>
0435         BOOST_UBLAS_INLINE
0436         hermitian_matrix& operator += (const matrix_expression<AE> &ae) {
0437             self_type temporary (*this + ae);
0438             return assign_temporary (temporary);
0439         }
0440         template<class AE>
0441         BOOST_UBLAS_INLINE
0442         hermitian_matrix &plus_assign (const matrix_expression<AE> &ae) {
0443             matrix_assign<scalar_plus_assign> (*this, ae);
0444             return *this;
0445         }
0446         template<class AE>
0447         BOOST_UBLAS_INLINE
0448         hermitian_matrix& operator -= (const matrix_expression<AE> &ae) {
0449             self_type temporary (*this - ae);
0450             return assign_temporary (temporary);
0451         }
0452         template<class AE>
0453         BOOST_UBLAS_INLINE
0454         hermitian_matrix &minus_assign (const matrix_expression<AE> &ae) {
0455             matrix_assign<scalar_minus_assign> (*this, ae);
0456             return *this;
0457         }
0458         template<class AT>
0459         BOOST_UBLAS_INLINE
0460         hermitian_matrix& operator *= (const AT &at) {
0461             // Multiplication is only allowed for real scalars,
0462             // otherwise the resulting matrix isn't hermitian.
0463             // Thanks to Peter Schmitteckert for spotting this.
0464             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
0465             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
0466             return *this;
0467         }
0468         template<class AT>
0469         BOOST_UBLAS_INLINE
0470         hermitian_matrix& operator /= (const AT &at) {
0471             // Multiplication is only allowed for real scalars,
0472             // otherwise the resulting matrix isn't hermitian.
0473             // Thanks to Peter Schmitteckert for spotting this.
0474             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
0475             matrix_assign_scalar<scalar_divides_assign> (*this, at);
0476             return *this;
0477         }
0478
0479         // Swapping
0480         BOOST_UBLAS_INLINE
0481         void swap (hermitian_matrix &m) {
0482             if (this != &m) {
0483                 std::swap (size_, m.size_);
0484                 data ().swap (m.data ());
0485             }
0486         }
0487         BOOST_UBLAS_INLINE
0488         friend void swap (hermitian_matrix &m1, hermitian_matrix &m2) {
0489             m1.swap (m2);
0490         }
0491
0492         // Iterator types
0493 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
0494         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
0495         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
0496         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
0497         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
0498 #else
0499         class const_iterator1;
0500         class iterator1;
0501         class const_iterator2;
0502         class iterator2;
0503 #endif
0504         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
0505         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
0506         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
0507         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
0508
0509         // Element lookup
0510         BOOST_UBLAS_INLINE
0511         const_iterator1 find1 (int /* rank */, size_type i, size_type j) const {
0512             return const_iterator1 (*this, i, j);
0513         }
0514         BOOST_UBLAS_INLINE
0515         iterator1 find1 (int rank, size_type i, size_type j) {
0516             if (rank == 1)
0517                 i = triangular_type::mutable_restrict1 (i, j, size1(), size2());
0518             if (rank == 0)
0519                 i = triangular_type::global_mutable_restrict1 (i, size1(), j, size2());
0520             return iterator1 (*this, i, j);
0521         }
0522         BOOST_UBLAS_INLINE
0523         const_iterator2 find2 (int /* rank */, size_type i, size_type j) const {
0524             return const_iterator2 (*this, i, j);
0525         }
0526         BOOST_UBLAS_INLINE
0527         iterator2 find2 (int rank, size_type i, size_type j) {
0528             if (rank == 1)
0529                 j = triangular_type::mutable_restrict2 (i, j, size1(), size2());
0530             if (rank == 0)
0531                 j = triangular_type::global_mutable_restrict2 (i, size1(), j, size2());
0532             return iterator2 (*this, i, j);
0533         }
0534
0535         // Iterators simply are indices.
0536
0537 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
0538         class const_iterator1:
0539             public container_const_reference<hermitian_matrix>,
0540             public random_access_iterator_base<packed_random_access_iterator_tag,
0541                                                const_iterator1, value_type> {
0542         public:
0543             typedef typename hermitian_matrix::value_type value_type;
0544             typedef typename hermitian_matrix::difference_type difference_type;
0545             typedef typename hermitian_matrix::const_reference reference;
0546             typedef const typename hermitian_matrix::pointer pointer;
0547
0548             typedef const_iterator2 dual_iterator_type;
0549             typedef const_reverse_iterator2 dual_reverse_iterator_type;
0550
0551             // Construction and destruction
0552             BOOST_UBLAS_INLINE
0553             const_iterator1 ():
0554                 container_const_reference<self_type> (), it1_ (), it2_ () {}
0555             BOOST_UBLAS_INLINE
0556             const_iterator1 (const self_type &m, size_type it1, size_type it2):
0557                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
0558             BOOST_UBLAS_INLINE
0559             const_iterator1 (const iterator1 &it):
0560                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
0561
0562             // Arithmetic
0563             BOOST_UBLAS_INLINE
0564             const_iterator1 &operator ++ () {
0565                 ++ it1_;
0566                 return *this;
0567             }
0568             BOOST_UBLAS_INLINE
0569             const_iterator1 &operator -- () {
0570                 -- it1_;
0571                 return *this;
0572             }
0573             BOOST_UBLAS_INLINE
0574             const_iterator1 &operator += (difference_type n) {
0575                 it1_ += n;
0576                 return *this;
0577             }
0578             BOOST_UBLAS_INLINE
0579             const_iterator1 &operator -= (difference_type n) {
0580                 it1_ -= n;
0581                 return *this;
0582             }
0583             BOOST_UBLAS_INLINE
0584             difference_type operator - (const const_iterator1 &it) const {
0585                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0586                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0587                 return it1_ - it.it1_;
0588             }
0589
0590             // Dereference
0591             BOOST_UBLAS_INLINE
0592             const_reference operator * () const {
0593                 return (*this) () (it1_, it2_);
0594             }
0595             BOOST_UBLAS_INLINE
0596             const_reference operator [] (difference_type n) const {
0597                 return *(*this + n);
0598             }
0599
0600 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
0601             BOOST_UBLAS_INLINE
0602 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0603             typename self_type::
0604 #endif
0605             const_iterator2 begin () const {
0606                 return (*this) ().find2 (1, it1_, 0);
0607             }
0608             BOOST_UBLAS_INLINE
0609 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0610             typename self_type::
0611 #endif
0612             const_iterator2 cbegin () const {
0613                 return begin ();
0614             }
0615             BOOST_UBLAS_INLINE
0616 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0617             typename self_type::
0618 #endif
0619             const_iterator2 end () const {
0620                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
0621             }
0622             BOOST_UBLAS_INLINE
0623 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0624             typename self_type::
0625 #endif
0626             const_iterator2 cend () const {
0627                 return end ();
0628             }
0629             BOOST_UBLAS_INLINE
0630 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0631             typename self_type::
0632 #endif
0633             const_reverse_iterator2 rbegin () const {
0634                 return const_reverse_iterator2 (end ());
0635             }
0636             BOOST_UBLAS_INLINE
0637 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0638             typename self_type::
0639 #endif
0640             const_reverse_iterator2 crbegin () const {
0641                 return rbegin ();
0642             }
0643             BOOST_UBLAS_INLINE
0644 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0645             typename self_type::
0646 #endif
0647             const_reverse_iterator2 rend () const {
0648                 return const_reverse_iterator2 (begin ());
0649             }
0650             BOOST_UBLAS_INLINE
0651 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0652             typename self_type::
0653 #endif
0654             const_reverse_iterator2 crend () const {
0655                 return rend ();
0656             }
0657 #endif
0658
0659             // Indices
0660             BOOST_UBLAS_INLINE
0661             size_type index1 () const {
0662                 return it1_;
0663             }
0664             BOOST_UBLAS_INLINE
0665             size_type index2 () const {
0666                 return it2_;
0667             }
0668
0669             // Assignment
0670             BOOST_UBLAS_INLINE
0671             const_iterator1 &operator = (const const_iterator1 &it) {
0672                 container_const_reference<self_type>::assign (&it ());
0673                 it1_ = it.it1_;
0674                 it2_ = it.it2_;
0675                 return *this;
0676             }
0677
0678             // Comparison
0679             BOOST_UBLAS_INLINE
0680             bool operator == (const const_iterator1 &it) const {
0681                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0682                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0683                 return it1_ == it.it1_;
0684             }
0685             BOOST_UBLAS_INLINE
0686             bool operator < (const const_iterator1 &it) const {
0687                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0688                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0689                 return it1_ < it.it1_;
0690             }
0691
0692         private:
0693             size_type it1_;
0694             size_type it2_;
0695         };
0696 #endif
0697
0698         BOOST_UBLAS_INLINE
0699         const_iterator1 begin1 () const {
0700             return find1 (0, 0, 0);
0701         }
0702         BOOST_UBLAS_INLINE
0703         const_iterator1 cbegin1 () const {
0704             return begin1 ();
0705         }
0706         BOOST_UBLAS_INLINE
0707         const_iterator1 end1 () const {
0708             return find1 (0, size_, 0);
0709         }
0710         BOOST_UBLAS_INLINE
0711         const_iterator1 cend1 () const {
0712             return end1 ();
0713         }
0714
0715 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
0716         class iterator1:
0717             public container_reference<hermitian_matrix>,
0718             public random_access_iterator_base<packed_random_access_iterator_tag,
0719                                                iterator1, value_type> {
0720         public:
0721             typedef typename hermitian_matrix::value_type value_type;
0722             typedef typename hermitian_matrix::difference_type difference_type;
0723             typedef typename hermitian_matrix::true_reference reference;
