The templated class matrix_expression<E>
forms the base
for all static derived matrix expression classes including class matrix
itself.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None.
None.
None.
Member | Description |
---|---|
const expression_type &operator () () const |
Returns a const reference of the expression.
|
expression_type &operator () () |
Returns a reference of the expression. |
// Base class for the Barton Nackman trick
template<class E>
struct matrix_expression {
typedef E expression_type;
typedef matrix_tag type_category;
// This class could define an common interface for all
// statically derived expression type classes.
// Due to a compiler deficiency - one can not reference class typedefs of E
// on MSVC 6.0 (error C2027) - we only implement the casts.
const expression_type &operator () () const;
expression_type &operator () ();
};
The templated class matrix_const_reference<E>
contains
a constant reference to a matrix expression.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_const_reference<E> >
Member | Description |
---|---|
matrix_const_reference (const expression_type
&e) |
Constructs a constant reference of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
Interface
template<class E>
class matrix_const_reference:
public matrix_expression<matrix_const_reference<E> > {
public:
typedef E expression_type;
typedef typename E::size_type size_type;
typedef typename E::difference_type difference_type;
typedef typename E::value_type value_type;
typedef typename E::const_reference const_reference;
typedef const_reference reference;
typedef typename E::const_pointer const_pointer;
typedef const_pointer pointer;
typedef typename E::orientation_category orientation_category;
typedef typename E::const_iterator1 const_iterator1_type;
typedef typename E::const_iterator2 const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_const_reference ();
matrix_const_reference (const expression_type &e);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression_type &expression () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
typedef const_iterator1_type const_iterator1;
typedef const_iterator1 iterator1;
typedef const_iterator2_type const_iterator2;
typedef const_iterator2 iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators are the iterators of the referenced expression.
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
The templated class matrix_reference<E>
contains a reference
to a matrix expression.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_reference<E> >
Member | Description |
---|---|
matrix_reference (expression_type &e)
|
Constructs a constant reference of the expression. |
void resize (size_type size1, size2) |
Resizes the expression to hold at most size1 rows
of size2 elements. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
reference operator () (size_type i, size_type
j) |
Returns a reference of the j -th element
in the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning
of the expression. |
iterator1 end1 () |
Returns a iterator1 pointing to the end
of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning
of the expression. |
iterator2 end2 () |
Returns a iterator2 pointing to the end
of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to
the beginning of the reversed expression. |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to
the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to
the beginning of the reversed expression. |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to
the end of the reversed expression. |
template<class E>
class matrix_reference:
public matrix_expression<matrix_reference<E> > {
public:
typedef E expression_type;
typedef typename E::size_type size_type;
typedef typename E::difference_type difference_type;
typedef typename E::value_type value_type;
typedef typename E::const_reference const_reference;
typedef typename E::reference reference;
typedef typename E::const_pointer const_pointer;
typedef typename E::pointer pointer;
typedef typename E::orientation_category orientation_category;
typedef typename E::const_iterator1 const_iterator1_type;
typedef typename E::iterator1 iterator1_type;
typedef typename E::const_iterator2 const_iterator2_type;
typedef typename E::iterator2 iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_reference ();
matrix_reference (expression_type &e);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression_type &expression () const;
expression_type &expression ();
// Resizing
void resize (size_type size1, size_type size2);
// Element access
const_reference operator () (size_type i, size_type j) const;
reference operator () (size_type i, size_type j);
typedef const_iterator1_type const_iterator1;
typedef iterator1_type iterator1;
typedef const_iterator2_type const_iterator2;
typedef iterator2_type iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
iterator1 find_first1 (int rank, size_type i, size_type j);
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
iterator1 find_last1 (int rank, size_type i, size_type j);
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
iterator2 find_first2 (int rank, size_type i, size_type j);
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
iterator2 find_last2 (int rank, size_type i, size_type j);
// Iterators are the iterators of the referenced expression.
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
iterator1 begin1 ();
iterator1 end1 ();
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
iterator2 begin2 ();
iterator2 end2 ();
// Reverse iterators
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
typedef reverse_iterator_base1<iterator1> reverse_iterator1;
reverse_iterator1 rbegin1 ();
reverse_iterator1 rend1 ();
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
typedef reverse_iterator_base2<iterator2> reverse_iterator2;
reverse_iterator2 rbegin2 ();
reverse_iterator2 rend2 ();
};
The templated classes matrix_unary1<E, F>
and
matrix_unary2<E, F>
describe unary matrix operations.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_unary1<E, F> >
and
matrix_expression<matrix_unary2<E, F> >
resp.
