Matrix Proxies

Matrix Row

Description

The templated class matrix_row<M> allows addressing a row of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i) {

        matrix_row<matrix<double> > mr (m, i);

        for (unsigned j = 0; j < mr.size (); ++ j)

            mr (j) = 3 * i + j;

        std::cout << mr << std::endl;

    }

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Vector Expression .

Type requirements

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

Public base classes

vector_expression<matrix_row<M> >

Members

Member	Description
`matrix_row (matrix_type &data, size_type i)`	Constructs a sub vector.
`size_type size () const`	Returns the size of the sub vector.
`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.
`matrix_row &operator = (const matrix_row &mr)`	The assignment operator.
`matrix_row &assign_temporary (matrix_row &mr)`	Assigns a temporary. May change the matrix row `mr` .
`template<class AE> matrix_row &operator = (const vector_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_row &assign (const vector_expression<AE> &ae)`	Assigns a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_row &operator += (const vector_expression<AE> &ae)`	A computed assignment operator. Adds the vector expression to the sub vector.
`template<class AE> matrix_row &plus_assign (const vector_expression<AE> &ae)`	Adds a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_row &operator -= (const vector_expression<AE> &ae)`	A computed assignment operator. Subtracts the vector expression from the sub vector.
`template<class AE> matrix_row &minus_assign (const vector_expression<AE> &ae)`	Subtracts a vector expression from the sub vector. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_row &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub vector with a scalar.
`template<class AT> matrix_row &operator /= (const AT &at)`	A computed assignment operator. Divides the sub vector through a scalar.
`void swap (matrix_row &mr)`	Swaps the contents of the sub vectors.
`const_iterator begin () const`	Returns a `const_iterator` pointing to the beginning of the `matrix_row`.
`const_iterator end () const`	Returns a `const_iterator` pointing to the end of the `matrix_row`.
`iterator begin ()`	Returns a `iterator` pointing to the beginning of the `matrix_row`.
`iterator end ()`	Returns a `iterator` pointing to the end of the `matrix_row`.
`const_reverse_iterator rbegin () const`	Returns a `const_reverse_iterator` pointing to the beginning of the reversed `matrix_row`.
`const_reverse_iterator rend () const`	Returns a `const_reverse_iterator` pointing to the end of the reversed `matrix_row`.
`reverse_iterator rbegin ()`	Returns a `reverse_iterator` pointing to the beginning of the reversed `matrix_row`.
`reverse_iterator rend ()`	Returns a `reverse_iterator` pointing to the end of the reversed `matrix_row`.

Interface

// Matrix based row vector class

    template<class M>

    class matrix_row:

        public vector_expression<matrix_row<M> > {

    public:

        typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const vector_const_reference<const matrix_row<matrix_type> > const_closure_type;

        typedef vector_reference<matrix_row<matrix_type> > closure_type;

        typedef typename M::const_iterator2 const_iterator_type;

        typedef typename M::iterator2 iterator_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;



        // Construction and destruction

        matrix_row ();

        matrix_row (matrix_type &data, size_type i);



        // Accessors

        size_type size () const;

        const_matrix_type &data () const;

        matrix_type &data ();





        // Element access

        const_reference operator () (size_type j) const;

        reference operator () (size_type j);



        const_reference operator [] (size_type j) const;

        reference operator [] (size_type j);



        // Assignment

        matrix_row &operator = (const matrix_row &mr);

        matrix_row &assign_temporary (matrix_row &mr);

        template<class AE>

        matrix_row &operator = (const vector_expression<AE> &ae);

        template<class AE>

        matrix_row &assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_row &operator += (const vector_expression<AE> &ae);

        template<class AE>

        matrix_row &plus_assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_row &operator -= (const vector_expression<AE> &ae);

        template<class AE>

        matrix_row &minus_assign (const vector_expression<AE> &ae);

        template<class AT>

        matrix_row &operator *= (const AT &at);

        template<class AT>

        matrix_row &operator /= (const AT &at);



        // Swapping

        void swap (matrix_row &mr);

        friend void swap (matrix_row &mr1, matrix_row &mr2);



        class const_iterator;

        class iterator;



        // Element lookup

        const_iterator find_first (size_type j) const;

        iterator find_first (size_type j);

        const_iterator find_last (size_type j) const;

        iterator find_last (size_type j);



        // Iterators simply are pointers.



        class const_iterator:

            public container_const_reference<matrix_row>,

            public random_access_iterator_base<const_iterator, value_type> {

        public:

            typedef typename const_iterator_type::iterator_category iterator_category;

            typedef typename const_iterator_type::difference_type difference_type;

            typedef typename const_iterator_type::value_type value_type;

            typedef typename const_iterator_type::reference reference;

            typedef typename const_iterator_type::pointer pointer;



            // Construction and destruction

            const_iterator ();

            const_iterator (const matrix_row &mr, const const_iterator_type &it);

            const_iterator (const iterator &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;



        class iterator:

            public container_reference<matrix_row>,

            public random_access_iterator_base<iterator, value_type> {

        public:

            typedef typename iterator_type::iterator_category iterator_category;

            typedef typename iterator_type::difference_type difference_type;

            typedef typename iterator_type::value_type value_type;

            typedef typename iterator_type::reference reference;

            typedef typename iterator_type::pointer pointer;



            // Construction and destruction

            iterator ();

            iterator (matrix_row &mr, const iterator_type &it);



            // Arithmetic

            iterator &operator ++ ();

            iterator &operator -- ();

            iterator &operator += (difference_type n);

            iterator &operator -= (difference_type n);

            difference_type operator - (const iterator &it) const;



            // Dereference

            reference operator * () const;



            // Index

            size_type index () const;



            // Assignment

             iterator &operator = (const iterator &it);



            // Comparison

            bool operator == (const iterator &it) const;

            bool operator <(const iterator &it) 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 ();

    };

Projections

Prototypes

template<class M>

    matrix_row<M> row (M &data, std::size_t i);

    template<class M>

    const matrix_row<const M> row (const M &data, std::size_t i);

Description

The free row functions support the construction of matrix rows.

