c++boost.gif 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

    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

    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

    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

    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