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ecency-mobile/ios/Pods/boost-for-react-native/boost/numeric/ublas/triangular.hpp

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//
// Copyright (c) 2000-2002
// Joerg Walter, Mathias Koch
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
// The authors gratefully acknowledge the support of
// GeNeSys mbH & Co. KG in producing this work.
//
#ifndef _BOOST_UBLAS_TRIANGULAR_
#define _BOOST_UBLAS_TRIANGULAR_
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/detail/temporary.hpp>
#include <boost/type_traits/remove_const.hpp>
// Iterators based on ideas of Jeremy Siek
namespace boost { namespace numeric { namespace ublas {
namespace detail {
using namespace boost::numeric::ublas;
// Matrix resizing algorithm
template <class L, class T, class M>
BOOST_UBLAS_INLINE
void matrix_resize_preserve (M& m, M& temporary) {
typedef L layout_type;
typedef T triangular_type;
typedef typename M::size_type size_type;
const size_type msize1 (m.size1 ()); // original size
const size_type msize2 (m.size2 ());
const size_type size1 (temporary.size1 ()); // new size is specified by temporary
const size_type size2 (temporary.size2 ());
// Common elements to preserve
const size_type size1_min = (std::min) (size1, msize1);
const size_type size2_min = (std::min) (size2, msize2);
// Order for major and minor sizes
const size_type major_size = layout_type::size_M (size1_min, size2_min);
const size_type minor_size = layout_type::size_m (size1_min, size2_min);
// Indexing copy over major
for (size_type major = 0; major != major_size; ++major) {
for (size_type minor = 0; minor != minor_size; ++minor) {
// find indexes - use invertability of element_ functions
const size_type i1 = layout_type::index_M(major, minor);
const size_type i2 = layout_type::index_m(major, minor);
if ( triangular_type::other(i1,i2) ) {
temporary.data () [triangular_type::element (layout_type (), i1, size1, i2, size2)] =
m.data() [triangular_type::element (layout_type (), i1, msize1, i2, msize2)];
}
}
}
m.assign_temporary (temporary);
}
}
/** \brief A triangular matrix of values of type \c T.
*
* For a \f$(n \times n )\f$-dimensional lower triangular matrix and if \f$0 \leq i < n\f$, \f$0 \leq j < n\f$ and \f$i>j\f$ holds,
* \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit lower triangular.
*
* For a \f$(n \times n )\f$-dimensional upper triangular matrix and if \f$0 \leq i < n\f$, \f$0 \leq j < n\f$ and \f$i<j\f$ holds,
* \f$m_{i,j}=0\f$. Furthermore if \f$m_{i,i}=1\f$, the matrix is called unit upper triangular.
*
* The default storage for triangular matrices is packed. Orientation and storage can also be specified.
* Default is \c row_major and and unbounded_array. It is \b not required by the storage to initialize
* elements of the matrix.
*
* \tparam T the type of object stored in the matrix (like double, float, complex, etc...)
* \tparam TRI the type of the triangular matrix. It can either be \c lower or \c upper. Default is \c lower
* \tparam L the storage organization. It can be either \c row_major or \c column_major. Default is \c row_major
* \tparam A the type of Storage array. Default is \c unbounded_array
*/
template<class T, class TRI, class L, class A>
class triangular_matrix:
public matrix_container<triangular_matrix<T, TRI, L, A> > {
typedef T *pointer;
typedef TRI triangular_type;
typedef L layout_type;
typedef triangular_matrix<T, TRI, L, A> self_type;
public:
#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
using matrix_container<self_type>::operator ();
#endif
typedef typename A::size_type size_type;
typedef typename A::difference_type difference_type;
typedef T value_type;
typedef const T &const_reference;
typedef T &reference;
typedef A array_type;
typedef const matrix_reference<const self_type> const_closure_type;
typedef matrix_reference<self_type> closure_type;
typedef vector<T, A> vector_temporary_type;
typedef matrix<T, L, A> matrix_temporary_type; // general sub-matrix
typedef packed_tag storage_category;
typedef typename L::orientation_category orientation_category;
// Construction and destruction
BOOST_UBLAS_INLINE
triangular_matrix ():
matrix_container<self_type> (),
size1_ (0), size2_ (0), data_ (0) {}
BOOST_UBLAS_INLINE
triangular_matrix (size_type size1, size_type size2):
matrix_container<self_type> (),
size1_ (size1), size2_ (size2), data_ (triangular_type::packed_size (layout_type (), size1, size2)) {
}
BOOST_UBLAS_INLINE