Definition

Defined in the header matrix_proxy.hpp.

Type requirements

M is a model of Matrix Expression .

Preconditions

i < data.size1 ()

Complexity

Linear depending from the size of the row.

Examples

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i) {

        for (unsigned j = 0; j < m.size2 (); ++ j)

            row (m, i) (j) = 3 * i + j;

        std::cout << row (m, i) << std::endl;

    }

}

Matrix Column

Description

The templated class matrix_column<M> allows addressing a column of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned j = 0; j < m.size2 (); ++ j) {

        matrix_column<matrix<double> > mc (m, j);

        for (unsigned i = 0; i < mc.size (); ++ i)

            mc (i) = 3 * i + j;

        std::cout << mc << std::endl;

    }

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Vector Expression .

Type requirements

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

Public base classes

vector_expression<matrix_column<M> >

Members

Member	Description
`matrix_column (matrix_type &data, size_type j)`	Constructs a sub vector.
`size_type size () const`	Returns the size of the sub vector.
`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.
`matrix_column &operator = (const matrix_column &mc)`	The assignment operator.
`matrix_column &assign_temporary (matrix_column &mc)`	Assigns a temporary. May change the matrix column `mc` .
`template<class AE> matrix_column &operator = (const vector_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_column &assign (const vector_expression<AE> &ae)`	Assigns a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_column &operator += (const vector_expression<AE> &ae)`	A computed assignment operator. Adds the vector expression to the sub vector.
`template<class AE> matrix_column &plus_assign (const vector_expression<AE> &ae)`	Adds a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_column &operator -= (const vector_expression<AE> &ae)`	A computed assignment operator. Subtracts the vector expression from the sub vector.
`template<class AE> matrix_column &minus_assign (const vector_expression<AE> &ae)`	Subtracts a vector expression from the sub vector. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_column &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub vector with a scalar.
`template<class AT> matrix_column &operator /= (const AT &at)`	A computed assignment operator. Divides the sub vector through a scalar.
`void swap (matrix_column &mc)`	Swaps the contents of the sub vectors.
`const_iterator begin () const`	Returns a `const_iterator` pointing to the beginning of the `matrix_column`.
`const_iterator end () const`	Returns a `const_iterator` pointing to the end of the `matrix_column`.
`iterator begin ()`	Returns a `iterator` pointing to the beginning of the `matrix_column`.
`iterator end ()`	Returns a `iterator` pointing to the end of the `matrix_column`.
`const_reverse_iterator rbegin () const`	Returns a `const_reverse_iterator` pointing to the beginning of the reversed `matrix_column`.
`const_reverse_iterator rend () const`	Returns a `const_reverse_iterator` pointing to the end of the reversed `matrix_column`.
`reverse_iterator rbegin ()`	Returns a `reverse_iterator` pointing to the beginning of the reversed `matrix_column`.
`reverse_iterator rend ()`	Returns a `reverse_iterator` pointing to the end of the reversed `matrix_column`.

Interface

// Matrix based column vector class

    template<class M>

    class matrix_column:

        public vector_expression<matrix_column<M> > {

    public:     

         typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const vector_const_reference<const matrix_column<matrix_type> > const_closure_type;

        typedef vector_reference<matrix_column<matrix_type> > closure_type;

        typedef typename M::const_iterator1 const_iterator_type;

        typedef typename M::iterator1 iterator_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;



        // Construction and destruction

        matrix_column ();

        matrix_column (matrix_type &data, size_type j);



        // Accessors

        size_type size () const;

        const_matrix_type &data () const;

        matrix_type &data ();





        // 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);



        // Assignment

        matrix_column &operator = (const matrix_column &mc);

        matrix_column &assign_temporary (matrix_column &mc);

        template<class AE>

        matrix_column &operator = (const vector_expression<AE> &ae);

        template<class AE>

        matrix_column &assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_column &operator += (const vector_expression<AE> &ae);

        template<class AE>

        matrix_column &plus_assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_column &operator -= (const vector_expression<AE> &ae);

        template<class AE>

        matrix_column &minus_assign (const vector_expression<AE> &ae);

        template<class AT>

        matrix_column &operator *= (const AT &at);

        template<class AT>

        matrix_column &operator /= (const AT &at);



        // Swapping

        void swap (matrix_column &mc);

        friend void swap (matrix_column &mc1, matrix_column &mc2);



        class const_iterator;

        class 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);



        // Iterators simply are pointers.



        class const_iterator:

            public container_const_reference<matrix_column>,

            public random_access_iterator_base<const_iterator, value_type> {

        public:

            typedef typename const_iterator_type::iterator_category iterator_category;

            typedef typename const_iterator_type::difference_type difference_type;

            typedef typename const_iterator_type::value_type value_type;

            typedef typename const_iterator_type::reference reference;

            typedef typename const_iterator_type::pointer pointer;