Member | Description |
---|---|
matrix_unary1 (const expression_type &e)
|
Constructs a description of the expression. |
matrix_unary2 (const expression_type &e) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
template<class E, class F>
class matrix_unary1:
public matrix_expression<matrix_unary1<E, F> > {
public:
typedef E expression_type;
typedef F functor_type;
typedef typename E::size_type size_type;
typedef typename E::difference_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_unary1<E, F> const_closure_type;
typedef typename E::orientation_category orientation_category;
typedef typename E::const_iterator1 const_iterator1_type;
typedef typename E::const_iterator2 const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_unary1 ();
matrix_unary1 (const expression_type &e);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression_type &expression () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators enhance the iterators of the referenced expression
// with the unary functor.
class const_iterator1:
public container_const_reference<matrix_unary1>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename E::const_iterator1::iterator_category iterator_category;
typedef typename matrix_unary1::difference_type difference_type;
typedef typename matrix_unary1::value_type value_type;
typedef typename matrix_unary1::const_reference reference;
typedef typename matrix_unary1::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_unary1 &mu, const const_iterator1_type &it);
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_unary1>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename E::const_iterator2::iterator_category iterator_category;
typedef typename matrix_unary1::difference_type difference_type;
typedef typename matrix_unary1::value_type value_type;
typedef typename matrix_unary1::const_reference reference;
typedef typename matrix_unary1::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_unary1 &mu, const const_iterator2_type &it);
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class E, class F>
class matrix_unary2:
public matrix_expression<matrix_unary2<E, F> > {
public:
typedef E expression_type;
typedef F functor_type;
typedef typename E::size_type size_type;
typedef typename E::difference_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_unary2<E, F> const_closure_type;
typedef typename E::orientation_category orientation_category;
typedef typename E::const_iterator1 const_iterator2_type;
typedef typename E::const_iterator2 const_iterator1_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_unary2 ();
matrix_unary2 (const expression_type &e);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression_type &expression () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators enhance the iterators of the referenced expression
// with the unary functor.
class const_iterator1:
public container_const_reference<matrix_unary2>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename E::const_iterator2::iterator_category iterator_category;
typedef typename matrix_unary2::difference_type difference_type;
typedef typename matrix_unary2::value_type value_type;
typedef typename matrix_unary2::const_reference reference;
typedef typename matrix_unary2::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_unary2 &mu, const const_iterator1_type &it);
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_unary2>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename E::const_iterator1::iterator_catego
ry iterator_category;
typedef typename matrix_unary2::difference_type difference_type;
typedef typename matrix_unary2::value_type value_type;
typedef typename matrix_unary2::const_reference reference;
typedef typename matrix_unary2::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_unary2 &mu, const const_iterator2_type &it);
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class E, class F>
struct matrix_unary1_traits {
typedef matrix_unary1<typename E::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (- m) [i] [j] = - m [i] [j]
template<class E>
typename matrix_unary1_traits<E, scalar_negate<typename E::value_type> >::result_type
operator - (const matrix_expression<E> &e);
// (conj m) [i] [j] = conj (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_conj<typename E::value_type> >::result_type
conj (const matrix_expression<E> &e);
// (real m) [i] [j] = real (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_real<typename E::value_type> >::result_type
real (const matrix_expression<E> &e);
// (imag m) [i] [j] = imag (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_imag<typename E::value_type> >::result_type
imag (const matrix_expression<E> &e);
template<class E, class F>
struct matrix_unary2_traits {
typedef matrix_unary2<typename E::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (trans m) [i] [j] = m [j] [i]
template<class E>
typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type
trans (const matrix_expression<E> &e);
// (herm m) [i] [j] = conj (m [j] [i])
template<class E>
typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type
herm (const matrix_expression<E> &e);
operator -
computes the additive inverse of a matrix expression.
conj
computes the complex conjugate of a matrix expression.
real
and imag
compute the real and imaginary parts
of a matrix expression. trans
computes the transpose of a matrix
expression. herm
computes the hermitian, i.e. the complex conjugate
of the transpose of a matrix expression.
Defined in the header matrix_expression.hpp.
E
is a model of
Matrix Expression
.None.