0724             typedef typename hermitian_matrix::pointer pointer;
0725
0726             typedef iterator2 dual_iterator_type;
0727             typedef reverse_iterator2 dual_reverse_iterator_type;
0728
0729             // Construction and destruction
0730             BOOST_UBLAS_INLINE
0731             iterator1 ():
0732                 container_reference<self_type> (), it1_ (), it2_ () {}
0733             BOOST_UBLAS_INLINE
0734             iterator1 (self_type &m, size_type it1, size_type it2):
0735                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
0736
0737             // Arithmetic
0738             BOOST_UBLAS_INLINE
0739             iterator1 &operator ++ () {
0740                 ++ it1_;
0741                 return *this;
0742             }
0743             BOOST_UBLAS_INLINE
0744             iterator1 &operator -- () {
0745                 -- it1_;
0746                 return *this;
0747             }
0748             BOOST_UBLAS_INLINE
0749             iterator1 &operator += (difference_type n) {
0750                 it1_ += n;
0751                 return *this;
0752             }
0753             BOOST_UBLAS_INLINE
0754             iterator1 &operator -= (difference_type n) {
0755                 it1_ -= n;
0756                 return *this;
0757             }
0758             BOOST_UBLAS_INLINE
0759             difference_type operator - (const iterator1 &it) const {
0760                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0761                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0762                 return it1_ - it.it1_;
0763             }
0764
0765             // Dereference
0766             BOOST_UBLAS_INLINE
0767             reference operator * () const {
0768                 return (*this) ().at_element (it1_, it2_);
0769             }
0770             BOOST_UBLAS_INLINE
0771             reference operator [] (difference_type n) const {
0772                 return *(*this + n);
0773             }
0774
0775 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
0776             BOOST_UBLAS_INLINE
0777 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0778             typename self_type::
0779 #endif
0780             iterator2 begin () const {
0781                 return (*this) ().find2 (1, it1_, 0);
0782             }
0783             BOOST_UBLAS_INLINE
0784 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0785             typename self_type::
0786 #endif
0787             iterator2 end () const {
0788                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
0789             }
0790             BOOST_UBLAS_INLINE
0791 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0792             typename self_type::
0793 #endif
0794             reverse_iterator2 rbegin () const {
0795                 return reverse_iterator2 (end ());
0796             }
0797             BOOST_UBLAS_INLINE
0798 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0799             typename self_type::
0800 #endif
0801             reverse_iterator2 rend () const {
0802                 return reverse_iterator2 (begin ());
0803             }
0804 #endif
0805
0806             // Indices
0807             BOOST_UBLAS_INLINE
0808             size_type index1 () const {
0809                 return it1_;
0810             }
0811             BOOST_UBLAS_INLINE
0812             size_type index2 () const {
0813                 return it2_;
0814             }
0815
0816             // Assignment
0817             BOOST_UBLAS_INLINE
0818             iterator1 &operator = (const iterator1 &it) {
0819                 container_reference<self_type>::assign (&it ());
0820                 it1_ = it.it1_;
0821                 it2_ = it.it2_;
0822                 return *this;
0823             }
0824
0825             // Comparison
0826             BOOST_UBLAS_INLINE
0827             bool operator == (const iterator1 &it) const {
0828                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0829                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0830                 return it1_ == it.it1_;
0831             }
0832             BOOST_UBLAS_INLINE
0833             bool operator < (const iterator1 &it) const {
0834                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0835                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
0836                 return it1_ < it.it1_;
0837             }
0838
0839         private:
0840             size_type it1_;
0841             size_type it2_;
0842
0843             friend class const_iterator1;
0844         };
0845 #endif
0846
0847         BOOST_UBLAS_INLINE
0848         iterator1 begin1 () {
0849             return find1 (0, 0, 0);
0850         }
0851         BOOST_UBLAS_INLINE
0852         iterator1 end1 () {
0853             return find1 (0, size_, 0);
0854         }
0855
0856 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
0857         class const_iterator2:
0858             public container_const_reference<hermitian_matrix>,
0859             public random_access_iterator_base<packed_random_access_iterator_tag,
0860                                                const_iterator2, value_type> {
0861         public:
0862             typedef typename hermitian_matrix::value_type value_type;
0863             typedef typename hermitian_matrix::difference_type difference_type;
0864             typedef typename hermitian_matrix::const_reference reference;
0865             typedef const typename hermitian_matrix::pointer pointer;
0866
0867             typedef const_iterator1 dual_iterator_type;
0868             typedef const_reverse_iterator1 dual_reverse_iterator_type;
0869
0870             // Construction and destruction
0871             BOOST_UBLAS_INLINE
0872             const_iterator2 ():
0873                 container_const_reference<self_type> (), it1_ (), it2_ () {}
0874             BOOST_UBLAS_INLINE
0875             const_iterator2 (const self_type &m, size_type it1, size_type it2):
0876                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
0877             BOOST_UBLAS_INLINE
0878             const_iterator2 (const iterator2 &it):
0879                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
0880
0881             // Arithmetic
0882             BOOST_UBLAS_INLINE
0883             const_iterator2 &operator ++ () {
0884                 ++ it2_;
0885                 return *this;
0886             }
0887             BOOST_UBLAS_INLINE
0888             const_iterator2 &operator -- () {
0889                 -- it2_;
0890                 return *this;
0891             }
0892             BOOST_UBLAS_INLINE
0893             const_iterator2 &operator += (difference_type n) {
0894                 it2_ += n;
0895                 return *this;
0896             }
0897             BOOST_UBLAS_INLINE
0898             const_iterator2 &operator -= (difference_type n) {
0899                 it2_ -= n;
0900                 return *this;
0901             }
0902             BOOST_UBLAS_INLINE
0903             difference_type operator - (const const_iterator2 &it) const {
0904                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
0905                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
0906                 return it2_ - it.it2_;
0907             }
0908
0909             // Dereference
0910             BOOST_UBLAS_INLINE
0911             const_reference operator * () const {
0912                 return (*this) () (it1_, it2_);
0913             }
0914             BOOST_UBLAS_INLINE
0915             const_reference operator [] (difference_type n) const {
0916                 return *(*this + n);
0917             }
0918
0919 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
0920             BOOST_UBLAS_INLINE
0921 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0922             typename self_type::
0923 #endif
0924             const_iterator1 begin () const {
0925                 return (*this) ().find1 (1, 0, it2_);
0926             }
0927             BOOST_UBLAS_INLINE
0928 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0929             typename self_type::
0930 #endif
0931             const_iterator1 cbegin () const {
0932                 return begin ();
0933             }
0934             BOOST_UBLAS_INLINE
0935 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0936             typename self_type::
0937 #endif
0938             const_iterator1 end () const {
0939                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
0940             }
0941             BOOST_UBLAS_INLINE
0942 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0943             typename self_type::
0944 #endif
0945             const_iterator1 cend () const {
0946                 return end ();
0947             }
0948             BOOST_UBLAS_INLINE
0949 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0950             typename self_type::
0951 #endif
0952             const_reverse_iterator1 rbegin () const {
0953                 return const_reverse_iterator1 (end ());
0954             }
0955             BOOST_UBLAS_INLINE
0956 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0957             typename self_type::
0958 #endif
0959             const_iterator1 crbegin () const {
0960                 return rbegin ();
0961             }
0962             BOOST_UBLAS_INLINE
0963 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0964             typename self_type::
0965 #endif
0966             const_reverse_iterator1 rend () const {
0967                 return const_reverse_iterator1 (begin ());
0968             }
0969             BOOST_UBLAS_INLINE
0970 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
0971             typename self_type::
0972 #endif
0973             const_iterator1 crend () const {
0974                 return rend ();
0975             }
0976 #endif
0977
0978             // Indices
0979             BOOST_UBLAS_INLINE
0980             size_type index1 () const {
0981                 return it1_;
0982             }
0983             BOOST_UBLAS_INLINE
0984             size_type index2 () const {
0985                 return it2_;
0986             }
0987
0988             // Assignment
0989             BOOST_UBLAS_INLINE
0990             const_iterator2 &operator = (const const_iterator2 &it) {
0991                 container_const_reference<self_type>::assign (&it ());
0992                 it1_ = it.it1_;
0993                 it2_ = it.it2_;
0994                 return *this;
0995             }
0996
0997             // Comparison
0998             BOOST_UBLAS_INLINE
0999             bool operator == (const const_iterator2 &it) const {
1000                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1001                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
1002                 return it2_ == it.it2_;
1003             }
1004             BOOST_UBLAS_INLINE
1005             bool operator < (const const_iterator2 &it) const {
1006                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1007                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
1008                 return it2_ < it.it2_;
1009             }
1010
1011         private:
1012             size_type it1_;
1013             size_type it2_;
1014         };
1015 #endif
1016
1017         BOOST_UBLAS_INLINE
1018         const_iterator2 begin2 () const {
1019             return find2 (0, 0, 0);
1020         }
1021         BOOST_UBLAS_INLINE
1022         const_iterator2 cbegin2 () const {
1023             return begin2 ();
1024         }
1025         BOOST_UBLAS_INLINE
1026         const_iterator2 end2 () const {
1027             return find2 (0, 0, size_);
1028         }
1029         BOOST_UBLAS_INLINE
1030         const_iterator2 cend2 () const {
1031             return end2 ();
1032         }
1033
1034 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
1035         class iterator2:
1036             public container_reference<hermitian_matrix>,
1037             public random_access_iterator_base<packed_random_access_iterator_tag,