            // Construction and destruction

            const_iterator ();

            const_iterator (const matrix_column &mc, const const_iterator_type &it);

            const_iterator (const iterator &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;



        class iterator:

            public container_reference<matrix_column>,

            public random_access_iterator_base<iterator, value_type> {

        public:

            typedef typename iterator_type::iterator_category iterator_category;

            typedef typename iterator_type::difference_type difference_type;

            typedef typename iterator_type::value_type value_type;

            typedef typename iterator_type::reference reference;

            typedef typename iterator_type::pointer pointer;



            // Construction and destruction

            iterator ();

            iterator (matrix_column &mc, const iterator_type &it);



            // Arithmetic

            iterator &operator ++ ();

            iterator &operator -- ();

            iterator &operator += (difference_type n);

            iterator &operator -= (difference_type n);

            difference_type operator - (const iterator &it) const;



            // Dereference

            reference operator * () const;



            // Index

            size_type index () const;



            // Assignment

             iterator &operator = (const iterator &it);



            // Comparison

            bool operator == (const iterator &it) const;

            bool operator <(const iterator &it) 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 ();

    };

Projections

Prototypes

template<class M>

    matrix_column<M> column (M &data, std::size_t j);

    template<class M>

    const matrix_column<const M> column (const M &data, std::size_t j);

Description

The free column functions support the construction of matrix columns.

Definition

Defined in the header matrix_proxy.hpp.

Type requirements

M is a model of Matrix Expression .

Preconditions

j < data.size2 ()

Complexity

Linear depending from the size of the column.

Examples

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned j = 0; j < m.size2 (); ++ j) {

        for (unsigned i = 0; i < m.size1 (); ++ i)

            column (m, j) (i) = 3 * i + j;

        std::cout << column (m, j) << std::endl;

    }

}

Vector Range

Description

The templated class matrix_vector_range<M> allows addressing a sub vector of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i)

        for (unsigned j = 0; j < m.size2 (); ++ j)

            m (i, j) = 3 * i + j;



    matrix_vector_range<matrix<double> > mvr (m, range (0, 3), range (0, 3));

    std::cout << mvr << std::endl;

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Vector Expression .

Type requirements

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

Public base classes

vector_expression<matrix_vector_range<M> >

Members

Member	Description
`matrix_vector_range (matrix_type &data, const range &r1, const range &r2)`	Constructs a sub vector.
`size_type size () const`	Returns the size of the sub vector.
`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.
`matrix_vector_range &operator = (const matrix_vector_range &mvr)`	The assignment operator.
`matrix_vector_range &assign_temporary (matrix_vector_range &mvr)`	Assigns a temporary. May change the matrix vector range `mvr`.
`template<class AE> matrix_vector_range &operator = (const vector_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_vector_range &assign (const vector_expression<AE> &ae)`	Assigns a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_vector_range &operator += (const vector_expression<AE> &ae)`	A computed assignment operator. Adds the vector expression to the sub vector.
`template<class AE> matrix_vector_range &plus_assign (const vector_expression<AE> &ae)`	Adds a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_vector_range &operator -= (const vector_expression<AE> &ae)`	A computed assignment operator. Subtracts the vector expression from the sub vector.
`template<class AE> matrix_vector_range &minus_assign (const vector_expression<AE> &ae)`	Subtracts a vector expression from the sub vector. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_vector_range &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub vector with a scalar.
`template<class AT> matrix_vector_range &operator /= (const AT &at)`	A computed assignment operator. Divides the sub vector through a scalar.
`void swap (matrix_vector_range &mvr)`	Swaps the contents of the sub vectors.
`const_iterator begin () const`	Returns a `const_iterator` pointing to the beginning of the `matrix_vector_range`.
`const_iterator end () const`	Returns a `const_iterator` pointing to the end of the `matrix_vector_range`.
`iterator begin ()`	Returns a `iterator` pointing to the beginning of the `matrix_vector_range`.
`iterator end ()`	Returns a `iterator` pointing to the end of the `matrix_vector_range`.
`const_reverse_iterator rbegin () const`	Returns a `const_reverse_iterator` pointing to the beginning of the `matrix_vector_range`.
`const_reverse_iterator rend () const`	Returns a `const_reverse_iterator` pointing to the end of the reversed `matrix_vector_range`.
`reverse_iterator rbegin ()`	Returns a `reverse_iterator` pointing to the beginning of the reversed `matrix_vector_range`.
`reverse_iterator rend ()`	Returns a `reverse_iterator` pointing to the end of the reversed `matrix_vector_range`.

Interface

// Matrix based vector range class

    template<class M>

    class matrix_vector_range:

        public vector_expression<matrix_vector_range<M> > {

    public:     

         typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const vector_const_reference<const matrix_vector_range<matrix_type> > const_closure_type;

        typedef vector_reference<matrix_vector_range<matrix_type> > closure_type;

        typedef range::const_iterator const_iterator1_type;

        typedef range::const_iterator iterator1_type;

        typedef range::const_iterator const_iterator2_type;

        typedef range::const_iterator iterator2_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;



        // Construction and destruction

        matrix_vector_range ();

        matrix_vector_range (matrix_type &data, const range &r1, const range &r2);



        // Accessors

        size_type size () const;

        const_matrix_type &data () const;

        matrix_type &data ();





        // 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);



        // Assignment

        matrix_vector_range &operator = (const matrix_vector_range &mvr);

        matrix_vector_range &assign_temporary (matrix_vector_range &mvr);

        template<class AE>

        matrix_vector_range &operator = (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_range &assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_range &operator += (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_range &plus_assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_range &operator -= (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_range &minus_assign (const vector_expression<AE> &ae);

        template<class AT>

        matrix_vector_range &operator *= (const AT &at);

        template<class AT>

        matrix_vector_range &operator /= (const AT &at);