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<std::complex<double> > m (3, 3);
for (unsigned i = 0; i < m.size1 (); ++ i)
for (unsigned j = 0; j < m.size2 (); ++ j)
m (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
std::cout << - m << std::endl;
std::cout << conj (m) << std::endl;
std::cout << real (m) << std::endl;
std::cout << imag (m) << std::endl;
std::cout << trans (m) << std::endl;
std::cout << herm (m) << std::endl;
}
The templated class matrix_binary<E1, E2, F>
describes
a binary matrix operation.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first matrix expression. | |
E2 |
The type of the second matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_binary<E1, E2, F> >
.
Member | Description |
---|---|
matrix_binary (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
template<class E1, class E2, class F>
class matrix_binary:
public matrix_expression<matrix_binary<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_binary<E1, E2, F> const_closure_type;
typedef unknown_orientation_tag orientation_category;
typedef typename E1::const_iterator1 const_iterator11_type;
typedef typename E1::const_iterator2 const_iterator12_type;
typedef typename E2::const_iterator1 const_iterator21_type;
typedef typename E2::const_iterator2 const_iterator22_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_binary ();
matrix_binary (const E1 &e1, const E2 &e2);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators enhance the iterators of the referenced expression
// with the binary functor.
class const_iterator1:
public container_const_reference<matrix_binary>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
typename E2::const_iterator1::iterator_category>::iterator_category iterator_category;
typedef typename matrix_binary::difference_type difference_type;
typedef typename matrix_binary::value_type value_type;
typedef typename matrix_binary::const_reference reference;
typedef typename matrix_binary::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_binary &mb, size_type i, size_type j,
const const_iterator11_type &it1, const const_iterator11_type &it1_end,
const const_iterator21_type &it2, const const_iterator21_type &it2_end);
// Dense specializations
void increment (dense_random_access_iterator_tag);
void decrement (dense_random_access_iterator_tag);
value_type dereference (dense_random_access_iterator_tag) const;
// Packed specializations
void increment (packed_random_access_iterator_tag);
void decrement (packed_random_access_iterator_tag);
value_type dereference (packed_random_access_iterator_tag) const;
// Sparse specializations
void increment (sparse_bidirectional_iterator_tag);
void decrement (sparse_bidirectional_iterator_tag);
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_binary>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator2::iterator_category,
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
typedef typename matrix_binary::difference_type difference_type;
typedef typename matrix_binary::value_type value_type;
typedef typename matrix_binary::const_reference reference;
typedef typename matrix_binary::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_binary &mb, size_type i, size_type j,
const const_iterator12_type &it1, const const_iterator12_type &it1_end,
const const_iterator22_type &it2, const const_iterator22_type &it2_end);
// Dense specializations
void increment (dense_random_access_iterator_tag);
void decrement (dense_random_access_iterator_tag);
value_type dereference (dense_random_access_iterator_tag) const;
// Packed specializations
void increment (packed_random_access_iterator_tag);
void decrement (packed_random_access_iterator_tag);
value_type dereference (packed_random_access_iterator_tag) const;
// Sparse specializations
void increment (sparse_bidirectional_iterator_tag);
void decrement (sparse_bidirectional_iterator_tag);
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class E1, class E2, class F>
struct matrix_binary_traits {
typedef matrix_binary<typename E1::const_closure_type,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (m1 + m2) [i] [j] = m1 [i] [j] + m2 [i] [j]
template<class E1, class E2>
typename matrix_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
typename E2::value_type> >::result_type
operator + (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
// (m1 - m2) [i] [j] = m1 [i] [j] - m2 [i] [j]
template<class E1, class E2>
typename matrix_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
typename E2::value_type> >::result_type
operator - (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
operator +
computes the sum of two matrix expressions.
operator -
computes the difference of two matrix expressions.
Defined in the header matrix_expression.hpp.
E1
is a model of
Matrix Expression
. E2
is a model of
Matrix Expression
. e1 ().size1 () == e2 ().size1 ()
e1 ().size2 () == e2 ().size2 ()
Quadratic depending from the size of the matrix expressions.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m1 (3, 3), m2 (3, 3);
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
m1 (i, j) = m2 (i, j) = 3 * i + j;
std::cout << m1 + m2 << std::endl;
std::cout << m1 - m2 << std::endl;
}
The templated classes matrix_binary_scalar1<E1, E2, F>
and matrix_binary_scalar2<E1, E2, F>
describe binary
operations between a scalar and a matrix.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1/E2 |
The type of the scalar expression. | |
E2/E1 |
The type of the matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_binary_scalar1<E1, E2, F> >
and matrix_expression<matrix_binary_scalar2<E1, E2, F> >
resp.