1038                                                iterator2, value_type> {
1039         public:
1040             typedef typename hermitian_matrix::value_type value_type;
1041             typedef typename hermitian_matrix::difference_type difference_type;
1042             typedef typename hermitian_matrix::true_reference reference;
1043             typedef typename hermitian_matrix::pointer pointer;
1044
1045             typedef iterator1 dual_iterator_type;
1046             typedef reverse_iterator1 dual_reverse_iterator_type;
1047
1048             // Construction and destruction
1049             BOOST_UBLAS_INLINE
1050             iterator2 ():
1051                 container_reference<self_type> (), it1_ (), it2_ () {}
1052             BOOST_UBLAS_INLINE
1053             iterator2 (self_type &m, size_type it1, size_type it2):
1054                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
1055
1056             // Arithmetic
1057             BOOST_UBLAS_INLINE
1058             iterator2 &operator ++ () {
1059                 ++ it2_;
1060                 return *this;
1061             }
1062             BOOST_UBLAS_INLINE
1063             iterator2 &operator -- () {
1064                 -- it2_;
1065                 return *this;
1066             }
1067             BOOST_UBLAS_INLINE
1068             iterator2 &operator += (difference_type n) {
1069                 it2_ += n;
1070                 return *this;
1071             }
1072             BOOST_UBLAS_INLINE
1073             iterator2 &operator -= (difference_type n) {
1074                 it2_ -= n;
1075                 return *this;
1076             }
1077             BOOST_UBLAS_INLINE
1078             difference_type operator - (const iterator2 &it) const {
1079                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1080                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
1081                 return it2_ - it.it2_;
1082             }
1083
1084             // Dereference
1085             BOOST_UBLAS_INLINE
1086             reference operator * () const {
1087                 return (*this) ().at_element (it1_, it2_);
1088             }
1089             BOOST_UBLAS_INLINE
1090             reference operator [] (difference_type n) const {
1091                 return *(*this + n);
1092             }
1093
1094 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
1095             BOOST_UBLAS_INLINE
1096 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1097             typename self_type::
1098 #endif
1099             iterator1 begin () const {
1100                 return (*this) ().find1 (1, 0, it2_);
1101             }
1102             BOOST_UBLAS_INLINE
1103 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1104             typename self_type::
1105 #endif
1106             iterator1 end () const {
1107                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
1108             }
1109             BOOST_UBLAS_INLINE
1110 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1111             typename self_type::
1112 #endif
1113             reverse_iterator1 rbegin () const {
1114                 return reverse_iterator1 (end ());
1115             }
1116             BOOST_UBLAS_INLINE
1117 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1118             typename self_type::
1119 #endif
1120             reverse_iterator1 rend () const {
1121                 return reverse_iterator1 (begin ());
1122             }
1123 #endif
1124
1125             // Indices
1126             BOOST_UBLAS_INLINE
1127             size_type index1 () const {
1128                 return it1_;
1129             }
1130             BOOST_UBLAS_INLINE
1131             size_type index2 () const {
1132                 return it2_;
1133             }
1134
1135             // Assignment
1136             BOOST_UBLAS_INLINE
1137             iterator2 &operator = (const iterator2 &it) {
1138                 container_reference<self_type>::assign (&it ());
1139                 it1_ = it.it1_;
1140                 it2_ = it.it2_;
1141                 return *this;
1142             }
1143
1144             // Comparison
1145             BOOST_UBLAS_INLINE
1146             bool operator == (const iterator2 &it) const {
1147                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1148                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
1149                 return it2_ == it.it2_;
1150             }
1151             BOOST_UBLAS_INLINE
1152             bool operator < (const iterator2 &it) const {
1153                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1154                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
1155                 return it2_ < it.it2_;
1156             }
1157
1158         private:
1159             size_type it1_;
1160             size_type it2_;
1161
1162             friend class const_iterator2;
1163         };
1164 #endif
1165
1166         BOOST_UBLAS_INLINE
1167         iterator2 begin2 () {
1168             return find2 (0, 0, 0);
1169         }
1170         BOOST_UBLAS_INLINE
1171         iterator2 end2 () {
1172             return find2 (0, 0, size_);
1173         }
1174
1175         // Reverse iterators
1176
1177         BOOST_UBLAS_INLINE
1178         const_reverse_iterator1 rbegin1 () const {
1179             return const_reverse_iterator1 (end1 ());
1180         }
1181         BOOST_UBLAS_INLINE
1182         const_reverse_iterator1 crbegin1 () const {
1183             return rbegin1 ();
1184         }
1185         BOOST_UBLAS_INLINE
1186         const_reverse_iterator1 rend1 () const {
1187             return const_reverse_iterator1 (begin1 ());
1188         }
1189         BOOST_UBLAS_INLINE
1190         const_reverse_iterator1 crend1 () const {
1191             return rend1 ();
1192         }
1193
1194         BOOST_UBLAS_INLINE
1195         reverse_iterator1 rbegin1 () {
1196             return reverse_iterator1 (end1 ());
1197         }
1198         BOOST_UBLAS_INLINE
1199         reverse_iterator1 rend1 () {
1200             return reverse_iterator1 (begin1 ());
1201         }
1202
1203         BOOST_UBLAS_INLINE
1204         const_reverse_iterator2 rbegin2 () const {
1205             return const_reverse_iterator2 (end2 ());
1206         }
1207         BOOST_UBLAS_INLINE
1208         const_reverse_iterator2 crbegin2 () const {
1209             return rbegin2();
1210         }
1211         BOOST_UBLAS_INLINE
1212         const_reverse_iterator2 rend2 () const {
1213             return const_reverse_iterator2 (begin2 ());
1214         }
1215         BOOST_UBLAS_INLINE
1216         const_reverse_iterator2 crend2 () const {
1217             return rend2 ();
1218         }
1219
1220         BOOST_UBLAS_INLINE
1221         reverse_iterator2 rbegin2 () {
1222             return reverse_iterator2 (end2 ());
1223         }
1224         BOOST_UBLAS_INLINE
1225         reverse_iterator2 rend2 () {
1226             return reverse_iterator2 (begin2 ());
1227         }
1228
1229     private:
1230         size_type size_;
1231         array_type data_;
1232     };
1233
1234     /** \brief A Hermitian matrix adaptator: convert a any matrix into a Hermitian matrix expression
1235      *
1236      * For a \f$(m\times n)\f$-dimensional matrix, the \c hermitian_adaptor will provide a hermitian matrix.
1237      * Storage and location are based on those of the underlying matrix. This is important because
1238      * a \c hermitian_adaptor does not copy the matrix data to a new place. Therefore, modifying values
1239      * in a \c hermitian_adaptor matrix will also modify the underlying matrix too.
1240      *
1241      * \tparam M the type of matrix used to generate a hermitian matrix
1242      */
1243     template<class M, class TRI>
1244     class hermitian_adaptor:
1245         public matrix_expression<hermitian_adaptor<M, TRI> > {
1246
1247         typedef hermitian_adaptor<M, TRI> self_type;
1248         typedef typename M::value_type &true_reference;
1249     public:
1250 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
1251         using matrix_expression<self_type>::operator ();
1252 #endif
1253         typedef const M const_matrix_type;
1254         typedef M matrix_type;
1255         typedef TRI triangular_type;
1256         typedef typename M::size_type size_type;
1257         typedef typename M::difference_type difference_type;
1258         typedef typename M::value_type value_type;
1259         typedef typename M::value_type const_reference;
1260 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
1261         typedef typename boost::mpl::if_<boost::is_const<M>,
1262                                           typename M::value_type,
1263                                           typename M::reference>::type reference;
1264 #else
1265         typedef typename boost::mpl::if_<boost::is_const<M>,
1266                                           typename M::value_type,
1267                                           hermitian_matrix_element<self_type> >::type reference;
1268 #endif
1269         typedef typename boost::mpl::if_<boost::is_const<M>,
1270                                           typename M::const_closure_type,
1271                                           typename M::closure_type>::type matrix_closure_type;
1272         typedef const self_type const_closure_type;
1273         typedef self_type closure_type;
1274         // Replaced by _temporary_traits to avoid type requirements on M
1275         //typedef typename M::vector_temporary_type vector_temporary_type;
1276         //typedef typename M::matrix_temporary_type matrix_temporary_type;
1277         typedef typename storage_restrict_traits<typename M::storage_category,
1278                                                  packed_proxy_tag>::storage_category storage_category;
1279         typedef typename M::orientation_category orientation_category;
1280
1281         // Construction and destruction
1282         BOOST_UBLAS_INLINE
1283         hermitian_adaptor (matrix_type &data):
1284             matrix_expression<self_type> (),
1285             data_ (data) {
1286             BOOST_UBLAS_CHECK (data_.size1 () == data_.size2 (), bad_size ());
1287         }
1288         BOOST_UBLAS_INLINE
1289         hermitian_adaptor (const hermitian_adaptor &m):
1290             matrix_expression<self_type> (),
1291             data_ (m.data_) {
1292             BOOST_UBLAS_CHECK (data_.size1 () == data_.size2 (), bad_size ());
1293         }
1294
1295         // Accessors
1296         BOOST_UBLAS_INLINE
1297         size_type size1 () const {
1298             return data_.size1 ();
1299         }
1300         BOOST_UBLAS_INLINE
1301         size_type size2 () const {
1302             return data_.size2 ();
1303         }
1304
1305         // Storage accessors
1306         BOOST_UBLAS_INLINE
1307         const matrix_closure_type &data () const {
1308             return data_;
1309         }
1310         BOOST_UBLAS_INLINE
1311         matrix_closure_type &data () {
1312             return data_;
1313         }
1314
1315         // Element access
1316 #ifndef BOOST_UBLAS_PROXY_CONST_MEMBER
1317         BOOST_UBLAS_INLINE
1318         const_reference operator () (size_type i, size_type j) const {
1319             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
1320             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
1321             // if (i == j)
1322             //     return type_traits<value_type>::real (data () (i, i));
1323             // else
1324             if (triangular_type::other (i, j))
1325                 return data () (i, j);
1326             else
1327                 return type_traits<value_type>::conj (data () (j, i));
1328         }
1329         BOOST_UBLAS_INLINE
1330         reference operator () (size_type i, size_type j) {
1331             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
1332             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
1333 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
1334             if (triangular_type::other (i, j))
