boost/numeric/ublas/triangular.hpp
// // Copyright (c) 2000-2002 // Joerg Walter, Mathias Koch // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // // The authors gratefully acknowledge the support of // GeNeSys mbH & Co. KG in producing this work. // #ifndef _BOOST_UBLAS_TRIANGULAR_ #define _BOOST_UBLAS_TRIANGULAR_ #include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/detail/temporary.hpp> #include <boost/type_traits/remove_const.hpp> // Iterators based on ideas of Jeremy Siek namespace boost { namespace numeric { namespace ublas { namespace detail { using namespace boost::numeric::ublas; // Matrix resizing algorithm template <class L, class T, class M> BOOST_UBLAS_INLINE void matrix_resize_preserve (M& m, M& temporary) { typedef L layout_type; typedef T triangular_type; typedef typename M::size_type size_type; const size_type msize1 (m.size1 ()); // original size const size_type msize2 (m.size2 ()); const size_type size1 (temporary.size1 ()); // new size is specified by temporary const size_type size2 (temporary.size2 ()); // Common elements to preserve const size_type size1_min = (std::min) (size1, msize1); const size_type size2_min = (std::min) (size2, msize2); // Order for major and minor sizes const size_type major_size = layout_type::size_M (size1_min, size2_min); const size_type minor_size = layout_type::size_m (size1_min, size2_min); // Indexing copy over major for (size_type major = 0; major != major_size; ++major) { for (size_type minor = 0; minor != minor_size; ++minor) { // find indexes - use invertability of element_ functions const size_type i1 = layout_type::index_M(major, minor); const size_type i2 = layout_type::index_m(major, minor); if ( triangular_type::other(i1,i2) ) { temporary.data () [triangular_type::element (layout_type (), i1, size1, i2, size2)] = m.data() [triangular_type::element (layout_type (), i1, msize1, i2, msize2)]; } } } m.assign_temporary (temporary); } } /** \brief A triangular matrix of values of type \c T. * * For a \f$(n \times n )\f$-dimensional lower triangular matrix and if \f$0 \leq i < n\f$, \f$0 \leq j < n\f$ and \f$i>j\f$ holds, * \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit lower triangular. * * For a \f$(n \times n )\f$-dimensional upper triangular matrix and if \f$0 \leq i < n\f$, \f$0 \leq j < n\f$ and \f$i<j\f$ holds, * \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit upper triangular. * * The default storage for triangular matrices is packed. Orientation and storage can also be specified. * Default is \c row_major and and unbounded_array. It is \b not required by the storage to initialize * elements of the matrix. * * \tparam T the type of object stored in the matrix (like double, float, complex, etc...) * \tparam TRI the type of the triangular matrix. It can either be \c lower or \c upper. Default is \c lower * \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major * \tparam A the type of Storage array. Default is \c unbounded_array */ template<class T, class TRI, class L, class A> class triangular_matrix: public matrix_container<triangular_matrix<T, TRI, L, A> > { typedef T *pointer; typedef TRI triangular_type; typedef L layout_type; typedef triangular_matrix<T, TRI, L, A> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using matrix_container<self_type>::operator (); #endif typedef typename A::size_type size_type; typedef typename A::difference_type difference_type; typedef T value_type; typedef const T &const_reference; typedef T &reference; typedef A array_type; typedef const matrix_reference<const self_type> const_closure_type; typedef matrix_reference<self_type> closure_type; typedef vector<T, A> vector_temporary_type; typedef matrix<T, L, A> matrix_temporary_type; // general sub-matrix typedef packed_tag storage_category; typedef typename L::orientation_category orientation_category; // Construction and destruction BOOST_UBLAS_INLINE triangular_matrix (): matrix_container<self_type> (), size1_ (0), size2_ (0), data_ (0) {} BOOST_UBLAS_INLINE triangular_matrix (size_type size1, size_type size2): matrix_container<self_type> (), size1_ (size1), size2_ (size2), data_ (triangular_type::packed_size (layout_type (), size1, size2)) { } BOOST_UBLAS_INLINE triangular_matrix (size_type size1, size_type size2, const array_type &data): matrix_container<self_type> (), size1_ (size1), size2_ (size2), data_ (data) {} BOOST_UBLAS_INLINE triangular_matrix (const triangular_matrix &m): matrix_container<self_type> (), size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {} template<class AE> BOOST_UBLAS_INLINE triangular_matrix (const matrix_expression<AE> &ae): matrix_container<self_type> (), size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), data_ (triangular_type::packed_size (layout_type (), size1_, size2_)) { matrix_assign<scalar_assign> (*this, ae); } // Accessors BOOST_UBLAS_INLINE size_type size1 () const { return size1_; } BOOST_UBLAS_INLINE size_type size2 () const { return size2_; } // Storage accessors BOOST_UBLAS_INLINE const array_type &data () const { return data_; } BOOST_UBLAS_INLINE array_type &data () { return data_; } // Resizing BOOST_UBLAS_INLINE void resize (size_type size1, size_type size2, bool preserve = true) { if (preserve) { self_type temporary (size1, size2); detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary); } else { data ().resize (triangular_type::packed_size (layout_type (), size1, size2)); size1_ = size1; size2_ = size2; } } BOOST_UBLAS_INLINE void resize_packed_preserve (size_type size1, size_type size2) { size1_ = size1; size2_ = size2; data ().resize (triangular_type::packed_size (layout_type (), size1_, size2_), value_type ()); } // Element access BOOST_UBLAS_INLINE const_reference operator () (size_type i, size_type j) const { BOOST_UBLAS_CHECK (i < size1_, bad_index ()); BOOST_UBLAS_CHECK (j < size2_, bad_index ()); if (triangular_type::other (i, j)) return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; else if (triangular_type::one (i, j)) return one_; else return zero_; } BOOST_UBLAS_INLINE reference at_element (size_type i, size_type j) { BOOST_UBLAS_CHECK (i < size1_, bad_index ()); BOOST_UBLAS_CHECK (j < size2_, bad_index ()); return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; } BOOST_UBLAS_INLINE reference operator () (size_type i, size_type j) { BOOST_UBLAS_CHECK (i < size1_, bad_index ()); BOOST_UBLAS_CHECK (j < size2_, bad_index ()); if (!triangular_type::other (i, j)) { bad_index ().raise (); // NEVER reached } return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; } // Element assignment BOOST_UBLAS_INLINE reference insert_element (size_type i, size_type j, const_reference t) { return (operator () (i, j) = t); } BOOST_UBLAS_INLINE void erase_element (size_type i, size_type j) { operator () (i, j) = value_type/*zero*/(); } // Zeroing BOOST_UBLAS_INLINE