Member | Description |
---|---|
matrix_binary_scalar1 (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
matrix_binary_scalar1 (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
template<class E1, class E2, class F>
class matrix_binary_scalar1:
public matrix_expression<matrix_binary_scalar1<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename E2::size_type size_type;
typedef typename E2::difference_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_binary_scalar1<E1, E2, F> const_closure_type;
typedef typename E2::orientation_category orientation_category;
typedef typename E1::value_type const_iterator1_type;
typedef typename E2::const_iterator1 const_iterator21_type;
typedef typename E2::const_iterator2 const_iterator22_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_binary_scalar1 ();
matrix_binary_scalar1 (const expression1_type &e1, const expression2_type &e2);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators enhance the iterators of the referenced expression
// with the binary functor.
class const_iterator1:
public container_const_reference<matrix_binary_scalar1>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename E2::const_iterator1::iterator_category iterator_category;
typedef typename matrix_binary_scalar1::difference_type difference_type;
typedef typename matrix_binary_scalar1::value_type value_type;
typedef typename matrix_binary_scalar1::const_reference reference;
typedef typename matrix_binary_scalar1::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_binary_scalar1 &mbs, const const_iterator1_type &it1, const const_iterator21_type &it2);
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_binary_scalar1>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename E2::const_iterator2::iterator_category iterator_category;
typedef typename matrix_binary_scalar1::difference_type difference_type;
typedef typename matrix_binary_scalar1::value_type value_type;
typedef typename matrix_binary_scalar1::const_reference reference;
typedef typename matrix_binary_scalar1::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_binary_scalar1 &mbs, const const_iterator1_type &it1, const const_iterator22_type &it2);
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class E1, class E2, class F>
class matrix_binary_scalar2:
public matrix_expression<matrix_binary_scalar2<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename E1::size_type size_type;
typedef typename E1::difference_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_binary_scalar2<E1, E2, F> const_closure_type;
typedef typename E1::orientation_category orientation_category;
typedef typename E1::const_iterator1 const_iterator11_type;
typedef typename E1::const_iterator2 const_iterator12_type;
typedef typename E2::value_type const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_binary_scalar2 ();
matrix_binary_scalar2 (const expression1_type &e1, const expression2_type &e2);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators enhance the iterators of the referenced expression
// with the binary functor.
class const_iterator1:
public container_const_reference<matrix_binary_scalar2>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename E1::const_iterator1::iterator_category iterator_category;
typedef typename matrix_binary_scalar2::difference_type difference_type;
typedef typename matrix_binary_scalar2::value_type value_type;
typedef typename matrix_binary_scalar2::const_reference reference;
typedef typename matrix_binary_scalar2::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_binary_scalar2 &mbs, const const_iterator11_type &it1, const const_iterator2_type &it2);
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_binary_scalar2>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename E1::const_iterator2::iterator_category iterator_category;
typedef typename matrix_binary_scalar2::difference_type difference_type;
typedef typename matrix_binary_scalar2::value_type value_type;
typedef typename matrix_binary_scalar2::const_reference reference;
typedef typename matrix_binary_scalar2::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_binary_scalar2 &mbs, const const_iterator12_type &it1, const const_iterator2_type &it2);
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class T1, class E2, class F>
struct matrix_binary_scalar1_traits {
typedef matrix_binary_scalar1<scalar_const_reference<T1>,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (t * m) [i] [j] = t * m [i] [j]
template<class T1, class E2>
typename matrix_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
operator * (const T1 &e1,
const matrix_expression<E2> &e2);
template<class E1, class T2, class F>
struct matrix_binary_scalar2_traits {
typedef matrix_binary_scalar2<typename E1::const_closure_type,
scalar_const_reference<T2>, F> expression_type;
typedef expression_type result_type;
};
// (m * t) [i] [j] = m [i] [j] * t
template<class E1, class T2>
typename matrix_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
operator * (const matrix_expression<E1> &e1,
const T2 &e2);
// (m / t) [i] [j] = m [i] [j] / t
template<class E1, class T2>
typename matrix_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
operator / (const matrix_expression<E1> &e1,
const T2 &e2);
operator *
computes the product of a scalar and a matrix expression.
operator /
multiplies the matrix with the reciprocal of the
scalar.
