# Symmetric Matrix

#### Description

The templated class `symmetric_matrix<T, F1, F2, A>` is the base container adaptor for symmetric matrices. For a (n x n )-dimensional symmetric matrix and 0 <= i < n, 0 <= j < n holds si, j = s j, i. The storage of symmetric matrices is packed.

#### Example

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

    int main () {
        using namespace boost::numeric::ublas;
        symmetric_matrix<double, lower> ml (3, 3);
        for (unsigned i = 0; i < ml.size1 (); ++ i)
            for (unsigned j = 0; j <= i; ++ j)
                ml (i, j) = 3 * i + j;
        std::cout << ml << std::endl;
        symmetric_matrix<double, upper> mu (3, 3);
        for (unsigned i = 0; i < mu.size1 (); ++ i)
            for (unsigned j = i; j < mu.size2 (); ++ j)
                mu (i, j) = 3 * i + j;
        std::cout << mu << std::endl;
    }

#### Definition

Defined in the header symmetric.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the matrix. |
`F1` | Functor describing the type of the symmetric matrix. [1] | `lower`
`F2` | Functor describing the storage organization. [2] | `row_major`
`A` | The type of the adapted array. [3] | `unbounded_array<T>`

#### Model of

Matrix .

#### Type requirements

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

#### Public base classes

`matrix_expression<symmetric_matrix<T, F1, F2, A> >`

#### Members

Member | Description
--- | ---
`symmetric_matrix ()` | Allocates an uninitialized `symmetric_matrix` that holds zero rows of zero elements.
`symmetric_matrix (size_type size)` | Allocates an uninitialized `symmetric_matrix` that holds `size` rows of `size` elements.
`symmetric_matrix (const symmetric_matrix &m)` | The copy constructor.
`template<class AE> symmetric_matrix (const matrix_expression<AE> &ae)` | The extended copy constructor.
`void resize (size_type size)` | Reallocates a `symmetric_matrix` to hold `size` rows of `size` elements. The content of the `symmetric_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.
`symmetric_matrix &operator = (const symmetric_matrix &m)` | The assignment operator.
`symmetric_matrix &assign_temporary (symmetric_matrix &m)` | Assigns a temporary. May change the symmetric matrix `m` .
`template<class AE> symmetric_matrix &operator = (const matrix_expression<AE> &ae)` | The extended assignment operator.
`template<class AE> symmetric_matrix &assign (const matrix_expression<AE> &ae)` | Assigns a matrix expression to the symmetric matrix. Left and right hand side of the assignment should be independent.
`template<class AE> symmetric_matrix &operator += (const matrix_expression<AE> &ae)` | A computed assignment operator. Adds the matrix expression to the symmetric matrix.
`template<class AE> symmetric_matrix &plus_assign (const matrix_expression<AE> &ae)` | Adds a matrix expression to the symmetric matrix. Left and right hand side of the assignment should be independent.
`template<class AE> symmetric_matrix &operator -= (const matrix_expression<AE> &ae)` | A computed assignment operator. Subtracts the matrix expression from the symmetric matrix.
`template<class AE> symmetric_matrix &minus_assign (const matrix_expression<AE> &ae)` | Subtracts a matrix expression from the symmetric matrix. Left and right hand side of the assignment should be independent.
`template<class AT> symmetric_matrix &operator *= (const AT &at)` | A computed assignment operator. Multiplies the symmetric matrix with a scalar.
`template<class AT> symmetric_matrix &operator /= (const AT &at)` | A computed assignment operator. Divides the symmetric matrix through a scalar.
`void swap (symmetric_matrix &m)` | Swaps the contents of the symmetric 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 elemenst of the `i`-th row.
`void clear ()` | Clears the matrix.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `symmetric_matrix`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `symmetric_matrix`.
`iterator1 begin1 ()` | Returns a `iterator1` pointing to the beginning of the `symmetric_matrix`.
`iterator1 end1 ()` | Returns a `iterator1` pointing to the end of the `symmetric_matrix`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `symmetric_matrix`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `symmetric_matrix`.
`iterator2 begin2 ()` | Returns a `iterator2` pointing to the beginning of the `symmetric_matrix`.
`iterator2 end2 ()` | Returns a `iterator2` pointing to the end of the `symmetric_matrix`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `symmetric_matrix`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `symmetric_matrix`.
`reverse_iterator1 rbegin1 ()` | Returns a `reverse_iterator1` pointing to the beginning of the reversed `symmetric_matrix`.
`reverse_iterator1 rend1 ()` | Returns a `reverse_iterator1` pointing to the end of the reversed `symmetric_matrix`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `symmetric_matrix`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `symmetric_matrix`.
`reverse_iterator2 rbegin2 ()` | Returns a `reverse_iterator2` pointing to the beginning of the reversed `symmetric_matrix`.
`reverse_iterator2 rend2 ()` | Returns a `reverse_iterator2` pointing to the end of the reversed `symmetric_matrix`.

