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2593 lines
98 KiB
2593 lines
98 KiB
// |
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// Copyright (c) 2000-2002 |
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// Joerg Walter, Mathias Koch |
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// |
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// Distributed under the Boost Software License, Version 1.0. (See |
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// accompanying file LICENSE_1_0.txt or copy at |
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// http://www.boost.org/LICENSE_1_0.txt) |
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// |
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// The authors gratefully acknowledge the support of |
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// GeNeSys mbH & Co. KG in producing this work. |
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// |
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#ifndef _BOOST_UBLAS_TRIANGULAR_ |
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#define _BOOST_UBLAS_TRIANGULAR_ |
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|
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#include <boost/numeric/ublas/matrix.hpp> |
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#include <boost/numeric/ublas/detail/temporary.hpp> |
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#include <boost/type_traits/remove_const.hpp> |
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// Iterators based on ideas of Jeremy Siek |
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|
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namespace boost { namespace numeric { namespace ublas { |
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namespace detail { |
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using namespace boost::numeric::ublas; |
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// Matrix resizing algorithm |
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template <class L, class T, class M> |
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BOOST_UBLAS_INLINE |
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void matrix_resize_preserve (M& m, M& temporary) { |
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typedef L layout_type; |
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typedef T triangular_type; |
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typedef typename M::size_type size_type; |
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const size_type msize1 (m.size1 ()); // original size |
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const size_type msize2 (m.size2 ()); |
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const size_type size1 (temporary.size1 ()); // new size is specified by temporary |
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const size_type size2 (temporary.size2 ()); |
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// Common elements to preserve |
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const size_type size1_min = (std::min) (size1, msize1); |
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const size_type size2_min = (std::min) (size2, msize2); |
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// Order for major and minor sizes |
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const size_type major_size = layout_type::size_M (size1_min, size2_min); |
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const size_type minor_size = layout_type::size_m (size1_min, size2_min); |
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// Indexing copy over major |
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for (size_type major = 0; major != major_size; ++major) { |
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for (size_type minor = 0; minor != minor_size; ++minor) { |
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// find indexes - use invertability of element_ functions |
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const size_type i1 = layout_type::index_M(major, minor); |
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const size_type i2 = layout_type::index_m(major, minor); |
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if ( triangular_type::other(i1,i2) ) { |
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temporary.data () [triangular_type::element (layout_type (), i1, size1, i2, size2)] = |
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m.data() [triangular_type::element (layout_type (), i1, msize1, i2, msize2)]; |
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} |
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} |
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} |
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m.assign_temporary (temporary); |
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} |
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} |
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/** \brief A triangular matrix of values of type \c T. |
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* |
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* 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, |
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* \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit lower triangular. |
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* |
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* 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, |
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* \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit upper triangular. |
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* |
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* The default storage for triangular matrices is packed. Orientation and storage can also be specified. |
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* Default is \c row_major and and unbounded_array. It is \b not required by the storage to initialize |
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* elements of the matrix. |
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* |
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* \tparam T the type of object stored in the matrix (like double, float, complex, etc...) |
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* \tparam TRI the type of the triangular matrix. It can either be \c lower or \c upper. Default is \c lower |
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* \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major |
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* \tparam A the type of Storage array. Default is \c unbounded_array |
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*/ |
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template<class T, class TRI, class L, class A> |
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class triangular_matrix: |
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public matrix_container<triangular_matrix<T, TRI, L, A> > { |
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typedef T *pointer; |
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typedef TRI triangular_type; |
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typedef L layout_type; |
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typedef triangular_matrix<T, TRI, L, A> self_type; |
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public: |
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#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS |
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using matrix_container<self_type>::operator (); |
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#endif |
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typedef typename A::size_type size_type; |
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typedef typename A::difference_type difference_type; |
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typedef T value_type; |
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typedef const T &const_reference; |
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typedef T &reference; |
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typedef A array_type; |
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typedef const matrix_reference<const self_type> const_closure_type; |
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typedef matrix_reference<self_type> closure_type; |
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typedef vector<T, A> vector_temporary_type; |
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typedef matrix<T, L, A> matrix_temporary_type; // general sub-matrix |
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typedef packed_tag storage_category; |
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typedef typename L::orientation_category orientation_category; |
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// Construction and destruction |