        // Swapping

        void swap (matrix_vector_range &mvr);

        friend void swap (matrix_vector_range &mvr1, matrix_vector_range &mvr2);



        class const_iterator;

        class 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);



        // Iterators simply are indices.



        class const_iterator:

            public container_const_reference<matrix_vector_range>,

            public random_access_iterator_base<const_iterator, value_type> {

        public:

            typedef typename restrict_traits<typename M::const_iterator1::iterator_category,

                                             typename M::const_iterator2::iterator_category>::iterator_category iterator_category;

             typedef typename matrix_vector_range::difference_type difference_type;

            typedef typename matrix_vector_range::value_type value_type;

            typedef typename matrix_vector_range::const_reference reference;

            typedef typename matrix_vector_range::const_pointer pointer;



            // Construction and destruction

            const_iterator ();

            const_iterator (const matrix_vector_range &mvr, const const_iterator1_type &it1, const const_iterator2_type &it2);

            const_iterator (const iterator &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;



        class iterator:

            public container_reference<matrix_vector_range>,

            public random_access_iterator_base<iterator, value_type> {

        public:

            typedef typename restrict_traits<typename M::iterator1::iterator_category,

                                             typename M::iterator2::iterator_category>::iterator_category iterator_category;

             typedef typename matrix_vector_range::difference_type difference_type;

            typedef typename matrix_vector_range::value_type value_type;

            typedef typename matrix_vector_range::reference reference;

            typedef typename matrix_vector_range::pointer pointer;



            // Construction and destruction

            iterator ();

            iterator (matrix_vector_range &mvr, const iterator1_type &it1, const iterator2_type &it2);



            // Arithmetic

            iterator &operator ++ ();

            iterator &operator -- ();

            iterator &operator += (difference_type n);

            iterator &operator -= (difference_type n);

            difference_type operator - (const iterator &it) const;



            // Dereference

            reference operator * () const;



            // Index

            size_type index () const;



            // Assignment

             iterator &operator = (const iterator &it);



            // Comparison

            bool operator == (const iterator &it) const;

            bool operator <(const iterator &it) 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 Slice

Description

The templated class matrix_vector_slice<M> allows addressing a sliced sub vector of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i)

        for (unsigned j = 0; j < m.size2 (); ++ j)

            m (i, j) = 3 * i + j;



    matrix_vector_slice<matrix<double> > mvs (m, slice (0, 1, 3), slice (0, 1, 3));

    std::cout << mvs << std::endl;

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Vector Expression .

Type requirements

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

Public base classes

vector_expression<matrix_vector_slice<M> >

Members

Member	Description
`matrix_vector_slice (matrix_type &data, const slice &s1, const slice &s2)`	Constructs a sub vector.
`size_type size () const`	Returns the size of the sub vector.
`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.
`matrix_vector_slice &operator = (const matrix_vector_slice &mvs)`	The assignment operator.
`matrix_vector_slice &assign_temporary (matrix_vector_slice &mvs)`	Assigns a temporary. May change the matrix vector slice `vs`.
`template<class AE> matrix_vector_slice &operator = (const vector_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_vector_slice &assign (const vector_expression<AE> &ae)`	Assigns a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_vector_slice &operator += (const vector_expression<AE> &ae)`	A computed assignment operator. Adds the vector expression to the sub vector.
`template<class AE> matrix_vector_slice &plus_assign (const vector_expression<AE> &ae)`	Adds a vector expression to the sub vector. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_vector_slice &operator -= (const vector_expression<AE> &ae)`	A computed assignment operator. Subtracts the vector expression from the sub vector.
`template<class AE> matrix_vector_slice &minus_assign (const vector_expression<AE> &ae)`	Subtracts a vector expression from the sub vector. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_vector_slice &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub vector with a scalar.
`template<class AT> matrix_vector_slice &operator /= (const AT &at)`	A computed assignment operator. Divides the sub vector through a scalar.
`void swap (matrix_vector_slice &mvs)`	Swaps the contents of the sub vectors.
`const_iterator begin () const`	Returns a `const_iterator` pointing to the beginning of the `matrix_vector_slice`.
`const_iterator end () const`	Returns a `const_iterator` pointing to the end of the `matrix_vector_slice`.
`iterator begin ()`	Returns a `iterator` pointing to the beginning of the `matrix_vector_slice`.
`iterator end ()`	Returns a `iterator` pointing to the end of the `matrix_vector_slice`.
`const_reverse_iterator rbegin () const`	Returns a `const_reverse_iterator` pointing to the beginning of the reversed `matrix_vector_slice`.
`const_reverse_iterator rend () const`	Returns a `const_reverse_iterator` pointing to the end of the reversed `matrix_vector_slice`.
`reverse_iterator rbegin ()`	Returns a `reverse_iterator` pointing to the beginning of the reversed `matrix_vector_slice`.
`reverse_iterator rend ()`	Returns a `reverse_iterator` pointing to the end of the reversed `matrix_vector_slice`.