1335                 return data () (i, j);
1336             else {
1337                 external_logic ().raise ();
1338                 return conj_ = type_traits<value_type>::conj (data () (j, i));
1339             }
1340 #else
1341             if (triangular_type::other (i, j))
1342                 return reference (*this, i, j, data () (i, j));
1343             else
1344                 return reference (*this, i, j, type_traits<value_type>::conj (data () (j, i)));
1345 #endif
1346         }
1347         BOOST_UBLAS_INLINE
1348         true_reference insert_element (size_type i, size_type j, value_type t) {
1349             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
1350             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
1351             // if (i == j)
1352             //     data () (i, i) = type_traits<value_type>::real (t);
1353             // else
1354             if (triangular_type::other (i, j))
1355                 return data () (i, j) = t;
1356             else
1357                 return data () (j, i) = type_traits<value_type>::conj (t);
1358         }
1359 #else
1360         BOOST_UBLAS_INLINE
1361         reference operator () (size_type i, size_type j) {
1362             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
1363             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
1364 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
1365             if (triangular_type::other (i, j))
1366                 return data () (i, j);
1367             else {
1368                 external_logic ().raise ();
1369                 return conj_ = type_traits<value_type>::conj (data () (j, i));
1370             }
1371 #else
1372             if (triangular_type::other (i, j))
1373                 return reference (*this, i, j, data () (i, j));
1374             else
1375                 return reference (*this, i, j, type_traits<value_type>::conj (data () (j, i)));
1376 #endif
1377         }
1378         BOOST_UBLAS_INLINE
1379         true_reference insert_element (size_type i, size_type j, value_type t) {
1380             BOOST_UBLAS_CHECK (i < size1 (), bad_index ());
1381             BOOST_UBLAS_CHECK (j < size2 (), bad_index ());
1382             // if (i == j)
1383             //     data () (i, i) = type_traits<value_type>::real (t);
1384             // else
1385             if (triangular_type::other (i, j))
1386                 return data () (i, j) = t;
1387             else
1388                 return data () (j, i) = type_traits<value_type>::conj (t);
1389         }
1390 #endif
1391
1392         // Assignment
1393         BOOST_UBLAS_INLINE
1394         hermitian_adaptor &operator = (const hermitian_adaptor &m) {
1395             matrix_assign<scalar_assign, triangular_type> (*this, m);
1396             return *this;
1397         }
1398         BOOST_UBLAS_INLINE
1399         hermitian_adaptor &assign_temporary (hermitian_adaptor &m) {
1400             *this = m;
1401             return *this;
1402         }
1403         template<class AE>
1404         BOOST_UBLAS_INLINE
1405         hermitian_adaptor &operator = (const matrix_expression<AE> &ae) {
1406             matrix_assign<scalar_assign, triangular_type> (*this, matrix<value_type> (ae));
1407             return *this;
1408         }
1409         template<class AE>
1410         BOOST_UBLAS_INLINE
1411         hermitian_adaptor &assign (const matrix_expression<AE> &ae) {
1412             matrix_assign<scalar_assign, triangular_type> (*this, ae);
1413             return *this;
1414         }
1415         template<class AE>
1416         BOOST_UBLAS_INLINE
1417         hermitian_adaptor& operator += (const matrix_expression<AE> &ae) {
1418             matrix_assign<scalar_assign, triangular_type> (*this, matrix<value_type> (*this + ae));
1419             return *this;
1420         }
1421         template<class AE>
1422         BOOST_UBLAS_INLINE
1423         hermitian_adaptor &plus_assign (const matrix_expression<AE> &ae) {
1424             matrix_assign<scalar_plus_assign, triangular_type> (*this, ae);
1425             return *this;
1426         }
1427         template<class AE>
1428         BOOST_UBLAS_INLINE
1429         hermitian_adaptor& operator -= (const matrix_expression<AE> &ae) {
1430             matrix_assign<scalar_assign, triangular_type> (*this, matrix<value_type> (*this - ae));
1431             return *this;
1432         }
1433         template<class AE>
1434         BOOST_UBLAS_INLINE
1435         hermitian_adaptor &minus_assign (const matrix_expression<AE> &ae) {
1436             matrix_assign<scalar_minus_assign, triangular_type> (*this, ae);
1437             return *this;
1438         }
1439         template<class AT>
1440         BOOST_UBLAS_INLINE
1441         hermitian_adaptor& operator *= (const AT &at) {
1442             // Multiplication is only allowed for real scalars,
1443             // otherwise the resulting matrix isn't hermitian.
1444             // Thanks to Peter Schmitteckert for spotting this.
1445             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
1446             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
1447             return *this;
1448         }
1449         template<class AT>
1450         BOOST_UBLAS_INLINE
1451         hermitian_adaptor& operator /= (const AT &at) {
1452             // Multiplication is only allowed for real scalars,
1453             // otherwise the resulting matrix isn't hermitian.
1454             // Thanks to Peter Schmitteckert for spotting this.
1455             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
1456             matrix_assign_scalar<scalar_divides_assign> (*this, at);
1457             return *this;
1458         }
1459
1460         // Closure comparison
1461         BOOST_UBLAS_INLINE
1462         bool same_closure (const hermitian_adaptor &ha) const {
1463             return (*this).data ().same_closure (ha.data ());
1464         }
1465
1466         // Swapping
1467         BOOST_UBLAS_INLINE
1468         void swap (hermitian_adaptor &m) {
1469             if (this != &m)
1470                 matrix_swap<scalar_swap, triangular_type> (*this, m);
1471         }
1472         BOOST_UBLAS_INLINE
1473         friend void swap (hermitian_adaptor &m1, hermitian_adaptor &m2) {
1474             m1.swap (m2);
1475         }
1476
1477         // Iterator types
1478     private:
1479         // Use matrix iterator
1480         typedef typename M::const_iterator1 const_subiterator1_type;
1481         typedef typename boost::mpl::if_<boost::is_const<M>,
1482                                           typename M::const_iterator1,
1483                                           typename M::iterator1>::type subiterator1_type;
1484         typedef typename M::const_iterator2 const_subiterator2_type;
1485         typedef typename boost::mpl::if_<boost::is_const<M>,
1486                                           typename M::const_iterator2,
1487                                           typename M::iterator2>::type subiterator2_type;
1488
1489     public:
1490 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
1491         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
1492         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
1493         typedef indexed_const_iterator1<self_type, dense_random_access_iterator_tag> const_iterator1;
1494         typedef indexed_const_iterator2<self_type, dense_random_access_iterator_tag> const_iterator2;
1495 #else
1496         class const_iterator1;
1497         class iterator1;
1498         class const_iterator2;
1499         class iterator2;
1500 #endif
1501         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
1502         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
1503         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
1504         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
1505
1506         // Element lookup
1507         BOOST_UBLAS_INLINE
1508         const_iterator1 find1 (int rank, size_type i, size_type j) const {
1509             if (triangular_type::other (i, j)) {
1510                 if (triangular_type::other (size1 (), j)) {
1511                     return const_iterator1 (*this, 0, 0,
1512                                             data ().find1 (rank, i, j), data ().find1 (rank, size1 (), j),
1513                                             data ().find2 (rank, size2 (), size1 ()), data ().find2 (rank, size2 (), size1 ()));
1514                 } else {
1515                     return const_iterator1 (*this, 0, 1,
1516                                             data ().find1 (rank, i, j), data ().find1 (rank, j, j),
1517                                             data ().find2 (rank, j, j), data ().find2 (rank, j, size1 ()));
1518                 }
1519             } else {
1520                 if (triangular_type::other (size1 (), j)) {
1521                     return const_iterator1 (*this, 1, 0,
1522                                             data ().find1 (rank, j, j), data ().find1 (rank, size1 (), j),
1523                                             data ().find2 (rank, j, i), data ().find2 (rank, j, j));
1524                 } else {
1525                     return const_iterator1 (*this, 1, 1,
1526                                             data ().find1 (rank, size1 (), size2 ()), data ().find1 (rank, size1 (), size2 ()),
1527                                             data ().find2 (rank, j, i), data ().find2 (rank, j, size1 ()));
1528                 }
1529             }
1530         }
1531         BOOST_UBLAS_INLINE
1532         iterator1 find1 (int rank, size_type i, size_type j) {
1533             if (rank == 1)
1534                 i = triangular_type::mutable_restrict1 (i, j, size1(), size2());
1535             if (rank == 0)
1536                 i = triangular_type::global_mutable_restrict1 (i, size1(), j, size2());
1537             return iterator1 (*this, data ().find1 (rank, i, j));
1538         }
1539         BOOST_UBLAS_INLINE
1540         const_iterator2 find2 (int rank, size_type i, size_type j) const {
1541             if (triangular_type::other (i, j)) {
1542                 if (triangular_type::other (i, size2 ())) {
1543                     return const_iterator2 (*this, 1, 1,
1544                                             data ().find1 (rank, size2 (), size1 ()), data ().find1 (rank, size2 (), size1 ()),
1545                                             data ().find2 (rank, i, j), data ().find2 (rank, i, size2 ()));
1546                 } else {
1547                     return const_iterator2 (*this, 1, 0,
1548                                             data ().find1 (rank, i, i), data ().find1 (rank, size2 (), i),
1549                                             data ().find2 (rank, i, j), data ().find2 (rank, i, i));
1550                 }
1551             } else {
1552                 if (triangular_type::other (i, size2 ())) {
1553                     return const_iterator2 (*this, 0, 1,
1554                                             data ().find1 (rank, j, i), data ().find1 (rank, i, i),
1555                                             data ().find2 (rank, i, i), data ().find2 (rank, i, size2 ()));
1556                 } else {
1557                     return const_iterator2 (*this, 0, 0,
1558                                             data ().find1 (rank, j, i), data ().find1 (rank, size2 (), i),
1559                                             data ().find2 (rank, size1 (), size2 ()), data ().find2 (rank, size2 (), size2 ()));
1560                 }
1561             }
1562         }
1563         BOOST_UBLAS_INLINE
1564         iterator2 find2 (int rank, size_type i, size_type j) {
1565             if (rank == 1)
1566                 j = triangular_type::mutable_restrict2 (i, j, size1(), size2());
1567             if (rank == 0)
1568                 j = triangular_type::global_mutable_restrict2 (i, size1(), j, size2());
1569             return iterator2 (*this, data ().find2 (rank, i, j));
1570         }
1571
1572         // Iterators simply are indices.
