# Matrix

#### Description

The templated class `matrix<T, F, A>` is the base container adaptor for dense matrices. For a (m x n)-dimensional matrix and 0 <= i < m, 0 <= j < n every element mi, j is mapped to the (i x n + j)-th element of the container for row major orientation or the (i + j x m)-th element of the container for column major orientation.

#### 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;
        std::cout << m << std::endl;
    }

#### Definition

Defined in the header matrix.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the matrix. |
`F` | Functor describing the storage organization. [1] | `row_major`
`A` | The type of the adapted array. [2] | `unbounded_array<T>`

#### Model of

Matrix .

#### Type requirements

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

#### Public base classes

`matrix_expression<matrix<T, F, A> >`

#### Members

Member | Description
--- | ---
`matrix ()` | Allocates an uninitialized `matrix` that holds zero rows of zero elements.
`matrix (size_type size1, size_type size2)` | Allocates an uninitialized `matrix` that holds `size1` rows of `size2` elements.
`matrix (const matrix &m)` | The copy constructor.
`template<class AE> matrix (const matrix_expression<AE> &ae)` | The extended copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)` | Reallocates a `matrix` to hold `size1` rows of `size2` elements. The existing elements of the `matrix` are preseved when specified.
`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 a `const` reference 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 &operator = (const matrix &m)` | The assignment operator.
`matrix &assign_temporary (matrix &m)` | Assigns a temporary. May change the matrix `m`.
`template<class AE> matrix &operator = (const matrix_expression<AE> &ae)` | The extended assignment operator.
`template<class AE> matrix &assign (const matrix_expression<AE> &ae)` | Assigns a matrix expression to the matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix &operator += (const matrix_expression<AE> &ae)` | A computed assignment operator. Adds the matrix expression to the matrix.
`template<class AE> matrix &plus_assign (const matrix_expression<AE> &ae)` | Adds a matrix expression to the matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix &operator -= (const matrix_expression<AE> &ae)` | A computed assignment operator. Subtracts the matrix expression from the matrix.
`template<class AE> matrix &minus_assign (const matrix_expression<AE> &ae)` | Subtracts a matrix expression from the matrix. Left and right hand side of the assignment should be independent.
`template<class AT> matrix &operator *= (const AT &at)` | A computed assignment operator. Multiplies the matrix with a scalar.
`template<class AT> matrix &operator /= (const AT &at)` | A computed assignment operator. Divides the matrix through a scalar.
`void swap (matrix &m)` | Swaps the contents of the matrices.
`void insert (size_type i, size_type j, const_reference t)` | Inserts the value `t` at the `j`-th element of the `i`-th row.
`void erase (size_type i, size_type j)` | Erases the value at the `j`-th element of the `i`-th row.
`void clear ()` | Clears the matrix.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `matrix`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `matrix`.
`iterator1 begin1 ()` | Returns a `iterator1` pointing to the beginning of the `matrix`.
`iterator1 end1 ()` | Returns a `iterator1` pointing to the end of the `matrix`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `matrix`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `matrix`.
`iterator2 begin2 ()` | Returns a `iterator2` pointing to the beginning of the `matrix`.
`iterator2 end2 ()` | Returns a `iterator2` pointing to the end of the `matrix`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `matrix`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `matrix`.
`reverse_iterator1 rbegin1 ()` | Returns a `reverse_iterator1` pointing to the beginning of the reversed `matrix`.
`reverse_iterator1 rend1 ()` | Returns a `reverse_iterator1` pointing to the end of the reversed `matrix`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `matrix`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `matrix`.
`reverse_iterator2 rbegin2 ()` | Returns a `reverse_iterator2` pointing to the beginning of the reversed `matrix`.
`reverse_iterator2 rend2 ()` | Returns a `reverse_iterator2` pointing to the end of the reversed `matrix`.

#### Notes

[1] Supported parameters for the storage organization are `row_major` and `column_major`.

[2] Supported parameters for the adapted array are `unbounded_array<T>` , `bounded_array<T>` and `std::vector<T>` .

## Identity Matrix

#### Description

The templated class `identity_matrix<T>` represents identity matrices. For a (m x n)-dimensional identity matrix and 0 <= i < m, 0 <= j < n holds idi, j = 0, if i <> j, and idi, i= 1.

