1 //
2 //  Copyright (c) 2000-2010
3 //  Joerg Walter, Mathias Koch, David Bellot
4 //
5 //  Distributed under the Boost Software License, Version 1.0. (See
6 //  accompanying file LICENSE_1_0.txt or copy at
7 //  http://www.boost.org/LICENSE_1_0.txt)
8 //
9 //  The authors gratefully acknowledge the support of
10 //  GeNeSys mbH & Co. KG in producing this work.
11 //
12 
13 #ifndef BOOST_UBLAS_HERMITIAN_H
14 #define BOOST_UBLAS_HERMITIAN_H
15 
16 #include <boost/numeric/ublas/matrix.hpp>
17 #include <boost/numeric/ublas/triangular.hpp>  // for resize_preserve
18 #include <boost/numeric/ublas/detail/temporary.hpp>
19 
20 // Iterators based on ideas of Jeremy Siek
21 // Hermitian matrices are square. Thanks to Peter Schmitteckert for spotting this.
22 
23 namespace boost { namespace numeric { namespace ublas {
24 
25     template<class M>
is_hermitian(const M & m)26     bool is_hermitian (const M &m) {
27         typedef typename M::size_type size_type;
28 
29         if (m.size1 () != m.size2 ())
30             return false;
31         size_type size = BOOST_UBLAS_SAME (m.size1 (), m.size2 ());
32         for (size_type i = 0; i < size; ++ i) {
33             for (size_type j = i; j < size; ++ j) {
34                 if (m (i, j) != conj (m (j, i)))
35                     return false;
36             }
37         }
38         return true;
39     }
40 
41 #ifdef BOOST_UBLAS_STRICT_HERMITIAN
42 
43     template<class M>
44     class hermitian_matrix_element:
45        public container_reference<M> {
46     public:
47         typedef M matrix_type;
48         typedef typename M::size_type size_type;
49         typedef typename M::value_type value_type;
50         typedef const value_type &const_reference;
51         typedef value_type &reference;
52         typedef value_type *pointer;
53 
54         // Construction and destruction
55         BOOST_UBLAS_INLINE
hermitian_matrix_element(matrix_type & m,size_type i,size_type j,value_type d)56         hermitian_matrix_element (matrix_type &m, size_type i, size_type j, value_type d):
57             container_reference<matrix_type> (m), i_ (i), j_ (j), d_ (d), dirty_ (false) {}
58         BOOST_UBLAS_INLINE
~hermitian_matrix_element()59         ~hermitian_matrix_element () {
60             if (dirty_)
61                 (*this) ().insert_element (i_, j_, d_);
62         }
63 
64         // Assignment
65         BOOST_UBLAS_INLINE
operator =(const hermitian_matrix_element & p)66         hermitian_matrix_element &operator = (const hermitian_matrix_element &p) {
67             // Overide the implict copy assignment
68             d_ = p.d_;
69             dirty_ = true;
70             return *this;
71         }
72         template<class D>
73         BOOST_UBLAS_INLINE
operator =(const D & d)74         hermitian_matrix_element &operator = (const D &d) {
75             d_ = d;
76             dirty_ = true;
77             return *this;
78         }
79         template<class D>
80         BOOST_UBLAS_INLINE
operator +=(const D & d)81         hermitian_matrix_element &operator += (const D &d) {
82             d_ += d;
83             dirty_ = true;
84             return *this;
85         }
86         template<class D>
87         BOOST_UBLAS_INLINE
operator -=(const D & d)88         hermitian_matrix_element &operator -= (const D &d) {
89             d_ -= d;
90             dirty_ = true;
91             return *this;
92         }
93         template<class D>
94         BOOST_UBLAS_INLINE
operator *=(const D & d)95         hermitian_matrix_element &operator *= (const D &d) {
96             d_ *= d;
97             dirty_ = true;
98             return *this;
99         }
100         template<class D>
101         BOOST_UBLAS_INLINE
operator /=(const D & d)102         hermitian_matrix_element &operator /= (const D &d) {
103             d_ /= d;
104             dirty_ = true;
105             return *this;
106         }
107 
108         // Comparison
109         template<class D>
110         BOOST_UBLAS_INLINE
operator ==(const D & d) const111         bool operator == (const D &d) const {
112             return d_ == d;
113         }
114         template<class D>
115         BOOST_UBLAS_INLINE
operator !=(const D & d) const116         bool operator != (const D &d) const {
117             return d_ != d;
118         }
119 
120         // Conversion
121         BOOST_UBLAS_INLINE
operator const_reference() const122         operator const_reference () const {
123             return d_;
124         }
125 
126         // Swapping
127         BOOST_UBLAS_INLINE
swap(hermitian_matrix_element p)128         void swap (hermitian_matrix_element p) {
129             if (this != &p) {
130                 dirty_ = true;
131                 p.dirty_ = true;
132                 std::swap (d_, p.d_);
133             }
134         }
135         BOOST_UBLAS_INLINE
swap(hermitian_matrix_element p1,hermitian_matrix_element p2)136         friend void swap (hermitian_matrix_element p1, hermitian_matrix_element p2) {
137             p1.swap (p2);
138         }
139 
140     private:
141         size_type i_;
142         size_type j_;
143         value_type d_;
144         bool dirty_;
145     };
146 
147     template<class M>
148     struct type_traits<hermitian_matrix_element<M> > {
149         typedef typename M::value_type element_type;
150         typedef type_traits<hermitian_matrix_element<M> > self_type;
151         typedef typename type_traits<element_type>::value_type value_type;
152         typedef typename type_traits<element_type>::const_reference const_reference;
153         typedef hermitian_matrix_element<M> reference;
154         typedef typename type_traits<element_type>::real_type real_type;
155         typedef typename type_traits<element_type>::precision_type precision_type;
156 
157         static const unsigned plus_complexity = type_traits<element_type>::plus_complexity;
158         static const unsigned multiplies_complexity = type_traits<element_type>::multiplies_complexity;
159 
160         static
161         BOOST_UBLAS_INLINE
realboost::numeric::ublas::type_traits162         real_type real (const_reference t) {
163             return type_traits<element_type>::real (t);
164         }
165         static
166         BOOST_UBLAS_INLINE
imagboost::numeric::ublas::type_traits167         real_type imag (const_reference t) {
168             return type_traits<element_type>::imag (t);
169         }
170         static
171         BOOST_UBLAS_INLINE
conjboost::numeric::ublas::type_traits172         value_type conj (const_reference t) {
173             return type_traits<element_type>::conj (t);
174         }
175 
176         static
177         BOOST_UBLAS_INLINE
type_absboost::numeric::ublas::type_traits178         real_type type_abs (const_reference t) {
179             return type_traits<element_type>::type_abs (t);
180         }
181         static
182         BOOST_UBLAS_INLINE
type_sqrtboost::numeric::ublas::type_traits183         value_type type_sqrt (const_reference t) {
184             return type_traits<element_type>::type_sqrt (t);
185         }
186 
187         static