1573
1574 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
1575         class const_iterator1:
1576             public container_const_reference<hermitian_adaptor>,
1577             public random_access_iterator_base<typename iterator_restrict_traits<
1578                                                    typename const_subiterator1_type::iterator_category, dense_random_access_iterator_tag>::iterator_category,
1579                                                const_iterator1, value_type> {
1580         public:
1581             typedef typename const_subiterator1_type::value_type value_type;
1582             typedef typename const_subiterator1_type::difference_type difference_type;
1583             // FIXME no better way to not return the address of a temporary?
1584             // typedef typename const_subiterator1_type::reference reference;
1585             typedef typename const_subiterator1_type::value_type reference;
1586             typedef typename const_subiterator1_type::pointer pointer;
1587
1588             typedef const_iterator2 dual_iterator_type;
1589             typedef const_reverse_iterator2 dual_reverse_iterator_type;
1590
1591             // Construction and destruction
1592             BOOST_UBLAS_INLINE
1593             const_iterator1 ():
1594                 container_const_reference<self_type> (),
1595                 begin_ (-1), end_ (-1), current_ (-1),
1596                 it1_begin_ (), it1_end_ (), it1_ (),
1597                 it2_begin_ (), it2_end_ (), it2_ () {}
1598             BOOST_UBLAS_INLINE
1599             const_iterator1 (const self_type &m, int begin, int end,
1600                              const const_subiterator1_type &it1_begin, const const_subiterator1_type &it1_end,
1601                              const const_subiterator2_type &it2_begin, const const_subiterator2_type &it2_end):
1602                 container_const_reference<self_type> (m),
1603                 begin_ (begin), end_ (end), current_ (begin),
1604                 it1_begin_ (it1_begin), it1_end_ (it1_end), it1_ (it1_begin_),
1605                 it2_begin_ (it2_begin), it2_end_ (it2_end), it2_ (it2_begin_) {
1606                 if (current_ == 0 && it1_ == it1_end_)
1607                     current_ = 1;
1608                 if (current_ == 1 && it2_ == it2_end_)
1609                     current_ = 0;
1610                 if ((current_ == 0 && it1_ == it1_end_) ||
1611                     (current_ == 1 && it2_ == it2_end_))
1612                     current_ = end_;
1613                 BOOST_UBLAS_CHECK (current_ == end_ ||
1614                                    (current_ == 0 && it1_ != it1_end_) ||
1615                                    (current_ == 1 && it2_ != it2_end_), internal_logic ());
1616             }
1617             // FIXME cannot compile
1618             //  iterator1 does not have these members!
1619             BOOST_UBLAS_INLINE
1620             const_iterator1 (const iterator1 &it):
1621                 container_const_reference<self_type> (it ()),
1622                 begin_ (it.begin_), end_ (it.end_), current_ (it.current_),
1623                 it1_begin_ (it.it1_begin_), it1_end_ (it.it1_end_), it1_ (it.it1_),
1624                 it2_begin_ (it.it2_begin_), it2_end_ (it.it2_end_), it2_ (it.it2_) {
1625                 BOOST_UBLAS_CHECK (current_ == end_ ||
1626                                    (current_ == 0 && it1_ != it1_end_) ||
1627                                    (current_ == 1 && it2_ != it2_end_), internal_logic ());
1628             }
1629
1630             // Arithmetic
1631             BOOST_UBLAS_INLINE
1632             const_iterator1 &operator ++ () {
1633                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1634                 if (current_ == 0) {
1635                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
1636                     ++ it1_;
1637                     if (it1_ == it1_end_ && end_ == 1) {
1638                         it2_ = it2_begin_;
1639                         current_ = 1;
1640                     }
1641                 } else /* if (current_ == 1) */ {
1642                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
1643                     ++ it2_;
1644                     if (it2_ == it2_end_ && end_ == 0) {
1645                         it1_ = it1_begin_;
1646                         current_ = 0;
1647                     }
1648                 }
1649                 return *this;
1650             }
1651             BOOST_UBLAS_INLINE
1652             const_iterator1 &operator -- () {
1653                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1654                 if (current_ == 0) {
1655                     if (it1_ == it1_begin_ && begin_ == 1) {
1656                         it2_ = it2_end_;
1657                         BOOST_UBLAS_CHECK (it2_ != it2_begin_, internal_logic ());
1658                         -- it2_;
1659                         current_ = 1;
1660                     } else {
1661                         -- it1_;
1662                     }
1663                 } else /* if (current_ == 1) */ {
1664                     if (it2_ == it2_begin_ && begin_ == 0) {
1665                         it1_ = it1_end_;
1666                         BOOST_UBLAS_CHECK (it1_ != it1_begin_, internal_logic ());
1667                         -- it1_;
1668                         current_ = 0;
1669                     } else {
1670                         -- it2_;
1671                     }
1672                 }
1673                 return *this;
1674             }
1675             BOOST_UBLAS_INLINE
1676             const_iterator1 &operator += (difference_type n) {
1677                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1678                 if (current_ == 0) {
1679                     size_type d = (std::min) (n, it1_end_ - it1_);
1680                     it1_ += d;
1681                     n -= d;
1682                     if (n > 0 || (end_ == 1 && it1_ == it1_end_)) {
1683                         BOOST_UBLAS_CHECK (end_ == 1, external_logic ());
1684                         d = (std::min) (n, it2_end_ - it2_begin_);
1685                         it2_ = it2_begin_ + d;
1686                         n -= d;
1687                         current_ = 1;
1688                     }
1689                 } else /* if (current_ == 1) */ {
1690                     size_type d = (std::min) (n, it2_end_ - it2_);
1691                     it2_ += d;
1692                     n -= d;
1693                     if (n > 0 || (end_ == 0 && it2_ == it2_end_)) {
1694                         BOOST_UBLAS_CHECK (end_ == 0, external_logic ());
1695                         d = (std::min) (n, it1_end_ - it1_begin_);
1696                         it1_ = it1_begin_ + d;
1697                         n -= d;
1698                         current_ = 0;
1699                     }
1700                 }
1701                 BOOST_UBLAS_CHECK (n == 0, external_logic ());
1702                 return *this;
1703             }
1704             BOOST_UBLAS_INLINE
1705             const_iterator1 &operator -= (difference_type n) {
1706                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1707                 if (current_ == 0) {
1708                     size_type d = (std::min) (n, it1_ - it1_begin_);
1709                     it1_ -= d;
1710                     n -= d;
1711                     if (n > 0) {
1712                         BOOST_UBLAS_CHECK (end_ == 1, external_logic ());
1713                         d = (std::min) (n, it2_end_ - it2_begin_);
1714                         it2_ = it2_end_ - d;
1715                         n -= d;
1716                         current_ = 1;
1717                     }
1718                 } else /* if (current_ == 1) */ {
1719                     size_type d = (std::min) (n, it2_ - it2_begin_);
1720                     it2_ -= d;
1721                     n -= d;
1722                     if (n > 0) {
1723                         BOOST_UBLAS_CHECK (end_ == 0, external_logic ());
1724                         d = (std::min) (n, it1_end_ - it1_begin_);
1725                         it1_ = it1_end_ - d;
1726                         n -= d;
1727                         current_ = 0;
1728                     }
1729                 }
1730                 BOOST_UBLAS_CHECK (n == 0, external_logic ());
1731                 return *this;
1732             }
1733             BOOST_UBLAS_INLINE
1734             difference_type operator - (const const_iterator1 &it) const {
1735                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1736                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1737                 BOOST_UBLAS_CHECK (it.current_ == 0 || it.current_ == 1, internal_logic ());
1738                 BOOST_UBLAS_CHECK (/* begin_ == it.begin_ && */ end_ == it.end_, internal_logic ());
1739                 if (current_ == 0 && it.current_ == 0) {
1740                     return it1_ - it.it1_;
1741                 } else if (current_ == 0 && it.current_ == 1) {
1742                     if (end_ == 1 && it.end_ == 1) {
1743                         return (it1_ - it.it1_end_) + (it.it2_begin_ - it.it2_);
1744                     } else /* if (end_ == 0 && it.end_ == 0) */ {
1745                         return (it1_ - it.it1_begin_) + (it.it2_end_ - it.it2_);
1746                     }
1747
1748                 } else if (current_ == 1 && it.current_ == 0) {
1749                     if (end_ == 1 && it.end_ == 1) {
1750                         return (it2_ - it.it2_begin_) + (it.it1_end_ - it.it1_);
1751                     } else /* if (end_ == 0 && it.end_ == 0) */ {
1752                         return (it2_ - it.it2_end_) + (it.it1_begin_ - it.it1_);
1753                     }
1754                 } else /* if (current_ == 1 && it.current_ == 1) */ {
1755                     return it2_ - it.it2_;
1756                 }
1757             }
1758
1759             // Dereference
1760             BOOST_UBLAS_INLINE
1761             const_reference operator * () const {
1762                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1763                 if (current_ == 0) {
1764                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
1765                     if (triangular_type::other (index1 (), index2 ()))
1766                         return *it1_;
1767                     else
1768                         return type_traits<value_type>::conj (*it1_);
1769                 } else /* if (current_ == 1) */ {
1770                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
1771                     if (triangular_type::other (index1 (), index2 ()))
1772                         return *it2_;
1773                     else
1774                         return type_traits<value_type>::conj (*it2_);
1775                 }
1776             }
1777             BOOST_UBLAS_INLINE
1778             const_reference operator [] (difference_type n) const {
1779                 return *(*this + n);
1780             }
1781
1782 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
1783             BOOST_UBLAS_INLINE
1784 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1785             typename self_type::
1786 #endif
1787             const_iterator2 begin () const {
1788                 return (*this) ().find2 (1, index1 (), 0);
1789             }
1790             BOOST_UBLAS_INLINE
1791 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1792             typename self_type::
1793 #endif
1794             const_iterator2 cbegin () const {
1795                 return begin ();
1796             }
1797             BOOST_UBLAS_INLINE
1798 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1799             typename self_type::
1800 #endif
1801             const_iterator2 end () const {
1802                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
1803             }
1804             BOOST_UBLAS_INLINE
1805 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1806             typename self_type::
1807 #endif
1808             const_iterator2 cend () const {
1809                 return end ();
1810             }
1811             BOOST_UBLAS_INLINE
1812 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1813             typename self_type::
1814 #endif
1815             const_reverse_iterator2 rbegin () const {
1816                 return const_reverse_iterator2 (end ());
1817             }
1818             BOOST_UBLAS_INLINE
