The templated class sparse_matrix<T, F, A>
is the base
container adaptor for sparse matrices. For a (m x n)-dimensional
sparse matrix and 0 <= i < m, 0 <= j < n the
non-zero elements mi, j are mapped via (i
x n + j) for row major orientation or via (i + j x m) for column
major orientation to consecutive elements of the associative container, i.e.
for elements k = mi1
,j1 and
k + 1 = mi2
,j2 of the
container holds i1 < i2
or (i1 = i2 and
j1 < j2)
with row major orientation or j1 < j
2 or (j1 = j2
and i1 < i2
) with column major orientation.
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
sparse_matrix<double> m (3, 3, 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;
}
Defined in the header matrix_sparse.hpp.
Parameter | Description | Default |
---|---|---|
T |
The type of object stored in the sparse matrix. | |
F |
Functor describing the storage organization. [1] | row_major |
A |
The type of the adapted array. [2] | map_array<std::size_t, T> |
Matrix .
None, except for those imposed by the requirements of Matrix .
matrix_expression<sparse_matrix<T, F, A> >
Member | Description |
---|---|
sparse_matrix () |
Allocates a sparse_matrix that holds at
most zero rows of zero elements. |
sparse_matrix (size_type size1, size_type2, size_type
non_zeros) |
Allocates a sparse_matrix that holds at
most size1 rows of size2 elements. |
sparse_matrix (const sparse_matrix &m) |
The copy constructor. |
template<class AE> |
The extended copy constructor. |
void resize (size_type size1, size_type size2,
size_type non_zeros) |
Reallocates a sparse_matrix to hold at
most size1 rows of size2 elements. The
content of the sparse_matrix is 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 the value 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. |
sparse_matrix &operator = (const sparse_matrix
&m) |
The assignment operator. |
sparse_matrix &assign_temporary (sparse_matrix
&m) |
Assigns a temporary. May change the sparse matrix m
. |
template<class AE> |
The extended assignment operator. |
template<class AE> |
Assigns a matrix expression to the sparse matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Adds the matrix expression to the sparse matrix. |
template<class AE> |
Adds a matrix expression to the sparse matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Subtracts the matrix expression from the sparse matrix. |
template<class AE> |
Subtracts a matrix expression from the sparse matrix. Left and right hand side of the assignment should be independent. |
template<class AT> |
A computed assignment operator. Multiplies the sparse matrix with a scalar. |
template<class AT> |
A computed assignment operator. Divides the sparse matrix through a scalar. |
void swap (sparse_matrix &m) |
Swaps the contents of the sparse 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 sparse matrix. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the sparse_matrix . |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the
end of the sparse_matrix . |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning
of the sparse_matrix . |
iterator1 end1 () |
Returns a iterator1 pointing to the end
of the sparse_matrix . |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the sparse_matrix . |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the
end of the sparse_matrix . |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning
of the sparse_matrix . |
iterator2 end2 () |
Returns a iterator2 pointing to the end
of the sparse_matrix . |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed sparse_matrix . |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed sparse_matrix . |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to
the beginning of the reversed sparse_matrix . |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to
the end of the reversed sparse_matrix . |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed sparse_matrix . |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed sparse_matrix . |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to
the beginning of the reversed sparse_matrix . |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to
the end of the reversed sparse_matrix . |
[1]
Supported parameters for the storage organization are row_major
and column_major
.
[2]
Supported parameters for the adapted array are map_array<std::size_t,
T>
and std::map<std::size_t, T>
.
// Array based sparse matrix class
template<class T, class F, class A>
class sparse_matrix:
public matrix_expression<sparse_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 sparse_matrix<T, F, A> const_self_type;
typedef sparse_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 sparse_tag storage_category;
typedef typename F::orientation_category orientation_category;
// Construction and destruction
sparse_matrix ();
sparse_matrix (size_type size1, size_type size2, size_type non_zeros = 0);
sparse_matrix (const sparse_matrix &m);
template<class AE>
sparse_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);
// Accessors
size_type size1 () const;
size_type size2 () const;
size_type non_zeros () const;
const_array_type &data () const;
array_type &data ();
// Resizing
void resize (size_type size1, size_type size2, size_type non_zeros = 0);
// Element access
const_reference operator () (size_type i, size_type j) const;
reference operator () (size_type i, size_type j);
// Assignment
sparse_matrix &operator = (const sparse_matrix &m);
sparse_matrix &assign_temporary (sparse_matrix &m);
template<class AE>
sparse_matrix &operator = (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix &reset (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix &assign (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix& operator += (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix &plus_assign (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix& operator -= (const matrix_expression<AE> &ae);
template<class AE>
sparse_matrix &minus_assign (const matrix_expression<AE> &ae);
template<class AT>
sparse_matrix& operator *= (const AT &at);
template<class AT>
sparse_matrix& operator /= (const AT &at);
// Swapping
void swap (sparse_matrix &m);
friend void swap (sparse_matrix &m1, sparse_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<sparse_matrix>,
public bidirectional_iterator_base<const_iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_matrix::difference_type difference_type;
typedef typename sparse_matrix::value_type value_type;
typedef typename sparse_matrix::const_reference reference;
typedef typename sparse_matrix::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator1 (const iterator1 &it);
// 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;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class iterator1:
public container_reference<sparse_matrix>,
public bidirectional_iterator_base<iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_matrix::difference_type difference_type;
typedef typename sparse_matrix::value_type value_type;
typedef typename sparse_matrix::reference reference;
typedef typename sparse_matrix::pointer pointer;
typedef iterator2 dual_iterator_type;
typedef reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
iterator1 ();
iterator1 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator1 &operator ++ ();
iterator1 &operator -- ();
// 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;
};
iterator1 begin1 ();
iterator1 end1 ();
class const_iterator2:
public container_const_reference<sparse_matrix>,
public bidirectional_iterator_base<const_iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_matrix::difference_type difference_type;
typedef typename sparse_matrix::value_type value_type;
typedef typename sparse_matrix::const_reference reference;
typedef typename sparse_matrix::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator2 (const iterator2 &it);
// 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;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
class iterator2:
public container_reference<sparse_matrix>,
public bidirectional_iterator_base<iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_matrix::difference_type difference_type;
typedef typename sparse_matrix::value_type value_type;
typedef typename sparse_matrix::reference reference;
typedef typename sparse_matrix::pointer pointer;
typedef iterator1 dual_iterator_type;
typedef reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
iterator2 ();
iterator2 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator2 &operator ++ ();
iterator2 &operator -- ();
// 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;
};
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 ();
};
The templated class compressed_matrix<T, F, IB, IA, TA>
is the base container adaptor for compressed matrices. For a (m x n
)-dimensional compressed matrix and 0 <= i < m, 0 <=
j < n the non-zero elements mi, j are
mapped via (i x n + j) for row major orientation or via (i +
j x m) for column major orientation to consecutive elements of the index
and value containers, i.e. for elements k = mi
1,j1
and k + 1 = mi2
,j2 of the
container holds i1 < i2
or (i1 = i2 and
j1 < j2)
with row major orientation or j1 < j
2 or (j1 = j2
and i1 < i2
) with column major orientation.
