c++boost.gif Matrix

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 m i, j is mapped to the (i x n + j)-th element of the container for row major orientation or the (i + j x m)-th element of the container for column major orientation.

Example

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

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

Definition

Defined in the header matrix.hpp.

Template parameters

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

Model of

Matrix .

Type requirements

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

Public base classes

matrix_expression<matrix<T, F, A> >

Members

Member Description
matrix () Allocates an uninitialized matrix that holds zero rows of zero elements.
matrix (size_type size1, size_type size2) Allocates an uninitialized matrix that holds size1 rows of size2 elements.
matrix (const matrix &m) The copy constructor.
template<class AE>
matrix (const matrix_expression<AE> &ae)
The extended copy constructor.
void resize (size_type size1, size_type size2) 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

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

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

Definition

Defined in the header matrix.hpp.

Template parameters

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

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<identity_matrix<T> >

Members

Member Description
identity_matrix () Constructs an identity_matrix that holds zero rows of zero elements.
identity_matrix (size_type size) Constructs an identity_matrix that holds size rows of size elements.
identity_matrix (const identity_matrix &m) The copy constructor.
void resize (size_type size) 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

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

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

Definition

Defined in the header matrix.hpp.

Template parameters

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

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<zero_matrix<T> >

Members

Member Description
zero_matrix () Constructs a zero_matrix that holds zero rows of zero elements.
zero_matrix (size_type size1, size_type size2) Constructs a zero_matrix that holds size1 rows of size2 elements.
zero_matrix (const zero_matrix &m) The copy constructor.
void resize (size_type size1, size_type size2) 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: 1/15/2003