#### Notes

[1] Supported parameters for the type of the symmetric matrix are `lower` and `upper`.

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

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

#### Interface

        // Array based symmetric matrix class
        template<class T, class F1, class F2, class A>
        class symmetric_matrix:
            public matrix_expression<symmetric_matrix<T, F1, F2, 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 F1 functor1_type;
            typedef F2 functor2_type;
            typedef A array_type;
            typedef const A const_array_type;
            typedef const symmetric_matrix<T, F1, F2, A> const_self_type;
            typedef symmetric_matrix<T, F1, F2, A> self_type;
            typedef const matrix_const_reference<const_self_type> const_closure_type;
            typedef matrix_reference<self_type> closure_type;
            typedef packed_tag storage_category;
            typedef typename F1::packed_category packed_category;
            typedef typename F2::orientation_category orientation_category;

            // Construction and destruction
            symmetric_matrix ();
            symmetric_matrix (size_type size);
            symmetric_matrix (size_type size1, size_type size2);
            symmetric_matrix (const symmetric_matrix &m);
            template<class AE>
            symmetric_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 size);
            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
            symmetric_matrix &operator = (const symmetric_matrix &m);
            symmetric_matrix &assign_temporary (symmetric_matrix &m);
            template<class AE>
            symmetric_matrix &operator = (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix &reset (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix &assign (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix& operator += (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix &plus_assign (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix& operator -= (const matrix_expression<AE> &ae);
            template<class AE>
            symmetric_matrix &minus_assign (const matrix_expression<AE> &ae);
            template<class AT>
            symmetric_matrix& operator *= (const AT &at);
            template<class AT>
            symmetric_matrix& operator /= (const AT &at);

            // Swapping
            void swap (symmetric_matrix &m);
            friend void swap (symmetric_matrix &m1, symmetric_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 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<symmetric_matrix>,
                public random_access_iterator_base<const_iterator1, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_matrix::difference_type difference_type;
                typedef typename symmetric_matrix::value_type value_type;
                typedef typename symmetric_matrix::const_reference reference;
                typedef typename symmetric_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 symmetric_matrix &m, size_type it1, size_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<symmetric_matrix>,
                public random_access_iterator_base<iterator1, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_matrix::difference_type difference_type;
                typedef typename symmetric_matrix::value_type value_type;
                typedef typename symmetric_matrix::reference reference;
                typedef typename symmetric_matrix::pointer pointer;
                typedef iterator2 dual_iterator_type;
                typedef reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                iterator1 ();
                iterator1 (symmetric_matrix &m, size_type it1, size_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<symmetric_matrix>,
                public random_access_iterator_base<const_iterator2, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_matrix::difference_type difference_type;
                typedef typename symmetric_matrix::value_type value_type;
                typedef typename symmetric_matrix::const_reference reference;
                typedef typename symmetric_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 symmetric_matrix &m, size_type it1, size_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<symmetric_matrix>,
                public random_access_iterator_base<iterator2, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_matrix::difference_type difference_type;
                typedef typename symmetric_matrix::value_type value_type;
                typedef typename symmetric_matrix::reference reference;
                typedef typename symmetric_matrix::pointer pointer;
                typedef iterator1 dual_iterator_type;
                typedef reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                iterator2 ();
                iterator2 (symmetric_matrix &m, size_type it1, size_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_iter
    ator1 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 ();
        };

## Symmetric Adaptor

#### Description

The templated class `symmetric_adaptor<M, F>` is a symmetric matrix adaptor for other matrices.