triangular_matrix (size_type size1, size_type size2, const array_type &data):
matrix_container<self_type> (),
size1_ (size1), size2_ (size2), data_ (data) {}
BOOST_UBLAS_INLINE
triangular_matrix (const triangular_matrix &m):
matrix_container<self_type> (),
size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix (const matrix_expression<AE> &ae):
matrix_container<self_type> (),
size1_ (ae ().size1 ()), size2_ (ae ().size2 ()),
data_ (triangular_type::packed_size (layout_type (), size1_, size2_)) {
matrix_assign<scalar_assign> (*this, ae);
}
// Accessors
BOOST_UBLAS_INLINE
size_type size1 () const {
return size1_;
}
BOOST_UBLAS_INLINE
size_type size2 () const {
return size2_;
}
// Storage accessors
BOOST_UBLAS_INLINE
const array_type &data () const {
return data_;
}
BOOST_UBLAS_INLINE
array_type &data () {
return data_;
}
// Resizing
BOOST_UBLAS_INLINE
void resize (size_type size1, size_type size2, bool preserve = true) {
if (preserve) {
self_type temporary (size1, size2);
detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary);
}
else {
data ().resize (triangular_type::packed_size (layout_type (), size1, size2));
size1_ = size1;
size2_ = size2;
}
}
BOOST_UBLAS_INLINE
void resize_packed_preserve (size_type size1, size_type size2) {
size1_ = size1;
size2_ = size2;
data ().resize (triangular_type::packed_size (layout_type (), size1_, size2_), value_type ());
}
// Element access
BOOST_UBLAS_INLINE
const_reference operator () (size_type i, size_type j) const {
BOOST_UBLAS_CHECK (i < size1_, bad_index ());
BOOST_UBLAS_CHECK (j < size2_, bad_index ());
if (triangular_type::other (i, j))
return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
else if (triangular_type::one (i, j))
return one_;
else
return zero_;
}
BOOST_UBLAS_INLINE
reference at_element (size_type i, size_type j) {
BOOST_UBLAS_CHECK (i < size1_, bad_index ());
BOOST_UBLAS_CHECK (j < size2_, bad_index ());
return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
}
BOOST_UBLAS_INLINE
reference operator () (size_type i, size_type j) {
BOOST_UBLAS_CHECK (i < size1_, bad_index ());
BOOST_UBLAS_CHECK (j < size2_, bad_index ());
if (!triangular_type::other (i, j)) {
bad_index ().raise ();
// NEVER reached
}
return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
}
// Element assignment
BOOST_UBLAS_INLINE
reference insert_element (size_type i, size_type j, const_reference t) {
return (operator () (i, j) = t);
}
BOOST_UBLAS_INLINE
void erase_element (size_type i, size_type j) {
operator () (i, j) = value_type/*zero*/();
}
// Zeroing
BOOST_UBLAS_INLINE
void clear () {
// data ().clear ();
std::fill (data ().begin (), data ().end (), value_type/*zero*/());
}
// Assignment
BOOST_UBLAS_INLINE
triangular_matrix &operator = (const triangular_matrix &m) {
size1_ = m.size1_;
size2_ = m.size2_;
data () = m.data ();
return *this;
}
BOOST_UBLAS_INLINE
triangular_matrix &assign_temporary (triangular_matrix &m) {
swap (m);
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix &operator = (const matrix_expression<AE> &ae) {
self_type temporary (ae);
return assign_temporary (temporary);
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix &assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_assign> (*this, ae);
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix& operator += (const matrix_expression<AE> &ae) {
self_type temporary (*this + ae);
return assign_temporary (temporary);
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix &plus_assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_plus_assign> (*this, ae);
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix& operator -= (const matrix_expression<AE> &ae) {
self_type temporary (*this - ae);
return assign_temporary (temporary);
}
template<class AE>
BOOST_UBLAS_INLINE
triangular_matrix &minus_assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_minus_assign> (*this, ae);
return *this;
}
template<class AT>
BOOST_UBLAS_INLINE
triangular_matrix& operator *= (const AT &at) {
matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
return *this;
}
template<class AT>
BOOST_UBLAS_INLINE
triangular_matrix& operator /= (const AT &at) {
matrix_assign_scalar<scalar_divides_assign> (*this, at);
return *this;
}
// Swapping
BOOST_UBLAS_INLINE
void swap (triangular_matrix &m) {
if (this != &m) {
// BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ());
std::swap (size1_, m.size1_);
std::swap (size2_, m.size2_);
data ().swap (m.data ());
}
}