1819 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1820             typename self_type::
1821 #endif
1822             const_reverse_iterator2 crbegin () const {
1823                 return rbegin ();
1824             }
1825             BOOST_UBLAS_INLINE
1826 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1827             typename self_type::
1828 #endif
1829             const_reverse_iterator2 rend () const {
1830                 return const_reverse_iterator2 (begin ());
1831             }
1832             BOOST_UBLAS_INLINE
1833 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1834             typename self_type::
1835 #endif
1836             const_reverse_iterator2 crend () const {
1837                 return rend ();
1838             }
1839 #endif
1840
1841             // Indices
1842             BOOST_UBLAS_INLINE
1843             size_type index1 () const {
1844                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1845                 if (current_ == 0) {
1846                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
1847                     return it1_.index1 ();
1848                 } else /* if (current_ == 1) */ {
1849                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
1850                     return it2_.index2 ();
1851                 }
1852             }
1853             BOOST_UBLAS_INLINE
1854             size_type index2 () const {
1855                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1856                 if (current_ == 0) {
1857                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
1858                     return it1_.index2 ();
1859                 } else /* if (current_ == 1) */ {
1860                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
1861                     return it2_.index1 ();
1862                 }
1863             }
1864
1865             // Assignment
1866             BOOST_UBLAS_INLINE
1867             const_iterator1 &operator = (const const_iterator1 &it) {
1868                 container_const_reference<self_type>::assign (&it ());
1869                 begin_ = it.begin_;
1870                 end_ = it.end_;
1871                 current_ = it.current_;
1872                 it1_begin_ = it.it1_begin_;
1873                 it1_end_ = it.it1_end_;
1874                 it1_ = it.it1_;
1875                 it2_begin_ = it.it2_begin_;
1876                 it2_end_ = it.it2_end_;
1877                 it2_ = it.it2_;
1878                 return *this;
1879             }
1880
1881             // Comparison
1882             BOOST_UBLAS_INLINE
1883             bool operator == (const const_iterator1 &it) const {
1884                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1885                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
1886                 BOOST_UBLAS_CHECK (it.current_ == 0 || it.current_ == 1, internal_logic ());
1887                 BOOST_UBLAS_CHECK (/* begin_ == it.begin_ && */ end_ == it.end_, internal_logic ());
1888                 return (current_ == 0 && it.current_ == 0 && it1_ == it.it1_) ||
1889                        (current_ == 1 && it.current_ == 1 && it2_ == it.it2_);
1890             }
1891             BOOST_UBLAS_INLINE
1892             bool operator < (const const_iterator1 &it) const {
1893                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1894                 return it - *this > 0;
1895             }
1896
1897         private:
1898             int begin_;
1899             int end_;
1900             int current_;
1901             const_subiterator1_type it1_begin_;
1902             const_subiterator1_type it1_end_;
1903             const_subiterator1_type it1_;
1904             const_subiterator2_type it2_begin_;
1905             const_subiterator2_type it2_end_;
1906             const_subiterator2_type it2_;
1907         };
1908 #endif
1909
1910         BOOST_UBLAS_INLINE
1911         const_iterator1 begin1 () const {
1912             return find1 (0, 0, 0);
1913         }
1914         BOOST_UBLAS_INLINE
1915         const_iterator1 cbegin1 () const {
1916             return begin1 ();
1917         }
1918         BOOST_UBLAS_INLINE
1919         const_iterator1 end1 () const {
1920             return find1 (0, size1 (), 0);
1921         }
1922         BOOST_UBLAS_INLINE
1923         const_iterator1 cend1 () const {
1924             return end1 ();
1925         }
1926
1927 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
1928         class iterator1:
1929             public container_reference<hermitian_adaptor>,
1930             public random_access_iterator_base<typename iterator_restrict_traits<
1931                                                    typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
1932                                                iterator1, value_type> {
1933         public:
1934             typedef typename subiterator1_type::value_type value_type;
1935             typedef typename subiterator1_type::difference_type difference_type;
1936             typedef typename subiterator1_type::reference reference;
1937             typedef typename subiterator1_type::pointer pointer;
1938
1939             typedef iterator2 dual_iterator_type;
1940             typedef reverse_iterator2 dual_reverse_iterator_type;
1941
1942             // Construction and destruction
1943             BOOST_UBLAS_INLINE
1944             iterator1 ():
1945                 container_reference<self_type> (), it1_ () {}
1946             BOOST_UBLAS_INLINE
1947             iterator1 (self_type &m, const subiterator1_type &it1):
1948                 container_reference<self_type> (m), it1_ (it1) {}
1949
1950             // Arithmetic
1951             BOOST_UBLAS_INLINE
1952             iterator1 &operator ++ () {
1953                 ++ it1_;
1954                 return *this;
1955             }
1956             BOOST_UBLAS_INLINE
1957             iterator1 &operator -- () {
1958                 -- it1_;
1959                 return *this;
1960             }
1961             BOOST_UBLAS_INLINE
1962             iterator1 &operator += (difference_type n) {
1963                 it1_ += n;
1964                 return *this;
1965             }
1966             BOOST_UBLAS_INLINE
1967             iterator1 &operator -= (difference_type n) {
1968                 it1_ -= n;
1969                 return *this;
1970             }
1971             BOOST_UBLAS_INLINE
1972             difference_type operator - (const iterator1 &it) const {
1973                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
1974                 return it1_ - it.it1_;
1975             }
1976
1977             // Dereference
1978             BOOST_UBLAS_INLINE
1979             reference operator * () const {
1980                 return *it1_;
1981             }
1982             BOOST_UBLAS_INLINE
1983             reference operator [] (difference_type n) const {
1984                 return *(*this + n);
1985             }
1986
1987 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
1988             BOOST_UBLAS_INLINE
1989 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1990             typename self_type::
1991 #endif
1992             iterator2 begin () const {
1993                 return (*this) ().find2 (1, index1 (), 0);
1994             }
1995             BOOST_UBLAS_INLINE
1996 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
1997             typename self_type::
1998 #endif
1999             iterator2 end () const {
2000                 return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
2001             }
2002             BOOST_UBLAS_INLINE
2003 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2004             typename self_type::
2005 #endif
2006             reverse_iterator2 rbegin () const {
2007                 return reverse_iterator2 (end ());
2008             }
2009             BOOST_UBLAS_INLINE
2010 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2011             typename self_type::
2012 #endif
2013             reverse_iterator2 rend () const {
2014                 return reverse_iterator2 (begin ());
2015             }
2016 #endif
2017
2018             // Indices
2019             BOOST_UBLAS_INLINE
2020             size_type index1 () const {
2021                 return it1_.index1 ();
2022             }
2023             BOOST_UBLAS_INLINE
2024             size_type index2 () const {
2025                 return it1_.index2 ();
2026             }
2027
2028             // Assignment
2029             BOOST_UBLAS_INLINE
2030             iterator1 &operator = (const iterator1 &it) {
2031                 container_reference<self_type>::assign (&it ());
2032                 it1_ = it.it1_;
2033                 return *this;
2034             }
2035
2036             // Comparison
2037             BOOST_UBLAS_INLINE
2038             bool operator == (const iterator1 &it) const {
2039                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2040                 return it1_ == it.it1_;
2041             }
2042             BOOST_UBLAS_INLINE
2043             bool operator < (const iterator1 &it) const {
2044                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2045                 return it1_ < it.it1_;
2046             }
2047
2048         private:
2049             subiterator1_type it1_;
2050
2051             friend class const_iterator1;
2052         };
2053 #endif
2054
2055         BOOST_UBLAS_INLINE
2056         iterator1 begin1 () {
2057             return find1 (0, 0, 0);
2058         }
2059         BOOST_UBLAS_INLINE
2060         iterator1 end1 () {
2061             return find1 (0, size1 (), 0);
2062         }
2063
2064 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
2065         class const_iterator2:
2066             public container_const_reference<hermitian_adaptor>,
2067             public random_access_iterator_base<typename iterator_restrict_traits<
2068             typename const_subiterator2_type::iterator_category, dense_random_access_iterator_tag>::iterator_category,
2069                                                const_iterator2, value_type> {
2070         public:
2071             typedef typename const_subiterator2_type::value_type value_type;
2072             typedef typename const_subiterator2_type::difference_type difference_type;
2073             // FIXME no better way to not return the address of a temporary?
2074             // typedef typename const_subiterator2_type::reference reference;
2075             typedef typename const_subiterator2_type::value_type reference;
2076             typedef typename const_subiterator2_type::pointer pointer;
2077
2078             typedef const_iterator1 dual_iterator_type;
2079             typedef const_reverse_iterator1 dual_reverse_iterator_type;
2080
2081             // Construction and destruction
2082             BOOST_UBLAS_INLINE
2083             const_iterator2 ():
2084                 container_const_reference<self_type> (),
2085                 begin_ (-1), end_ (-1), current_ (-1),
2086                 it1_begin_ (), it1_end_ (), it1_ (),
2087                 it2_begin_ (), it2_end_ (), it2_ () {}
2088             BOOST_UBLAS_INLINE
2089             const_iterator2 (const self_type &m, int begin, int end,
2090                              const const_subiterator1_type &it1_begin, const const_subiterator1_type &it1_end,
2091                              const const_subiterator2_type &it2_begin, const const_subiterator2_type &it2_end):
2092                 container_const_reference<self_type> (m),
2093                 begin_ (begin), end_ (end), current_ (begin),
2094                 it1_begin_ (it1_begin), it1_end_ (it1_end), it1_ (it1_begin_),
2095                 it2_begin_ (it2_begin), it2_end_ (it2_end), it2_ (it2_begin_) {
2096                 if (current_ == 0 && it1_ == it1_end_)
2097                     current_ = 1;
2098                 if (current_ == 1 && it2_ == it2_end_)
2099                     current_ = 0;
2100                 if ((current_ == 0 && it1_ == it1_end_) ||
2101                     (current_ == 1 && it2_ == it2_end_))
2102                     current_ = end_;
2103                 BOOST_UBLAS_CHECK (current_ == end_ ||
2104                                    (current_ == 0 && it1_ != it1_end_) ||
2105                                    (current_ == 1 && it2_ != it2_end_), internal_logic ());
2106             }
2107             // FIXME cannot compiler
2108             //  iterator2 does not have these members!
