...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
The templated class vector_expression<E>
is required to be a public base of all classes which model the Vector Expression concept.
Defined in the header expression_types.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the vector expression. |
None. Not a Vector Expression!
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. |
The range
, slice
and project
functions have been removed. Use the free functions defined in vector proxy instead.
The templated class vector_container<C>
is required to be a public base of all classes which model the Vector concept.
This includes the class vector
itself.
Defined in the header expression_types.hpp.
Parameter | Description | Default |
---|---|---|
C |
The type of the vector container. |
None. Not a Vector Expression OR Vector!
None.
vector_expression<C>
Member | Description |
---|---|
const container_type &operator () ()
const |
Returns a const reference of the container. |
container_type &operator () () |
Returns a reference of the container. |
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. |
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>
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>
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>
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 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_2_square v = sum (v [i] * v [i])
template<class E>
typename vector_scalar_unary_traits<E, vector_norm_2_square<typename E::value_type> >::result_type
norm_2_square (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
Use, modification and distribution are subject to the
Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt
or copy at
http://www.boost.org/LICENSE_1_0.txt
).