BOOST_UBLAS_INLINE
friend void swap (triangular_matrix &m1, triangular_matrix &m2) {
m1.swap (m2);
}
// Iterator types
#ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
#else
class const_iterator1;
class iterator1;
class const_iterator2;
class iterator2;
#endif
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base1<iterator1> reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
typedef reverse_iterator_base2<iterator2> reverse_iterator2;
// Element lookup
BOOST_UBLAS_INLINE
const_iterator1 find1 (int rank, size_type i, size_type j) const {
if (rank == 1)
i = triangular_type::restrict1 (i, j, size1_, size2_);
if (rank == 0)
i = triangular_type::global_restrict1 (i, size1_, j, size2_);
return const_iterator1 (*this, i, j);
}
BOOST_UBLAS_INLINE
iterator1 find1 (int rank, size_type i, size_type j) {
if (rank == 1)
i = triangular_type::mutable_restrict1 (i, j, size1_, size2_);
if (rank == 0)
i = triangular_type::global_mutable_restrict1 (i, size1_, j, size2_);
return iterator1 (*this, i, j);
}
BOOST_UBLAS_INLINE
const_iterator2 find2 (int rank, size_type i, size_type j) const {
if (rank == 1)
j = triangular_type::restrict2 (i, j, size1_, size2_);
if (rank == 0)
j = triangular_type::global_restrict2 (i, size1_, j, size2_);
return const_iterator2 (*this, i, j);
}
BOOST_UBLAS_INLINE
iterator2 find2 (int rank, size_type i, size_type j) {
if (rank == 1)
j = triangular_type::mutable_restrict2 (i, j, size1_, size2_);
if (rank == 0)
j = triangular_type::global_mutable_restrict2 (i, size1_, j, size2_);
return iterator2 (*this, i, j);
}
// Iterators simply are indices.
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class const_iterator1:
public container_const_reference<triangular_matrix>,
public random_access_iterator_base<packed_random_access_iterator_tag,
const_iterator1, value_type> {
public:
typedef typename triangular_matrix::value_type value_type;
typedef typename triangular_matrix::difference_type difference_type;
typedef typename triangular_matrix::const_reference reference;
typedef const typename triangular_matrix::pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
BOOST_UBLAS_INLINE
const_iterator1 ():
container_const_reference<self_type> (), it1_ (), it2_ () {}
BOOST_UBLAS_INLINE
const_iterator1 (const self_type &m, size_type it1, size_type it2):
container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
BOOST_UBLAS_INLINE
const_iterator1 (const iterator1 &it):
container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
// Arithmetic
BOOST_UBLAS_INLINE
const_iterator1 &operator ++ () {
++ it1_;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator1 &operator -- () {
-- it1_;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator1 &operator += (difference_type n) {
it1_ += n;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator1 &operator -= (difference_type n) {
it1_ -= n;
return *this;
}
BOOST_UBLAS_INLINE
difference_type operator - (const const_iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ - it.it1_;
}
// Dereference
BOOST_UBLAS_INLINE
const_reference operator * () const {
return (*this) () (it1_, it2_);
}
BOOST_UBLAS_INLINE
const_reference operator [] (difference_type n) const {
return *(*this + n);
}
#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 begin () const {
return (*this) ().find2 (1, it1_, 0);
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 cbegin () const {
return begin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 end () const {
return (*this) ().find2 (1, it1_, (*this) ().size2 ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 cend () const {
return end ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 rbegin () const {
return const_reverse_iterator2 (end ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 crbegin () const {
return rbegin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 rend () const {
return const_reverse_iterator2 (begin ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 crend () const {
return rend ();
}
#endif
// Indices
BOOST_UBLAS_INLINE
size_type index1 () const {
return it1_;
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it2_;
}
// Assignment
BOOST_UBLAS_INLINE
const_iterator1 &operator = (const const_iterator1 &it) {
container_const_reference<self_type>::assign (&it ());
it1_ = it.it1_;
it2_ = it.it2_;
return *this;
}
// Comparison
BOOST_UBLAS_INLINE
bool operator == (const const_iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ == it.it1_;
}