188         BOOST_UBLAS_INLINE
norm_1boost::numeric::ublas::type_traits189         real_type norm_1 (const_reference t) {
190             return type_traits<element_type>::norm_1 (t);
191         }
192         static
193         BOOST_UBLAS_INLINE
norm_2boost::numeric::ublas::type_traits194         real_type norm_2 (const_reference t) {
195             return type_traits<element_type>::norm_2 (t);
196         }
197         static
198         BOOST_UBLAS_INLINE
norm_infboost::numeric::ublas::type_traits199         real_type norm_inf (const_reference t) {
200             return type_traits<element_type>::norm_inf (t);
201         }
202 
203         static
204         BOOST_UBLAS_INLINE
equalsboost::numeric::ublas::type_traits205         bool equals (const_reference t1, const_reference t2) {
206             return type_traits<element_type>::equals (t1, t2);
207         }
208     };
209 
210     template<class M1, class T2>
211     struct promote_traits<hermitian_matrix_element<M1>, T2> {
212         typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type, T2>::promote_type promote_type;
213     };
214     template<class T1, class M2>
215     struct promote_traits<T1, hermitian_matrix_element<M2> > {
216         typedef typename promote_traits<T1, typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
217     };
218     template<class M1, class M2>
219     struct promote_traits<hermitian_matrix_element<M1>, hermitian_matrix_element<M2> > {
220         typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type,
221                                         typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
222     };
223 
224 #endif
225     /** \brief A hermitian matrix of values of type \c T
226      *
227      * For a \f$(n \times n)\f$-dimensional matrix and \f$ 0 \leq i < n, 0 \leq j < n\f$, every element
228      * \f$m_{i,j}\f$ is mapped to the \f$(i.n + j)\f$-th element of the container for row major orientation
229      * or the \f$(i + j.m)\f$-th element of the container for column major orientation. And
230      * \f$\forall i,j\f$, \f$m_{i,j} = \overline{m_{i,j}}\f$.
231      *
232      * Orientation and storage can also be specified, otherwise a row major and unbounded array are used.
233      * It is \b not required by the storage to initialize elements of the matrix.
234      * Moreover, only the given triangular matrix is stored and the storage of hermitian matrices is packed.
235      *
236      * See http://en.wikipedia.org/wiki/Hermitian_matrix for more details on hermitian matrices.
237      *
238      * \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
239      * \tparam TRI the type of triangular matrix is either \c lower or \c upper. Default is \c lower
240      * \tparam L the storage organization. It is either \c row_major or \c column_major. Default is \c row_major
241      * \tparam A the type of Storage array. Default is \unbounded_array.
242      */
243     template<class T, class TRI, class L, class A>
244     class hermitian_matrix:
245         public matrix_container<hermitian_matrix<T, TRI, L, A> > {
246 
247         typedef T &true_reference;
248         typedef T *pointer;
249         typedef TRI triangular_type;
250         typedef L layout_type;
251         typedef hermitian_matrix<T, TRI, L, A> self_type;
252     public:
253 #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
254         using matrix_container<self_type>::operator ();
255 #endif
256         typedef typename A::size_type size_type;
257         typedef typename A::difference_type difference_type;
258         typedef T value_type;
259         // FIXME no better way to not return the address of a temporary?
260         // typedef const T &const_reference;
261         typedef const T const_reference;
262 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
263         typedef T &reference;
264 #else
265         typedef hermitian_matrix_element<self_type> reference;
266 #endif
267         typedef A array_type;
268 
269         typedef const matrix_reference<const self_type> const_closure_type;
270         typedef matrix_reference<self_type> closure_type;
271         typedef vector<T, A> vector_temporary_type;
272         typedef matrix<T, L, A> matrix_temporary_type;  // general sub-matrix
273         typedef packed_tag storage_category;
274         typedef typename L::orientation_category orientation_category;
275 
276         // Construction and destruction
277         BOOST_UBLAS_INLINE
hermitian_matrix()278         hermitian_matrix ():
279             matrix_container<self_type> (),
280             size_ (0), data_ (0) {}
281         BOOST_UBLAS_INLINE
hermitian_matrix(size_type size)282         hermitian_matrix (size_type size):
283             matrix_container<self_type> (),
284             size_ (BOOST_UBLAS_SAME (size, size)), data_ (triangular_type::packed_size (layout_type (), size, size)) {
285         }
286         BOOST_UBLAS_INLINE
hermitian_matrix(size_type size1,size_type size2)287         hermitian_matrix (size_type size1, size_type size2):
288             matrix_container<self_type> (),
289             size_ (BOOST_UBLAS_SAME (size1, size2)), data_ (triangular_type::packed_size (layout_type (), size1, size2)) {
290         }
291         BOOST_UBLAS_INLINE
hermitian_matrix(size_type size,const array_type & data)292         hermitian_matrix (size_type size, const array_type &data):
293             matrix_container<self_type> (),
294             size_ (size), data_ (data) {}
295         BOOST_UBLAS_INLINE
hermitian_matrix(const hermitian_matrix & m)296         hermitian_matrix (const hermitian_matrix &m):
297             matrix_container<self_type> (),
298             size_ (m.size_), data_ (m.data_) {}
299         template<class AE>
300         BOOST_UBLAS_INLINE
hermitian_matrix(const matrix_expression<AE> & ae)301         hermitian_matrix (const matrix_expression<AE> &ae):
302             matrix_container<self_type> (),
303             size_ (BOOST_UBLAS_SAME (ae ().size1 (), ae ().size2 ())),
304             data_ (triangular_type::packed_size (layout_type (), size_, size_)) {
305             matrix_assign<scalar_assign> (*this, ae);
306         }
307 
308         // Accessors
309         BOOST_UBLAS_INLINE
size1() const310         size_type size1 () const {
311             return size_;
312         }
313         BOOST_UBLAS_INLINE
size2() const314         size_type size2 () const {
315             return size_;
316         }
317 
318         // Storage accessors
319         BOOST_UBLAS_INLINE
data() const320         const array_type &data () const {
321             return data_;
322         }
323         BOOST_UBLAS_INLINE
data()324         array_type &data () {
325             return data_;
326         }
327 
328         // Resizing
329         BOOST_UBLAS_INLINE
resize(size_type size,bool preserve=true)330         void resize (size_type size, bool preserve = true) {
331             if (preserve) {
332                 self_type temporary (size, size);
333                 detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary);
334             }
335             else {
