The templated class vector_expression<E>
forms the base
for all static derived vector expression classes including class vector
itself.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the vector 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 vector_expression {
typedef E expression_type;
typedef vector_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 vector_const_reference<E>
contains
a constant reference to a vector expression.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the vector expression. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<vector_const_reference<E> >
Member | Description |
---|---|
vector_const_reference (const expression_type
&e) |
Constructs a constant reference 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 E>
class vector_const_reference:
public vector_expression<vector_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::const_iterator const_iterator_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_const_reference ();
vector_const_reference (const expression_type &e);
// Accessors
size_type size () const;
const expression_type &expression () const;
// Element access
const_reference operator () (size_type i) const;
const_reference operator [] (size_type i) const;
typedef const_iterator_type 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 is the iterator of the referenced expression.
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;
};
The templated class vector_reference<E>
contains a reference
to a vector expression.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the vector expression. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<vector_reference<E> >
Member | Description |
---|---|
vector_reference (expression_type &e) |
Constructs a reference of the expression. |
void resize (size_type size) |
Resizes the expression to hold at most size
elements. |
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. |
reference operator () (size_type i) |
Returns a reference 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. |
iterator begin () |
Returns a iterator pointing to the beginning
of the expression. |
iterator end () |
Returns a 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. |
reverse_iterator rbegin () |
Returns a reverse_iterator pointing to
the beginning of the reversed expression. |
reverse_iterator rend () |
Returns a reverse_iterator pointing to
the end of the reversed expression. |
template<class E>
class vector_reference:
public vector_expression<vector_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::const_iterator const_iterator_type;
typedef typename E::iterator iterator_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_reference ();
vector_reference (expression_type &e);
// Accessors
size_type size () const;
const expression_type &expression () const;
expression_type &expression ();
// Resizing
void resize (size_type size);
// Element access
const_reference operator () (size_type i) const;
reference operator () (size_type i);
const_reference operator [] (size_type i) const;
reference operator [] (size_type i);
typedef const_iterator_type const_iterator;
typedef iterator_type iterator;
// Element lookup
const_iterator find_first (size_type i) const;
iterator find_first (size_type i);
const_iterator find_last (size_type i) const;
iterator find_last (size_type i);
// Iterator is the iterator of the referenced expression.
const_iterator begin () const;
const_iterator end () const;
iterator begin ();
iterator end ();
// Reverse iterator
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
const_reverse_iterator rbegin () const;
const_reverse_iterator rend () const;
typedef reverse_iterator_base<iterator> reverse_iterator;
reverse_iterator rbegin ();
reverse_iterator rend ();
};
The templated class vector_unary<E, F>
describes a unary
vector operation.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the vector expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<vector_unary<E, F> >
Member | Description |
---|---|
vector_unary (const expression_type &e) |
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 E, class F>
class vector_unary:
public vector_expression<vector_unary<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 vector_unary<E, F> const_closure_type;
typedef typename E::const_iterator const_iterator_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_unary ();
vector_unary (const expression_type &e);
// Accessors
size_type size () const;
const expression_type &expression () const;
// Element access
const_reference operator () (size_type i) const;
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 enhances the iterator of the referenced expression
// with the unary functor.
class const_iterator:
public container_const_reference<vector_unary>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename E::const_iterator::iterator_category iterator_category;
typedef typename vector_unary::difference_type difference_type;
typedef typename vector_unary::value_type value_type;
typedef typename vector_unary::const_reference reference;
typedef typename vector_unary::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const vector_unary &vu, const const_iterator_type &it);
// 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 E, class F>
struct vector_unary_traits {
typedef vector_unary<typename E::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (- v) [i] = - v [i]
template<class E>
typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type
operator - (const vector_expression<E> &e);
// (conj v) [i] = conj (v [i])
template<class E>
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
conj (const vector_expression<E> &e);
// (real v) [i] = real (v [i])
template<class E>
typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type
real (const vector_expression<E> &e);
// (imag v) [i] = imag (v [i])
template<class E>
typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type
imag (const vector_expression<E> &e);
// (trans v) [i] = v [i]
template<class E>
typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type
trans (const vector_expression<E> &e);
// (herm v) [i] = conj (v [i])
template<class E>
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
herm (const vector_expression<E> &e);
operator -
computes the additive inverse of a vector expression.
conj
computes the complex conjugate of a vector expression.
real
and imag
compute the real and imaginary parts of
a vector expression. trans
computes the transpose of a vector
expression. herm
computes the hermitian, i.e. the complex conjugate
of the transpose of a vector expression.
Defined in the header vector_expression.hpp.
E
is a model of
Vector Expression
.None.
Linear depending from the size of the vector expression.
