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From: James N. Knight (nate_at_[hidden])
Date: 2006-11-10 13:30:42
I've seen this discussed on the message board a few times before. So I thought I would post
the code I've been using. I hope this is okay.
The attached file diagonal_from_vector.hpp includes some helpful code for
dealing with diagonal matrices. The diagonal_vector_adaptor<V> creates
a matrix adaptor that is a square diagonal matrix view with the vector
on the diagonal.
The free function diagm takes a vector and returns a diagonal_vector_adaptor.
The free function diag takes a matrix and returns a matrix_vector_slice corresponding
to the diagonal.
I've also included a the file ublas_banded1.hpp which should go in bindings/traits
and allows a diagonal_matrix to be used in place of a vector. In other words, you could
do something like lapack::gesdd(A,S,U,Vt); where S is a diagonal_matrix and not a vector
which is what is expected by the call. This however, might not really be needed as
the call could be done like lapack::gesdd(A,diag(S),U,Vt) without the new traits file.
Any thoughts?
Nate
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Sample Usage:
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/banded.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <iostream>
#include "diagonal_from_vector.hpp"
namespace ublas = boost::numeric::ublas;
int main(){
typedef ublas::vector<double> vector;
typedef ublas::matrix<double, ublas::column_major> matrix;
vector s(5);
s(0) = 1.2; s(1) = 2.2; s(2) = 3.3; s(3) = 5; s(4) = -1;
std::cout << "s = " << s << std::endl;
std::cout << "diag(s) = " << ublas::diagm(s) << std::endl;
std::cout << "diag(diagm(s)) = " << ublas::diag(ublas::diagm(s)) << std::endl;
std::cout << "diagm(2*s) = " << ublas::diagm(2*s) << std::endl;
ublas::diagonal_matrix<double> m(5,5);
ublas::diag(m) = s;
std::cout << "diag(m) = s; m = " << m << std::endl;
}
/*
*
* Copyright (c) 2002, 2003 Kresimir Fresl, Toon Knapen and Karl Meerbergen
*
* Permission to copy, modify, use and distribute this software
* for any non-commercial or commercial purpose is granted provided
* that this license appear on all copies of the software source code.
*
* Authors assume no responsibility whatsoever for its use and makes
* no guarantees about its quality, correctness or reliability.
*
* KF acknowledges the support of the Faculty of Civil Engineering,
* University of Zagreb, Croatia.
*
*/
#ifndef BOOST_NUMERIC_BINDINGS_TRAITS_UBLAS_BANDED1_H
#define BOOST_NUMERIC_BINDINGS_TRAITS_UBLAS_BANDED1_H
#include <boost/numeric/bindings/traits/traits.hpp>
#ifndef BOOST_NUMERIC_BINDINGS_POOR_MANS_TRAITS
#ifndef BOOST_UBLAS_HAVE_BINDINGS
# include <boost/numeric/ublas/banded.hpp>
#endif
#include <boost/numeric/bindings/traits/detail/ublas_ordering.hpp>
#if defined (BOOST_NUMERIC_BINDINGS_FORTRAN) || !defined (BOOST_NUMERIC_BINDINGS_NO_STRUCTURE_CHECK)
# include <boost/static_assert.hpp>
# include <boost/type_traits/same_traits.hpp>
#endif
namespace boost { namespace numeric { namespace bindings { namespace traits {
// ublas::matrix_banded<>
// When orientation_category==row_major_tag then the ublas banded format corresponds to
// the LAPACK band format.
// Specialization using matrix_detail_traits so that we can specialize for
// matrix_detail_traits< banded<T, F, ArrT>, banded<T, F, ArrT> >
// matrix_detail_traits< banded<T, F, ArrT>, banded<T, F, ArrT> const >
// at once.