336                 data ().resize (triangular_type::packed_size (layout_type (), size, size));
337                 size_ = size;
338             }
339         }
340         BOOST_UBLAS_INLINE
resize(size_type size1,size_type size2,bool preserve=true)341         void resize (size_type size1, size_type size2, bool preserve = true) {
342             resize (BOOST_UBLAS_SAME (size1, size2), preserve);
343         }
344         BOOST_UBLAS_INLINE
resize_packed_preserve(size_type size)345         void resize_packed_preserve (size_type size) {
346             size_ = BOOST_UBLAS_SAME (size, size);
347             data ().resize (triangular_type::packed_size (layout_type (), size_, size_), value_type ());
348         }
349 
350         // Element access
351         BOOST_UBLAS_INLINE
operator ()(size_type i,size_type j) const352         const_reference operator () (size_type i, size_type j) const {
353             BOOST_UBLAS_CHECK (i < size_, bad_index ());
354             BOOST_UBLAS_CHECK (j < size_, bad_index ());
355             // if (i == j)
356             //    return type_traits<value_type>::real (data () [triangular_type::element (layout_type (), i, size_, i, size_)]);
357             // else
358             if (triangular_type::other (i, j))
359                 return data () [triangular_type::element (layout_type (), i, size_, j, size_)];
360             else
361                 return type_traits<value_type>::conj (data () [triangular_type::element (layout_type (), j, size_, i, size_)]);
362         }
363         BOOST_UBLAS_INLINE
at_element(size_type i,size_type j)364         true_reference at_element (size_type i, size_type j) {
365             BOOST_UBLAS_CHECK (i < size_, bad_index ());
366             BOOST_UBLAS_CHECK (j < size_, bad_index ());
367             BOOST_UBLAS_CHECK (triangular_type::other (i, j), bad_index ());
368             return data () [triangular_type::element (layout_type (), i, size_, j, size_)];
369         }
370         BOOST_UBLAS_INLINE
operator ()(size_type i,size_type j)371         reference operator () (size_type i, size_type j) {
372 #ifndef BOOST_UBLAS_STRICT_HERMITIAN
373             if (!triangular_type::other (i, j)) {
374                 bad_index ().raise ();
375                 // NEVER reached
376             }
377             return at_element (i, j);
378 #else
379         if (triangular_type::other (i, j))
380             return reference (*this, i, j, data () [triangular_type::element (layout_type (), i, size_, j, size_)]);
381         else
382             return reference (*this, i, j, type_traits<value_type>::conj (data () [triangular_type::element (layout_type (), j, size_, i, size_)]));
383 #endif
384         }
385 
386         // Element assignemnt
387         BOOST_UBLAS_INLINE
insert_element(size_type i,size_type j,const_reference t)388         true_reference insert_element (size_type i, size_type j, const_reference t) {
389             BOOST_UBLAS_CHECK (i < size_, bad_index ());
390             BOOST_UBLAS_CHECK (j < size_, bad_index ());
391             if (triangular_type::other (i, j)) {
392                 return (data () [triangular_type::element (layout_type (), i, size_, j, size_)] = t);
393             } else {
394                 return (data () [triangular_type::element (layout_type (), j, size_, i, size_)] = type_traits<value_type>::conj (t));
395             }
396         }
397         BOOST_UBLAS_INLINE
erase_element(size_type i,size_type j)398         void erase_element (size_type i, size_type j) {
399             BOOST_UBLAS_CHECK (i < size_, bad_index ());
400             BOOST_UBLAS_CHECK (j < size_, bad_index ());
401             data () [triangular_type::element (layout_type (), i, size_, j, size_)] = value_type/*zero*/();
402         }
403 
404         // Zeroing
405         BOOST_UBLAS_INLINE
clear()406         void clear () {
407             std::fill (data ().begin (), data ().end (), value_type/*zero*/());
408         }
409 
410         // Assignment
411         BOOST_UBLAS_INLINE
operator =(const hermitian_matrix & m)412         hermitian_matrix &operator = (const hermitian_matrix &m) {
413             size_ = m.size_;
414             data () = m.data ();
415             return *this;
416         }
417         BOOST_UBLAS_INLINE
assign_temporary(hermitian_matrix & m)418         hermitian_matrix &assign_temporary (hermitian_matrix &m) {
419             swap (m);
420             return *this;
421         }
422         template<class AE>
423         BOOST_UBLAS_INLINE
operator =(const matrix_expression<AE> & ae)424         hermitian_matrix &operator = (const matrix_expression<AE> &ae) {
425             self_type temporary (ae);
426             return assign_temporary (temporary);
427         }
428         template<class AE>
429         BOOST_UBLAS_INLINE
assign(const matrix_expression<AE> & ae)430         hermitian_matrix &assign (const matrix_expression<AE> &ae) {
431             matrix_assign<scalar_assign> (*this, ae);
432             return *this;
433         }
434         template<class AE>
435         BOOST_UBLAS_INLINE
operator +=(const matrix_expression<AE> & ae)436         hermitian_matrix& operator += (const matrix_expression<AE> &ae) {
437             self_type temporary (*this + ae);
438             return assign_temporary (temporary);
439         }
440         template<class AE>
441         BOOST_UBLAS_INLINE
plus_assign(const matrix_expression<AE> & ae)442         hermitian_matrix &plus_assign (const matrix_expression<AE> &ae) {
443             matrix_assign<scalar_plus_assign> (*this, ae);
444             return *this;
445         }
446         template<class AE>
447         BOOST_UBLAS_INLINE
operator -=(const matrix_expression<AE> & ae)448         hermitian_matrix& operator -= (const matrix_expression<AE> &ae) {
449             self_type temporary (*this - ae);
450             return assign_temporary (temporary);
451         }
452         template<class AE>
453         BOOST_UBLAS_INLINE
minus_assign(const matrix_expression<AE> & ae)454         hermitian_matrix &minus_assign (const matrix_expression<AE> &ae) {
455             matrix_assign<scalar_minus_assign> (*this, ae);
456             return *this;
457         }
458         template<class AT>
459         BOOST_UBLAS_INLINE
operator *=(const AT & at)460         hermitian_matrix& operator *= (const AT &at) {
461             // Multiplication is only allowed for real scalars,
462             // otherwise the resulting matrix isn't hermitian.
463             // Thanks to Peter Schmitteckert for spotting this.
464             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
465             matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
466             return *this;
467         }
468         template<class AT>
469         BOOST_UBLAS_INLINE
operator /=(const AT & at)470         hermitian_matrix& operator /= (const AT &at) {
471             // Multiplication is only allowed for real scalars,
472             // otherwise the resulting matrix isn't hermitian.
473             // Thanks to Peter Schmitteckert for spotting this.