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<std::complex<double> > v (3);
for (unsigned i = 0; i < v.size (); ++ i)
v (i) = std::complex<double> (i, i);
std::cout << - v << std::endl;
std::cout << conj (v) << std::endl;
std::cout << real (v) << std::endl;
std::cout << imag (v) << std::endl;
std::cout << trans (v) << std::endl;
std::cout << herm (v) << std::endl;
}
The templated class vector_binary<E1, E2, F>
describes
a binary vector operation.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first vector expression. | |
E2 |
The type of the second vector expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<vector_binary<E1, E2, F> >
Member | Description |
---|---|
vector_binary (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 vector_binary:
public vector_expression<vector_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 vector_binary<E1, E2, F> const_closure_type;
typedef typename E1::const_iterator const_iterator1_type;
typedef typename E2::const_iterator const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_binary ();
vector_binary (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;
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 merges the iterators of the referenced expressions and
// enhances them with the binary functor.
class const_iterator:
public container_const_reference<vector_binary>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
typedef typename vector_binary::difference_type difference_type;
typedef typename vector_binary::value_type value_type;
typedef typename vector_binary::const_reference reference;
typedef typename vector_binary::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const vector_binary &vb, size_type i,
const const_iterator1_type &it1, const const_iterator1_type &it1_end,
const const_iterator2_type &it2, const const_iterator2_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_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>
struct vector_binary_traits {
typedef vector_binary<typename E1::const_closure_type,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (v1 + v2) [i] = v1 [i] + v2 [i]
template<class E1, class E2>
typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
typename E2::value_type> >::result_type
operator + (const vector_expression<E1> &e1,
const vector_expression<E2> &e2);
// (v1 - v2) [i] = v1 [i] - v2 [i]
template<class E1, class E2>
typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
typename E2::value_type> >::result_type
operator - (const vector_expression<E1> &e1,
const vector_expression<E2> &e2);
operator +
computes the sum of two vector expressions.
operator -
computes the difference of two vector expressions.
Defined in the header vector_expression.hpp.
E1
is a model of
Vector Expression
.E2
is a model of
Vector Expression
.e1 ().size () == e2 ().size ()
Linear depending from the size of the vector expressions.
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<double> v1 (3), v2 (3);
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
v1 (i) = v2 (i) = i;
std::cout << v1 + v2 << std::endl;
std::cout << v1 - v2 << std::endl;
}
The templated class vector_matrix_binary<E1, E2, F>
describes a binary outer vector operation.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first vector expression. | |
E2 |
The type of the second vector expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<vector_matrix_binary<E1, E2, F> >
Member | Description |
---|---|
vector_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 vector_matrix_binary:
public matrix_expression<vector_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 vector_matrix_binary<E1, E2, F> const_closure_type;
typedef unknown_orientation_tag orientation_category;
typedef typename E1::const_iterator const_iterator1_type;
typedef typename E2::const_iterator const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_matrix_binary ();
vector_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;
// 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 expressions
// with the binary functor.
class const_iterator1:
public container_const_reference<vector_matrix_binary>,
public random_access_iterator_base<const_iterator1, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
typedef typename vector_matrix_binary::difference_type difference_type;
typedef typename vector_matrix_binary::value_type value_type;
typedef typename vector_matrix_binary::const_reference reference;
typedef typename vector_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 vector_matrix_binary &vmb, const const_iterator1_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<vector_matrix_binary>,
public random_access_iterator_base<const_iterator2, value_type> {
public:
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
typedef typename vector_matrix_binary::difference_type difference_type;
typedef typename vector_matrix_binary::value_type value_type;
typedef typename vector_matrix_binary::const_reference reference;
typedef typename vector_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 vector_matrix_binary &vmb, const const_iterator1_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 E1, class E2, class F>
struct vector_matrix_binary_traits {
typedef vector_matrix_binary<typename E1::const_closure_type,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j]
template<class E1, class E2>
typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type
outer_prod (const vector_expression<E1> &e1,
const vector_expression<E2> &e2);
outer_prod
computes the outer product of two vector expressions.
Defined in the header matrix_expression.hpp.
E1
is a model of
Vector Expression
.E2
is a model of
Vector Expression
.None.
Quadratic depending from the size of the vector expressions.
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<double> v1 (3), v2 (3);
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
v1 (i) = v2 (i) = i;
std::cout << outer_prod (v1, v2) << std::endl;
}
The templated classes vector_binary_scalar1<E1, E2, F>
and vector_binary_scalar2<E1, E2, F>
describe binary
operations between a scalar and a vector.
Defined in the header vector_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1/E2 |
The type of the scalar expression. | |
E2/E1 |
The type of the vector expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<vector_binary_scalar1<E1, E2, F> >
and vector_expression<vector_binary_scalar2<E1, E2, F> >
resp.
Member | Description |
---|---|
vector_binary_scalar1 (const expression1_type
&e1, const expression2_type &e2) |
Constructs a description of the expression. |
vector_binary_scalar2 (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 vector_binary_scalar1:
public vector_expression<vector_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 vector_binary_scalar1<E1, E2, F> const_closure_type;
typedef typename E1::value_type const_iterator1_type;
typedef typename E2::const_iterator const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_binary_scalar1 ();
vector_binary_scalar1 (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;
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 enhances the iterator of the referenced vector expression
// with the binary functor.
