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.

Interface

    // 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 () ();
};

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.

Interface

    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;
};

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.

Interface

    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 ();
};

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.

Interface

    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;
};

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

  • E is a model of Vector Expression .
  • 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.

    Interface

        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;
    };

    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

  • E1 is a model of Vector Expression .
  • E2 is a model of Vector Expression .
  • Preconditions

  • e1 ().size () == e2 ().size ()
  • 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.

    Interface

        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;
    };

    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

  • E1 is a model of Vector Expression .
  • E2 is a model of Vector Expression .
  • 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.

    Interface

        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;
    };

    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

  • T1/T2 is a model of Scalar Expression .
  • E2/E1 is a model of Vector Expression .
  • 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

  • E is a model of Vector Expression .
  • 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

  • E1 is a model of Vector Expression .
  • E2 is a model of Vector Expression .
  • Preconditions

  • e1 ().size () == e2 ().size ()
  • 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