void clear () { // data ().clear (); std::fill (data ().begin (), data ().end (), value_type/*zero*/()); } // Assignment BOOST_UBLAS_INLINE triangular_matrix &operator = (const triangular_matrix &m) { size1_ = m.size1_; size2_ = m.size2_; data () = m.data (); return *this; } BOOST_UBLAS_INLINE triangular_matrix &assign_temporary (triangular_matrix &m) { swap (m); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_matrix &operator = (const matrix_expression<AE> &ae) { self_type temporary (ae); return assign_temporary (temporary); } template<class AE> BOOST_UBLAS_INLINE triangular_matrix &assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_assign> (*this, ae); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_matrix& operator += (const matrix_expression<AE> &ae) { self_type temporary (*this + ae); return assign_temporary (temporary); } template<class AE> BOOST_UBLAS_INLINE triangular_matrix &plus_assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_plus_assign> (*this, ae); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_matrix& operator -= (const matrix_expression<AE> &ae) { self_type temporary (*this - ae); return assign_temporary (temporary); } template<class AE> BOOST_UBLAS_INLINE triangular_matrix &minus_assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_minus_assign> (*this, ae); return *this; } template<class AT> BOOST_UBLAS_INLINE triangular_matrix& operator *= (const AT &at) { matrix_assign_scalar<scalar_multiplies_assign> (*this, at); return *this; } template<class AT> BOOST_UBLAS_INLINE triangular_matrix& operator /= (const AT &at) { matrix_assign_scalar<scalar_divides_assign> (*this, at); return *this; } // Swapping BOOST_UBLAS_INLINE void swap (triangular_matrix &m) { if (this != &m) { // BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ()); std::swap (size1_, m.size1_); std::swap (size2_, m.size2_); data ().swap (m.data ()); } } BOOST_UBLAS_INLINE friend void swap (triangular_matrix &m1, triangular_matrix &m2) { m1.swap (m2); } // Iterator types #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1; typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2; typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1; typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2; #else class const_iterator1; class iterator1; class const_iterator2; class iterator2; #endif typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1; typedef reverse_iterator_base1<iterator1> reverse_iterator1; typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2; typedef reverse_iterator_base2<iterator2> reverse_iterator2; // Element lookup BOOST_UBLAS_INLINE const_iterator1 find1 (int rank, size_type i, size_type j) const { if (rank == 1) i = triangular_type::restrict1 (i, j, size1_, size2_); if (rank == 0) i = triangular_type::global_restrict1 (i, size1_, j, size2_); return const_iterator1 (*this, i, j); } BOOST_UBLAS_INLINE iterator1 find1 (int rank, size_type i, size_type j) { if (rank == 1) i = triangular_type::mutable_restrict1 (i, j, size1_, size2_); if (rank == 0) i = triangular_type::global_mutable_restrict1 (i, size1_, j, size2_); return iterator1 (*this, i, j); } BOOST_UBLAS_INLINE const_iterator2 find2 (int rank, size_type i, size_type j) const { if (rank == 1) j = triangular_type::restrict2 (i, j, size1_, size2_); if (rank == 0) j = triangular_type::global_restrict2 (i, size1_, j, size2_); return const_iterator2 (*this, i, j); } BOOST_UBLAS_INLINE iterator2 find2 (int rank, size_type i, size_type j) { if (rank == 1) j = triangular_type::mutable_restrict2 (i, j, size1_, size2_); if (rank == 0) j = triangular_type::global_mutable_restrict2 (i, size1_, j, size2_); return iterator2 (*this, i, j); } // Iterators simply are indices. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator1: public container_const_reference<triangular_matrix>, public random_access_iterator_base<packed_random_access_iterator_tag, const_iterator1, value_type> { public: typedef typename triangular_matrix::value_type value_type; typedef typename triangular_matrix::difference_type difference_type; typedef typename triangular_matrix::const_reference reference; typedef const typename triangular_matrix::pointer pointer; typedef const_iterator2 dual_iterator_type; typedef const_reverse_iterator2 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE const_iterator1 (): container_const_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE const_iterator1 (const self_type &m, size_type it1, size_type it2): container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {} BOOST_UBLAS_INLINE const_iterator1 (const iterator1 &it): container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator1 &operator ++ () { ++ it1_; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator -- () { -- it1_; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator += (difference_type n) { it1_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator -= (difference_type n) { it1_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ - it.it1_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return (*this) () (it1_, it2_); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator2 begin () const { return (*this) ().find2 (1, it1_, 0); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator2 end () const { return (*this) ().find2 (1, it1_, (*this) ().size2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator2 rbegin () const { return const_reverse_iterator2 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator2 rend () const { return const_reverse_iterator2 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_; } BOOST_UBLAS_INLINE size_type index2 () const { return it2_; } // Assignment BOOST_UBLAS_INLINE const_iterator1 &operator = (const const_iterator1 &it) { container_const_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ == it.it1_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ < it.it1_; } private: size_type it1_; size_type it2_; }; #endif BOOST_UBLAS_INLINE const_iterator1 begin1 () const { return find1 (0, 0, 0); } BOOST_UBLAS_INLINE const_iterator1 end1 () const { return find1 (0, size1_, 0); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class iterator1: public container_reference<triangular_matrix>, public random_access_iterator_base<packed_random_access_iterator_tag, iterator1, value_type> { public: typedef typename triangular_matrix::value_type value_type; typedef typename triangular_matrix::difference_type difference_type; typedef typename triangular_matrix::reference reference; typedef typename triangular_matrix::pointer pointer; typedef iterator2 dual_iterator_type; typedef reverse_iterator2 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE iterator1 (): container_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE iterator1 (self_type &m, size_type it1, size_type it2): container_reference<self_type> (m), it1_ (it1), it2_ (it2) {} // Arithmetic BOOST_UBLAS_INLINE iterator1 &operator ++ () { ++ it1_; return *this; } BOOST_UBLAS_INLINE iterator1 &operator -- () { -- it1_; return *this; } BOOST_UBLAS_INLINE iterator1 &operator += (difference_type n) { it1_ += n; return *this; } BOOST_UBLAS_INLINE iterator1 &operator -= (difference_type n) { it1_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ - it.it1_; } // Dereference BOOST_UBLAS_INLINE reference operator * () const { return (*this) () (it1_, it2_); } BOOST_UBLAS_INLINE reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator2 begin () const { return (*this) ().find2 (1, it1_, 0); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator2 end () const { return (*this) ().find2 (1, it1_, (*this) ().size2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator2 rbegin () const { return reverse_iterator2 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator2 rend () const { return reverse_iterator2 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_; } BOOST_UBLAS_INLINE size_type index2 () const { return it2_; } // Assignment BOOST_UBLAS_INLINE iterator1 &operator = (const iterator1 &it) { container_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ == it.it1_; } BOOST_UBLAS_INLINE bool operator < (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); return it1_ < it.it1_; } private: size_type it1_; size_type it2_; friend class const_iterator1; }; #endif BOOST_UBLAS_INLINE iterator1 begin1 () { return find1 (0, 0, 0); } BOOST_UBLAS_INLINE iterator1 end1 () { return find1 (0, size1_, 0); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator2: public container_const_reference<triangular_matrix>, public random_access_iterator_base<packed_random_access_iterator_tag, const_iterator2, value_type> { public: typedef typename triangular_matrix::value_type value_type; typedef typename triangular_matrix::difference_type difference_type; typedef typename triangular_matrix::const_reference reference; typedef const typename triangular_matrix::pointer pointer; typedef const_iterator1 dual_iterator_type; typedef const_reverse_iterator1 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE const_iterator2 (): container_const_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE const_iterator2 (const self_type &m, size_type it1, size_type it2): container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {} BOOST_UBLAS_INLINE const_iterator2 (const iterator2 &it): container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator2 &operator ++ () { ++ it2_; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator -- () { -- it2_; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator += (difference_type n) { it2_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator -= (difference_type n) { it2_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ - it.it2_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { return (*this) () (it1_, it2_); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator1 begin () const { return (*this) ().find1 (1, 0, it2_); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator1 end () const { return (*this) ().find1 (1, (*this) ().size1 (), it2_); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator1 rbegin () const { return const_reverse_iterator1 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator1 rend () const { return const_reverse_iterator1 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_; } BOOST_UBLAS_INLINE size_type index2 () const { return it2_; } // Assignment BOOST_UBLAS_INLINE const_iterator2 &operator = (const const_iterator2 &it) { container_const_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ == it.it2_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ < it.it2_; } private: size_type it1_; size_type it2_; }; #endif BOOST_UBLAS_INLINE const_iterator2 begin2 () const { return find2 (0, 0, 0); } BOOST_UBLAS_INLINE const_iterator2 end2 () const { return find2 (0, 0, size2_); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class iterator2: public container_reference<triangular_matrix>, public random_access_iterator_base<packed_random_access_iterator_tag, iterator2, value_type> { public: typedef typename triangular_matrix::value_type value_type; typedef typename triangular_matrix::difference_type difference_type; typedef typename triangular_matrix::reference reference; typedef typename triangular_matrix::pointer pointer; typedef iterator1 dual_iterator_type; typedef reverse_iterator1 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE iterator2 (): container_reference<self_type> (), it1_ (), it2_ () {} BOOST_UBLAS_INLINE iterator2 (self_type &m, size_type it1, size_type it2): container_reference<self_type> (m), it1_ (it1), it2_ (it2) {} // Arithmetic BOOST_UBLAS_INLINE iterator2 &operator ++ () { ++ it2_; return *this; } BOOST_UBLAS_INLINE iterator2 &operator -- () { -- it2_; return *this; } BOOST_UBLAS_INLINE iterator2 &operator += (difference_type n) { it2_ += n; return *this; } BOOST_UBLAS_INLINE iterator2 &operator -= (difference_type n) { it2_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ - it.it2_; } // Dereference BOOST_UBLAS_INLINE reference operator * () const { return (*this) () (it1_, it2_); } BOOST_UBLAS_INLINE reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator1 begin () const { return (*this) ().find1 (1, 0, it2_); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator1 end () const { return (*this) ().find1 (1, (*this) ().size1 (), it2_); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator1 rbegin () const { return reverse_iterator1 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator1 rend () const { return reverse_iterator1 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_; } BOOST_UBLAS_INLINE size_type index2 () const { return it2_; } // Assignment BOOST_UBLAS_INLINE iterator2 &operator = (const iterator2 &it) { container_reference<self_type>::assign (&it ()); it1_ = it.it1_; it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ == it.it2_; } BOOST_UBLAS_INLINE bool operator < (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ()); return it2_ < it.it2_; } private: size_type it1_; size_type it2_; friend class const_iterator2; }; #endif BOOST_UBLAS_INLINE iterator2 begin2 () { return find2 (0, 0, 0); } BOOST_UBLAS_INLINE iterator2 end2 () { return find2 (0, 0, size2_); } // Reverse iterators BOOST_UBLAS_INLINE const_reverse_iterator1 rbegin1 () const { return const_reverse_iterator1 (end1 ()); } BOOST_UBLAS_INLINE const_reverse_iterator1 rend1 () const { return const_reverse_iterator1 (begin1 ()); } BOOST_UBLAS_INLINE reverse_iterator1 rbegin1 () { return reverse_iterator1 (end1 ()); } BOOST_UBLAS_INLINE reverse_iterator1 rend1 () { return reverse_iterator1 (begin1 ()); } BOOST_UBLAS_INLINE const_reverse_iterator2 rbegin2 () const { return const_reverse_iterator2 (end2 ()); } BOOST_UBLAS_INLINE const_reverse_iterator2 rend2 () const { return const_reverse_iterator2 (begin2 ()); } BOOST_UBLAS_INLINE reverse_iterator2 rbegin2 () { return reverse_iterator2 (end2 ()); } BOOST_UBLAS_INLINE reverse_iterator2 rend2 () { return reverse_iterator2 (begin2 ()); } private: size_type size1_; size_type size2_; array_type data_; static const value_type zero_; static const value_type one_; }; template<class T, class TRI, class L, class A> const typename triangular_matrix<T, TRI, L, A>::value_type triangular_matrix<T, TRI, L, A>::zero_ = value_type/*zero*/(); template<class T, class TRI, class L, class A> const typename triangular_matrix<T, TRI, L, A>::value_type triangular_matrix<T, TRI, L, A>::one_ (1); // Triangular matrix adaptor class template<class M, class TRI> class triangular_adaptor: public matrix_expression<triangular_adaptor<M, TRI> > { typedef triangular_adaptor<M, TRI> self_type; public: #ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS using matrix_expression<self_type>::operator (); #endif typedef const M const_matrix_type; typedef M matrix_type; typedef TRI triangular_type; typedef typename M::size_type size_type; typedef typename M::difference_type difference_type; typedef typename M::value_type value_type; typedef typename M::const_reference const_reference; typedef typename boost::mpl::if_<boost::is_const<M>, typename M::const_reference, typename M::reference>::type reference; typedef typename boost::mpl::if_<boost::is_const<M>, typename M::const_closure_type, typename M::closure_type>::type matrix_closure_type; typedef const self_type const_closure_type; typedef self_type closure_type; // Replaced by _temporary_traits to avoid type requirements on M //typedef typename M::vector_temporary_type vector_temporary_type; //typedef typename M::matrix_temporary_type matrix_temporary_type; typedef typename storage_restrict_traits<typename M::storage_category, packed_proxy_tag>::storage_category storage_category; typedef typename M::orientation_category orientation_category; // Construction and destruction BOOST_UBLAS_INLINE triangular_adaptor (matrix_type &data): matrix_expression<self_type> (), data_ (data) {} BOOST_UBLAS_INLINE triangular_adaptor (const triangular_adaptor &m): matrix_expression<self_type> (), data_ (m.data_) {} // Accessors BOOST_UBLAS_INLINE size_type size1 () const { return data_.size1 (); } BOOST_UBLAS_INLINE size_type size2 () const { return data_.size2 (); } // Storage accessors BOOST_UBLAS_INLINE const matrix_closure_type &data () const { return data_; } BOOST_UBLAS_INLINE matrix_closure_type &data () { return data_; } // Element access #ifndef BOOST_UBLAS_PROXY_CONST_MEMBER BOOST_UBLAS_INLINE const_reference operator () (size_type i, size_type j) const { BOOST_UBLAS_CHECK (i < size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < size2 (), bad_index ()); if (triangular_type::other (i, j)) return data () (i, j); else if (triangular_type::one (i, j)) return one_; else return zero_; } BOOST_UBLAS_INLINE reference operator () (size_type i, size_type j) { BOOST_UBLAS_CHECK (i < size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < size2 (), bad_index ()); if (!triangular_type::other (i, j)) { bad_index ().raise (); // NEVER reached } return data () (i, j); } #else BOOST_UBLAS_INLINE reference operator () (size_type i, size_type j) const { BOOST_UBLAS_CHECK (i < size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < size2 (), bad_index ()); if (!triangular_type::other (i, j)) { bad_index ().raise (); // NEVER reached } return data () (i, j); } #endif // Assignment BOOST_UBLAS_INLINE triangular_adaptor &operator = (const triangular_adaptor &m) { matrix_assign<scalar_assign> (*this, m); return *this; } BOOST_UBLAS_INLINE triangular_adaptor &assign_temporary (triangular_adaptor &m) { *this = m; return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor &operator = (const matrix_expression<AE> &ae) { matrix_assign<scalar_assign> (*this, matrix<value_type> (ae)); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor &assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_assign> (*this, ae); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor& operator += (const matrix_expression<AE> &ae) { matrix_assign<scalar_assign> (*this, matrix<value_type> (*this + ae)); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor &plus_assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_plus_assign> (*this, ae); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor& operator -= (const matrix_expression<AE> &ae) { matrix_assign<scalar_assign> (*this, matrix<value_type> (*this - ae)); return *this; } template<class AE> BOOST_UBLAS_INLINE triangular_adaptor &minus_assign (const matrix_expression<AE> &ae) { matrix_assign<scalar_minus_assign> (*this, ae); return *this; } template<class AT> BOOST_UBLAS_INLINE triangular_adaptor& operator *= (const AT &at) { matrix_assign_scalar<scalar_multiplies_assign> (*this, at); return *this; } template<class AT> BOOST_UBLAS_INLINE triangular_adaptor& operator /= (const AT &at) { matrix_assign_scalar<scalar_divides_assign> (*this, at); return *this; } // Closure comparison BOOST_UBLAS_INLINE bool same_closure (const triangular_adaptor &ta) const { return (*this).data ().same_closure (ta.data ()); } // Swapping BOOST_UBLAS_INLINE void swap (triangular_adaptor &m) { if (this != &m) matrix_swap<scalar_swap> (*this, m); } BOOST_UBLAS_INLINE friend void swap (triangular_adaptor &m1, triangular_adaptor &m2) { m1.swap (m2); } // Iterator types private: typedef typename M::const_iterator1 const_subiterator1_type; typedef typename boost::mpl::if_<boost::is_const<M>, typename M::const_iterator1, typename M::iterator1>::type subiterator1_type; typedef typename M::const_iterator2 const_subiterator2_type; typedef typename boost::mpl::if_<boost::is_const<M>, typename M::const_iterator2, typename M::iterator2>::type subiterator2_type; public: #ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1; typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2; typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1; typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2; #else class const_iterator1; class iterator1; class const_iterator2; class iterator2; #endif typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1; typedef reverse_iterator_base1<iterator1> reverse_iterator1; typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2; typedef reverse_iterator_base2<iterator2> reverse_iterator2; // Element lookup BOOST_UBLAS_INLINE const_iterator1 find1 (int rank, size_type i, size_type j) const { if (rank == 1) i = triangular_type::restrict1 (i, j, size1(), size2()); if (rank == 0) i = triangular_type::global_restrict1 (i, size1(), j, size2()); return const_iterator1 (*this, data ().find1 (rank, i, j)); } BOOST_UBLAS_INLINE