Defined in the header matrix_expression.hpp.
T1/T2
is a model of
Scalar Expression
. E2/E1
is a model of
Matrix Expression
.None.
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m (3, 3);
for (unsigned i = 0; i < m.size1 (); ++ i)
for (unsigned j = 0; j < m.size2 (); ++ j)
m (i, j) = 3 * i + j;
std::cout << 2.0 * m << std::endl;
std::cout << m * 2.0 << std::endl;
}
The templated classes matrix_vector_binary1<E1, E2, F>
and matrix_vector_binary2<E1, E2, F>
describe binary
matrix vector operations.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the matrix or vector expression. | |
E2 |
The type of the vector or matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<matrix_vector_binary1<E1, E2, F> >
and vector_expression<matrix_vector_binary2<E1, E2, F> >
resp.
Member | Description |
---|---|
matrix_vector_binary1 (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
matrix_vector_binary2 (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
size_type size () const |
Returns the size of the expression. |
const_reference operator () (size_type i) const |
Returns the value of the i -th element. |
const_iterator begin () const |
Returns a const_iterator pointing to the
beginning of the expression. |
const_iterator end () const |
Returns a const_iterator pointing to the
end of the expression. |
const_reverse_iterator rbegin () const |
Returns a const_reverse_iterator pointing
to the beginning of the reversed expression. |
const_reverse_iterator rend () const |
Returns a const_reverse_iterator pointing
to the end of the reversed expression. |
template<class E1, class E2, class F>
class matrix_vector_binary1:
public vector_expression<matrix_vector_binary1<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_vector_binary1<E1, E2, F> const_closure_type;
typedef typename E1::const_iterator1 const_iterator1_type;
typedef typename E2::const_iterator const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_vector_binary1 ();
matrix_vector_binary1 (const expression1_type &e1, const expression2_type &e2);
// Accessors
size_type size () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type i) const;
class const_iterator;
typedef const_iterator iterator;
// Element lookup
const_iterator find_first (size_type i) const;
const_iterator find_last (size_type i) const;
// Iterator simply is a pointer.
class const_iterator:
public container_const_reference<matrix_vector_binary1>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
typedef typename matrix_vector_binary1::difference_type difference_type;
typedef typename matrix_vector_binary1::value_type value_type;
typedef typename matrix_vector_binary1::const_reference reference;
typedef typename matrix_vector_binary1::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const matrix_vector_binary1 &mvb, const const_iterator1_type &it1);
// Dense random access specialization
value_type dereference (dense_random_access_iterator_tag) const;
// Packed bidirectional specialization
value_type dereference (packed_bidirectional_iterator_tag) const;
// Sparse bidirectional specialization
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator &operator ++ ();
const_iterator &operator -- ();
const_iterator &operator += (difference_type n);
const_iterator &operator -= (difference_type n);
difference_type operator - (const const_iterator &it) const;
// Dereference
reference operator * () const;
// Index
size_type index () const;
// Assignment
const_iterator &operator = (const const_iterator &it);
// Comparison
bool operator == (const const_iterator &it) const;
bool operator <(const const_iterator &it) const;
};
const_iterator begin () const;
const_iterator end () const;
// Reverse iterator
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
const_reverse_iterator rbegin () const;
const_reverse_iterator rend () const;
};
template<class E1, class E2, class F>
class matrix_vector_binary2:
public vector_expression<matrix_vector_binary2<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_vector_binary2<E1, E2, F> const_closure_type;
typedef typename E1::const_iterator const_iterator1_type;
typedef typename E2::const_iterator2 const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_vector_binary2 ();
matrix_vector_binary2 (const expression1_type &e1, const expression2_type &e2);
// Accessors
size_type size () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type j) const;
class const_iterator;
typedef const_iterator iterator;
// Element lookup
const_iterator find_first (size_type j) const;
const_iterator find_last (size_type j) const;
// Iterator simply is a pointer.