BOOST_UBLAS_INLINE
bool operator < (const const_iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ < it.it1_;
}
private:
size_type it1_;
size_type it2_;
};
#endif
BOOST_UBLAS_INLINE
const_iterator1 begin1 () const {
return find1 (0, 0, 0);
}
BOOST_UBLAS_INLINE
const_iterator1 cbegin1 () const {
return begin1 ();
}
BOOST_UBLAS_INLINE
const_iterator1 end1 () const {
return find1 (0, size1_, 0);
}
BOOST_UBLAS_INLINE
const_iterator1 cend1 () const {
return end1 ();
}
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class iterator1:
public container_reference<triangular_matrix>,
public random_access_iterator_base<packed_random_access_iterator_tag,
iterator1, value_type> {
public:
typedef typename triangular_matrix::value_type value_type;
typedef typename triangular_matrix::difference_type difference_type;
typedef typename triangular_matrix::reference reference;
typedef typename triangular_matrix::pointer pointer;
typedef iterator2 dual_iterator_type;
typedef reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
BOOST_UBLAS_INLINE
iterator1 ():
container_reference<self_type> (), it1_ (), it2_ () {}
BOOST_UBLAS_INLINE
iterator1 (self_type &m, size_type it1, size_type it2):
container_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
// Arithmetic
BOOST_UBLAS_INLINE
iterator1 &operator ++ () {
++ it1_;
return *this;
}
BOOST_UBLAS_INLINE
iterator1 &operator -- () {
-- it1_;
return *this;
}
BOOST_UBLAS_INLINE
iterator1 &operator += (difference_type n) {
it1_ += n;
return *this;
}
BOOST_UBLAS_INLINE
iterator1 &operator -= (difference_type n) {
it1_ -= n;
return *this;
}
BOOST_UBLAS_INLINE
difference_type operator - (const iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ - it.it1_;
}
// Dereference
BOOST_UBLAS_INLINE
reference operator * () const {
return (*this) () (it1_, it2_);
}
BOOST_UBLAS_INLINE
reference operator [] (difference_type n) const {
return *(*this + n);
}
#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
iterator2 begin () const {
return (*this) ().find2 (1, it1_, 0);
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
iterator2 end () const {
return (*this) ().find2 (1, it1_, (*this) ().size2 ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
reverse_iterator2 rbegin () const {
return reverse_iterator2 (end ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
reverse_iterator2 rend () const {
return reverse_iterator2 (begin ());
}
#endif
// Indices
BOOST_UBLAS_INLINE
size_type index1 () const {
return it1_;
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it2_;
}
// Assignment
BOOST_UBLAS_INLINE
iterator1 &operator = (const iterator1 &it) {
container_reference<self_type>::assign (&it ());
it1_ = it.it1_;
it2_ = it.it2_;
return *this;
}
// Comparison
BOOST_UBLAS_INLINE
bool operator == (const iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ == it.it1_;
}
BOOST_UBLAS_INLINE
bool operator < (const iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it2_ == it.it2_, external_logic ());
return it1_ < it.it1_;
}
private:
size_type it1_;
size_type it2_;
friend class const_iterator1;
};
#endif
BOOST_UBLAS_INLINE
iterator1 begin1 () {
return find1 (0, 0, 0);
}
BOOST_UBLAS_INLINE
iterator1 end1 () {
return find1 (0, size1_, 0);
}
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class const_iterator2:
public container_const_reference<triangular_matrix>,
public random_access_iterator_base<packed_random_access_iterator_tag,
const_iterator2, value_type> {
public:
typedef typename triangular_matrix::value_type value_type;
typedef typename triangular_matrix::difference_type difference_type;
typedef typename triangular_matrix::const_reference reference;
typedef const typename triangular_matrix::pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
BOOST_UBLAS_INLINE
const_iterator2 ():
container_const_reference<self_type> (), it1_ (), it2_ () {}
BOOST_UBLAS_INLINE
const_iterator2 (const self_type &m, size_type it1, size_type it2):
container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
BOOST_UBLAS_INLINE
const_iterator2 (const iterator2 &it):
container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}
// Arithmetic
BOOST_UBLAS_INLINE
const_iterator2 &operator ++ () {
++ it2_;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator2 &operator -- () {
-- it2_;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator2 &operator += (difference_type n) {
it2_ += n;
return *this;
}
BOOST_UBLAS_INLINE
const_iterator2 &operator -= (difference_type n) {