474             BOOST_UBLAS_CHECK (type_traits<value_type>::imag (at) == 0, non_real ());
475             matrix_assign_scalar<scalar_divides_assign> (*this, at);
476             return *this;
477         }
478 
479         // Swapping
480         BOOST_UBLAS_INLINE
swap(hermitian_matrix & m)481         void swap (hermitian_matrix &m) {
482             if (this != &m) {
483                 std::swap (size_, m.size_);
484                 data ().swap (m.data ());
485             }
486         }
487         BOOST_UBLAS_INLINE
swap(hermitian_matrix & m1,hermitian_matrix & m2)488         friend void swap (hermitian_matrix &m1, hermitian_matrix &m2) {
489             m1.swap (m2);
490         }
491 
492         // Iterator types
493 #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
494         typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
495         typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
496         typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
497         typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
498 #else
499         class const_iterator1;
500         class iterator1;
501         class const_iterator2;
502         class iterator2;
503 #endif
504         typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
505         typedef reverse_iterator_base1<iterator1> reverse_iterator1;
506         typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
507         typedef reverse_iterator_base2<iterator2> reverse_iterator2;
508 
509         // Element lookup
510         BOOST_UBLAS_INLINE
find1(int,size_type i,size_type j) const511         const_iterator1 find1 (int /* rank */, size_type i, size_type j) const {
512             return const_iterator1 (*this, i, j);
513         }
514         BOOST_UBLAS_INLINE
find1(int rank,size_type i,size_type j)515         iterator1 find1 (int rank, size_type i, size_type j) {
516             if (rank == 1)
517                 i = triangular_type::mutable_restrict1 (i, j, size1(), size2());
518             if (rank == 0)
519                 i = triangular_type::global_mutable_restrict1 (i, size1(), j, size2());
520             return iterator1 (*this, i, j);
521         }
522         BOOST_UBLAS_INLINE
find2(int,size_type i,size_type j) const523         const_iterator2 find2 (int /* rank */, size_type i, size_type j) const {
524             return const_iterator2 (*this, i, j);
525         }
526         BOOST_UBLAS_INLINE
find2(int rank,size_type i,size_type j)527         iterator2 find2 (int rank, size_type i, size_type j) {
528             if (rank == 1)
529                 j = triangular_type::mutable_restrict2 (i, j, size1(), size2());
530             if (rank == 0)
531                 j = triangular_type::global_mutable_restrict2 (i, size1(), j, size2());
532             return iterator2 (*this, i, j);
533         }
534 
535         // Iterators simply are indices.
536 
537 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
538         class const_iterator1:
539             public container_const_reference<hermitian_matrix>,
540             public random_access_iterator_base<packed_random_access_iterator_tag,
541                                                const_iterator1, value_type> {
542         public:
543             typedef typename hermitian_matrix::value_type value_type;
544             typedef typename hermitian_matrix::difference_type difference_type;
545             typedef typename hermitian_matrix::const_reference reference;
546             typedef const typename hermitian_matrix::pointer pointer;
547 
548             typedef const_iterator2 dual_iterator_type;
549             typedef const_reverse_iterator2 dual_reverse_iterator_type;
550 
551             // Construction and destruction
552             BOOST_UBLAS_INLINE
const_iterator1()553             const_iterator1 ():
554                 container_const_reference<self_type> (), it1_ (), it2_ () {}
555             BOOST_UBLAS_INLINE
const_iterator1(const self_type & m,size_type it1,size_type it2)556             const_iterator1 (const self_type &m, size_type it1, size_type it2):
557                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
558             BOOST_UBLAS_INLINE
const_iterator1(const iterator1 & it)559             const_iterator1 (const iterator1 &it):
560                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
561 
562             // Arithmetic
563             BOOST_UBLAS_INLINE
operator ++()564             const_iterator1 &operator ++ () {
565                 ++ it1_;
566                 return *this;
567             }
568             BOOST_UBLAS_INLINE
operator --()569             const_iterator1 &operator -- () {
570                 -- it1_;
571                 return *this;
572             }
573             BOOST_UBLAS_INLINE
operator +=(difference_type n)574             const_iterator1 &operator += (difference_type n) {
575                 it1_ += n;
576                 return *this;
577             }
578             BOOST_UBLAS_INLINE
operator -=(difference_type n)579             const_iterator1 &operator -= (difference_type n) {
580                 it1_ -= n;
581                 return *this;
582             }
583             BOOST_UBLAS_INLINE
operator -(const const_iterator1 & it) const584             difference_type operator - (const const_iterator1 &it) const {
585                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
586                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
587                 return it1_ - it.it1_;
588             }
589 
590             // Dereference
591             BOOST_UBLAS_INLINE
operator *() const592             const_reference operator * () const {
593                 return (*this) () (it1_, it2_);
594             }
595             BOOST_UBLAS_INLINE
operator [](difference_type n) const596             const_reference operator [] (difference_type n) const {
597                 return *(*this + n);
598             }
599 
600 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
601             BOOST_UBLAS_INLINE
602 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
603             typename self_type::
604 #endif
begin() const605             const_iterator2 begin () const {
606                 return (*this) ().find2 (1, it1_, 0);
607             }
608             BOOST_UBLAS_INLINE
609 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
610             typename self_type::
611 #endif
cbegin() const612             const_iterator2 cbegin () const {
613                 return begin ();
614             }
615             BOOST_UBLAS_INLINE
616 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
617             typename self_type::
618 #endif
end() const619             const_iterator2 end () const {
620                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
621             }
622             BOOST_UBLAS_INLINE
623 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
624             typename self_type::
625 #endif
cend() const626             const_iterator2 cend () const {
627                 return end ();
628             }
629             BOOST_UBLAS_INLINE
630 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
631             typename self_type::
632 #endif
rbegin() const633             const_reverse_iterator2 rbegin () const {
634                 return const_reverse_iterator2 (end ());
635             }
636             BOOST_UBLAS_INLINE
637 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
638             typename self_type::
639 #endif
crbegin() const640             const_reverse_iterator2 crbegin () const {
641                 return rbegin ();
642             }
643             BOOST_UBLAS_INLINE
644 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
645             typename self_type::
646 #endif
rend() const647             const_reverse_iterator2 rend () const {
648                 return const_reverse_iterator2 (begin ());
649             }
650             BOOST_UBLAS_INLINE
651 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
652             typename self_type::
653 #endif
crend() const654             const_reverse_iterator2 crend () const {
655                 return rend ();
656             }
657 #endif
658 
659             // Indices
660             BOOST_UBLAS_INLINE
index1() const661             size_type index1 () const {
662                 return it1_;
663             }
664             BOOST_UBLAS_INLINE
index2() const665             size_type index2 () const {
666                 return it2_;
667             }
668 
669             // Assignment
670             BOOST_UBLAS_INLINE
operator =(const const_iterator1 & it)671             const_iterator1 &operator = (const const_iterator1 &it) {
672                 container_const_reference<self_type>::assign (&it ());
673                 it1_ = it.it1_;
674                 it2_ = it.it2_;
675                 return *this;
676             }
677 
678             // Comparison