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BOOST_UBLAS_INLINE |
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triangular_matrix (): |
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matrix_container<self_type> (), |
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size1_ (0), size2_ (0), data_ (0) {} |
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BOOST_UBLAS_INLINE |
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triangular_matrix (size_type size1, size_type size2): |
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matrix_container<self_type> (), |
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size1_ (size1), size2_ (size2), data_ (triangular_type::packed_size (layout_type (), size1, size2)) { |
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} |
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BOOST_UBLAS_INLINE |
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triangular_matrix (size_type size1, size_type size2, const array_type &data): |
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matrix_container<self_type> (), |
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size1_ (size1), size2_ (size2), data_ (data) {} |
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BOOST_UBLAS_INLINE |
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triangular_matrix (const triangular_matrix &m): |
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matrix_container<self_type> (), |
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size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix (const matrix_expression<AE> &ae): |
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matrix_container<self_type> (), |
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size1_ (ae ().size1 ()), size2_ (ae ().size2 ()), |
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data_ (triangular_type::packed_size (layout_type (), size1_, size2_)) { |
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matrix_assign<scalar_assign> (*this, ae); |
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} |
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// Accessors |
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BOOST_UBLAS_INLINE |
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size_type size1 () const { |
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return size1_; |
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} |
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BOOST_UBLAS_INLINE |
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size_type size2 () const { |
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return size2_; |
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} |
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// Storage accessors |
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BOOST_UBLAS_INLINE |
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const array_type &data () const { |
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return data_; |
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} |
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BOOST_UBLAS_INLINE |
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array_type &data () { |
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return data_; |
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} |
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// Resizing |
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BOOST_UBLAS_INLINE |
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void resize (size_type size1, size_type size2, bool preserve = true) { |
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if (preserve) { |
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self_type temporary (size1, size2); |
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detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary); |
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} |
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else { |
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data ().resize (triangular_type::packed_size (layout_type (), size1, size2)); |
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size1_ = size1; |
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size2_ = size2; |
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} |
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} |
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BOOST_UBLAS_INLINE |
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void resize_packed_preserve (size_type size1, size_type size2) { |
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size1_ = size1; |
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size2_ = size2; |
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data ().resize (triangular_type::packed_size (layout_type (), size1_, size2_), value_type ()); |
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} |
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// Element access |
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BOOST_UBLAS_INLINE |
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const_reference operator () (size_type i, size_type j) const { |
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BOOST_UBLAS_CHECK (i < size1_, bad_index ()); |
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BOOST_UBLAS_CHECK (j < size2_, bad_index ()); |
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if (triangular_type::other (i, j)) |
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return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; |
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else if (triangular_type::one (i, j)) |
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return one_; |
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else |
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return zero_; |
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} |
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BOOST_UBLAS_INLINE |
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reference at_element (size_type i, size_type j) { |
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BOOST_UBLAS_CHECK (i < size1_, bad_index ()); |
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BOOST_UBLAS_CHECK (j < size2_, bad_index ()); |
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return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; |
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} |
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BOOST_UBLAS_INLINE |
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reference operator () (size_type i, size_type j) { |
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BOOST_UBLAS_CHECK (i < size1_, bad_index ()); |
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BOOST_UBLAS_CHECK (j < size2_, bad_index ()); |
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if (!triangular_type::other (i, j)) { |
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bad_index ().raise (); |
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// NEVER reached |
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} |
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return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)]; |
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} |
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// Element assignment |
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BOOST_UBLAS_INLINE |
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reference insert_element (size_type i, size_type j, const_reference t) { |
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return (operator () (i, j) = t); |
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} |
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BOOST_UBLAS_INLINE |
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void erase_element (size_type i, size_type j) { |
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operator () (i, j) = value_type/*zero*/(); |
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} |
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// Zeroing |
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BOOST_UBLAS_INLINE |
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void clear () { |
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// data ().clear (); |
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std::fill (data ().begin (), data ().end (), value_type/*zero*/()); |
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} |
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// Assignment |
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BOOST_UBLAS_INLINE |
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triangular_matrix &operator = (const triangular_matrix &m) { |
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size1_ = m.size1_; |
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size2_ = m.size2_; |