iterator1 find1 (int rank, size_type i, size_type j) { if (rank == 1) i = triangular_type::mutable_restrict1 (i, j, size1(), size2()); if (rank == 0) i = triangular_type::global_mutable_restrict1 (i, size1(), j, size2()); return iterator1 (*this, data ().find1 (rank, i, j)); } BOOST_UBLAS_INLINE const_iterator2 find2 (int rank, size_type i, size_type j) const { if (rank == 1) j = triangular_type::restrict2 (i, j, size1(), size2()); if (rank == 0) j = triangular_type::global_restrict2 (i, size1(), j, size2()); return const_iterator2 (*this, data ().find2 (rank, i, j)); } BOOST_UBLAS_INLINE iterator2 find2 (int rank, size_type i, size_type j) { if (rank == 1) j = triangular_type::mutable_restrict2 (i, j, size1(), size2()); if (rank == 0) j = triangular_type::global_mutable_restrict2 (i, size1(), j, size2()); return iterator2 (*this, data ().find2 (rank, i, j)); } // Iterators simply are indices. #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator1: public container_const_reference<triangular_adaptor>, public random_access_iterator_base<typename iterator_restrict_traits< typename const_subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category, const_iterator1, value_type> { public: typedef typename const_subiterator1_type::value_type value_type; typedef typename const_subiterator1_type::difference_type difference_type; typedef typename const_subiterator1_type::reference reference; typedef typename const_subiterator1_type::pointer pointer; typedef const_iterator2 dual_iterator_type; typedef const_reverse_iterator2 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE const_iterator1 (): container_const_reference<self_type> (), it1_ () {} BOOST_UBLAS_INLINE const_iterator1 (const self_type &m, const const_subiterator1_type &it1): container_const_reference<self_type> (m), it1_ (it1) {} BOOST_UBLAS_INLINE const_iterator1 (const iterator1 &it): container_const_reference<self_type> (it ()), it1_ (it.it1_) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator1 &operator ++ () { ++ it1_; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator -- () { -- it1_; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator += (difference_type n) { it1_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator1 &operator -= (difference_type n) { it1_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ - it.it1_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { size_type i = index1 (); size_type j = index2 (); BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ()); if (triangular_type::other (i, j)) return *it1_; else return (*this) () (i, j); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator2 begin () const { return (*this) ().find2 (1, index1 (), 0); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator2 end () const { return (*this) ().find2 (1, index1 (), (*this) ().size2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator2 rbegin () const { return const_reverse_iterator2 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator2 rend () const { return const_reverse_iterator2 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_.index1 (); } BOOST_UBLAS_INLINE size_type index2 () const { return it1_.index2 (); } // Assignment BOOST_UBLAS_INLINE const_iterator1 &operator = (const const_iterator1 &it) { container_const_reference<self_type>::assign (&it ()); it1_ = it.it1_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ == it.it1_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ < it.it1_; } private: const_subiterator1_type it1_; }; #endif BOOST_UBLAS_INLINE const_iterator1 begin1 () const { return find1 (0, 0, 0); } BOOST_UBLAS_INLINE const_iterator1 end1 () const { return find1 (0, size1 (), 0); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class iterator1: public container_reference<triangular_adaptor>, public random_access_iterator_base<typename iterator_restrict_traits< typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category, iterator1, value_type> { public: typedef typename subiterator1_type::value_type value_type; typedef typename subiterator1_type::difference_type difference_type; typedef typename subiterator1_type::reference reference; typedef typename subiterator1_type::pointer pointer; typedef iterator2 dual_iterator_type; typedef reverse_iterator2 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE iterator1 (): container_reference<self_type> (), it1_ () {} BOOST_UBLAS_INLINE iterator1 (self_type &m, const subiterator1_type &it1): container_reference<self_type> (m), it1_ (it1) {} // Arithmetic BOOST_UBLAS_INLINE iterator1 &operator ++ () { ++ it1_; return *this; } BOOST_UBLAS_INLINE iterator1 &operator -- () { -- it1_; return *this; } BOOST_UBLAS_INLINE iterator1 &operator += (difference_type n) { it1_ += n; return *this; } BOOST_UBLAS_INLINE iterator1 &operator -= (difference_type n) { it1_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ - it.it1_; } // Dereference BOOST_UBLAS_INLINE reference operator * () const { size_type i = index1 (); size_type j = index2 (); BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ()); if (triangular_type::other (i, j)) return *it1_; else return (*this) () (i, j); } BOOST_UBLAS_INLINE reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator2 begin () const { return (*this) ().find2 (1, index1 (), 0); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator2 end () const { return (*this) ().find2 (1, index1 (), (*this) ().size2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator2 rbegin () const { return reverse_iterator2 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator2 rend () const { return reverse_iterator2 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it1_.index1 (); } BOOST_UBLAS_INLINE size_type index2 () const { return it1_.index2 (); } // Assignment BOOST_UBLAS_INLINE iterator1 &operator = (const iterator1 &it) { container_reference<self_type>::assign (&it ()); it1_ = it.it1_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ == it.it1_; } BOOST_UBLAS_INLINE bool operator < (const iterator1 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it1_ < it.it1_; } private: subiterator1_type it1_; friend class const_iterator1; }; #endif BOOST_UBLAS_INLINE iterator1 begin1 () { return find1 (0, 0, 0); } BOOST_UBLAS_INLINE iterator1 end1 () { return find1 (0, size1 (), 0); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class const_iterator2: public container_const_reference<triangular_adaptor>, public random_access_iterator_base<typename iterator_restrict_traits< typename const_subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category, const_iterator2, value_type> { public: typedef typename const_subiterator2_type::value_type value_type; typedef typename const_subiterator2_type::difference_type difference_type; typedef typename const_subiterator2_type::reference reference; typedef