# 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`.

### 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`.

### 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`.

## 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`.

## 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`.

### 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`.

### 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