#### Example

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

    int main () {
        using namespace boost::numeric::ublas;
        identity_matrix<double> m (3);
        std::cout << m << std::endl;
    }

#### Definition

Defined in the header matrix.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the matrix. |

#### Model of

Matrix Expression .

#### Type requirements

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

#### Public base classes

`matrix_expression<identity_matrix<T> >`

#### Members

Member | Description
--- | ---
`identity_matrix ()` | Constructs an `identity_matrix` that holds zero rows of zero elements.
`identity_matrix (size_type size)` | Constructs an `identity_matrix` that holds `size` rows of `size` elements.
`identity_matrix (const identity_matrix &m)` | The copy constructor.
`void resize (size_type size, bool preserve = true)` | Resizes a `identity_matrix` to hold `size` rows of `size` elements. Therefore the existing elements of the `itendity_matrix` are always preseved.
`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.
`identity_matrix &operator = (const identity_matrix &m)` | The assignment operator.
`identity_matrix &assign_temporary (identity_matrix &m)` | Assigns a temporary. May change the identity matrix `m` .
`void swap (identity_matrix &m)` | Swaps the contents of the identity matrices.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `identity_matrix`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `identity_matrix`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `identity_matrix`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `identity_matrix`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `identity_matrix`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `identity_matrix`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `identity_matrix`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `identity_matrix`.

## Zero Matrix

#### Description

The templated class `zero_matrix<T>` represents zero matrices. For a (m x n)-dimensional zero matrix and 0 <= i < m, 0 <= j < n holds zi, j = 0.

#### Example

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

    int main () {
        using namespace boost::numeric::ublas;
        zero_matrix<double> m (3, 3);
        std::cout << m << std::endl;
    }

#### Definition

Defined in the header matrix.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the matrix. |

#### Model of

Matrix Expression .

#### Type requirements

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

#### Public base classes

`matrix_expression<zero_matrix<T> >`

#### Members

Member | Description
--- | ---
`zero_matrix ()` | Constructs a `zero_matrix` that holds zero rows of zero elements.
`zero_matrix (size_type size1, size_type size2)` | Constructs a `zero_matrix` that holds `size1` rows of `size2` elements.
`zero_matrix (const zero_matrix &m)` | The copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)` | Resizes a `zero_matrix` to hold `size1` rows of `size2` elements. Therefore the existing elements of the `zero_matrix` are always preseved.
`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.
`zero_matrix &operator = (const zero_matrix &m)` | The assignment operator.
`zero_matrix &assign_temporary (zero_matrix &m)` | Assigns a temporary. May change the zero matrix `m` .
`void swap (zero_matrix &m)` | Swaps the contents of the zero matrices.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `zero_matrix`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `zero_matrix`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `zero_matrix`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `zero_matrix`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `zero_matrix`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `zero_matrix`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `zero_matrix`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `zero_matrix`.

## scalar Matrix

#### Description

The templated class `scalar_matrix<T>` represents scalar matrices. For a (m x n)-dimensional scalar matrix and 0 <= i < m, 0 <= j < n holds zi, j = s.

#### Example

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

    int main () {
        using namespace boost::numeric::ublas;
        scalar_matrix<double> m (3, 3);
        std::cout << m << std::endl;
    }

#### Definition

Defined in the header matrix.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the matrix. |

#### Model of

Matrix Expression .

#### Type requirements

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

#### Public base classes

`matrix_expression<scalar_matrix<T> >`

#### Members

Member | Description
--- | ---
`scalar_matrix ()` | Constructs a `scalar_matrix` that holds scalar rows of zero elements.
`scalar_matrix (size_type size1, size_type size2, const value_type &value)` | Constructs a `scalar_matrix` that holds `size1` rows of `size2` elements each of the specified value.
`scalar_matrix (const scalar_matrix &m)` | The copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)` | Resizes a `scalar_matrix` to hold `size1` rows of `size2` elements. Therefore the existing elements of the `scalar_matrix` are always preseved.
`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.
`scalar_matrix &operator = (const scalar_matrix &m)` | The assignment operator.
`scalar_matrix &assign_temporary (scalar_matrix &m)` | Assigns a temporary. May change the scalar matrix `m` .
`void swap (scalar_matrix &m)` | Swaps the contents of the scalar matrices.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `scalar_matrix`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `scalar_matrix`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `scalar_matrix`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `scalar_matrix`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `scalar_matrix`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `scalar_matrix`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `scalar_matrix`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `scalar_matrix`.

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