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data () = m.data (); |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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triangular_matrix &assign_temporary (triangular_matrix &m) { |
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swap (m); |
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return *this; |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix &operator = (const matrix_expression<AE> &ae) { |
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self_type temporary (ae); |
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return assign_temporary (temporary); |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix &assign (const matrix_expression<AE> &ae) { |
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matrix_assign<scalar_assign> (*this, ae); |
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return *this; |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix& operator += (const matrix_expression<AE> &ae) { |
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self_type temporary (*this + ae); |
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return assign_temporary (temporary); |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix &plus_assign (const matrix_expression<AE> &ae) { |
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matrix_assign<scalar_plus_assign> (*this, ae); |
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return *this; |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix& operator -= (const matrix_expression<AE> &ae) { |
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self_type temporary (*this - ae); |
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return assign_temporary (temporary); |
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} |
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template<class AE> |
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BOOST_UBLAS_INLINE |
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triangular_matrix &minus_assign (const matrix_expression<AE> &ae) { |
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matrix_assign<scalar_minus_assign> (*this, ae); |
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return *this; |
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} |
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template<class AT> |
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BOOST_UBLAS_INLINE |
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triangular_matrix& operator *= (const AT &at) { |
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matrix_assign_scalar<scalar_multiplies_assign> (*this, at); |
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return *this; |
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} |
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template<class AT> |
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BOOST_UBLAS_INLINE |
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triangular_matrix& operator /= (const AT &at) { |
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matrix_assign_scalar<scalar_divides_assign> (*this, at); |
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return *this; |
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} |
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// Swapping |
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BOOST_UBLAS_INLINE |
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void swap (triangular_matrix &m) { |
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if (this != &m) { |
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// BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ()); |
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std::swap (size1_, m.size1_); |
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std::swap (size2_, m.size2_); |
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data ().swap (m.data ()); |
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} |
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} |
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BOOST_UBLAS_INLINE |
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friend void swap (triangular_matrix &m1, triangular_matrix &m2) { |
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m1.swap (m2); |
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} |
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// Iterator types |
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#ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR |
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typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1; |
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typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2; |
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typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1; |
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typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2; |
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#else |
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class const_iterator1; |
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class iterator1; |
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class const_iterator2; |
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class iterator2; |
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#endif |
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typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1; |
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typedef reverse_iterator_base1<iterator1> reverse_iterator1; |
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typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2; |
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typedef reverse_iterator_base2<iterator2> reverse_iterator2; |
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|
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// Element lookup |
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BOOST_UBLAS_INLINE |
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const_iterator1 find1 (int rank, size_type i, size_type j) const { |
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if (rank == 1) |
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i = triangular_type::restrict1 (i, j, size1_, size2_); |
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if (rank == 0) |
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i = triangular_type::global_restrict1 (i, size1_, j, size2_); |
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return const_iterator1 (*this, i, j); |
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} |
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BOOST_UBLAS_INLINE |
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iterator1 find1 (int rank, size_type i, size_type j) { |
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if (rank == 1) |
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i = triangular_type::mutable_restrict1 (i, j, size1_, size2_); |
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if (rank == 0) |
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i = triangular_type::global_mutable_restrict1 (i, size1_, j, size2_); |
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return iterator1 (*this, i, j); |
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} |
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BOOST_UBLAS_INLINE |
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const_iterator2 find2 (int rank, size_type i, size_type j) const { |
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if (rank == 1) |
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j = triangular_type::restrict2 (i, j, size1_, size2_); |
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if (rank == 0) |
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j = triangular_type::global_restrict2 (i, size1_, j, size2_); |
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return const_iterator2 (*this, i, j); |
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} |
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BOOST_UBLAS_INLINE |
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iterator2 find2 (int rank, size_type i, size_type j) { |
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if (rank == 1) |
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j = triangular_type::mutable_restrict2 (i, j, size1_, size2_); |
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if (rank == 0) |
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j = triangular_type::global_mutable_restrict2 (i, size1_, j, size2_); |
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return iterator2 (*this, i, j); |
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} |
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// Iterators simply are indices. |
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|
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#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR |
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class const_iterator1: |
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public container_const_reference<triangular_matrix>, |
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public random_access_iterator_base<packed_random_access_iterator_tag, |
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const_iterator1, value_type> { |
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public: |
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typedef typename triangular_matrix::value_type value_type; |
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typedef typename triangular_matrix::difference_type difference_type; |
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typedef typename triangular_matrix::const_reference reference; |
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typedef const typename triangular_matrix::pointer pointer; |
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typedef const_iterator2 dual_iterator_type; |
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typedef const_reverse_iterator2 dual_reverse_iterator_type; |
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// Construction and destruction |
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BOOST_UBLAS_INLINE |
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const_iterator1 (): |
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container_const_reference<self_type> (), it1_ (), it2_ () {} |
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BOOST_UBLAS_INLINE |
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const_iterator1 (const self_type &m, size_type it1, size_type it2): |
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container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {} |
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BOOST_UBLAS_INLINE |
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const_iterator1 (const iterator1 &it): |
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container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {} |
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// Arithmetic |
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BOOST_UBLAS_INLINE |
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const_iterator1 &operator ++ () { |
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++ it1_; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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const_iterator1 &operator -- () { |
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-- it1_; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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const_iterator1 &operator += (difference_type n) { |
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it1_ += n; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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const_iterator1 &operator -= (difference_type n) { |
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it1_ -= n; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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difference_type operator - (const const_iterator1 &it) const { |
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BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); |
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BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); |
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return it1_ - it.it1_; |
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} |
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// Dereference |
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BOOST_UBLAS_INLINE |
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const_reference operator * () const { |
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return (*this) () (it1_, it2_); |
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} |
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BOOST_UBLAS_INLINE |
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const_reference operator [] (difference_type n) const { |
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return *(*this + n); |
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} |
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#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
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BOOST_UBLAS_INLINE |
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#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION |
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typename self_type:: |
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#endif |
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const_iterator2 begin () const { |
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return (*this) ().find2 (1, it1_, 0); |
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} |
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BOOST_UBLAS_INLINE |
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#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION |
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typename self_type:: |
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#endif |
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const_iterator2 end () const { |
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return (*this) ().find2 (1, it1_, (*this) ().size2 ()); |
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} |
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BOOST_UBLAS_INLINE |
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#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION |
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typename self_type:: |
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#endif |
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const_reverse_iterator2 rbegin () const { |
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return const_reverse_iterator2 (end ()); |
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} |
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BOOST_UBLAS_INLINE |
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#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION |
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typename self_type:: |
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#endif |
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const_reverse_iterator2 rend () const { |
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return const_reverse_iterator2 (begin ()); |
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} |
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#endif |
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|
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// Indices |
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BOOST_UBLAS_INLINE |
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size_type index1 () const { |
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return it1_; |
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} |
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BOOST_UBLAS_INLINE |
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size_type index2 () const { |
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return it2_; |
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} |
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|
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// Assignment |
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BOOST_UBLAS_INLINE |
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const_iterator1 &operator = (const const_iterator1 &it) { |
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container_const_reference<self_type>::assign (&it ()); |
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it1_ = it.it1_; |
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it2_ = it.it2_; |
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return *this; |
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} |
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|
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// Comparison |
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BOOST_UBLAS_INLINE |
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bool operator == (const const_iterator1 &it) const { |
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BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); |
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BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); |
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return it1_ == it.it1_; |
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} |
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BOOST_UBLAS_INLINE |
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bool operator < (const const_iterator1 &it) const { |
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BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ()); |
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BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ()); |