template <typename T, typename F, typename ArrT, typename M>
struct vector_detail_traits< boost::numeric::ublas::diagonal_matrix<T, F, ArrT>, M >
{
#ifndef BOOST_NUMERIC_BINDINGS_NO_SANITY_CHECK
BOOST_STATIC_ASSERT( (boost::is_same<boost::numeric::ublas::diagonal_matrix<T, F, ArrT>, typename boost::remove_const<M>::type>::value) );
#endif
#ifdef BOOST_NUMERIC_BINDINGS_FORTRAN
BOOST_STATIC_ASSERT((boost::is_same<
typename F::orientation_category,
boost::numeric::ublas::row_major_tag
>::value));
#endif
typedef boost::numeric::ublas::diagonal_matrix<T, F, ArrT> identifier_type ;
typedef M vector_type;
typedef T value_type;
typedef typename detail::generate_const<M,T>::type* pointer;
static pointer storage (vector_type& m) {
typedef typename detail::generate_const<M,ArrT>::type array_type ;
return vector_traits<array_type>::storage (m.data());
}
static int size (vector_type& m) { return m.size1(); }
static int lower_bandwidth (vector_type& m) { return m.lower() ; }
static int upper_bandwidth (vector_type& m) { return m.upper() ; }
static int storage_size (vector_type& m) { return size1 (m) * size2 (m); }
static int leading_dimension (vector_type& m) {
// g++ 2.95.4 and 3.0.4 (with -pedantic) dislike
// identifier_type::functor_type::size2()
return lower_bandwidth(m) + upper_bandwidth(m) + 1 ;
}
// stride1 == distance (m (i, j), m (i+1, j))
static int stride (vector_type& m) {
typedef typename identifier_type::orientation_category orientation_category;
typedef typename detail::ublas_ordering<orientation_category>::functor_type functor_t ;
return functor_t::one2 ( std::max(m.size1(), m.size2()), leading_dimension(m)-1 ) ;
}
// stride2 == distance (m (i, j), m (i, j+1))
static int stride2 (vector_type& m) {
typedef typename identifier_type::orientation_category orientation_category;
typedef typename detail::ublas_ordering<orientation_category>::functor_type functor_t ;
return functor_t::one1 ( std::max(m.size1(), m.size2()), leading_dimension(m)-1 ) ;
}
};
}}}}
#endif // BOOST_NUMERIC_BINDINGS_POOR_MANS_TRAITS
#endif // BOOST_NUMERIC_BINDINGS_TRAITS_UBLAS_BANDED_H
#ifndef _BOOST_UBLAS_DIAGONAL_FROM_VECTOR_
#define _BOOST_UBLAS_DIAGONAL_FROM_VECTOR_
// create by James Knight 10/18/2006
// diagonal_vector_adaptor is a modified version of banded_adaptor in banded.hpp
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/detail/temporary.hpp>
// Iterators based on ideas of Jeremy Siek
namespace boost { namespace numeric { namespace ublas {
template<class M>
class diagonal_vector_adaptor :
public matrix_expression<diagonal_vector_adaptor<M> > {
typedef diagonal_vector_adaptor<M> 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 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;
// Construction and destruction
BOOST_UBLAS_INLINE
diagonal_vector_adaptor(matrix_type &data):
matrix_expression<self_type> (),
data_ (data), lower_ (0), upper_ (0) {}
BOOST_UBLAS_INLINE
diagonal_vector_adaptor (const diagonal_vector_adaptor &m):
matrix_expression<self_type> (),
data_ (m.data_), lower_ (m.lower_), upper_ (m.upper_) {}
// Accessors
BOOST_UBLAS_INLINE
size_type size1 () const {
return data_.size ();
}
BOOST_UBLAS_INLINE
size_type size2 () const {
return data_.size ();
}
BOOST_UBLAS_INLINE
size_type lower () const {
return size_type();
}
BOOST_UBLAS_INLINE
size_type upper () const {
return size_type();
}
// 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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
if (i == j)
return data () (i);
#else
if (i == j)
return data () (i);
#endif
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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
if (i == j)
return data () (i);
#else
if (i == j)
return data () (i);
#endif
#ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER
bad_index ().raise ();
#endif
return const_cast<reference>(zero_);
}
#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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
if (i == j)
return data () (i);
#else
if (i == j)
return data () (i);
#endif
#ifndef BOOST_UBLAS_REFERENCE_CONST_MEMBER
bad_index ().raise ();
#endif
return const_cast<reference>(zero_);
}
#endif
// Assignment
BOOST_UBLAS_INLINE
diagonal_vector_adaptor &operator = (const diagonal_vector_adaptor &m) {
matrix_assign<scalar_assign> (*this, m);
return *this;
}
BOOST_UBLAS_INLINE
diagonal_vector_adaptor &assign_temporary (diagonal_vector_adaptor &m) {
*this = m;
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
diagonal_vector_adaptor &operator = (const matrix_expression<AE> &ae) {
matrix_assign<scalar_assign> (*this, matrix<value_type> (ae));
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
diagonal_vector_adaptor &assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_assign> (*this, ae);
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
diagonal_vector_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
diagonal_vector_adaptor &plus_assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_plus_assign> (*this, ae);
return *this;
}
template<class AE>
BOOST_UBLAS_INLINE
diagonal_vector_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
diagonal_vector_adaptor &minus_assign (const matrix_expression<AE> &ae) {
matrix_assign<scalar_minus_assign> (*this, ae);
return *this;
}
template<class AT>
BOOST_UBLAS_INLINE
diagonal_vector_adaptor& operator *= (const AT &at) {
matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
return *this;
}
template<class AT>
BOOST_UBLAS_INLINE
diagonal_vector_adaptor& operator /= (const AT &at) {
matrix_assign_scalar<scalar_divides_assign> (*this, at);
return *this;
}
// Closure comparison
BOOST_UBLAS_INLINE
bool same_closure (const diagonal_vector_adaptor &ba) const {
return (*this).data ().same_closure (ba.data ());
}
// Swapping
BOOST_UBLAS_INLINE
void swap (diagonal_vector_adaptor &m) {