679             BOOST_UBLAS_INLINE
operator ==(const const_iterator1 & it) const680             bool operator == (const const_iterator1 &it) const {
681                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
682                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
683                 return it1_ == it.it1_;
684             }
685             BOOST_UBLAS_INLINE
operator <(const const_iterator1 & it) const686             bool operator < (const const_iterator1 &it) const {
687                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
688                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
689                 return it1_ < it.it1_;
690             }
691 
692         private:
693             size_type it1_;
694             size_type it2_;
695         };
696 #endif
697 
698         BOOST_UBLAS_INLINE
begin1() const699         const_iterator1 begin1 () const {
700             return find1 (0, 0, 0);
701         }
702         BOOST_UBLAS_INLINE
cbegin1() const703         const_iterator1 cbegin1 () const {
704             return begin1 ();
705         }
706         BOOST_UBLAS_INLINE
end1() const707         const_iterator1 end1 () const {
708             return find1 (0, size_, 0);
709         }
710         BOOST_UBLAS_INLINE
cend1() const711         const_iterator1 cend1 () const {
712             return end1 ();
713         }
714 
715 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
716         class iterator1:
717             public container_reference<hermitian_matrix>,
718             public random_access_iterator_base<packed_random_access_iterator_tag,
719                                                iterator1, value_type> {
720         public:
721             typedef typename hermitian_matrix::value_type value_type;
722             typedef typename hermitian_matrix::difference_type difference_type;
723             typedef typename hermitian_matrix::true_reference reference;
724             typedef typename hermitian_matrix::pointer pointer;
725 
726             typedef iterator2 dual_iterator_type;
727             typedef reverse_iterator2 dual_reverse_iterator_type;
728 
729             // Construction and destruction
730             BOOST_UBLAS_INLINE
iterator1()731             iterator1 ():
732                 container_reference<self_type> (), it1_ (), it2_ () {}
733             BOOST_UBLAS_INLINE
iterator1(self_type & m,size_type it1,size_type it2)734             iterator1 (self_type &m, size_type it1, size_type it2):
735                 container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
736 
737             // Arithmetic
738             BOOST_UBLAS_INLINE
operator ++()739             iterator1 &operator ++ () {
740                 ++ it1_;
741                 return *this;
742             }
743             BOOST_UBLAS_INLINE
operator --()744             iterator1 &operator -- () {
745                 -- it1_;
746                 return *this;
747             }
748             BOOST_UBLAS_INLINE
operator +=(difference_type n)749             iterator1 &operator += (difference_type n) {
750                 it1_ += n;
751                 return *this;
752             }
753             BOOST_UBLAS_INLINE
operator -=(difference_type n)754             iterator1 &operator -= (difference_type n) {
755                 it1_ -= n;
756                 return *this;
757             }
758             BOOST_UBLAS_INLINE
operator -(const iterator1 & it) const759             difference_type operator - (const iterator1 &it) const {
760                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
761                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
762                 return it1_ - it.it1_;
763             }
764 
765             // Dereference
766             BOOST_UBLAS_INLINE
operator *() const767             reference operator * () const {
768                 return (*this) ().at_element (it1_, it2_);
769             }
770             BOOST_UBLAS_INLINE
operator [](difference_type n) const771             reference operator [] (difference_type n) const {
772                 return *(*this + n);
773             }
774 
775 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
776             BOOST_UBLAS_INLINE
777 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
778             typename self_type::
779 #endif
begin() const780             iterator2 begin () const {
781                 return (*this) ().find2 (1, it1_, 0);
782             }
783             BOOST_UBLAS_INLINE
784 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
785             typename self_type::
786 #endif
end() const787             iterator2 end () const {
788                 return (*this) ().find2 (1, it1_, (*this) ().size2 ());
789             }
790             BOOST_UBLAS_INLINE
791 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
792             typename self_type::
793 #endif
rbegin() const794             reverse_iterator2 rbegin () const {
795                 return reverse_iterator2 (end ());
796             }
797             BOOST_UBLAS_INLINE
798 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
799             typename self_type::
800 #endif
rend() const801             reverse_iterator2 rend () const {
802                 return reverse_iterator2 (begin ());
803             }
804 #endif
805 
806             // Indices
807             BOOST_UBLAS_INLINE
index1() const808             size_type index1 () const {
809                 return it1_;
810             }
811             BOOST_UBLAS_INLINE
index2() const812             size_type index2 () const {
813                 return it2_;
814             }
815 
816             // Assignment
817             BOOST_UBLAS_INLINE
operator =(const iterator1 & it)818             iterator1 &operator = (const iterator1 &it) {
819                 container_reference<self_type>::assign (&it ());
820                 it1_ = it.it1_;
821                 it2_ = it.it2_;
822                 return *this;
823             }
824 
825             // Comparison
826             BOOST_UBLAS_INLINE
operator ==(const iterator1 & it) const827             bool operator == (const iterator1 &it) const {
828                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
829                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
830                 return it1_ == it.it1_;
831             }
832             BOOST_UBLAS_INLINE
operator <(const iterator1 & it) const833             bool operator < (const iterator1 &it) const {
834                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
835                 BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
836                 return it1_ < it.it1_;
837             }
838 
839         private:
840             size_type it1_;
841             size_type it2_;
842 
843             friend class const_iterator1;
844         };
845 #endif
846 
847         BOOST_UBLAS_INLINE
begin1()848         iterator1 begin1 () {
849             return find1 (0, 0, 0);
850         }
851         BOOST_UBLAS_INLINE
end1()852         iterator1 end1 () {
853             return find1 (0, size_, 0);
854         }
855 
856 #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
857         class const_iterator2:
858             public container_const_reference<hermitian_matrix>,
859             public random_access_iterator_base<packed_random_access_iterator_tag,
860                                                const_iterator2, value_type> {
861         public:
862             typedef typename hermitian_matrix::value_type value_type;
863             typedef typename hermitian_matrix::difference_type difference_type;
864             typedef typename hermitian_matrix::const_reference reference;
865             typedef const typename hermitian_matrix::pointer pointer;
866 
867             typedef const_iterator1 dual_iterator_type;
868             typedef const_reverse_iterator1 dual_reverse_iterator_type;
869 
870             // Construction and destruction
871             BOOST_UBLAS_INLINE
const_iterator2()872             const_iterator2 ():
873                 container_const_reference<self_type> (), it1_ (), it2_ () {}
874             BOOST_UBLAS_INLINE
const_iterator2(const self_type & m,size_type it1,size_type it2)875             const_iterator2 (const self_type &m, size_type it1, size_type it2):
876                 container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
877             BOOST_UBLAS_INLINE
const_iterator2(const iterator2 & it)878             const_iterator2 (const iterator2 &it):
879                 container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
880 
881             // Arithmetic
882             BOOST_UBLAS_INLINE
operator ++()883             const_iterator2 &operator ++ () {
884                 ++ it2_;
885                 return *this;
886             }
887             BOOST_UBLAS_INLINE
operator --()888             const_iterator2 &operator -- () {
889                 -- it2_;
