c++boost.gifMatrix

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