Interface

// Matrix based vector slice class

    template<class M>

    class matrix_vector_slice:

        public vector_expression<matrix_vector_slice<M> > {

    public:     

         typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const vector_const_reference<const matrix_vector_slice<matrix_type> > const_closure_type;

        typedef vector_reference<matrix_vector_slice<matrix_type> > closure_type;

        typedef slice::const_iterator const_iterator1_type;

        typedef slice::const_iterator iterator1_type;

        typedef slice::const_iterator const_iterator2_type;

        typedef slice::const_iterator iterator2_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;



        // Construction and destruction

        matrix_vector_slice ();

        matrix_vector_slice (matrix_type &data, const slice &s1, const slice &s2);



        // Accessors

        size_type size () const;

        const_matrix_type &data () const;

        matrix_type &data ();





        // 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);



        // Assignment

        matrix_vector_slice &operator = (const matrix_vector_slice &mvs);

        matrix_vector_slice &assign_temporary (matrix_vector_slice &mvs);

        template<class AE>

        matrix_vector_slice &operator = (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_slice &assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_slice &operator += (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_slice &plus_assign (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_slice &operator -= (const vector_expression<AE> &ae);

        template<class AE>

        matrix_vector_slice &minus_assign (const vector_expression<AE> &ae);

        template<class AT>

        matrix_vector_slice &operator *= (const AT &at);

        template<class AT>

        matrix_vector_slice &operator /= (const AT &at);



        // Swapping

        void swap (matrix_vector_slice &mvs);

        friend void swap (matrix_vector_slice &mvs1, matrix_vector_slice &mvs2);



        class const_iterator;

        class 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);



        // Iterators simply are indices.



        class const_iterator:

            public container_const_reference<matrix_vector_slice>,

            public random_access_iterator_base<const_iterator, value_type> {

        public:

            typedef typename restrict_traits<typename M::const_iterator1::iterator_category,

                                             typename M::const_iterator2::iterator_category>::iterator_category iterator_category;

             typedef typename matrix_vector_slice::difference_type difference_type;

            typedef typename matrix_vector_slice::value_type value_type;

            typedef typename matrix_vector_slice::const_reference reference;

            typedef typename matrix_vector_slice::const_pointer pointer;



            // Construction and destruction

            const_iterator ();

            const_iterator (const matrix_vector_slice &mvs, const const_iterator1_type &it1, const const_iterator2_type &it2);

            const_iterator (const iterator &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;



        class iterator:

            public container_reference<matrix_vector_slice>,

            public random_access_iterator_base<iterator, value_type> {

        public:

            typedef typename restrict_traits<typename M::iterator1::iterator_category,

                                             typename M::iterator2::iterator_category>::iterator_category iterator_category;

             typedef typename matrix_vector_slice::difference_type difference_type;

            typedef typename matrix_vector_slice::value_type value_type;

            typedef typename matrix_vector_slice::reference reference;

            typedef typename matrix_vector_slice::pointer pointer;



            // Construction and destruction

            iterator ();

            iterator (matrix_vector_slice &mvs, const iterator1_type &it1, const iterator2_type &it2);



            // Arithmetic

            iterator &operator ++ ();

            iterator &operator -- ();

            iterator &operator += (difference_type n);

            iterator &operator -= (difference_type n);

            difference_type operator - (const iterator &it) const;



            // Dereference

            reference operator * () const;



            // Index

            size_type index () const;



            // Assignment

             iterator &operator = (const iterator &it);



            // Comparison

            bool operator == (const iterator &it) const;

            bool operator <(const iterator &it) 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 ();

    };

Matrix Range

Description

The templated class matrix_range<M> allows addressing a sub matrix of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    matrix_range<matrix<double> > mr (m, range (0, 3), range (0, 3));

    for (unsigned i = 0; i < mr.size1 (); ++ i)

        for (unsigned j = 0; j < mr.size2 (); ++ j)

            mr (i, j) = 3 * i + j;

    std::cout << mr << std::endl;

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<matrix_range<M> >

Members

Member	Description
`matrix_range (matrix_type &data, const range &r1, const range &r2)`	Constructs a sub matrix.
`size_type start1 () const`	Returns the index of the first row.
`size_type size1 () const`	Returns the number of rows.
`size_type start2 () const`	Returns the index of the first column.
`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.
`reference operator () (size_type i, size_type j)`	Returns a reference of the `j`-th element in the `i`-th row.
`matrix_range &operator = (const matrix_range &mr)`	The assignment operator.
`matrix_range &assign_temporary (matrix_range &mr)`	Assigns a temporary. May change the matrix range `mr` .
`template<class AE> matrix_range &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_range &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_range &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the sub matrix.
`template<class AE> matrix_range &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_range &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the sub matrix.
`template<class AE> matrix_range &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_range &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub matrix with a scalar.
`template<class AT> matrix_range &operator /= (const AT &at)`	A computed assignment operator. Divides the sub matrix through a scalar.
`void swap (matrix_range &mr)`	Swaps the contents of the sub matrices.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `matrix_range`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `matrix_range`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `matrix_range`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `matrix_range`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `matrix_range`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `matrix_range`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `matrix_range`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `matrix_range`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `matrix_range`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `matrix_range`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `matrix_range`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `matrix_range`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `matrix_range`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `matrix_range`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `matrix_range`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of reversed the `matrix_range`.

Interface

// Matrix based range class

    template<class M>

    class matrix_range:

        public matrix_expression<matrix_range<M> > {

    public:     

         typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const matrix_const_reference<const matrix_range<matrix_type> > const_closure_type;

        typedef matrix_reference<matrix_range<matrix_type> > closure_type;

        typedef typename M::const_iterator1 const_iterator1_type;

        typedef typename M::iterator1 iterator1_type;

        typedef typename M::const_iterator2 const_iterator2_type;

        typedef typename M::iterator2 iterator2_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;

        typedef typename M::orientation_category orientation_category;



        // Construction and destruction

        matrix_range ();

        matrix_range (matrix_type &data, const range &r1, const range &r2);



        // Accessors

        size_type start1 () const;

        size_type size1 () const;

        size_type start2() const;

        size_type size2 () const;

        const_matrix_type &data () const;

        matrix_type &data ();