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return it1_ < it.it1_; |
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} |
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|
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private: |
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size_type it1_; |
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size_type it2_; |
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}; |
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#endif |
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|
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BOOST_UBLAS_INLINE |
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const_iterator1 begin1 () const { |
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return find1 (0, 0, 0); |
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} |
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BOOST_UBLAS_INLINE |
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const_iterator1 end1 () const { |
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return find1 (0, size1_, 0); |
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} |
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|
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#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR |
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class iterator1: |
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public container_reference<triangular_matrix>, |
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public random_access_iterator_base<packed_random_access_iterator_tag, |
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iterator1, value_type> { |
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public: |
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typedef typename triangular_matrix::value_type value_type; |
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typedef typename triangular_matrix::difference_type difference_type; |
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typedef typename triangular_matrix::reference reference; |
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typedef typename triangular_matrix::pointer pointer; |
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|
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typedef iterator2 dual_iterator_type; |
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typedef reverse_iterator2 dual_reverse_iterator_type; |
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|
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// Construction and destruction |
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BOOST_UBLAS_INLINE |
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iterator1 (): |
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container_reference<self_type> (), it1_ (), it2_ () {} |
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BOOST_UBLAS_INLINE |
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iterator1 (self_type &m, size_type it1, size_type it2): |
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container_reference<self_type> (m), it1_ (it1), it2_ (it2) {} |
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|
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// Arithmetic |
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BOOST_UBLAS_INLINE |
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iterator1 &operator ++ () { |
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++ it1_; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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iterator1 &operator -- () { |
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-- it1_; |
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return *this; |
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} |
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BOOST_UBLAS_INLINE |
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iterator1 &operator += (difference_type n) { |
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it1_ += n; |
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return *this; |
|
} |
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BOOST_UBLAS_INLINE |
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iterator1 &operator -= (difference_type n) { |
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it1_ -= n; |
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return *this; |
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} |
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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; |
|
} |
|
} |
|
} |
|
// 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 (e2, trans (e1), |
|
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, |
|
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)); |
|
difference_type m (it1e1_rend - 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, |
|
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; |
|
} |
|
} |
|
} |
|
// 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 (e2, trans (e1), |
|
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, |
|
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; |
|
} |
|
|
|
// Dense (proxy) case |
|
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, dense_proxy_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (difference_type n = size - 1; n >= 0; -- n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
for (difference_type m = n - 1; m >= 0; -- m) |
|
e1 () (m) -= t * e2 () (n, m); |
|
} |
|
} |
|
} |
|
// Packed (proxy) case |
|
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, packed_proxy_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (difference_type n = size - 1; n >= 0; -- n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
typename E2::const_reverse_iterator2 it2e2 (e2 ().find2 (1, n, n)); |
|
typename E2::const_reverse_iterator2 it2e2_rend (e2 ().find2 (1, n, 0)); |
|
difference_type m (it2e2_rend - it2e2); |
|
while (-- m >= 0) |
|
e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2; |
|
} |
|
} |
|
} |
|
// Sparse (proxy) case |
|
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, unknown_storage_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (difference_type n = size - 1; n >= 0; -- n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
typename E2::const_reverse_iterator2 it2e2 (e2 ().find2 (1, n, n)); |
|
typename E2::const_reverse_iterator2 it2e2_rend (e2 ().find2 (1, n, 0)); |
|
while (it2e2 != it2e2_rend) |
|
e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2; |
|
} |
|
} |
|
} |
|
// 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 E1::storage_category storage_category; |
|
inplace_solve (e1, e2, |
|
lower_tag (), row_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 E1::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 ()); |
|
} |
|
|
|
// Dense (proxy) case |
|
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, dense_proxy_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (size_type n = 0; n < size; ++ n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
for (size_type m = n + 1; m < size; ++ m) |
|
e1 () (m) -= t * e2 () (n, m); |
|
} |
|
} |
|
} |
|
// Packed (proxy) case |
|
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, packed_proxy_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (size_type n = 0; n < size; ++ n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
typename E2::const_iterator2 it2e2 (e2 ().find2 (1, n, n + 1)); |
|
typename E2::const_iterator2 it2e2_end (e2 ().find2 (1, n, e2 ().size2 ())); |
|
difference_type m (it2e2_end - it2e2); |
|
while (-- m >= 0) |
|
e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2; |
|
} |
|
} |
|
} |
|
// Sparse (proxy) case |
|
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, unknown_storage_tag) { |
|
typedef typename E1::size_type size_type; |
|
typedef typename E1::difference_type difference_type; |
|
typedef typename E1::value_type value_type; |
|
|
|
BOOST_UBLAS_CHECK (e1 ().size () == e2 ().size1 (), bad_size ()); |
|
BOOST_UBLAS_CHECK (e2 ().size1 () == e2 ().size2 (), bad_size ()); |
|
size_type size = e1 ().size (); |
|
for (size_type n = 0; n < size; ++ n) { |
|
#ifndef BOOST_UBLAS_SINGULAR_CHECK |
|
BOOST_UBLAS_CHECK (e2 () (n, n) != value_type/*zero*/(), singular ()); |
|
#else |
|
if (e2 () (n, n) == value_type/*zero*/()) |
|
singular ().raise (); |
|
#endif |
|
value_type t = e1 () (n) /= e2 () (n, n); |
|
if (t != value_type/*zero*/()) { |
|
typename E2::const_iterator2 it2e2 (e2 ().find2 (1, n, n + 1)); |
|
typename E2::const_iterator2 it2e2_end (e2 ().find2 (1, n, e2 ().size2 ())); |
|
while (it2e2 != it2e2_end) |
|
e1 () (it2e2.index2 ()) -= *it2e2 * t, ++ it2e2; |
|
} |
|
} |
|
} |
|
// 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 E1::storage_category storage_category; |
|
inplace_solve (e1, e2, |
|
upper_tag (), row_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 E1::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
|
|
|