c++boost.gifVector 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

    int main () {
        using namespace boost::numeric::ublas;
        vector<std::complex<double> > v (3);
        for (int i = 0; i < v.size (); ++ i) 
            v (i) = std::complex (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

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v1 (3), v2 (3);
        for (int 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

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v1 (3), v2 (3);
        for (int 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

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v (3);
        for (int 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

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v (3);
        for (int 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

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v1 (3), v2 (3);
        for (int 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: 8/3/2002