# 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

    int main () {
        using namespace boost::numeric::ublas;
        matrix<double> m (3, 3);
        for (int i = 0; i < m.size1 (); ++ i)
            for (int 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)` | Reallocates a `matrix` to hold `size1` rows of `size2` elements. The content of the `matrix` is not preserved.
`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>`.

#### Interface

        // Array based matrix class
        template<class T, class F, class A>
        class matrix:
            public matrix_expression<matrix<T, F, A> > {
        public:
            typedef std::size_t size_type;
            typedef std::ptrdiff_t difference_type;
            typedef T value_type;
            typedef const T &const_reference;
            typedef T &reference;
            typedef const T *const_pointer;
            typedef T *pointer;
            typedef F functor_type;
            typedef A array_type;
            typedef const A const_array_type;
            typedef const matrix<T, F, A> const_self_type;
            typedef matrix<T, F, A> self_type;
            typedef const matrix_const_reference<const_self_type> const_closure_type;
            typedef matrix_reference<self_type> closure_type;
            typedef typename A::const_iterator const_iterator_type;
            typedef typename A::iterator iterator_type;
            typedef dense_tag storage_category;
            typedef typename F::orientation_category orientation_category;

            // Construction and destruction
            matrix ();
            matrix (size_type size1, size_type size2);
            matrix (const matrix &m);
            template<class AE>
            matrix (const matrix_expression<AE> &ae);

            // Accessors
            size_type size1 () const;
            size_type size2 () const;
            const_array_type &data () const;
            array_type &data ();

            // Resizing
            void resize (size_type size1, size_type size2);

            // Element access
            const_reference operator () (size_type i, size_type j) const;
            reference operator () (size_type i, size_type j);

            // Assignment
            matrix &operator = (const matrix &m);
            matrix &assign_temporary (matrix &m);
            template<class AE>
            matrix &operator = (const matrix_expression<AE> &ae);
            template<class AE>
            matrix &reset (const matrix_expression<AE> &ae);
            template<class AE>
            matrix &assign (const matrix_expression<AE> &ae);
            template<class AE>
            matrix& operator += (const matrix_expression<AE> &ae);
            template<class AE>
            matrix &plus_assign (const matrix_expression<AE> &ae);
            template<class AE>
            matrix& operator -= (const matrix_expression<AE> &ae);
            template<class AE>
            matrix &minus_assign (const matrix_expression<AE> &ae);
            template<class AT>
            matrix& operator *= (const AT &at);
            template<class AT>
            matrix& operator /= (const AT &at);

            // Swapping
            void swap (matrix &m);
            friend void swap (matrix &m1, matrix &m2);

            // Element insertion and erasure
            void insert (size_type i, size_type j, const_reference t);
            void erase (size_type i, size_type j);
            void clear ();

            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 find1 (int rank, size_type i, size_type j) const;
            iterator1 find1 (int rank, size_type i, size_type j);
            const_iterator2 find2 (int rank, size_type i, size_type j) const;
            iterator2 find2 (int rank, size_type i, size_type j);
            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>,
                public random_access_iterator_base<const_iterator1, value_type> {
            public:
                typedef dense_random_access_iterator_tag iterator_category;
                typedef typename matrix::difference_type difference_type;
                typedef typename matrix::value_type value_type;
                typedef typename matrix::const_reference reference;
                typedef typename matrix::const_pointer pointer;
                typedef const_iterator2 dual_iterator_type;
                typedef const_reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator1 ();
                const_iterator1 (const matrix &m, const const_iterator_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>,
                public random_access_iterator_base<iterator1, value_type> {
            public:
                typedef dense_random_access_iterator_tag iterator_category;
                typedef typename matrix::difference_type difference_type;
                typedef typename matrix::value_type value_type;
                typedef typename matrix::reference reference;
                typedef typename matrix::pointer pointer;
                typedef iterator2 dual_iterator_type;
                typedef reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                iterator1 ();
                iterator1 (matrix &m, const iterator_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>,
                public random_access_iterator_base<const_iterator2, value_type> {
            public:
                typedef dense_random_access_iterator_tag iterator_category;
                typedef typename matrix::difference_type difference_type;
                typedef typename matrix::value_type value_type;
                typedef typename matrix::const_reference reference;
                typedef typename matrix::const_pointer pointer;
                typedef const_iterator1 dual_iterator_type;
                typedef const_reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator2 ();
                const_iterator2 (const matrix &m, const const_iterator_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>,
                public random_access_iterator_base<iterator2, value_type> {
            public:
                typedef dense_random_access_iterator_tag iterator_category;
                typedef typename matrix::difference_type difference_type;
                typedef typename matrix::value_type value_type;
                typedef typename matrix::reference reference;
                typedef typename matrix::pointer pointer;
                typedef iterator1 dual_iterator_type;
                typedef reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                iterator2 ();
                iterator2 (matrix &m, const iterator_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 ();
        };

## 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

    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)` | Resizes a `identity_matrix` to hold `size` rows of `size` elements.
`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`.

