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