it2_ -= n;
return *this;
}
BOOST_UBLAS_INLINE
difference_type operator - (const const_iterator2 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
return it2_ - it.it2_;
}
// Dereference
BOOST_UBLAS_INLINE
const_reference operator * () const {
return (*this) () (it1_, it2_);
}
BOOST_UBLAS_INLINE
const_reference operator [] (difference_type n) const {
return *(*this + n);
}
#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 begin () const {
return (*this) ().find1 (1, 0, it2_);
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 cbegin () const {
return begin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 end () const {
return (*this) ().find1 (1, (*this) ().size1 (), it2_);
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 cend () const {
return end ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 rbegin () const {
return const_reverse_iterator1 (end ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 crbegin () const {
return rbegin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 rend () const {
return const_reverse_iterator1 (begin ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 crend () const {
return rend ();
}
#endif
// Indices
BOOST_UBLAS_INLINE
size_type index1 () const {
return it1_;
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it2_;
}
// Assignment
BOOST_UBLAS_INLINE
const_iterator2 &operator = (const const_iterator2 &it) {
container_const_reference<self_type>::assign (&it ());
it1_ = it.it1_;
it2_ = it.it2_;
return *this;
}
// Comparison
BOOST_UBLAS_INLINE
bool operator == (const const_iterator2 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
return it2_ == it.it2_;
}
BOOST_UBLAS_INLINE
bool operator < (const const_iterator2 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
BOOST_UBLAS_CHECK (it1_ == it.it1_, external_logic ());
return it2_ < it.it2_;
}
private:
size_type it1_;
size_type it2_;
};
#endif
BOOST_UBLAS_INLINE
const_iterator2 begin2 () const {
return find2 (0, 0, 0);
}
BOOST_UBLAS_INLINE
const_iterator2 cbegin2 () const {
return begin2 ();
}
BOOST_UBLAS_INLINE
const_iterator2 end2 () const {
return find2 (0, 0, size2_);
}
BOOST_UBLAS_INLINE
const_iterator2 cend2 () const {
return end2 ();
}
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class iterator2:
public container_reference<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 crbegin1 () const {
return rbegin1 ();
}
BOOST_UBLAS_INLINE
const_reverse_iterator1 rend1 () const {
return const_reverse_iterator1 (begin1 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator1 crend1 () const {
return rend1 ();
}
BOOST_UBLAS_INLINE
reverse_iterator1 rbegin1 () {
return reverse_iterator1 (end1 ());
}
BOOST_UBLAS_INLINE
reverse_iterator1 rend1 () {
return reverse_iterator1 (begin1 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 rbegin2 () const {
return const_reverse_iterator2 (end2 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 crbegin2 () const {
return rbegin2 ();
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 rend2 () const {
return const_reverse_iterator2 (begin2 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 crend2 () const {
return rend2 ();
}
BOOST_UBLAS_INLINE
reverse_iterator2 rbegin2 () {
return reverse_iterator2 (end2 ());
}
BOOST_UBLAS_INLINE
reverse_iterator2 rend2 () {
return reverse_iterator2 (begin2 ());
}
private:
size_type size1_;
size_type size2_;
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 cbegin () const {
return begin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 end () const {
return (*this) ().find2 (1, index1 (), (*this) ().size2 ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator2 cend () const {
return end ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 rbegin () const {
return const_reverse_iterator2 (end ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 crbegin () const {
return rbegin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 rend () const {
return const_reverse_iterator2 (begin ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator2 crend () const {
return rend ();
}
#endif
// Indices
BOOST_UBLAS_INLINE
size_type index1 () const {
return it1_.index1 ();
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it1_.index2 ();
}
// Assignment
BOOST_UBLAS_INLINE
const_iterator1 &operator = (const const_iterator1 &it) {
container_const_reference<self_type>::assign (&it ());
it1_ = it.it1_;
return *this;
}
// Comparison
BOOST_UBLAS_INLINE