2109             BOOST_UBLAS_INLINE
2110             const_iterator2 (const iterator2 &it):
2111                 container_const_reference<self_type> (it ()),
2112                 begin_ (it.begin_), end_ (it.end_), current_ (it.current_),
2113                 it1_begin_ (it.it1_begin_), it1_end_ (it.it1_end_), it1_ (it.it1_),
2114                 it2_begin_ (it.it2_begin_), it2_end_ (it.it2_end_), it2_ (it.it2_) {
2115                 BOOST_UBLAS_CHECK (current_ == end_ ||
2116                                    (current_ == 0 && it1_ != it1_end_) ||
2117                                    (current_ == 1 && it2_ != it2_end_), internal_logic ());
2118             }
2119
2120             // Arithmetic
2121             BOOST_UBLAS_INLINE
2122             const_iterator2 &operator ++ () {
2123                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2124                 if (current_ == 0) {
2125                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
2126                     ++ it1_;
2127                     if (it1_ == it1_end_ && end_ == 1) {
2128                         it2_ = it2_begin_;
2129                         current_ = 1;
2130                     }
2131                 } else /* if (current_ == 1) */ {
2132                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
2133                     ++ it2_;
2134                     if (it2_ == it2_end_ && end_ == 0) {
2135                         it1_ = it1_begin_;
2136                         current_ = 0;
2137                     }
2138                 }
2139                 return *this;
2140             }
2141             BOOST_UBLAS_INLINE
2142             const_iterator2 &operator -- () {
2143                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2144                 if (current_ == 0) {
2145                     if (it1_ == it1_begin_ && begin_ == 1) {
2146                         it2_ = it2_end_;
2147                         BOOST_UBLAS_CHECK (it2_ != it2_begin_, internal_logic ());
2148                         -- it2_;
2149                         current_ = 1;
2150                     } else {
2151                         -- it1_;
2152                     }
2153                 } else /* if (current_ == 1) */ {
2154                     if (it2_ == it2_begin_ && begin_ == 0) {
2155                         it1_ = it1_end_;
2156                         BOOST_UBLAS_CHECK (it1_ != it1_begin_, internal_logic ());
2157                         -- it1_;
2158                         current_ = 0;
2159                     } else {
2160                         -- it2_;
2161                     }
2162                 }
2163                 return *this;
2164             }
2165             BOOST_UBLAS_INLINE
2166             const_iterator2 &operator += (difference_type n) {
2167                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2168                 if (current_ == 0) {
2169                     size_type d = (std::min) (n, it1_end_ - it1_);
2170                     it1_ += d;
2171                     n -= d;
2172                     if (n > 0 || (end_ == 1 && it1_ == it1_end_)) {
2173                         BOOST_UBLAS_CHECK (end_ == 1, external_logic ());
2174                         d = (std::min) (n, it2_end_ - it2_begin_);
2175                         it2_ = it2_begin_ + d;
2176                         n -= d;
2177                         current_ = 1;
2178                     }
2179                 } else /* if (current_ == 1) */ {
2180                     size_type d = (std::min) (n, it2_end_ - it2_);
2181                     it2_ += d;
2182                     n -= d;
2183                     if (n > 0 || (end_ == 0 && it2_ == it2_end_)) {
2184                         BOOST_UBLAS_CHECK (end_ == 0, external_logic ());
2185                         d = (std::min) (n, it1_end_ - it1_begin_);
2186                         it1_ = it1_begin_ + d;
2187                         n -= d;
2188                         current_ = 0;
2189                     }
2190                 }
2191                 BOOST_UBLAS_CHECK (n == 0, external_logic ());
2192                 return *this;
2193             }
2194             BOOST_UBLAS_INLINE
2195             const_iterator2 &operator -= (difference_type n) {
2196                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2197                 if (current_ == 0) {
2198                     size_type d = (std::min) (n, it1_ - it1_begin_);
2199                     it1_ -= d;
2200                     n -= d;
2201                     if (n > 0) {
2202                         BOOST_UBLAS_CHECK (end_ == 1, external_logic ());
2203                         d = (std::min) (n, it2_end_ - it2_begin_);
2204                         it2_ = it2_end_ - d;
2205                         n -= d;
2206                         current_ = 1;
2207                     }
2208                 } else /* if (current_ == 1) */ {
2209                     size_type d = (std::min) (n, it2_ - it2_begin_);
2210                     it2_ -= d;
2211                     n -= d;
2212                     if (n > 0) {
2213                         BOOST_UBLAS_CHECK (end_ == 0, external_logic ());
2214                         d = (std::min) (n, it1_end_ - it1_begin_);
2215                         it1_ = it1_end_ - d;
2216                         n -= d;
2217                         current_ = 0;
2218                     }
2219                 }
2220                 BOOST_UBLAS_CHECK (n == 0, external_logic ());
2221                 return *this;
2222             }
2223             BOOST_UBLAS_INLINE
2224             difference_type operator - (const const_iterator2 &it) const {
2225                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2226                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2227                 BOOST_UBLAS_CHECK (it.current_ == 0 || it.current_ == 1, internal_logic ());
2228                 BOOST_UBLAS_CHECK (/* begin_ == it.begin_ && */ end_ == it.end_, internal_logic ());
2229                 if (current_ == 0 && it.current_ == 0) {
2230                     return it1_ - it.it1_;
2231                 } else if (current_ == 0 && it.current_ == 1) {
2232                     if (end_ == 1 && it.end_ == 1) {
2233                         return (it1_ - it.it1_end_) + (it.it2_begin_ - it.it2_);
2234                     } else /* if (end_ == 0 && it.end_ == 0) */ {
2235                         return (it1_ - it.it1_begin_) + (it.it2_end_ - it.it2_);
2236                     }
2237
2238                 } else if (current_ == 1 && it.current_ == 0) {
2239                     if (end_ == 1 && it.end_ == 1) {
2240                         return (it2_ - it.it2_begin_) + (it.it1_end_ - it.it1_);
2241                     } else /* if (end_ == 0 && it.end_ == 0) */ {
2242                         return (it2_ - it.it2_end_) + (it.it1_begin_ - it.it1_);
2243                     }
2244                 } else /* if (current_ == 1 && it.current_ == 1) */ {
2245                     return it2_ - it.it2_;
2246                 }
2247             }
2248
2249             // Dereference
2250             BOOST_UBLAS_INLINE
2251             const_reference operator * () const {
2252                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2253                 if (current_ == 0) {
2254                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
2255                     if (triangular_type::other (index1 (), index2 ()))
2256                         return *it1_;
2257                     else
2258                         return type_traits<value_type>::conj (*it1_);
2259                 } else /* if (current_ == 1) */ {
2260                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
2261                     if (triangular_type::other (index1 (), index2 ()))
2262                         return *it2_;
2263                     else
2264                         return type_traits<value_type>::conj (*it2_);
2265                 }
2266             }
2267             BOOST_UBLAS_INLINE
2268             const_reference operator [] (difference_type n) const {
2269                 return *(*this + n);
2270             }
2271
2272 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
2273             BOOST_UBLAS_INLINE
2274 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2275             typename self_type::
2276 #endif
2277             const_iterator1 begin () const {
2278                 return (*this) ().find1 (1, 0, index2 ());
2279             }
2280             BOOST_UBLAS_INLINE
2281 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2282             typename self_type::
2283 #endif
2284             const_iterator1 cbegin () const {
2285                 return begin ();
2286             }
2287             BOOST_UBLAS_INLINE
2288 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2289             typename self_type::
2290 #endif
2291             const_iterator1 end () const {
2292                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
2293             }
2294             BOOST_UBLAS_INLINE
2295 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2296             typename self_type::
2297 #endif
2298             const_iterator1 cend () const {
2299                 return end ();
2300             }
2301             BOOST_UBLAS_INLINE
2302 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2303             typename self_type::
2304 #endif
2305             const_reverse_iterator1 rbegin () const {
2306                 return const_reverse_iterator1 (end ());
2307             }
2308             BOOST_UBLAS_INLINE
2309 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2310             typename self_type::
2311 #endif
2312             const_reverse_iterator1 crbegin () const {
2313                 return rbegin ();
2314             }
2315             BOOST_UBLAS_INLINE
2316 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2317             typename self_type::
2318 #endif
2319             const_reverse_iterator1 rend () const {
2320                 return const_reverse_iterator1 (begin ());
2321             }
2322             BOOST_UBLAS_INLINE
2323 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2324             typename self_type::
2325 #endif
2326             const_reverse_iterator1 crend () const {
2327                 return end ();
2328             }
2329 #endif
2330
2331             // Indices
2332             BOOST_UBLAS_INLINE
2333             size_type index1 () const {
2334                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2335                 if (current_ == 0) {
2336                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
2337                     return it1_.index2 ();
2338                 } else /* if (current_ == 1) */ {
2339                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
2340                     return it2_.index1 ();
2341                 }
2342             }
2343             BOOST_UBLAS_INLINE
2344             size_type index2 () const {
