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c++boost.gif Vector Expressions

Vector Expression

Description

The templated class vector_expression<E> forms the base for all static derived vector expression classes including class vector itself.

Definition

Defined in the header vector_expression.hpp.

Template parameters

Parameter Description Default
E The type of the vector expression.  

Model of

None.

Type requirements

None.

Public base classes

None.

Members

Member Description
const expression_type &operator () () const Returns a const reference of the expression.
expression_type &operator () () Returns a reference of the expression.

Vector References

Constant Reference

Description

The templated class vector_const_reference<E> contains a constant reference to a vector expression.

Definition

Defined in the header vector_expression.hpp.

Template parameters

Parameter Description Default
E The type of the vector expression.  

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<vector_const_reference<E> >

Members

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.

Reference

Description

The templated class vector_reference<E> contains a reference to a vector expression.

Definition

Defined in the header vector_expression.hpp.

Template parameters

Parameter Description Default
E The type of the vector expression.  

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<vector_reference<E> >

Members

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.

Vector Operations

Unary Operation Description

Description

The templated class vector_unary<E, F> describes a unary vector operation.

Definition

Defined in the header vector_expression.hpp.

Template parameters

Parameter Description Default
E The type of the vector expression.  
F The type of the operation.  

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<vector_unary<E, F> >

Members

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.

Unary Operations

Prototypes

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);

Description

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.

Definition

Defined in the header vector_expression.hpp.

Type requirements

Preconditions

None.

Complexity

Linear depending from the size of the vector expression.

Examples

#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;
}

Binary Operation Description

Description

The templated class vector_binary<E1, E2, F> describes a binary vector operation.

Definition

Defined in the header vector_expression.hpp.

Template parameters

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.  

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<vector_binary<E1, E2, F> >

Members

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.

Binary Operations

Prototypes

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);

Description

operator + computes the sum of two vector expressions. operator - computes the difference of two vector expressions.

Definition

Defined in the header vector_expression.hpp.

Type requirements

Preconditions

Complexity

Linear depending from the size of the vector expressions.

Examples

#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;
}

Binary Outer Operation Description

Description

The templated class vector_matrix_binary<E1, E2, F> describes a binary outer vector operation.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

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.  

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<vector_matrix_binary<E1, E2, F> >

Members

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.

Binary Outer Operations

Prototypes

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);

Description

outer_prod computes the outer product of two vector expressions.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

Preconditions

None.

Complexity

Quadratic depending from the size of the vector expressions.

Examples

#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;
}

Scalar Vector Operation Description

Description

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.

Definition

Defined in the header vector_expression.hpp.

Template parameters

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.  

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<vector_binary_scalar1<E1, E2, F> > and vector_expression<vector_binary_scalar2<E1, E2, F> > resp.

Members

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.

Scalar Vector Operations

Prototypes

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);

Description

operator * computes the product of a scalar and a vector expression. operator / multiplies the vector with the reciprocal of the scalar.

Definition

Defined in the header vector_expression.hpp.

Type requirements

Preconditions

None.

Complexity

Linear depending from the size of the vector expression.

Examples

#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;
}

Vector Reductions

Unary Reductions

Prototypes

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);

Description

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.

Definition

Defined in the header vector_expression.hpp.

Type requirements

Preconditions

None.

Complexity

Linear depending from the size of the vector expression.

Examples

#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;
}

Binary Reductions

Prototypes

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);

Description

inner_prod computes the inner product of the vector expressions. prec_inner_prod computes the double precision inner product of the vector expressions.

Definition

Defined in the header vector_expression.hpp.

Type requirements

Preconditions

Complexity

Linear depending from the size of the vector expressions.

Examples

#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