bool operator == (const const_iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
return it1_ == it.it1_;
}
BOOST_UBLAS_INLINE
bool operator < (const const_iterator1 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
return it1_ < it.it1_;
}
private:
const_subiterator1_type it1_;
};
#endif
BOOST_UBLAS_INLINE
const_iterator1 begin1 () const {
return find1 (0, 0, 0);
}
BOOST_UBLAS_INLINE
const_iterator1 cbegin1 () const {
return begin1 ();
}
BOOST_UBLAS_INLINE
const_iterator1 end1 () const {
return find1 (0, size1 (), 0);
}
BOOST_UBLAS_INLINE
const_iterator1 cend1 () const {
return end1 ();
}
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class iterator1:
public container_reference<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 cbegin () const {
return begin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 end () const {
return (*this) ().find1 (1, (*this) ().size1 (), index2 ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_iterator1 cend () const {
return end ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 rbegin () const {
return const_reverse_iterator1 (end ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 crbegin () const {
return rbegin ();
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 rend () const {
return const_reverse_iterator1 (begin ());
}
BOOST_UBLAS_INLINE
#ifdef BOOST_UBLAS_MSVC_NESTED_CLASS_RELATION
typename self_type::
#endif
const_reverse_iterator1 crend () const {
return rend ();
}
#endif
// Indices
BOOST_UBLAS_INLINE
size_type index1 () const {
return it2_.index1 ();
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it2_.index2 ();
}
// Assignment
BOOST_UBLAS_INLINE
const_iterator2 &operator = (const const_iterator2 &it) {
container_const_reference<self_type>::assign (&it ());
it2_ = it.it2_;
return *this;
}
// Comparison
BOOST_UBLAS_INLINE
bool operator == (const const_iterator2 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
return it2_ == it.it2_;
}
BOOST_UBLAS_INLINE
bool operator < (const const_iterator2 &it) const {
BOOST_UBLAS_CHECK (&(*this) () == &it (), external_logic ());
return it2_ < it.it2_;
}
private:
const_subiterator2_type it2_;
};
#endif
BOOST_UBLAS_INLINE
const_iterator2 begin2 () const {
return find2 (0, 0, 0);
}
BOOST_UBLAS_INLINE
const_iterator2 cbegin2 () const {
return begin2 ();
}
BOOST_UBLAS_INLINE
const_iterator2 end2 () const {
return find2 (0, 0, size2 ());
}
BOOST_UBLAS_INLINE
const_iterator2 cend2 () const {
return end2 ();
}
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class iterator2:
public container_reference<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 crbegin1 () const {
return rbegin1 ();
}
BOOST_UBLAS_INLINE
const_reverse_iterator1 rend1 () const {
return const_reverse_iterator1 (begin1 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator1 crend1 () const {
return rend1 ();
}
BOOST_UBLAS_INLINE
reverse_iterator1 rbegin1 () {
return reverse_iterator1 (end1 ());
}
BOOST_UBLAS_INLINE
reverse_iterator1 rend1 () {
return reverse_iterator1 (begin1 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 rbegin2 () const {
return const_reverse_iterator2 (end2 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 crbegin2 () const {
return rbegin2 ();
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 rend2 () const {
return const_reverse_iterator2 (begin2 ());
}
BOOST_UBLAS_INLINE
const_reverse_iterator2 crend2 () const {
return rend2 ();
}
BOOST_UBLAS_INLINE
reverse_iterator2 rbegin2 () {
return reverse_iterator2 (end2 ());
}
BOOST_UBLAS_INLINE
reverse_iterator2 rend2 () {
return reverse_iterator2 (begin2 ());
}
private:
matrix_closure_type data_;
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::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::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (size_type n = 0; n < size; ++ n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n) /= e1 () (n, n);
if (t != value_type/*zero*/()) {
typename E1::const_iterator1 it1e1 (e1 ().find1 (1, n + 1, n));
typename E1::const_iterator1 it1e1_end (e1 ().find1 (1, e1 ().size1 (), n));
while (it1e1 != it1e1_end)
e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
}
}
}
// Dense (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag, row_major_tag, dense_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (size_type n = 0; n < size; ++ n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n) /= e1 () (n, n);
if (t != value_type/*zero*/()) {