2345                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2346                 if (current_ == 0) {
2347                     BOOST_UBLAS_CHECK (it1_ != it1_end_, internal_logic ());
2348                     return it1_.index1 ();
2349                 } else /* if (current_ == 1) */ {
2350                     BOOST_UBLAS_CHECK (it2_ != it2_end_, internal_logic ());
2351                     return it2_.index2 ();
2352                 }
2353             }
2354
2355             // Assignment
2356             BOOST_UBLAS_INLINE
2357             const_iterator2 &operator = (const const_iterator2 &it) {
2358                 container_const_reference<self_type>::assign (&it ());
2359                 begin_ = it.begin_;
2360                 end_ = it.end_;
2361                 current_ = it.current_;
2362                 it1_begin_ = it.it1_begin_;
2363                 it1_end_ = it.it1_end_;
2364                 it1_ = it.it1_;
2365                 it2_begin_ = it.it2_begin_;
2366                 it2_end_ = it.it2_end_;
2367                 it2_ = it.it2_;
2368                 return *this;
2369             }
2370
2371             // Comparison
2372             BOOST_UBLAS_INLINE
2373             bool operator == (const const_iterator2 &it) const {
2374                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2375                 BOOST_UBLAS_CHECK (current_ == 0 || current_ == 1, internal_logic ());
2376                 BOOST_UBLAS_CHECK (it.current_ == 0 || it.current_ == 1, internal_logic ());
2377                 BOOST_UBLAS_CHECK (/* begin_ == it.begin_ && */ end_ == it.end_, internal_logic ());
2378                 return (current_ == 0 && it.current_ == 0 && it1_ == it.it1_) ||
2379                        (current_ == 1 && it.current_ == 1 && it2_ == it.it2_);
2380             }
2381             BOOST_UBLAS_INLINE
2382             bool operator < (const const_iterator2 &it) const {
2383                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2384                 return it - *this > 0;
2385             }
2386
2387         private:
2388             int begin_;
2389             int end_;
2390             int current_;
2391             const_subiterator1_type it1_begin_;
2392             const_subiterator1_type it1_end_;
2393             const_subiterator1_type it1_;
2394             const_subiterator2_type it2_begin_;
2395             const_subiterator2_type it2_end_;
2396             const_subiterator2_type it2_;
2397         };
2398 #endif
2399
2400         BOOST_UBLAS_INLINE
2401         const_iterator2 begin2 () const {
2402             return find2 (0, 0, 0);
2403         }
2404         BOOST_UBLAS_INLINE
2405         const_iterator2 cbegin2 () const {
2406             return begin2 ();
2407         }
2408         BOOST_UBLAS_INLINE
2409         const_iterator2 end2 () const {
2410             return find2 (0, 0, size2 ());
2411         }
2412         BOOST_UBLAS_INLINE
2413         const_iterator2 cend2 () const {
2414             return end2 ();
2415         }
2416
2417 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
2418         class iterator2:
2419             public container_reference<hermitian_adaptor>,
2420             public random_access_iterator_base<typename iterator_restrict_traits<
2421                                                    typename subiterator2_type::iterator_category, packed_random_access_iterator_tag>::iterator_category,
2422                                                iterator2, value_type> {
2423         public:
2424             typedef typename subiterator2_type::value_type value_type;
2425             typedef typename subiterator2_type::difference_type difference_type;
2426             typedef typename subiterator2_type::reference reference;
2427             typedef typename subiterator2_type::pointer pointer;
2428
2429             typedef iterator1 dual_iterator_type;
2430             typedef reverse_iterator1 dual_reverse_iterator_type;
2431
2432             // Construction and destruction
2433             BOOST_UBLAS_INLINE
2434             iterator2 ():
2435                 container_reference<self_type> (), it2_ () {}
2436             BOOST_UBLAS_INLINE
2437             iterator2 (self_type &m, const subiterator2_type &it2):
2438                 container_reference<self_type> (m), it2_ (it2) {}
2439
2440             // Arithmetic
2441             BOOST_UBLAS_INLINE
2442             iterator2 &operator ++ () {
2443                 ++ it2_;
2444                 return *this;
2445             }
2446             BOOST_UBLAS_INLINE
2447             iterator2 &operator -- () {
2448                 -- it2_;
2449                 return *this;
2450             }
2451             BOOST_UBLAS_INLINE
2452             iterator2 &operator += (difference_type n) {
2453                 it2_ += n;
2454                 return *this;
2455             }
2456             BOOST_UBLAS_INLINE
2457             iterator2 &operator -= (difference_type n) {
2458                 it2_ -= n;
2459                 return *this;
2460             }
2461             BOOST_UBLAS_INLINE
2462             difference_type operator - (const iterator2 &it) const {
2463                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2464                 return it2_ - it.it2_;
2465             }
2466
2467             // Dereference
2468             BOOST_UBLAS_INLINE
2469             reference operator * () const {
2470                 return *it2_;
2471             }
2472             BOOST_UBLAS_INLINE
2473             reference operator [] (difference_type n) const {
2474                 return *(*this + n);
2475             }
2476
2477 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
2478             BOOST_UBLAS_INLINE
2479 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2480             typename self_type::
2481 #endif
2482             iterator1 begin () const {
2483                 return (*this) ().find1 (1, 0, index2 ());
2484             }
2485             BOOST_UBLAS_INLINE
2486 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2487             typename self_type::
2488 #endif
2489             iterator1 end () const {
2490                 return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
2491             }
2492             BOOST_UBLAS_INLINE
2493 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2494             typename self_type::
2495 #endif
2496             reverse_iterator1 rbegin () const {
2497                 return reverse_iterator1 (end ());
2498             }
2499             BOOST_UBLAS_INLINE
2500 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
2501             typename self_type::
2502 #endif
2503             reverse_iterator1 rend () const {
2504                 return reverse_iterator1 (begin ());
2505             }
2506 #endif
2507
2508             // Indices
2509             BOOST_UBLAS_INLINE
2510             size_type index1 () const {
2511                 return it2_.index1 ();
2512             }
2513             BOOST_UBLAS_INLINE
2514             size_type index2 () const {
2515                 return it2_.index2 ();
2516             }
2517
2518             // Assignment
2519             BOOST_UBLAS_INLINE
2520             iterator2 &operator = (const iterator2 &it) {
2521                 container_reference<self_type>::assign (&it ());
2522                 it2_ = it.it2_;
2523                 return *this;
2524             }
2525
2526             // Comparison
2527             BOOST_UBLAS_INLINE
2528             bool operator == (const iterator2 &it) const {
2529                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2530                 return it2_ == it.it2_;
2531             }
2532             BOOST_UBLAS_INLINE
2533             bool operator < (const iterator2 &it) const {
2534                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2535                 return it2_ < it.it2_;
2536             }
2537
2538         private:
2539             subiterator2_type it2_;
2540
2541             friend class const_iterator2;
2542         };
2543 #endif
2544
2545         BOOST_UBLAS_INLINE
2546         iterator2 begin2 () {
2547             return find2 (0, 0, 0);
2548         }
2549         BOOST_UBLAS_INLINE
2550         iterator2 end2 () {
2551             return find2 (0, 0, size2 ());
2552         }
2553
2554         // Reverse iterators
2555
2556         BOOST_UBLAS_INLINE
2557         const_reverse_iterator1 rbegin1 () const {
2558             return const_reverse_iterator1 (end1 ());
2559         }
2560         BOOST_UBLAS_INLINE
2561         const_reverse_iterator1 crbegin1 () const {
2562             return rbegin1();
2563         }
2564         BOOST_UBLAS_INLINE
2565         const_reverse_iterator1 rend1 () const {
2566             return const_reverse_iterator1 (begin1 ());
2567         }
2568         BOOST_UBLAS_INLINE
2569         const_reverse_iterator1 crend1 () const {
2570             return rend1 ();
2571         }
2572
2573         BOOST_UBLAS_INLINE
2574         reverse_iterator1 rbegin1 () {
2575             return reverse_iterator1 (end1 ());
2576         }
2577         BOOST_UBLAS_INLINE
2578         reverse_iterator1 rend1 () {
2579             return reverse_iterator1 (begin1 ());
2580         }
2581
2582         BOOST_UBLAS_INLINE
2583         const_reverse_iterator2 rbegin2 () const {
2584             return const_reverse_iterator2 (end2 ());
2585         }
2586         BOOST_UBLAS_INLINE
2587         const_reverse_iterator2 crbegin2 () const {
2588             return rbegin2 ();
2589         }
2590         BOOST_UBLAS_INLINE
2591         const_reverse_iterator2 rend2 () const {
2592             return const_reverse_iterator2 (begin2 ());
2593         }
2594         BOOST_UBLAS_INLINE
2595         const_reverse_iterator2 crend2 () const {
2596             return rend2 ();
2597         }
2598
2599         BOOST_UBLAS_INLINE
2600         reverse_iterator2 rbegin2 () {
2601             return reverse_iterator2 (end2 ());
2602         }
2603         BOOST_UBLAS_INLINE
2604         reverse_iterator2 rend2 () {
2605             return reverse_iterator2 (begin2 ());
2606         }
2607
2608     private:
2609         matrix_closure_type data_;
2610         static value_type conj_;
2611     };
2612
2613     template<class M, class TRI>
2614     typename hermitian_adaptor<M, TRI>::value_type hermitian_adaptor<M, TRI>::conj_;
2615
2616     // Specialization for temporary_traits
2617     template <class M, class TRI>
2618     struct vector_temporary_traits< hermitian_adaptor<M, TRI> >
2619     : vector_temporary_traits< M > {} ;
2620     template <class M, class TRI>
2621     struct vector_temporary_traits< const hermitian_adaptor<M, TRI> >
2622     : vector_temporary_traits< M > {} ;
2623
2624     template <class M, class TRI>
2625     struct matrix_temporary_traits< hermitian_adaptor<M, TRI> >
2626     : matrix_temporary_traits< M > {} ;
2627     template <class M, class TRI>
2628     struct matrix_temporary_traits< const hermitian_adaptor<M, TRI> >
2629     : matrix_temporary_traits< M > {} ;
2630
2631 }}}
2632
2633 #endif