890                 return *this;
891             }
892             BOOST_UBLAS_INLINE
operator +=(difference_type n)893             const_iterator2 &operator += (difference_type n) {
894                 it2_ += n;
895                 return *this;
896             }
897             BOOST_UBLAS_INLINE
operator -=(difference_type n)898             const_iterator2 &operator -= (difference_type n) {
899                 it2_ -= n;
900                 return *this;
901             }
902             BOOST_UBLAS_INLINE
operator -(const const_iterator2 & it) const903             difference_type operator - (const const_iterator2 &it) const {
904                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
905                 BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
906                 return it2_ - it.it2_;
907             }
908 
909             // Dereference
910             BOOST_UBLAS_INLINE
operator *() const911             const_reference operator * () const {
912                 return (*this) () (it1_, it2_);
913             }
914             BOOST_UBLAS_INLINE
operator [](difference_type n) const915             const_reference operator [] (difference_type n) const {
916                 return *(*this + n);
917             }
918 
919 #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
920             BOOST_UBLAS_INLINE
921 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
922             typename self_type::
923 #endif
begin() const924             const_iterator1 begin () const {
925                 return (*this) ().find1 (1, 0, it2_);
926             }
927             BOOST_UBLAS_INLINE
928 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
929             typename self_type::
930 #endif
cbegin() const931             const_iterator1 cbegin () const {
932                 return begin ();
933             }
934             BOOST_UBLAS_INLINE
935 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
936             typename self_type::
937 #endif
end() const938             const_iterator1 end () const {
939                 return (*this) ().find1 (1, (*this) ().size1 (), it2_);
940             }
941             BOOST_UBLAS_INLINE
942 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
943             typename self_type::
944 #endif
cend() const945             const_iterator1 cend () const {
946                 return end ();
947             }
948             BOOST_UBLAS_INLINE
949 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
950             typename self_type::
951 #endif
rbegin() const952             const_reverse_iterator1 rbegin () const {
953                 return const_reverse_iterator1 (end ());
954             }
955             BOOST_UBLAS_INLINE
956 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
957             typename self_type::
958 #endif
crbegin() const959             const_iterator1 crbegin () const {
960                 return rbegin ();
961             }
962             BOOST_UBLAS_INLINE
963 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
964             typename self_type::
965 #endif
rend() const966             const_reverse_iterator1 rend () const {
967                 return const_reverse_iterator1 (begin ());
968             }
969             BOOST_UBLAS_INLINE
970 #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
971             typename self_type::
972 #endif
crend() const973             const_iterator1 crend () const {
974                 return rend ();
975             }
976 #endif
977 
978             // Indices
979             BOOST_UBLAS_INLINE
index1() const980             size_type index1 () const {
981                 return it1_;
982             }
983             BOOST_UBLAS_INLINE
index2() const984             size_type index2 () const {
985                 return it2_;
986             }
987 
988             // Assignment
989             BOOST_UBLAS_INLINE
operator =(const const_iterator2 & it)990             const_iterator2 &operator = (const const_iterator2 &it) {
991                 container_const_reference<self_type>::assign (&it ());
992                 it1_ = it.it1_;
993                 it2_ = it.it2_;
994                 return *this;
995             }
996 
997             // Comparison
998             BOOST_UBLAS_INLINE
operator ==(const const_iterator2 & it) const999             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
operator <(const const_iterator2 & it) const1005             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
begin2() const1018         const_iterator2 begin2 () const {
1019             return find2 (0, 0, 0);
1020         }
1021         BOOST_UBLAS_INLINE
cbegin2() const1022         const_iterator2 cbegin2 () const {
1023             return begin2 ();
1024         }
1025         BOOST_UBLAS_INLINE
end2() const1026         const_iterator2 end2 () const {
1027             return find2 (0, 0, size_);
1028         }
1029         BOOST_UBLAS_INLINE
cend2() const1030         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
iterator2()1050             iterator2 ():
1051                 container_reference<self_type> (), it1_ (), it2_ () {}
1052             BOOST_UBLAS_INLINE
iterator2(self_type & m,size_type it1,size_type it2)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
operator ++()1058             iterator2 &operator ++ () {
1059                 ++ it2_;
1060                 return *this;
1061             }
1062             BOOST_UBLAS_INLINE
operator --()1063             iterator2 &operator -- () {
1064                 -- it2_;
1065                 return *this;
1066             }
1067             BOOST_UBLAS_INLINE
operator +=(difference_type n)1068             iterator2 &operator += (difference_type n) {
1069                 it2_ += n;
1070                 return *this;
1071             }
1072             BOOST_UBLAS_INLINE
operator -=(difference_type n)1073             iterator2 &operator -= (difference_type n) {
1074                 it2_ -= n;
1075                 return *this;
1076             }
1077             BOOST_UBLAS_INLINE
operator -(const iterator2 & it) const1078             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
operator *() const1086             reference operator * () const {
1087                 return (*this) ().at_element (it1_, it2_);
1088             }
1089             BOOST_UBLAS_INLINE
operator [](difference_type n) const1090             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
begin() const1099             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
end() const1106             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
rbegin() const1113             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
rend() const1120             reverse_iterator1 rend () const {
1121                 return reverse_iterator1 (begin ());
1122             }
1123 #endif
1124 
1125             // Indices
1126             BOOST_UBLAS_INLINE
index1() const1127             size_type index1 () const {
1128                 return it1_;
1129             }
1130             BOOST_UBLAS_INLINE
index2() const1131             size_type index2 () const {
1132                 return it2_;
1133             }
1134 
1135             // Assignment
1136             BOOST_UBLAS_INLINE
operator =(const iterator2 & it)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
operator ==(const iterator2 & it) const1146             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
operator <(const iterator2 & it) const1152             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
begin2()1167         iterator2 begin2 () {
1168             return find2 (0, 0, 0);
1169         }
1170         BOOST_UBLAS_INLINE
end2()1171         iterator2 end2 () {
1172             return find2 (0, 0, size_);
1173         }
1174 
1175         // Reverse iterators
1176 
1177         BOOST_UBLAS_INLINE
rbegin1() const1178         const_reverse_iterator1 rbegin1 () const {
1179             return const_reverse_iterator1 (end1 ());
1180         }
1181         BOOST_UBLAS_INLINE
crbegin1() const1182         const_reverse_iterator1 crbegin1 () const {
1183             return rbegin1 ();
1184         }
1185         BOOST_UBLAS_INLINE
rend1() const1186         const_reverse_iterator1 rend1 () const {
1187             return const_reverse_iterator1 (begin1 ());
1188         }
1189         BOOST_UBLAS_INLINE
crend1() const1190         const_reverse_iterator1 crend1 () const {
1191             return rend1 ();
1192         }
1193 
1194         BOOST_UBLAS_INLINE
rbegin1()1195         reverse_iterator1 rbegin1 () {
1196             return reverse_iterator1 (end1 ());
1197         }
1198         BOOST_UBLAS_INLINE
rend1()1199         reverse_iterator1 rend1 () {
1200             return reverse_iterator1 (begin1 ());
1201         }
1202 
1203         BOOST_UBLAS_INLINE
rbegin2() const1204         const_reverse_iterator2 rbegin2 () const {
1205             return const_reverse_iterator2 (end2 ());