#### Interface

        // Identity matrix class
        template<class T>
        class identity_matrix:
            public matrix_expression<identity_matrix<T> > {
        public:
            typedef std::size_t size_type;
            typedef std::ptrdiff_t difference_type;
            typedef T value_type;
            typedef const T &const_reference;
            typedef T &reference;
            typedef const T *const_pointer;
            typedef T *pointer;
            typedef const identity_matrix<T> const_self_type;
            typedef identity_matrix<T> self_type;
            typedef const matrix_const_reference<const_self_type> const_closure_type;
            typedef size_type const_iterator_type;
            typedef packed_tag storage_category;
            typedef unknown_orientation_tag orientation_category;

            // Construction and destruction
            identity_matrix ();
            identity_matrix (size_type size);
            identity_matrix (size_type size1, size_type size2);
            identity_matrix (const identity_matrix &m);

            // Accessors
            size_type size1 () const;
            size_type size2 () const;

            // Resizing
            void resize (size_type size);
            void resize (size_type size1, size_type size2);

            // Element access
            const_reference operator () (size_type i, size_type j) const;

            // Assignment
            identity_matrix &operator = (const identity_matrix &m);
            identity_matrix &assign_temporary (identity_matrix &m);

            // Swapping
            void swap (identity_matrix &m);
            friend void swap (identity_matrix &m1, identity_matrix &m2);

            class const_iterator1;
            class const_iterator2;
            typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
            typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

            // Element lookup
            const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
            const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
            const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
            const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

            // Iterators simply are indices.

            class const_iterator1:
                public container_const_reference<identity_matrix>,
                public random_access_iterator_base<const_iterator1, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename identity_matrix::difference_type difference_type;
                typedef typename identity_matrix::value_type value_type;
                typedef typename identity_matrix::const_reference reference;
                typedef typename identity_matrix::const_pointer pointer;
                typedef const_iterator2 dual_iterator_type;
                typedef const_reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator1 ();
                const_iterator1 (const identity_matrix &m, const const_iterator_type &it1, const const_iterator_type &it2);

                // Arithmetic
                const_iterator1 &operator ++ ();
                const_iterator1 &operator -- ();
                const_iterator1 &operator += (difference_type n);
                const_iterator1 &operator -= (difference_type n);
                difference_type operator - (const const_iterator1 &it) const;

                // Dereference
                reference operator * () const;

                const_iterator2 begin () const;
                const_iterator2 end () const;
                const_reverse_iterator2 rbegin () const;
                const_reverse_iterator2 rend () const;

                // Indices
                size_type index1 () const;
                size_type index2 () const;

                // Assignment
                const_iterator1 &operator = (const const_iterator1 &it);

                // Comparison
                bool operator == (const const_iterator1 &it) const;
                bool operator <(const const_iterator1 &it) const;
            };

            typedef const_iterator1 iterator1;

            const_iterator1 begin1 () const;
            const_iterator1 end1 () const;

            class const_iterator2:
                public container_const_reference<identity_matrix>,
                public random_access_iterator_base<const_iterator2, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename identity_matrix::difference_type difference_type;
                typedef typename identity_matrix::value_type value_type;
                typedef typename identity_matrix::const_reference reference;
                typedef typename identity_matrix::const_pointer pointer;
                typedef const_iterator1 dual_iterator_type;
                typedef const_reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator2 ();
                const_iterator2 (const identity_matrix &m, const const_iterator_type &it1, const const_iterator_type &it2);

                // Arithmetic
                const_iterator2 &operator ++ ();
                const_iterator2 &operator -- ();
                const_iterator2 &operator += (difference_type n);
                const_iterator2 &operator -= (difference_type n);
                difference_type operator - (const const_iterator2 &it) const;