        // Element access

        const_reference operator () (size_type i, size_type j) const;

        reference operator () (size_type i, size_type j);



        matrix_range<matrix_type> project (const range &r1, const range &r2) const;



        // Assignment

        matrix_range &operator = (const matrix_range &mr);

        matrix_range &assign_temporary (matrix_range &mr);

        template<class AE>

        matrix_range &operator = (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_range &assign (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_range& operator += (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_range &plus_assign (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_range& operator -= (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_range &minus_assign (const matrix_expression<AE> &ae);

        template<class AT>

        matrix_range& operator *= (const AT &at);

        template<class AT>

        matrix_range& operator /= (const AT &at);



        // Swapping

        void swap (matrix_range &mr);

        friend void swap (matrix_range &mr1, matrix_range &mr2);



        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;

        typedef reverse_iterator_base1<iterator1> reverse_iterator1;

        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

        typedef reverse_iterator_base2<iterator2> reverse_iterator2;



        // Element lookup

        const_iterator1 find_first1 (int rank, size_type i, size_type j) const;

        iterator1 find_first1 (int rank, size_type i, size_type j);

        const_iterator1 find_last1 (int rank, size_type i, size_type j) const;

        iterator1 find_last1 (int rank, size_type i, size_type j);

        const_iterator2 find_first2 (int rank, size_type i, size_type j) const;

        iterator2 find_first2 (int rank, size_type i, size_type j);

        const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

        iterator2 find_last2 (int rank, size_type i, size_type j);



        // Iterators simply are pointers.



        class const_iterator1:

            public container_const_reference<matrix_range>,

            public random_access_iterator_base<const_iterator1, value_type> {

        public:

            typedef typename const_iterator1_type::iterator_category iterator_category;

            typedef typename const_iterator1_type::difference_type difference_type;

            typedef typename const_iterator1_type::value_type value_type;

            typedef typename const_iterator1_type::reference reference;

            typedef typename const_iterator1_type::pointer pointer;

            typedef const_iterator2 dual_iterator_type;

            typedef const_reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator1 ();

            const_iterator1 (const matrix_range &mr, const const_iterator1_type &it);

            const_iterator1 (const iterator1 &it);



            // 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 iterator1:

            public container_reference<matrix_range>,

            public random_access_iterator_base<iterator1, value_type> {

        public:

            typedef typename iterator1_type::iterator_category iterator_category;

            typedef typename iterator1_type::difference_type difference_type;

            typedef typename iterator1_type::value_type value_type;

            typedef typename iterator1_type::reference reference;

            typedef typename iterator1_type::pointer pointer;

            typedef iterator2 dual_iterator_type;

            typedef reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            iterator1 ();

            iterator1 (matrix_range &mr, const iterator1_type &it);



            // Arithmetic

            iterator1 &operator ++ ();

            iterator1 &operator -- ();

            iterator1 &operator += (difference_type n);

            iterator1 &operator -= (difference_type n);

            difference_type operator - (const iterator1 &it) const;



            // Dereference

            reference operator * () const;



            iterator2 begin () const;

            iterator2 end () const;

            reverse_iterator2 rbegin () const;

            reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment

             iterator1 &operator = (const iterator1 &it);



            // Comparison

            bool operator == (const iterator1 &it) const;

            bool operator <(const iterator1 &it) const;

        };



        iterator1 begin1 ();

        iterator1 end1 ();



        class const_iterator2:

            public container_const_reference<matrix_range>,

            public random_access_iterator_base<const_iterator2, value_type> {

        public:

            typedef typename const_iterator2_type::iterator_category iterator_category;

            typedef typename const_iterator2_type::difference_type difference_type;

            typedef typename const_iterator2_type::value_type value_type;

            typedef typename const_iterator2_type::reference reference;

            typedef typename const_iterator2_type::pointer pointer;

            typedef const_iterator1 dual_iterator_type;

            typedef const_reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator2 ();

            const_iterator2 (const matrix_range &mr, const const_iterator2_type &it);

            const_iterator2 (const iterator2 &it);



            // 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;



        class iterator2:

            public container_reference<matrix_range>,

            public random_access_iterator_base<iterator2, value_type> {

        public:

            typedef typename iterator2_type::iterator_category iterator_category;

            typedef typename iterator2_type::difference_type difference_type;

            typedef typename iterator2_type::value_type value_type;

            typedef typename iterator2_type::reference reference;

            typedef typename iterator2_type::pointer pointer;

            typedef iterator1 dual_iterator_type;

            typedef reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            iterator2 ();

            iterator2 (matrix_range &mr, const iterator2_type &it);



            // Arithmetic

            iterator2 &operator ++ ();

            iterator2 &operator -- ();

            iterator2 &operator += (difference_type n);

            iterator2 &operator -= (difference_type n);

            difference_type operator - (const iterator2 &it) const;



            // Dereference

            reference operator * () const;



            iterator1 begin () const;

            iterator1 end () const;

            reverse_iterator1 rbegin () const;

            reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment

             iterator2 &operator = (const iterator2 &it);



            // Comparison

            bool operator == (const iterator2 &it) const;

            bool operator <(const iterator2 &it) const;

        };



        iterator2 begin2 ();

        iterator2 end2 ();



        // Reverse iterators



        const_reverse_iterator1 rbegin1 () const;

        const_reverse_iterator1 rend1 () const;



        reverse_iterator1 rbegin1 ();

        reverse_iterator1 rend1 ();



        const_reverse_iterator2 rbegin2 () const;

        const_reverse_iterator2 rend2 () const;



        reverse_iterator2 rbegin2 ();

        reverse_iterator2 rend2 ();

    };

Projections

Prototypes

template<class M>

    matrix_range<M> project (M &data, const range &r1, const range &r2);

    template<class M>

    const matrix_range<const M> project (const M &data, const range &r1, const range &r2);

    template<class M>

    matrix_range<M> project (const matrix_range<M> &data, const range &r1, const range &r2);

Description

The free project functions support the construction of matrix ranges.