for (size_type m = n + 1; m < size; ++ m)
e2 () (m) -= e1 () (m, n) * t;
}
}
}
// Packed (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag, row_major_tag, packed_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (size_type n = 0; n < size; ++ n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n);
typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, 0));
typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, n));
while (it2e1 != it2e1_end) {
t -= *it2e1 * e2 () (it2e1.index2());
++ it2e1;
}
e2() (n) = t / e1 () (n, n);
}
}
// Sparse (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag, row_major_tag, unknown_storage_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (size_type n = 0; n < size; ++ n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n);
typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, 0));
typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, n));
while (it2e1 != it2e1_end) {
t -= *it2e1 * e2 () (it2e1.index2());
++ it2e1;
}
e2() (n) = t / e1 () (n, n);
}
}
// Redirectors :-)
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag, column_major_tag) {
typedef typename E1::storage_category storage_category;
inplace_solve (e1, e2,
lower_tag (), column_major_tag (), storage_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag, row_major_tag) {
typedef typename E1::storage_category storage_category;
inplace_solve (e1, e2,
lower_tag (), row_major_tag (), storage_category ());
}
// Dispatcher
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
lower_tag) {
typedef typename E1::orientation_category orientation_category;
inplace_solve (e1, e2,
lower_tag (), orientation_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
unit_lower_tag) {
typedef typename E1::orientation_category orientation_category;
inplace_solve (triangular_adaptor<const E1, unit_lower> (e1 ()), e2,
unit_lower_tag (), orientation_category ());
}
// Dense (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, column_major_tag, dense_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (difference_type n = size - 1; n >= 0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n) /= e1 () (n, n);
if (t != value_type/*zero*/()) {
for (difference_type m = n - 1; m >= 0; -- m)
e2 () (m) -= e1 () (m, n) * t;
}
}
}
// Packed (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, column_major_tag, packed_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (difference_type n = size - 1; n >= 0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n) /= e1 () (n, n);
if (t != value_type/*zero*/()) {
typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
while (it1e1 != it1e1_rend) {
e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
}
}
}
}
// Sparse (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, column_major_tag, unknown_storage_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e2 ().size ();
for (difference_type n = size - 1; n >= 0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n) /= e1 () (n, n);
if (t != value_type/*zero*/()) {
typename E1::const_reverse_iterator1 it1e1 (e1 ().find1 (1, n, n));
typename E1::const_reverse_iterator1 it1e1_rend (e1 ().find1 (1, 0, n));
while (it1e1 != it1e1_rend) {
e2 () (it1e1.index1 ()) -= *it1e1 * t, ++ it1e1;
}
}
}
}
// Dense (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, row_major_tag, dense_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e1 ().size1 ();
for (difference_type n = size-1; n >=0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n);
for (difference_type m = n + 1; m < static_cast<difference_type>(e1 ().size2()); ++ m) {
t -= e1 () (n, m) * e2 () (m);
}
e2() (n) = t / e1 () (n, n);
}
}
// Packed (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, row_major_tag, packed_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e1 ().size1 ();
for (difference_type n = size-1; n >=0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n);
typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, n+1));
typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, e1 ().size2 ()));
while (it2e1 != it2e1_end) {
t -= *it2e1 * e2 () (it2e1.index2());
++ it2e1;
}
e2() (n) = t / e1 () (n, n);
}
}
// Sparse (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, row_major_tag, unknown_storage_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename E2::value_type value_type;
BOOST_UBLAS_CHECK (e1 ().size1 () == e1 ().size2 (), bad_size ());
BOOST_UBLAS_CHECK (e1 ().size2 () == e2 ().size (), bad_size ());