class const_iterator:
public container_const_reference<matrix_vector_binary2>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
typedef typename matrix_vector_binary2::difference_type difference_type;
typedef typename matrix_vector_binary2::value_type value_type;
typedef typename matrix_vector_binary2::const_reference reference;
typedef typename matrix_vector_binary2::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const matrix_vector_binary2 &mvb, const const_iterator2_type &it2);
// Dense random access specialization
value_type dereference (dense_random_access_iterator_tag) const;
// Packed bidirectional specialization
value_type dereference (packed_bidirectional_iterator_tag) const;
// Sparse bidirectional specialization
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator &operator ++ ();
const_iterator &operator -- ();
const_iterator &operator += (difference_type n);
const_iterator &operator -= (difference_type n);
difference_type operator - (const const_iterator &it) const;
// Dereference
reference operator * () const;
// Index
size_type index () const;
// Assignment
const_iterator &operator = (const const_iterator &it);
// Comparison
bool operator == (const const_iterator &it) const;
bool operator <(const const_iterator &it) const;
};
const_iterator begin () const;
const_iterator end () const;
// Reverse iterator
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
const_reverse_iterator rbegin () const;
const_reverse_iterator rend () const;
};
template<class T1, class E1, class T2, class E2>
struct matrix_vector_binary1_traits {
typedef row_major_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_vector_binary1<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_vector_prod1<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
row_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
row_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class V, class E1, class E2>
V
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class V, class E1, class E2>
V
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class T1, class E1, class T2, class E2>
struct matrix_vector_binary2_traits {
typedef column_major_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_vector_binary2<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_vector_prod2<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
column_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
column_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class V, class E1, class E2>
V
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class V, class E1, class E2>
V
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
prod
computes the product of the matrix and the vector expression.
prec_prod
computes the double precision product of the matrix and
the vector expression.
Defined in the header matrix_expression.hpp.
E1
is a model of
Matrix Expression
or Vector
Expression
. E2
is a model of
Vector Expression
or Matrix Expression
.e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m (3, 3);
vector<double> v (3);
for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
for (unsigned j = 0; j < m.size2 (); ++ j)
m (i, j) = 3 * i + j;
v (i) = i;
}
std::cout << prod (m, v) << std::endl;
std::cout << prod (v, m) << std::endl;
}
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;
};
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
lower_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
upper_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_lower_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_upper_tag,
vector_tag);
template<class E1, class E2, class C>
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
C);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
lower_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
upper_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
unit_lower_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
unit_upper_tag);
template<class E1, class E2, class C>
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
C);
solve
solves a linear equation for lower or upper (unit) triangular
matrices.
Defined in the header triangular.hpp.
E1
is a model of
Matrix Expression
or Vector Expression
. E2
is a model of
Vector Expression
or Matrix Expression
.e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()
e2 ().size1 () == e2 ().size2 ()
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m (3, 3);
vector<double> v (3);
for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
for (unsigned j = 0; j <= i; ++ j)
m (i, j) = 3 * i + j + 1;
v (i) = i;
}
std::cout << solve (m, v, lower_tag ()) << std::endl;
std::cout << solve (v, m, lower_tag ()) << std::endl;
}
The templated class matrix_matrix_binary<E1, E2, F>
describes a binary matrix operation.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first matrix expression. | |
E2 |
The type of the second matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_matrix_binary<E1, E2, F> >
.
Member | Description |
---|---|
matrix_matrix_binary (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type
j) const |
Returns the value of the j -th element in
the i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to
the beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to
the end of the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to
the beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to
the end of the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed expression. |
template<class E1, class E2, class F>
class matrix_matrix_binary:
public matrix_expression<matrix_matrix_binary<E1, E2, F> > {
public:
typedef E1 expression1_type;
typedef E2 expression2_type;
typedef F functor_type;
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
typedef typename F::result_type value_type;
typedef value_type const_reference;
typedef const_reference reference;
typedef const value_type *const_pointer;
typedef const_pointer pointer;
typedef const matrix_matrix_binary<E1, E2, F> const_closure_type;
typedef unknown_orientation_tag orientation_category;
typedef typename E1::const_iterator1 const_iterator11_type;
typedef typename E1::const_iterator2 const_iterator12_type;
typedef typename E2::const_iterator1 const_iterator21_type;
typedef typename E2::const_iterator2 const_iterator22_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
matrix_matrix_binary ();
matrix_matrix_binary (const expression1_type &e1, const expression2_type &e2);
// Accessors
size_type size1 () const;
size_type size2 () const;
const expression1_type &expression1 () const;
const expression2_type &expression2 () const;
// Element access
const_reference operator () (size_type i, size_type j) const;
class const_iterator1;
typedef const_iterator1 iterator1;
class const_iterator2;
typedef const_iterator2 iterator2;
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
// Element lookup
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
// Iterators simply are pointers.