class const_iterator:
public container_const_reference<vector_binary_scalar1>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename E2::const_iterator::iterator_category iterator_category;
typedef typename vector_binary_scalar1::difference_type difference_type;
typedef typename vector_binary_scalar1::value_type value_type;
typedef typename vector_binary_scalar1::const_reference reference;
typedef typename vector_binary_scalar1::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const vector_binary_scalar1 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);
// 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 vector_binary_scalar2:
public vector_expression<vector_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 vector_binary_scalar2<E1, E2, F> const_closure_type;
typedef typename E1::const_iterator const_iterator1_type;
typedef typename E2::value_type const_iterator2_type;
typedef unknown_storage_tag storage_category;
// Construction and destruction
vector_binary_scalar2 ();
vector_binary_scalar2 (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;
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 enhances the iterator of the referenced vector expression
// with the binary functor.
class const_iterator:
public container_const_reference<vector_binary_scalar2>,
public random_access_iterator_base<const_iterator, value_type> {
public:
typedef typename E1::const_iterator::iterator_category iterator_category;
typedef typename vector_binary_scalar2::difference_type difference_type;
typedef typename vector_binary_scalar2::value_type value_type;
typedef typename vector_binary_scalar2::const_reference reference;
typedef typename vector_binary_scalar2::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const vector_binary_scalar2 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);
// 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 E2, class F>
struct vector_binary_scalar1_traits {
typedef vector_binary_scalar1<scalar_const_reference<T1>,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (t * v) [i] = t * v [i]
template<class T1, class E2>
typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
operator * (const T1 &e1,
const vector_expression<E2> &e2);
template<class E1, class T2, class F>
struct vector_binary_scalar2_traits {
typedef vector_binary_scalar2<typename E1::const_closure_type,
scalar_const_reference<T2>, F> expression_type;
typedef expression_type result_type;
};
// (v * t) [i] = v [i] * t
template<class E1, class T2>
typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
operator * (const vector_expression<E1> &e1,
const T2 &e2);
// (v / t) [i] = v [i] / t
template<class E1, class T2>
typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
operator / (const vector_expression<E1> &e1,
const T2 &e2);
operator *
computes the product of a scalar and a vector expression.
operator /
multiplies the vector with the reciprocal of the
scalar.
Defined in the header vector_expression.hpp.
T1/T2
is a model of
Scalar Expression
.E2/E1
is a model of
Vector Expression
.None.
Linear depending from the size of the vector expression.
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<double> v (3);
for (unsigned i = 0; i < v.size (); ++ i)
v (i) = i;
std::cout << 2.0 * v << std::endl;
std::cout << v * 2.0 << std::endl;
}
template<class E, class F>
struct vector_scalar_unary_traits {
typedef typename F::result_type result_type;
};
// sum v = sum (v [i])
template<class E>
typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type
sum (const vector_expression<E> &e);
// norm_1 v = sum (abs (v [i]))
template<class E>
typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type
norm_1 (const vector_expression<E> &e);
// norm_2 v = sqrt (sum (v [i] * v [i]))
template<class E>
typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type
norm_2 (const vector_expression<E> &e);
// norm_inf v = max (abs (v [i]))
template<class E>
typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type
norm_inf (const vector_expression<E> &e);
// index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i])))
template<class E>
typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type
index_norm_inf (const vector_expression<E> &e);
sum
computes the sum of the vector expression's elements.
norm_1
, norm_2
and norm_inf
compute
the corresponding ||.||1, ||.||
2 and ||.||inf vector norms.
index_norm_1
computes the index of the vector expression's first
element having maximal absolute value.
Defined in the header vector_expression.hpp.
E
is a model of Vector
Expression
.None.
Linear depending from the size of the vector expression.
#include <boost/numeric/ublas/vector.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<double> v (3);
for (unsigned i = 0; i < v.size (); ++ i)
v (i) = i;
std::cout << sum (v) << std::endl;
std::cout << norm_1 (v) << std::endl;
std::cout << norm_2 (v) << std::endl;
std::cout << norm_inf (v) << std::endl;
std::cout << index_norm_inf (v) << std::endl;
}
template<class E1, class E2, class F>
struct vector_scalar_binary_traits {
typedef typename F::result_type result_type;
};
// inner_prod (v1, v2) = sum (v1 [i] * v2 [i])
template<class E1, class E2>
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
typename E2::value_type,
typename promote_traits<typename E1::value_type,
typename E2::value_type>::promote_type> >::result_type
inner_prod (const vector_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class E1, class E2>
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
typename E2::value_type,
typename type_traits<typename promote_traits<typename E1::value_type,
typename E2::value_type>::promote_type>::precision_type> >::result_type
prec_inner_prod (const vector_expression<E1> &e1,
const vector_expression<E2> &e2);
inner_prod
computes the inner product of the vector expressions.
prec_inner_prod
computes the double precision inner product of
the vector expressions.
Defined in the header vector_expression.hpp.
E1
is a model of
Vector Expression
.E2
is a model of Vector
Expression
.e1 ().size () == e2 ().size ()
Linear depending from the size of the vector expressions.
#include <boost/numeric/ublas/vector.hpp>
int main () {
using namespace boost::numeric::ublas;
vector<double> v1 (3), v2 (3);
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
v1 (i) = v2 (i) = i;
std::cout << inner_prod (v1, v2) << 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