typename const_subiterator2_type::pointer pointer; typedef const_iterator1 dual_iterator_type; typedef const_reverse_iterator1 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE const_iterator2 (): container_const_reference<self_type> (), it2_ () {} BOOST_UBLAS_INLINE const_iterator2 (const self_type &m, const const_subiterator2_type &it2): container_const_reference<self_type> (m), it2_ (it2) {} BOOST_UBLAS_INLINE const_iterator2 (const iterator2 &it): container_const_reference<self_type> (it ()), it2_ (it.it2_) {} // Arithmetic BOOST_UBLAS_INLINE const_iterator2 &operator ++ () { ++ it2_; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator -- () { -- it2_; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator += (difference_type n) { it2_ += n; return *this; } BOOST_UBLAS_INLINE const_iterator2 &operator -= (difference_type n) { it2_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ - it.it2_; } // Dereference BOOST_UBLAS_INLINE const_reference operator * () const { size_type i = index1 (); size_type j = index2 (); BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ()); if (triangular_type::other (i, j)) return *it2_; else return (*this) () (i, j); } BOOST_UBLAS_INLINE const_reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator1 begin () const { return (*this) ().find1 (1, 0, index2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_iterator1 end () const { return (*this) ().find1 (1, (*this) ().size1 (), index2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator1 rbegin () const { return const_reverse_iterator1 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif const_reverse_iterator1 rend () const { return const_reverse_iterator1 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it2_.index1 (); } BOOST_UBLAS_INLINE size_type index2 () const { return it2_.index2 (); } // Assignment BOOST_UBLAS_INLINE const_iterator2 &operator = (const const_iterator2 &it) { container_const_reference<self_type>::assign (&it ()); it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ == it.it2_; } BOOST_UBLAS_INLINE bool operator < (const const_iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ < it.it2_; } private: const_subiterator2_type it2_; }; #endif BOOST_UBLAS_INLINE const_iterator2 begin2 () const { return find2 (0, 0, 0); } BOOST_UBLAS_INLINE const_iterator2 end2 () const { return find2 (0, 0, size2 ()); } #ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR class iterator2: public container_reference<triangular_adaptor>, public random_access_iterator_base<typename iterator_restrict_traits< typename subiterator1_type::iterator_category, packed_random_access_iterator_tag>::iterator_category, iterator2, value_type> { public: typedef typename subiterator2_type::value_type value_type; typedef typename subiterator2_type::difference_type difference_type; typedef typename subiterator2_type::reference reference; typedef typename subiterator2_type::pointer pointer; typedef iterator1 dual_iterator_type; typedef reverse_iterator1 dual_reverse_iterator_type; // Construction and destruction BOOST_UBLAS_INLINE iterator2 (): container_reference<self_type> (), it2_ () {} BOOST_UBLAS_INLINE iterator2 (self_type &m, const subiterator2_type &it2): container_reference<self_type> (m), it2_ (it2) {} // Arithmetic BOOST_UBLAS_INLINE iterator2 &operator ++ () { ++ it2_; return *this; } BOOST_UBLAS_INLINE iterator2 &operator -- () { -- it2_; return *this; } BOOST_UBLAS_INLINE iterator2 &operator += (difference_type n) { it2_ += n; return *this; } BOOST_UBLAS_INLINE iterator2 &operator -= (difference_type n) { it2_ -= n; return *this; } BOOST_UBLAS_INLINE difference_type operator - (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ - it.it2_; } // Dereference BOOST_UBLAS_INLINE reference operator * () const { size_type i = index1 (); size_type j = index2 (); BOOST_UBLAS_CHECK (i < (*this) ().size1 (), bad_index ()); BOOST_UBLAS_CHECK (j < (*this) ().size2 (), bad_index ()); if (triangular_type::other (i, j)) return *it2_; else return (*this) () (i, j); } BOOST_UBLAS_INLINE reference operator [] (difference_type n) const { return *(*this + n); } #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator1 begin () const { return (*this) ().find1 (1, 0, index2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif iterator1 end () const { return (*this) ().find1 (1, (*this) ().size1 (), index2 ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator1 rbegin () const { return reverse_iterator1 (end ()); } BOOST_UBLAS_INLINE #ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION typename self_type:: #endif reverse_iterator1 rend () const { return reverse_iterator1 (begin ()); } #endif // Indices BOOST_UBLAS_INLINE size_type index1 () const { return it2_.index1 (); } BOOST_UBLAS_INLINE size_type index2 () const { return it2_.index2 (); } // Assignment BOOST_UBLAS_INLINE iterator2 &operator = (const iterator2 &it) { container_reference<self_type>::assign (&it ()); it2_ = it.it2_; return *this; } // Comparison BOOST_UBLAS_INLINE bool operator == (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ == it.it2_; } BOOST_UBLAS_INLINE bool operator < (const iterator2 &it) const { BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); return it2_ < it.it2_; } private: subiterator2_type it2_; friend class const_iterator2; }; #endif BOOST_UBLAS_INLINE iterator2 begin2 () { return find2 (0, 0, 0); } BOOST_UBLAS_INLINE iterator2 end2 () { return find2 (0, 0, size2 ()); } // Reverse iterators BOOST_UBLAS_INLINE const_reverse_iterator1 rbegin1 () const { return const_reverse_iterator1 (end1 ()); } BOOST_UBLAS_INLINE const_reverse_iterator1 rend1 () const { return const_reverse_iterator1 (begin1 ()); } BOOST_UBLAS_INLINE reverse_iterator1 rbegin1 () { return reverse_iterator1 (end1 ()); } BOOST_UBLAS_INLINE reverse_iterator1 rend1 () { return reverse_iterator1 (begin1 ()); } BOOST_UBLAS_INLINE const_reverse_iterator2 rbegin2 () const { return const_reverse_iterator2 (end2 ()); } BOOST_UBLAS_INLINE const_reverse_iterator2 rend2 () const { return const_reverse_iterator2 (begin2 ()); } BOOST_UBLAS_INLINE reverse_iterator2 rbegin2 () { return reverse_iterator2 (end2 ()); } BOOST_UBLAS_INLINE reverse_iterator2 rend2 () { return reverse_iterator2 (begin2 ()); } private: matrix_closure_type data_; static const value_type zero_; static const value_type one_; }; template<class M, class TRI> const typename triangular_adaptor<M, TRI>::value_type triangular_adaptor<M, TRI>::zero_ = value_type/*zero*/(); template<class M, class TRI> const typename triangular_adaptor<M, TRI>::value_type triangular_adaptor<M, TRI>::one_ (1); template <class M, class TRI> struct vector_temporary_traits< triangular_adaptor<M, TRI> > : vector_temporary_traits< typename boost::remove_const<M>::type > {} ; template <class M, class TRI> struct