#### Example

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

    int main () {
        using namespace boost::numeric::ublas;
        matrix<double> m (3, 3);
        symmetric_adaptor<matrix<double>, lower> sal (m);
        for (unsigned i = 0; i < sal.size1 (); ++ i)
            for (unsigned j = 0; j <= i; ++ j)
                sal (i, j) = 3 * i + j;
        std::cout << sal << std::endl;
        symmetric_adaptor<matrix<double>, upper> sau (m);
        for (unsigned i = 0; i < sau.size1 (); ++ i)
            for (unsigned j = i; j < sau.size2 (); ++ j)
                sau (i, j) = 3 * i + j;
        std::cout << sau << std::endl;
    }

#### Definition

Defined in the header symmetric.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`M` | The type of the adapted matrix. |
`F` | Functor describing the type of the symmetric adaptor. [1] | `lower`

#### Model of

Matrix Expression .

#### Type requirements

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

#### Public base classes

`matrix_expression<symmetric_adaptor<M, F> >`

#### Members

Member | Description
--- | ---
`symmetric_adaptor ()` | Constructs a `symmetric_adaptor` that holds zero rows of zero elements.
`symmetric_adaptor (matrix_type &data)` | Constructs a `symmetric_adaptor` of a matrix.
`symmetric_adaptor (const symmetric_adaptor &m)` | The copy constructor.
`template<class AE> symmetric_adaptor (const matrix_expression<AE> &ae)` | The extended copy constructor.
`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.
`symmetric_adaptor &operator = (const symmetric_adaptor &m)` | The assignment operator.
`symmetric_adaptor &assign_temporary (symmetric_adaptor &m)` | Assigns a temporary. May change the symmetric adaptor `m`.
`template<class AE> symmetric_adaptor &operator = (const matrix_expression<AE> &ae)` | The extended assignment operator.
`template<class AE> symmetric_adaptor &assign (const matrix_expression<AE> &ae)` | Assigns a matrix expression to the symmetric adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> symmetric_adaptor &operator += (const matrix_expression<AE> &ae)` | A computed assignment operator. Adds the matrix expression to the symmetric adaptor.
`template<class AE> symmetric_adaptor &plus_assign (const matrix_expression<AE> &ae)` | Adds a matrix expression to the symmetric adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> symmetric_adaptor &operator -= (const matrix_expression<AE> &ae)` | A computed assignment operator. Subtracts the matrix expression from the symmetric adaptor.
`template<class AE> symmetric_adaptor &minus_assign (const matrix_expression<AE> &ae)` | Subtracts a matrix expression from the symmetric adaptor. Left and right hand side of the assignment should be independent.
`template<class AT> symmetric_adaptor &operator *= (const AT &at)` | A computed assignment operator. Multiplies the symmetric adaptor with a scalar.
`template<class AT> symmetric_adaptor &operator /= (const AT &at)` | A computed assignment operator. Divides the symmetric adaptor through a scalar.
`void swap (symmetric_adaptor &m)` | Swaps the contents of the symmetric adaptors.
`const_iterator1 begin1 () const` | Returns a `const_iterator1` pointing to the beginning of the `symmetric_adaptor`.
`const_iterator1 end1 () const` | Returns a `const_iterator1` pointing to the end of the `symmetric_adaptor`.
`iterator1 begin1 ()` | Returns a `iterator1` pointing to the beginning of the `symmetric_adaptor`.
`iterator1 end1 ()` | Returns a `iterator1` pointing to the end of the `symmetric_adaptor`.
`const_iterator2 begin2 () const` | Returns a `const_iterator2` pointing to the beginning of the `symmetric_adaptor`.
`const_iterator2 end2 () const` | Returns a `const_iterator2` pointing to the end of the `symmetric_adaptor`.
`iterator2 begin2 ()` | Returns a `iterator2` pointing to the beginning of the `symmetric_adaptor`.
`iterator2 end2 ()` | Returns a `iterator2` pointing to the end of the `symmetric_adaptor`.
`const_reverse_iterator1 rbegin1 () const` | Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `symmetric_adaptor`.
`const_reverse_iterator1 rend1 () const` | Returns a `const_reverse_iterator1` pointing to the end of the reversed `symmetric_adaptor`.
`reverse_iterator1 rbegin1 ()` | Returns a `reverse_iterator1` pointing to the beginning of the reversed `symmetric_adaptor`.
`reverse_iterator1 rend1 ()` | Returns a `reverse_iterator1` pointing to the end of the reversed `symmetric_adaptor`.
`const_reverse_iterator2 rbegin2 () const` | Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `symmetric_adaptor`.
`const_reverse_iterator2 rend2 () const` | Returns a `const_reverse_iterator2` pointing to the end of the reversed `symmetric_adaptor`.
`reverse_iterator2 rbegin2 ()` | Returns a `reverse_iterator2` pointing to the beginning of the reversed `symmetric_adaptor`.
`reverse_iterator2 rend2 ()` | Returns a `reverse_iterator2` pointing to the end of the reversed `symmetric_adaptor`.