1206         }
1207         BOOST_UBLAS_INLINE
crbegin2() const1208         const_reverse_iterator2 crbegin2 () const {
1209             return rbegin2();
1210         }
1211         BOOST_UBLAS_INLINE
rend2() const1212         const_reverse_iterator2 rend2 () const {
1213             return const_reverse_iterator2 (begin2 ());
1214         }
1215         BOOST_UBLAS_INLINE
crend2() const1216         const_reverse_iterator2 crend2 () const {
1217             return rend2 ();
1218         }
1219 
1220         BOOST_UBLAS_INLINE
rbegin2()1221         reverse_iterator2 rbegin2 () {
1222             return reverse_iterator2 (end2 ());
1223         }
1224         BOOST_UBLAS_INLINE
rend2()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
hermitian_adaptor(matrix_type & data)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
hermitian_adaptor(const hermitian_adaptor & m)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
size1() const1297         size_type size1 () const {
1298             return data_.size1 ();
1299         }
1300         BOOST_UBLAS_INLINE
size2() const1301         size_type size2 () const {
1302             return data_.size2 ();
1303         }
1304 
1305         // Storage accessors
1306         BOOST_UBLAS_INLINE
data() const1307         const matrix_closure_type &data () const {
1308             return data_;
1309         }
1310         BOOST_UBLAS_INLINE
data()1311         matrix_closure_type &data () {
1312             return data_;
1313         }
1314 
1315         // Element access
1316 #ifndef BOOST_UBLAS_PROXY_CONST_MEMBER
1317         BOOST_UBLAS_INLINE
operator ()(size_type i,size_type j) const1318         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
operator ()(size_type i,size_type j)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
insert_element(size_type i,size_type j,value_type t)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
operator ()(size_type i,size_type j)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
insert_element(size_type i,size_type j,value_type t)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
operator =(const hermitian_adaptor & m)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
assign_temporary(hermitian_adaptor & m)1399         hermitian_adaptor &assign_temporary (hermitian_adaptor &m) {
1400             *this = m;
1401             return *this;
1402         }
1403         template<class AE>
1404         BOOST_UBLAS_INLINE
operator =(const matrix_expression<AE> & ae)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
assign(const matrix_expression<AE> & ae)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
operator +=(const matrix_expression<AE> & ae)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
plus_assign(const matrix_expression<AE> & ae)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
operator -=(const matrix_expression<AE> & ae)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
minus_assign(const matrix_expression<AE> & ae)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
operator *=(const AT & at)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
operator /=(const AT & at)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
same_closure(const hermitian_adaptor & ha) const1462         bool same_closure (const hermitian_adaptor &ha) const {
1463             return (*this).data ().same_closure (ha.data ());
1464         }
1465 
1466         // Swapping
1467         BOOST_UBLAS_INLINE
swap(hermitian_adaptor & m)1468         void swap (hermitian_adaptor &m) {
1469             if (this != &m)
1470                 matrix_swap<scalar_swap, triangular_type> (*this, m);
1471         }
1472         BOOST_UBLAS_INLINE
swap(hermitian_adaptor & m1,hermitian_adaptor & m2)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
find1(int rank,size_type i,size_type j) const1508         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
find1(int rank,size_type i,size_type j)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
find2(int rank,size_type i,size_type j) const1540         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
find2(int rank,size_type i,size_type j)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
const_iterator1()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
const_iterator1(const self_type & m,int begin,int end,const const_subiterator1_type & it1_begin,const const_subiterator1_type & it1_end,const const_subiterator2_type & it2_begin,const const_subiterator2_type & it2_end)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
const_iterator1(const iterator1 & it)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
operator ++()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
operator --()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
operator +=(difference_type n)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
operator -=(difference_type n)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
operator -(const const_iterator1 & it) const1734             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
operator *() const1761             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
operator [](difference_type n) const1778             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
begin() const1787             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
cbegin() const1794             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
end() const1801             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
cend() const1808             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
rbegin() const1815             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
crbegin() const1822             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
rend() const1829             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
crend() const1836             const_reverse_iterator2 crend () const {
1837                 return rend ();
1838             }
1839 #endif
1840 
1841             // Indices
1842             BOOST_UBLAS_INLINE
index1() const1843             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
index2() const1854             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
operator =(const const_iterator1 & it)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
operator ==(const const_iterator1 & it) const1883             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
operator <(const const_iterator1 & it) const1892             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
begin1() const1911         const_iterator1 begin1 () const {
1912             return find1 (0, 0, 0);
1913         }
1914         BOOST_UBLAS_INLINE
cbegin1() const1915         const_iterator1 cbegin1 () const {
1916             return begin1 ();
1917         }
1918         BOOST_UBLAS_INLINE
end1() const1919         const_iterator1 end1 () const {
1920             return find1 (0, size1 (), 0);
1921         }
1922         BOOST_UBLAS_INLINE
cend1() const1923         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
iterator1()1944             iterator1 ():
1945                 container_reference<self_type> (), it1_ () {}
1946             BOOST_UBLAS_INLINE
iterator1(self_type & m,const subiterator1_type & it1)1947             iterator1 (self_type &m, const subiterator1_type &it1):
1948                 container_reference<self_type> (m), it1_ (it1) {}
1949 
1950             // Arithmetic
1951             BOOST_UBLAS_INLINE
operator ++()1952             iterator1 &operator ++ () {
1953                 ++ it1_;
1954                 return *this;
1955             }
1956             BOOST_UBLAS_INLINE
operator --()1957             iterator1 &operator -- () {
1958                 -- it1_;
1959                 return *this;
1960             }
1961             BOOST_UBLAS_INLINE
operator +=(difference_type n)1962             iterator1 &operator += (difference_type n) {
1963                 it1_ += n;
1964                 return *this;
1965             }
1966             BOOST_UBLAS_INLINE
operator -=(difference_type n)1967             iterator1 &operator -= (difference_type n) {
1968                 it1_ -= n;
1969                 return *this;
1970             }
1971             BOOST_UBLAS_INLINE
operator -(const iterator1 & it) const1972             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
operator *() const1979             reference operator * () const {
1980                 return *it1_;
1981             }
1982             BOOST_UBLAS_INLINE
operator [](difference_type n) const1983             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
begin() const1992             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
end() const1999             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
rbegin() const2006             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
rend() const2013             reverse_iterator2 rend () const {
2014                 return reverse_iterator2 (begin ());