class const_iterator1:
public container_const_reference<matrix_matrix_binary>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
typedef typename matrix_matrix_binary::difference_type difference_type;
typedef typename matrix_matrix_binary::value_type value_type;
typedef typename matrix_matrix_binary::const_reference reference;
typedef typename matrix_matrix_binary::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const matrix_matrix_binary &mmb, const const_iterator11_type &it1, const const_iterator22_type &it2);
// Random access specialization
value_type dereference (dense_random_access_iterator_tag) const;
// Packed bidirectional specialization
value_type dereference (packed_bidirectional_iterator_tag) const;
// Sparse bidirectional specialization
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator1 &operator ++ ();
const_iterator1 &operator -- ();
const_iterator1 &operator += (difference_type n);
const_iterator1 &operator -= (difference_type n);
difference_type operator - (const const_iterator1 &it) const;
// Dereference
reference operator * () const;
const_iterator2 begin () const;
const_iterator2 end () const;
const_reverse_iterator2 rbegin () const;
const_reverse_iterator2 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator1 &operator = (const const_iterator1 &it);
// Comparison
bool operator == (const const_iterator1 &it) const;
bool operator <(const const_iterator1 &it) const;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class const_iterator2:
public container_const_reference<matrix_matrix_binary>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
typedef typename matrix_matrix_binary::difference_type difference_type;
typedef typename matrix_matrix_binary::value_type value_type;
typedef typename matrix_matrix_binary::const_reference reference;
typedef typename matrix_matrix_binary::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const matrix_matrix_binary &mmb, const const_iterator11_type &it1, const const_iterator22_type &it2);
// Random access specialization
value_type dereference (dense_random_access_iterator_tag) const;
// Packed bidirectional specialization
value_type dereference (packed_bidirectional_iterator_tag) const;
// Sparse bidirectional specialization
value_type dereference (sparse_bidirectional_iterator_tag) const;
// Arithmetic
const_iterator2 &operator ++ ();
const_iterator2 &operator -- ();
const_iterator2 &operator += (difference_type n);
const_iterator2 &operator -= (difference_type n);
difference_type operator - (const const_iterator2 &it) const;
// Dereference
reference operator * () const;
const_iterator1 begin () const;
const_iterator1 end () const;
const_reverse_iterator1 rbegin () const;
const_reverse_iterator1 rend () const;
// Indices
size_type index1 () const;
size_type index2 () const;
// Assignment
const_iterator2 &operator = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
bool operator <(const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
// Reverse iterators
const_reverse_iterator1 rbegin1 () const;
const_reverse_iterator1 rend1 () const;
const_reverse_iterator2 rbegin2 () const;
const_reverse_iterator2 rend2 () const;
};
template<class T1, class E1, class T2, class E2>
struct matrix_matrix_binary_traits {
typedef unknown_orientation_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_matrix_binary<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_matrix_prod<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
unknown_orientation_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
unknown_orientation_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class M, class E1, class E2>
M
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class M, class E1, class E2>
M
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
prod
computes the product of the matrix expressions.
prec_prod
computes the double precision product of the matrix expressions.
Defined in the header matrix_expression.hpp.
E1
is a model of
Matrix Expression
. E2
is a model of
Matrix Expression
.e1 ().size2 () == e2 ().size1 ()
Cubic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m1 (3, 3), m2 (3, 3);
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
m1 (i, j) = m2 (i, j) = 3 * i + j;
std::cout << prod (m1, m2) << std::endl;
}
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;
};
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
lower_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
upper_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_lower_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_upper_tag,
matrix_tag);
template<class E1, class E2, class C>
typename matrix_matrix_solve_traits<E1, E2>::result_type
solve (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
C);
solve
solves a linear equation for lower or upper (unit) triangular
matrices.
Defined in the header triangular.hpp.
E1
is a model of
Matrix Expression
. E2
is a model of
Matrix Expression
.e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size1 ()
Cubic depending from the size of the matrix expressions.
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<double> m1 (3, 3), m2 (3, 3);
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
for (unsigned j = 0; j <= i; ++ j)
m1 (i, j) = m2 (i, j) = 3 * i + j + 1;
std::cout << solve (m1, m2, lower_tag ()) << std::endl;
}
Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted
provided this copyright notice appears in all copies. This document is provided
``as is'' without express or implied warranty, and with no claim as to its
suitability for any purpose.
Last revised: 1/15/2003