                // Dereference
                reference operator * () const;

                const_iterator1 begin () const;
                const_iterator1 end () const;
                const_reverse_iterator1 rbegin () const;
                const_reverse_iterator1 rend () const;

                // Indices
                size_type index1 () const;
                size_type index2 () const;

                // Assignment
                const_iterator2 &operator = (const const_iterator2 &it);

                // Comparison
                bool operator == (const const_iterator2 &it) const;
                bool operator <(const const_iterator2 &it) const;
            };

            typedef const_iterator2 iterator2;

            const_iterator2 begin2 () const;
            const_iterator2 end2 () const;

            // Reverse iterators

            const_reverse_iterator1 rbegin1 () const;
            const_reverse_iterator1 rend1 () const;

            const_reverse_iterator2 rbegin2 () const;
            const_reverse_iterator2 rend2 () const;
        };

## 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

    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)` | Resizes a `zero_matrix` to hold `size1` rows of `size2` elements.
`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`.

#### Interface

        // Zero matrix class
        template<class T>
        class zero_matrix:
            public matrix_expression<zero_matrix<T> > {
        public:
            typedef std::size_t size_type;
            typedef std::ptrdiff_t difference_type;
            typedef T value_type;
            typedef const T &const_reference;
            typedef T &reference;
            typedef const T *const_pointer;
            typedef T *pointer;
            typedef const zero_matrix<T> const_self_type;
            typedef zero_matrix<T> self_type;
            typedef const matrix_const_reference<const_self_type> const_closure_type;
            typedef size_type const_iterator_type;
            typedef sparse_tag storage_category;
            typedef unknown_orientation_tag orientation_category;

            // Construction and destruction
            zero_matrix ();
            zero_matrix (size_type size1, size_type size2);
            zero_matrix (const zero_matrix &m);

            // Accessors
            size_type size1 () const;
            size_type size2 () const;

            // Resizing
            void resize (size_type size1, size_type size2);

            // Element access
            const_reference operator () (size_type i, size_type j) const;

            // Assignment
            zero_matrix &operator = (const zero_matrix &m);
            zero_matrix &assign_temporary (zero_matrix &m);

            // Swapping
            void swap (zero_matrix &m);
            friend void swap (zero_matrix &m1, zero_matrix &m2);

            class const_iterator1;
            class const_iterator2;
            typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
            typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

            // Element lookup
            const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
            const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
            const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
            const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

            // Iterators simply are indices.

            class const_iterator1:
                public container_const_reference<zero_matrix>,
                public bidirectional_iterator_base<const_iterator1, value_type> {
            public:
                typedef sparse_bidirectional_iterator_tag iterator_category;
                typedef typename zero_matrix::difference_type difference_type;
                typedef typename zero_matrix::value_type value_type;
                typedef typename zero_matrix::const_reference reference;
                typedef typename zero_matrix::const_pointer pointer;
                typedef const_iterator2 dual_iterator_type;
                typedef const_reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator1 ();
                const_iterator1 (const zero_matrix &m, const const_iterator_type &it1, const const_iterator_type &it2);

                // Arithmetic
                const_iterator1 &operator ++ ();
                const_iterator1 &operator -- ();

                // 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;
            };

            typedef const_iterator1 iterator1;

            const_iterator1 begin1 () const;
            const_iterator1 end1 () const;

            class const_iterator2:
                public container_const_reference<zero_matrix>,
                public bidirectional_iterator_base<const_iterator2, value_type> {
            public:
                typedef sparse_bidirectional_iterator_tag iterator_category;
                typedef typename zero_matrix::difference_type difference_type;
                typedef typename zero_matrix::value_type value_type;
                typedef typename zero_matrix::const_reference reference;
                typedef typename zero_matrix::const_pointer pointer;
                typedef const_iterator1 dual_iterator_type;
                typedef const_reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                const_iterator2 ();
                const_iterator2 (const zero_matrix &m, const const_iterator_type &it1, const const_iterator_type &it2);

                // Arithmetic
                const_iterator2 &operator ++ ();
                const_iterator2 &operator -- ();

                // 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;
            };

            typedef const_iterator2 iterator2;

            const_iterator2 begin2 () const;
            const_iterator2 end2 () const;

            // Reverse iterators

            const_reverse_iterator1 rbegin1 () const;
            const_reverse_iterator1 rend1 () const;

            const_reverse_iterator2 rbegin2 () const;
            const_reverse_iterator2 rend2 () const;
        };

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: 8/3/2002