#### Notes

[1] Supported parameters for the type of the symmetric adaptor are `lower` and `upper`.

#### Interface

        // Symmetric matrix adaptor class
        template<class M, class F>
        class symmetric_adaptor:
            public matrix_expression<symmetric_adaptor<M, F> > {
        public:
            typedef const M const_matrix_type;
            typedef M matrix_type;
            typedef F functor_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 symmetric_adaptor<M, F> const_self_type;
            typedef symmetric_adaptor<M, F> self_type;
            typedef const matrix_const_reference<const_self_type> const_closure_type;
            typedef matrix_reference<self_type> closure_type;
            typedef typename storage_restrict_traits<typename M::storage_category,
                                                     packed_proxy_tag>::storage_category storage_category;
            typedef typename F::packed_category packed_category;
            typedef typename M::orientation_category orientation_category;

            // Construction and destruction
            symmetric_adaptor ();
            symmetric_adaptor (matrix_type &data);
            symmetric_adaptor (const symmetric_adaptor &m);

            // 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);

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

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

            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<symmetric_adaptor>,
                public random_access_iterator_base<const_iterator1, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_adaptor::difference_type difference_type;
                typedef typename symmetric_adaptor::value_type value_type;
                typedef typename symmetric_adaptor::const_reference reference;
                typedef typename symmetric_adaptor::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 symmetric_adaptor &m, size_type it1, size_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<symmetric_adaptor>,
                public random_access_iterator_base<iterator1, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_adaptor::difference_type difference_type;
                typedef typename symmetric_adaptor::value_type value_type;
                typedef typename symmetric_adaptor::reference reference;
                typedef typename symmetric_adaptor::pointer pointer;
                typedef iterator2 dual_iterator_type;
                typedef reverse_iterator2 dual_reverse_iterator_type;

                // Construction and destruction
                iterator1 ();
                iterator1 (symmetric_adaptor &m, size_type it1, size_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<symmetric_adaptor>,
                public random_access_iterator_base<const_iterator2, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_adaptor::difference_type difference_type;
                typedef typename symmetric_adaptor::value_type value_type;
                typedef typename symmetric_adaptor::const_reference reference;
                typedef typename symmetric_adaptor::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 symmetric_adaptor &m, size_type it1, size_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<symmetric_adaptor>,
                public random_access_iterator_base<iterator2, value_type> {
            public:
                typedef packed_random_access_iterator_tag iterator_category;
                typedef typename symmetric_adaptor::difference_type difference_type;
                typedef typename symmetric_adaptor::value_type value_type;
                typedef typename symmetric_adaptor::reference reference;
                typedef typename symmetric_adaptor::pointer pointer;
                typedef iterator1 dual_iterator_type;
                typedef reverse_iterator1 dual_reverse_iterator_type;

                // Construction and destruction
                iterator2 ();
                iterator2 (symmetric_adaptor &m, size_type it1, size_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 ();
        };

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