Definition

Defined in the header matrix_proxy.hpp.

Type requirements

M is a model of Matrix Expression .

Preconditions

r1.start () + r1.size () <= data.size1 ()
r2.start () + r2.size () <= data.size2 ()

Complexity

Quadratic depending from the size of the ranges.

Examples

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i)

        for (unsigned j = 0; j < m.size2 (); ++ j)

            project (m, range (0, 3), range (0, 3)) (i, j) = 3 * i + j;

    std::cout << project (m, range (0, 3), range (0, 3)) << std::endl;

}

Matrix Slice

Description

The templated class matrix_slice<M> allows addressing a sliced sub matrix of a matrix.

Example

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    matrix_slice<matrix<double> > ms (m, slice (0, 1, 3), slice (0, 1, 3));

    for (unsigned i = 0; i < ms.size1 (); ++ i)

        for (unsigned j = 0; j < ms.size2 (); ++ j)

            ms (i, j) = 3 * i + j;

    std::cout << ms << std::endl;

}

Definition

Defined in the header matrix_proxy.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of matrix referenced.

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<matrix_slice<M> >

Members

Member	Description
`matrix_slice (matrix_type &data, const slice &s1, const slice &s2)`	Constructs a sub matrix.
`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.
`reference operator () (size_type i, size_type j)`	Returns a reference of the `j`-th element in the `i`-th row.
`matrix_slice &operator = (const matrix_slice &ms)`	The assignment operator.
`matrix_slice &assign_temporary (matrix_slice &ms)`	Assigns a temporary. May change the matrix slice `ms` .
`template<class AE> matrix_slice &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix_slice &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_slice &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the sub matrix.
`template<class AE> matrix_slice &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix_slice &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the sub matrix.
`template<class AE> matrix_slice &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the sub matrix. Left and right hand side of the assignment should be independent.
`template<class AT> matrix_slice &operator *= (const AT &at)`	A computed assignment operator. Multiplies the sub matrix with a scalar.
`template<class AT> matrix_slice &operator /= (const AT &at)`	A computed assignment operator. Multiplies the sub matrix through a scalar.
`void swap (matrix_slice &ms)`	Swaps the contents of the sub matrices.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `matrix_slice`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `matrix_slice`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `matrix_slice`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `matrix_slice`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `matrix_slice`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `matrix_slice`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `matrix_slice`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `matrix_slice`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `matrix_slice`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `matrix_slice`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `matrix_slice`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `matrix_slice`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `matrix_slice`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `matrix_slice`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `matrix_slice`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `matrix_slice`.

Interface

// Matrix based slice class

    template<class M>

    class matrix_slice:

        public matrix_expression<matrix_slice<M> > {

    public:     

         typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::const_reference const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const matrix_const_reference<const matrix_slice<matrix_type> > const_closure_type;

        typedef matrix_reference<matrix_slice<matrix_type> > closure_type;

        typedef slice::const_iterator const_iterator1_type;

        typedef slice::const_iterator iterator1_type;

        typedef slice::const_iterator const_iterator2_type;

        typedef slice::const_iterator iterator2_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 dense_proxy_tag>::storage_category storage_category;

        typedef typename M::orientation_category orientation_category;



        // Construction and destruction

        matrix_slice ();

        matrix_slice (matrix_type &data, const slice &s1, const slice &s2);



        // Accessors

        size_type size1 () const;

        size_type size2 () const;

        const_matrix_type &data () const;

        matrix_type &data ();



        // Element access

        const_reference operator () (size_type i, size_type j) const;

        reference operator () (size_type i, size_type j);



        matrix_slice<matrix_type> project (const range &r1, const range &r2) const;

        matrix_slice<matrix_type> project (const slice &s1, const slice &s2) const;



        // Assignment

        matrix_slice &operator = (const matrix_slice &ms);

        matrix_slice &assign_temporary (matrix_slice &ms);

        template<class AE>

        matrix_slice &operator = (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_slice &assign (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_slice& operator += (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_slice &plus_assign (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_slice& operator -= (const matrix_expression<AE> &ae);

        template<class AE>

        matrix_slice &minus_assign (const matrix_expression<AE> &ae);

        template<class AT>

        matrix_slice& operator *= (const AT &at);

        template<class AT>

        matrix_slice& operator /= (const AT &at);



        // Swapping

        void swap (matrix_slice &ms);

        friend void swap (matrix_slice &ms1, matrix_slice &ms2);



        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;

        typedef reverse_iterator_base1<iterator1> reverse_iterator1;

        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

        typedef reverse_iterator_base2<iterator2> reverse_iterator2;



        // Element lookup

        const_iterator1 find_first1 (int rank, size_type i, size_type j) const;

        iterator1 find_first1 (int rank, size_type i, size_type j);

        const_iterator1 find_last1 (int rank, size_type i, size_type j) const;

        iterator1 find_last1 (int rank, size_type i, size_type j);

        const_iterator2 find_first2 (int rank, size_type i, size_type j) const;

        iterator2 find_first2 (int rank, size_type i, size_type j);

        const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

        iterator2 find_last2 (int rank, size_type i, size_type j);



        // Iterators simply are indices.