2015             }
2016 #endif
2017 
2018             // Indices
2019             BOOST_UBLAS_INLINE
index1() const2020             size_type index1 () const {
2021                 return it1_.index1 ();
2022             }
2023             BOOST_UBLAS_INLINE
index2() const2024             size_type index2 () const {
2025                 return it1_.index2 ();
2026             }
2027 
2028             // Assignment
2029             BOOST_UBLAS_INLINE
operator =(const iterator1 & it)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
operator ==(const iterator1 & it) const2038             bool operator == (const iterator1 &it) const {
2039                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2040                 return it1_ == it.it1_;
2041             }
2042             BOOST_UBLAS_INLINE
operator <(const iterator1 & it) const2043             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
begin1()2056         iterator1 begin1 () {
2057             return find1 (0, 0, 0);
2058         }
2059         BOOST_UBLAS_INLINE
end1()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
const_iterator2()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
const_iterator2(const self_type & m,int begin,int end,const const_subiterator1_type & it1_begin,const const_subiterator1_type & it1_end,const const_subiterator2_type & it2_begin,const const_subiterator2_type & it2_end)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
const_iterator2(const iterator2 & it)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
operator ++()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
operator --()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
operator +=(difference_type n)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
operator -=(difference_type n)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
operator -(const const_iterator2 & it) const2224             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
operator *() const2251             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
operator [](difference_type n) const2268             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
begin() const2277             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
cbegin() const2284             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
end() const2291             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
cend() const2298             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
rbegin() const2305             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
crbegin() const2312             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
rend() const2319             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
crend() const2326             const_reverse_iterator1 crend () const {
2327                 return end ();
2328             }
2329 #endif
2330 
2331             // Indices
2332             BOOST_UBLAS_INLINE
index1() const2333             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
index2() const2344             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
operator =(const const_iterator2 & it)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
operator ==(const const_iterator2 & it) const2373             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
operator <(const const_iterator2 & it) const2382             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
begin2() const2401         const_iterator2 begin2 () const {
2402             return find2 (0, 0, 0);
2403         }
2404         BOOST_UBLAS_INLINE
cbegin2() const2405         const_iterator2 cbegin2 () const {
2406             return begin2 ();
2407         }
2408         BOOST_UBLAS_INLINE
end2() const2409         const_iterator2 end2 () const {
2410             return find2 (0, 0, size2 ());
2411         }
2412         BOOST_UBLAS_INLINE
cend2() const2413         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
iterator2()2434             iterator2 ():
2435                 container_reference<self_type> (), it2_ () {}
2436             BOOST_UBLAS_INLINE
iterator2(self_type & m,const subiterator2_type & it2)2437             iterator2 (self_type &m, const subiterator2_type &it2):
2438                 container_reference<self_type> (m), it2_ (it2) {}
2439 
2440             // Arithmetic
2441             BOOST_UBLAS_INLINE
operator ++()2442             iterator2 &operator ++ () {
2443                 ++ it2_;
2444                 return *this;
2445             }
2446             BOOST_UBLAS_INLINE
operator --()2447             iterator2 &operator -- () {
2448                 -- it2_;
2449                 return *this;
2450             }
2451             BOOST_UBLAS_INLINE
operator +=(difference_type n)2452             iterator2 &operator += (difference_type n) {
2453                 it2_ += n;
2454                 return *this;
2455             }
2456             BOOST_UBLAS_INLINE
operator -=(difference_type n)2457             iterator2 &operator -= (difference_type n) {
2458                 it2_ -= n;
2459                 return *this;
2460             }
2461             BOOST_UBLAS_INLINE
operator -(const iterator2 & it) const2462             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
operator *() const2469             reference operator * () const {
2470                 return *it2_;
2471             }
2472             BOOST_UBLAS_INLINE
operator [](difference_type n) const2473             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
begin() const2482             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
end() const2489             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
rbegin() const2496             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
rend() const2503             reverse_iterator1 rend () const {
2504                 return reverse_iterator1 (begin ());
2505             }
2506 #endif
2507 
2508             // Indices
2509             BOOST_UBLAS_INLINE
index1() const2510             size_type index1 () const {
2511                 return it2_.index1 ();
2512             }
2513             BOOST_UBLAS_INLINE
index2() const2514             size_type index2 () const {
2515                 return it2_.index2 ();
2516             }
2517 
2518             // Assignment
2519             BOOST_UBLAS_INLINE
operator =(const iterator2 & it)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
operator ==(const iterator2 & it) const2528             bool operator == (const iterator2 &it) const {
2529                 BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
2530                 return it2_ == it.it2_;
2531             }
2532             BOOST_UBLAS_INLINE
operator <(const iterator2 & it) const2533             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
begin2()2546         iterator2 begin2 () {
2547             return find2 (0, 0, 0);
2548         }
2549         BOOST_UBLAS_INLINE
end2()2550         iterator2 end2 () {
2551             return find2 (0, 0, size2 ());
2552         }
2553 
2554         // Reverse iterators
2555 
2556         BOOST_UBLAS_INLINE
rbegin1() const2557         const_reverse_iterator1 rbegin1 () const {
2558             return const_reverse_iterator1 (end1 ());
2559         }
2560         BOOST_UBLAS_INLINE
crbegin1() const2561         const_reverse_iterator1 crbegin1 () const {
2562             return rbegin1();
2563         }
2564         BOOST_UBLAS_INLINE
rend1() const2565         const_reverse_iterator1 rend1 () const {
2566             return const_reverse_iterator1 (begin1 ());
2567         }
2568         BOOST_UBLAS_INLINE
crend1() const2569         const_reverse_iterator1 crend1 () const {
2570             return rend1 ();
2571         }
2572 
2573         BOOST_UBLAS_INLINE
rbegin1()2574         reverse_iterator1 rbegin1 () {
2575             return reverse_iterator1 (end1 ());
2576         }
2577         BOOST_UBLAS_INLINE
rend1()2578         reverse_iterator1 rend1 () {
2579             return reverse_iterator1 (begin1 ());
2580         }
2581 
2582         BOOST_UBLAS_INLINE
rbegin2() const2583         const_reverse_iterator2 rbegin2 () const {
2584             return const_reverse_iterator2 (end2 ());
2585         }
2586         BOOST_UBLAS_INLINE
crbegin2() const2587         const_reverse_iterator2 crbegin2 () const {
2588             return rbegin2 ();
2589         }
2590         BOOST_UBLAS_INLINE
rend2() const2591         const_reverse_iterator2 rend2 () const {
2592             return const_reverse_iterator2 (begin2 ());
2593         }
2594         BOOST_UBLAS_INLINE
crend2() const2595         const_reverse_iterator2 crend2 () const {
2596             return rend2 ();
2597         }
2598 
2599         BOOST_UBLAS_INLINE
rbegin2()2600         reverse_iterator2 rbegin2 () {
2601             return reverse_iterator2 (end2 ());
2602         }
2603         BOOST_UBLAS_INLINE
rend2()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
2634