if (this != &m) {
BOOST_UBLAS_CHECK (lower_ == m.lower_, bad_size ());
BOOST_UBLAS_CHECK (upper_ == m.upper_, bad_size ());
matrix_swap<scalar_swap> (*this, m);
}
}
BOOST_UBLAS_INLINE
friend void swap (diagonal_vector_adaptor &m1, diagonal_vector_adaptor &m2) {
m1.swap (m2);
}
// Iterator types
private:
// Use the matrix iterator
typedef typename M::const_iterator const_subiterator1_type;
typedef typename boost::mpl::if_<boost::is_const<M>,
typename M::const_iterator,
typename M::iterator>::type subiterator1_type;
typedef typename M::const_iterator const_subiterator2_type;
typedef typename boost::mpl::if_<boost::is_const<M>,
typename M::const_iterator,
typename M::iterator>::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) {
size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
i = (std::max) (i, lower_i);
size_type upper_i = (std::min) (j + 1 + lower_, size1 ());
i = (std::min) (i, upper_i);
}
return const_iterator1 (*this, data ().find (i));
}
BOOST_UBLAS_INLINE
iterator1 find1 (int rank, size_type i, size_type j) {
if (rank == 1) {
size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
i = (std::max) (i, lower_i);
size_type upper_i = (std::min) (j + 1 + lower_, size1 ());
i = (std::min) (i, upper_i);
}
return iterator1 (*this, data ().find (i));
}
BOOST_UBLAS_INLINE
const_iterator2 find2 (int rank, size_type i, size_type j) const {
if (rank == 1) {
size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
j = (std::max) (j, lower_j);
size_type upper_j = (std::min) (i + 1 + upper_, size2 ());
j = (std::min) (j, upper_j);
}
return const_iterator2 (*this, data ().find (j));
}
BOOST_UBLAS_INLINE
iterator2 find2 (int rank, size_type i, size_type j) {
if (rank == 1) {
size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
j = (std::max) (j, lower_j);
size_type upper_j = (std::min) (i + 1 + upper_, size2 ());
j = (std::min) (j, upper_j);
}
return iterator2 (*this, data ().find (j));
}
// Iterators simply are indices.
#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
class const_iterator1:
public container_const_reference<diagonal_vector_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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
size_type k = (std::max) (i, j);
size_type l = (*this) ().lower () + j - i;
if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it1_;
#else
size_type k = j;
size_type l = (*this) ().upper () + i - j;
if (k < (*this) ().size2 () &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it1_;
#endif
return (*this) () (i, j);
}
#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_.index ();
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it1_.index ();
}
// 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<diagonal_vector_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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
size_type k = (std::max) (i, j);
size_type l = (*this) ().lower () + j - i;
if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it1_;
#else
size_type k = j;
size_type l = (*this) ().upper () + i - j;
if (k < (*this) ().size2 () &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it1_;
#endif
return (*this) () (i, j);
}
#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<diagonal_vector_adaptor>,
public random_access_iterator_base<packed_random_access_iterator_tag,
const_iterator2, value_type> {
public:
typedef typename iterator_restrict_traits<typename const_subiterator2_type::iterator_category,
packed_random_access_iterator_tag>::iterator_category iterator_category;
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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
size_type k = (std::max) (i, j);
size_type l = (*this) ().lower () + j - i;
if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it2_;
#else
size_type k = j;
size_type l = (*this) ().upper () + i - j;
if (k < (*this) ().size2 () &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it2_;
#endif
return (*this) () (i, j);
}
#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_.index ();
}
BOOST_UBLAS_INLINE
size_type index2 () const {
return it2_.index ();
}
// 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<diagonal_vector_adaptor>,
public random_access_iterator_base<typename iterator_restrict_traits<
typename subiterator2_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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
size_type k = (std::max) (i, j);
size_type l = (*this) ().lower () + j - i;
if (k < (std::max) ((*this) ().size1 (), (*this) ().size2 ()) &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it2_;
#else
size_type k = j;
size_type l = (*this) ().upper () + i - j;
if (k < (*this) ().size2 () &&
l < (*this) ().lower () + 1 + (*this) ().upper ())
return *it2_;
#endif
return (*this) () (i, j);
}
#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_;
size_type lower_;
size_type upper_;
typedef const value_type const_value_type;
static const_value_type zero_;
};
template<class M>
typename diagonal_vector_adaptor<M>::const_value_type diagonal_vector_adaptor<M>::zero_ = value_type/*zero*/();
template<class M>
BOOST_UBLAS_INLINE
matrix_vector_slice<M> diag(M &data) {
const typename M::size_type s = std::min(data.size1(),data.size2());
return matrix_vector_slice<M>(data, slice(0,1,s), slice(0,1,s));
};
template<class M>
BOOST_UBLAS_INLINE
const matrix_vector_slice<const M> diag(const M &data) {
const typename M::size_type s = std::min(data.size1(),data.size2());
return matrix_vector_slice<const M>(data, slice(0,1,s), slice(0,1,s));
};
template<class V>
BOOST_UBLAS_INLINE
diagonal_vector_adaptor<V> diagm(V& data) {
return diagonal_vector_adaptor<V>(data);
};
template<class V>
BOOST_UBLAS_INLINE
const diagonal_vector_adaptor<const V> diagm(const V& data) {
return diagonal_vector_adaptor<const V>(data);
};
}}}
#endif