        class const_iterator1:

            public container_const_reference<matrix_slice>,

            public random_access_iterator_base<const_iterator1, value_type> {

        public:

            typedef typename M::const_iterator1::iterator_category iterator_category;

            typedef typename M::const_iterator1::difference_type difference_type;

            typedef typename M::const_iterator1::value_type value_type;

            typedef typename M::const_iterator1::reference reference;

            typedef typename M::const_iterator1::pointer pointer;

            typedef const_iterator2 dual_iterator_type;

            typedef const_reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator1 ();

            const_iterator1 (const matrix_slice &ms, const const_iterator1_type &it1, const const_iterator2_type &it2);

            const_iterator1 (const iterator1 &it);



            // 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 iterator1:

            public container_reference<matrix_slice>,

            public random_access_iterator_base<iterator1, value_type> {

        public:

            typedef typename M::iterator1::iterator_category iterator_category;

            typedef typename M::iterator1::difference_type difference_type;

            typedef typename M::iterator1::value_type value_type;

            typedef typename M::iterator1::reference reference;

            typedef typename M::iterator1::pointer pointer;

            typedef iterator2 dual_iterator_type;

            typedef reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            iterator1 ();

            iterator1 (matrix_slice &ms, const iterator1_type &it1, const iterator2_type &it2);



            // Arithmetic

            iterator1 &operator ++ ();

            iterator1 &operator -- ();

            iterator1 &operator += (difference_type n);

            iterator1 &operator -= (difference_type n);

            difference_type operator - (const iterator1 &it) const;



            // Dereference

            reference operator * () const;



            iterator2 begin () const;

            iterator2 end () const;

            reverse_iterator2 rbegin () const;

            reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment

            iterator1 &operator = (const iterator1 &it);



            // Comparison

            bool operator == (const iterator1 &it) const;

            bool operator <(const iterator1 &it) const;

        };



        iterator1 begin1 ();

        iterator1 end1 ();



        class const_iterator2:

            public container_const_reference<matrix_slice>,

            public random_access_iterator_base<const_iterator2, value_type> {

        public:

            typedef typename M::const_iterator2::iterator_category iterator_category;

            typedef typename M::const_iterator2::difference_type difference_type;

            typedef typename M::const_iterator2::value_type value_type;

            typedef typename M::const_iterator2::reference reference;

            typedef typename M::const_iterator2::pointer pointer;

            typedef const_iterator1 dual_iterator_type;

            typedef const_reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator2 ();

            const_iterator2 (const matrix_slice &ms, const const_iterator1_type &it1, const const_iterator2_type &it2);

            const_iterator2 (const iterator2 &it);



            // 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;



        class iterator2:

            public container_reference<matrix_slice>,

            public random_access_iterator_base<iterator2, value_type> {

        public:

            typedef typename M::iterator2::iterator_category iterator_category;

            typedef typename M::iterator2::difference_type difference_type;

            typedef typename M::iterator2::value_type value_type;

            typedef typename M::iterator2::reference reference;

            typedef typename M::iterator2::pointer pointer;

            typedef iterator1 dual_iterator_type;

            typedef reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            iterator2 ();

            iterator2 (matrix_slice &ms, const iterator1_type &it1, const iterator2_type &it2);



            // Arithmetic

            iterator2 &operator ++ ();

            iterator2 &operator -- ();

            iterator2 &operator += (difference_type n);

            iterator2 &operator -= (difference_type n);

            difference_type operator - (const iterator2 &it) const;



            // Dereference

            reference operator * () const;



            iterator1 begin () const;

            iterator1 end () const;

            reverse_iterator1 rbegin () const;

            reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment

            iterator2 &operator = (const iterator2 &it);



            // Comparison

            bool operator == (const iterator2 &it) const;

            bool operator <(const iterator2 &it) const;

        };



        iterator2 begin2 ();

        iterator2 end2 ();



        // Reverse iterators



        const_reverse_iterator1 rbegin1 () const;

        const_reverse_iterator1 rend1 () const;



        reverse_iterator1 rbegin1 ();

        reverse_iterator1 rend1 ();



        const_reverse_iterator2 rbegin2 () const;

        const_reverse_iterator2 rend2 () const;



        reverse_iterator2 rbegin2 ();

        reverse_iterator2 rend2 ();

    };

Projections

Prototypes

template<class M>

    matrix_slice<M> project (const matrix_slice<M> &data, const range &r1, const range &r2);

    template<class M>

    matrix_slice<M> project (M &data, const slice &s1, const slice &s2);

    template<class M>

    const matrix_slice<const M> project (const M &data, const slice &s1, const slice &s2);

    template<class M>

    matrix_slice<M> project (const matrix_slice<M> &data, const slice &s1, const slice &s2);

Description

The free project functions support the construction of matrix slices.

Definition

Defined in the header matrix_proxy.hpp.

Type requirements

M is a model of Matrix Expression .

Preconditions

s1.start () + s1.stride () * s1.size () <= data.size1 ()
s2.start () + s2.stride () * s2.size () <= data.size2 ()

Complexity

Quadratic depending from the size of the slices.

Examples

#include <boost/numeric/ublas/matrix.hpp>

#include <boost/numeric/ublas/io.hpp>



int main () {

    using namespace boost::numeric::ublas;

    matrix<double> m (3, 3);

    for (unsigned i = 0; i < m.size1 (); ++ i)

        for (unsigned j = 0; j < m.size2 (); ++ j)

            project (m, slice (0, 1, 3), slice (0, 1, 3)) (i, j) = 3 * i + j;

    std::cout << project (m, slice (0, 1, 3), slice (0, 1, 3)) << 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