size_type size = e1 ().size1 ();
for (difference_type n = size-1; n >=0; -- n) {
#ifndef BOOST_UBLAS_SINGULAR_CHECK
BOOST_UBLAS_CHECK (e1 () (n, n) != value_type/*zero*/(), singular ());
#else
if (e1 () (n, n) == value_type/*zero*/())
singular ().raise ();
#endif
value_type t = e2 () (n);
typename E1::const_iterator2 it2e1 (e1 ().find2 (1, n, n+1));
typename E1::const_iterator2 it2e1_end (e1 ().find2 (1, n, e1 ().size2 ()));
while (it2e1 != it2e1_end) {
t -= *it2e1 * e2 () (it2e1.index2());
++ it2e1;
}
e2() (n) = t / e1 () (n, n);
}
}
// Redirectors :-)
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, column_major_tag) {
typedef typename E1::storage_category storage_category;
inplace_solve (e1, e2,
upper_tag (), column_major_tag (), storage_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag, row_major_tag) {
typedef typename E1::storage_category storage_category;
inplace_solve (e1, e2,
upper_tag (), row_major_tag (), storage_category ());
}
// Dispatcher
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
upper_tag) {
typedef typename E1::orientation_category orientation_category;
inplace_solve (e1, e2,
upper_tag (), orientation_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, vector_expression<E2> &e2,
unit_upper_tag) {
typedef typename E1::orientation_category orientation_category;
inplace_solve (triangular_adaptor<const E1, unit_upper> (e1 ()), e2,
unit_upper_tag (), orientation_category ());
}
template<class E1, class E2, class C>
BOOST_UBLAS_INLINE
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
C) {
typename matrix_vector_solve_traits<E1, E2>::result_type r (e2);
inplace_solve (e1, r, C ());
return r;
}
// Redirectors :-)
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
lower_tag, row_major_tag) {
typedef typename E2::storage_category storage_category;
inplace_solve (trans(e2), e1,
upper_tag (), column_major_tag (), storage_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
lower_tag, column_major_tag) {
typedef typename E2::storage_category storage_category;
inplace_solve (trans (e2), e1,
upper_tag (), row_major_tag (), storage_category ());
}
// Dispatcher
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
lower_tag) {
typedef typename E2::orientation_category orientation_category;
inplace_solve (e1, e2,
lower_tag (), orientation_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
unit_lower_tag) {
typedef typename E2::orientation_category orientation_category;
inplace_solve (e1, triangular_adaptor<const E2, unit_lower> (e2 ()),
unit_lower_tag (), orientation_category ());
}
// Redirectors :-)
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
upper_tag, row_major_tag) {
typedef typename E2::storage_category storage_category;
inplace_solve (trans(e2), e1,
lower_tag (), column_major_tag (), storage_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
upper_tag, column_major_tag) {
typedef typename E2::storage_category storage_category;
inplace_solve (trans (e2), e1,
lower_tag (), row_major_tag (), storage_category ());
}
// Dispatcher
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
upper_tag) {
typedef typename E2::orientation_category orientation_category;
inplace_solve (e1, e2,
upper_tag (), orientation_category ());
}
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (vector_expression<E1> &e1, const matrix_expression<E2> &e2,
unit_upper_tag) {
typedef typename E2::orientation_category orientation_category;
inplace_solve (e1, triangular_adaptor<const E2, unit_upper> (e2 ()),
unit_upper_tag (), orientation_category ());
}
template<class E1, class E2, class C>
BOOST_UBLAS_INLINE
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
C) {
typename matrix_vector_solve_traits<E1, E2>::result_type r (e1);
inplace_solve (r, e2, C ());
return r;
}
template<class E1, class E2>
struct matrix_matrix_solve_traits {
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
typedef matrix<promote_type> result_type;
};
// Operations:
// k * n * (n - 1) / 2 + k * n = k * n * (n + 1) / 2 multiplications,
// k * n * (n - 1) / 2 additions
// Dense (proxy) case
template<class E1, class E2>
BOOST_UBLAS_INLINE
void inplace_solve (const matrix_expression<E1> &e1, matrix_expression<E2> &e2,
lower_tag, dense_proxy_tag) {
typedef typename E2::size_type size_type;
typedef typename E2::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::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
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