vector_temporary_traits< const triangular_adaptor<M, TRI> > : vector_temporary_traits< typename boost::remove_const<M>::type > {} ; template <class M, class TRI> struct matrix_temporary_traits< triangular_adaptor<M, TRI> > : matrix_temporary_traits< typename boost::remove_const<M>::type > {}; template <class M, class TRI> struct matrix_temporary_traits< const triangular_adaptor<M, TRI> > : matrix_temporary_traits< typename boost::remove_const<M>::type > {}; template<class E1, class E2> struct matrix_vector_solve_traits { typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type; typedef vector<promote_type> result_type; }; // Operations: // n * (n - 1) / 2 + n = n * (n + 1) / 2 multiplications, // n * (n - 1) / 2 additions // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, column_major_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { for (size_type m = n + 1; m < size; ++ m) e2 () (m) -= e1 () (m, n) * t; } } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, column_major_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n)); typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n)); difference_type m (it1e1_end - it1e1); while (-- m >= 0) e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1; } } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, column_major_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n)); typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n)); while (it1e1 != it1e1_end) e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1; } } } // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, row_major_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { for (size_type m = n + 1; m < size; ++ m) e2 () (m) -= e1 () (m, n) * t; } } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, row_major_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n); typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, 0)); typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, n)); while (it2e1 != it2e1_end) { t -= *it2e1 * e2 () (it2e1.index2()); ++ it2e1; } e2() (n) = t / e1 () (n, n); } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, row_major_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (size_type n = 0; n < size; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n); typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, 0)); typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, n)); while (it2e1 != it2e1_end) { t -= *it2e1 * e2 () (it2e1.index2()); ++ it2e1; } e2() (n) = t / e1 () (n, n); } } // Redirectors :-) template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, column_major_tag) { typedef typename E1::storage_category storage_category; inplace_solve (e1, e2, lower_tag (), column_major_tag (), storage_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag, row_major_tag) { typedef typename E1::storage_category storage_category; inplace_solve (e1, e2, lower_tag (), row_major_tag (), storage_category ()); } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, lower_tag) { typedef typename E1::orientation_category orientation_category; inplace_solve (e1, e2, lower_tag (), orientation_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, unit_lower_tag) { typedef typename E1::orientation_category orientation_category; inplace_solve (triangular_adaptor<const E1, unit_lower> (e1 ()), e2, unit_lower_tag (), orientation_category ()); } // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, column_major_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (difference_type n = size - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { for (difference_type m = n - 1; m >= 0; -- m) e2 () (m) -= e1 () (m, n) * t; } } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, column_major_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (difference_type n = size - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n)); typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n)); while (it1e1 != it1e1_rend) { e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1; } } } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, column_major_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e2 ().size (); for (difference_type n = size - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n)); typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n)); while (it1e1 != it1e1_rend) { e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1; } } } } // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, row_major_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e1 ().size1 (); for (difference_type n = size-1; n >=0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n); for (difference_type m = n + 1; m < e1 ().size2(); ++ m) { t -= e1 () (n, m) * e2 () (m); } e2() (n) = t / e1 () (n, n); } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, row_major_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e1 ().size1 (); for (difference_type n = size-1; n >=0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n); typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, n+1)); typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, e1 ().size2 ())); while (it2e1 != it2e1_end) { t -= *it2e1 * e2 () (it2e1.index2()); ++ it2e1; } e2() (n) = t / e1 () (n, n); } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, row_major_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ()); size_type size = e1 ().size1 (); for (difference_type n = size-1; n >=0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif value_type t = e2 () (n); typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, n+1)); typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, e1 ().size2 ())); while (it2e1 != it2e1_end) { t -= *it2e1 * e2 () (it2e1.index2()); ++ it2e1; } e2() (n) = t / e1 () (n, n); } } // Redirectors :-) template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, column_major_tag) { typedef typename E1::storage_category storage_category; inplace_solve (e1, e2, upper_tag (), column_major_tag (), storage_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag, row_major_tag) { typedef typename E1::storage_category storage_category; inplace_solve (e1, e2, upper_tag (), row_major_tag (), storage_category ()); } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, upper_tag) { typedef typename E1::orientation_category orientation_category; inplace_solve (e1, e2, upper_tag (), orientation_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2, unit_upper_tag) { typedef typename E1::orientation_category orientation_category; inplace_solve (triangular_adaptor<const E1, unit_upper> (e1 ()), e2, unit_upper_tag (), orientation_category ()); } template<class E1, class E2, class C> BOOST_UBLAS_INLINE typename matrix_vector_solve_traits<E1, E2>::result_type solve (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, C) { typename matrix_vector_solve_traits<E1, E2>::result_type r (e2); inplace_solve (e1, r, C ()); return r; } // Redirectors :-) template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, lower_tag, row_major_tag) { typedef typename E2::storage_category storage_category; inplace_solve (trans(e2), e1, upper_tag (), column_major_tag (), storage_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, lower_tag, column_major_tag) { typedef typename E2::storage_category storage_category; inplace_solve (trans (e2), e1, upper_tag (), row_major_tag (), storage_category ()); } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, lower_tag) { typedef typename E2::orientation_category orientation_category; inplace_solve (e1, e2, lower_tag (), orientation_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, unit_lower_tag) { typedef typename E2::orientation_category orientation_category; inplace_solve (e1, triangular_adaptor<const E2, unit_lower> (e2 ()), unit_lower_tag (), orientation_category ()); } // Redirectors :-) template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, upper_tag, row_major_tag) { typedef typename E2::storage_category storage_category; inplace_solve (trans(e2), e1, lower_tag (), column_major_tag (), storage_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, upper_tag, column_major_tag) { typedef typename E2::storage_category storage_category; inplace_solve (trans (e2), e1, lower_tag (), row_major_tag (), storage_category ()); } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, upper_tag) { typedef typename E2::orientation_category orientation_category; inplace_solve (e1, e2, upper_tag (), orientation_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2, unit_upper_tag) { typedef typename E2::orientation_category orientation_category; inplace_solve (e1, triangular_adaptor<const E2, unit_upper> (e2 ()), unit_upper_tag (), orientation_category ()); } template<class E1, class E2, class C> BOOST_UBLAS_INLINE typename matrix_vector_solve_traits<E1, E2>::result_type solve (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, C) { typename matrix_vector_solve_traits<E1, E2>::result_type r (e1); inplace_solve (r, e2, C ()); return r; } template<class E1, class E2> struct matrix_matrix_solve_traits { typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type; typedef matrix<promote_type> result_type; }; // Operations: // k * n * (n - 1) / 2 + k * n = k * n * (n + 1) / 2 multiplications, // k * n * (n - 1) / 2 additions // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, lower_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (size_type n = 0; n < size1; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (size_type l = 0; l < size2; ++ l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { for (size_type m = n + 1; m < size1; ++ m) e2 () (m, l) -= e1 () (m, n) * t; } } } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, lower_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (size_type n = 0; n < size1; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (size_type l = 0; l < size2; ++ l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n)); typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n)); difference_type m (it1e1_end - it1e1); while (-- m >= 0) e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1; } } } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, lower_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (size_type n = 0; n < size1; ++ n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (size_type l = 0; l < size2; ++ l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n)); typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n)); while (it1e1 != it1e1_end) e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1; } } } } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, lower_tag) { typedef typename E1::storage_category dispatch_category; inplace_solve (e1, e2, lower_tag (), dispatch_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, unit_lower_tag) { typedef typename E1::storage_category dispatch_category; inplace_solve (triangular_adaptor<const E1, unit_lower> (e1 ()), e2, unit_lower_tag (), dispatch_category ()); } // Dense (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, upper_tag, dense_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (difference_type n = size1 - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (difference_type l = size2 - 1; l >= 0; -- l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { for (difference_type m = n - 1; m >= 0; -- m) e2 () (m, l) -= e1 () (m, n) * t; } } } } // Packed (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, upper_tag, packed_proxy_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (difference_type n = size1 - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (difference_type l = size2 - 1; l >= 0; -- l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n)); typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n)); difference_type m (it1e1_rend - it1e1); while (-- m >= 0) e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1; } } } } // Sparse (proxy) case template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, upper_tag, unknown_storage_tag) { typedef typename E2::size_type size_type; typedef typename E2::difference_type difference_type; typedef typename E2::value_type value_type; BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ()); BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size1 (), bad_size ()); size_type size1 = e2 ().size1 (); size_type size2 = e2 ().size2 (); for (difference_type n = size1 - 1; n >= 0; -- n) { #ifndef BOOST_UBLAS_SINGULAR_CHECK BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ()); #else if (e1 () (n, n) == value_type/*zero*/()) singular ().raise (); #endif for (difference_type l = size2 - 1; l >= 0; -- l) { value_type t = e2 () (n, l) /= e1 () (n, n); if (t != value_type/*zero*/()) { typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n)); typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n)); while (it1e1 != it1e1_rend) e2 () (it1e1.index1 (), l) -= *it1e1 * t, ++ it1e1; } } } } // Dispatcher template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, upper_tag) { typedef typename E1::storage_category dispatch_category; inplace_solve (e1, e2, upper_tag (), dispatch_category ()); } template<class E1, class E2> BOOST_UBLAS_INLINE void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2, unit_upper_tag) { typedef typename E1::storage_category dispatch_category; inplace_solve (triangular_adaptor<const E1, unit_upper> (e1 ()), e2, unit_upper_tag (), dispatch_category ()); } template<class E1, class E2, class C> BOOST_UBLAS_INLINE typename matrix_matrix_solve_traits<E1, E2>::result_type solve (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, C) { typename matrix_matrix_solve_traits<E1, E2>::result_type r (e2); inplace_solve (e1, r, C ()); return r; } }}} #endif