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
compressed_matrix<double> m (3, 3, 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;
}
Defined in the header matrix_sparse.hpp.
Parameter | Description | Default |
---|---|---|
T |
The type of object stored in the compressed matrix. | |
F |
Functor describing the storage organization. [1] | row_major |
IB |
The index base of the compressed vector. [2] | 0 |
IA |
The type of the adapted array for indices. [3] | unbounded_array<std::size_t> |
TA |
The type of the adapted array for values. [3] | unbounded_array<T> |
Matrix .
None, except for those imposed by the requirements of Matrix .
matrix_expression<compressed_matrix<T, F, IB, IA, TA> >
Member | Description |
---|---|
compressed_matrix () |
Allocates a compressed_matrix that holds
at most zero rows of zero elements. |
compressed_matrix (size_type size1, size_type2,
size_type non_zeros) |
Allocates a compressed_matrix that holds
at most size1 rows of size2 elements. |
compressed_matrix (const compressed_matrix &m) |
The copy constructor. |
template<class AE> |
The extended copy constructor. |
void resize (size_type size1, size_type size2,
size_type non_zeros) |
Reallocates a compressed_matrix to hold
at most size1 rows of size2 elements.
The content of the compressed_matrix is 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 the value 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. |
compressed_matrix &operator = (const compressed_matrix
&m) |
The assignment operator. |
compressed_matrix &assign_temporary (compressed_matrix
&m) |
Assigns a temporary. May change the compressed matrix
m . |
template<class AE> |
The extended assignment operator. |
template<class AE> |
Assigns a matrix expression to the compressed matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Adds the matrix expression to the compressed matrix. |
template<class AE> |
Adds a matrix expression to the compressed matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Subtracts the matrix expression from the compressed matrix. |
template<class AE> |
Subtracts a matrix expression from the compressed matrix. Left and right hand side of the assignment should be independent. |
template<class AT> |
A computed assignment operator. Multiplies the compressed matrix with a scalar. |
template<class AT> |
A computed assignment operator. Divides the compressed matrix through a scalar. |
void swap (compressed_matrix &m) |
Swaps the contents of the compressed 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 compressed matrix. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the compressed_matrix . |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the
end of the compressed_matrix . |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning
of the compressed_matrix . |
iterator1 end1 () |
Returns a iterator1 pointing to the end
of the compressed_matrix . |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the compressed_matrix . |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the
end of the compressed_matrix . |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning
of the compressed_matrix . |
iterator2 end2 () |
Returns a iterator2 pointing to the end
of the compressed_matrix . |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed compressed_matrix .
|
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed compressed_matrix . |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to
the beginning of the reversed compressed_matrix . |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to
the end of the reversed compressed_matrix . |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed compressed_matrix .
|
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed compressed_matrix . |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to
the beginning of the reversed compressed_matrix . |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to
the end of the reversed compressed_matrix . |
[1]
Supported parameters for the storage organization are row_major
and column_major
.
[2]
Supported parameters for the index base are 0
and 1
at least.
[3]
Supported parameters for the adapted array are unbounded_array<>
, bounded_array<>
and std::vector<>
.
// Array based sparse matrix class
template<class T, class F, std::size_t IB, class IA, class TA>
class compressed_matrix:
public matrix_expression<compressed_matrix<T, F, IB, IA, TA> > {
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 IA index_array_type;
typedef TA value_array_type;
typedef const compressed_matrix<T, F, IB, IA, TA> const_self_type;
typedef compressed_matrix<T, F, IB, IA, TA> 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 sparse_tag storage_category;
typedef typename F::orientation_category orientation_category;
// Construction and destruction
compressed_matrix ();
compressed_matrix (size_type size1, size_type size2, size_type non_zeros = 0);
compressed_matrix (const compressed_matrix &m);
template<class AE>
compressed_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);
// Accessors
size_type size1 () const;
size_type size2 () const;
size_type non_zeros () const;
static size_type index_base ();
const index_array_type &index1_data () const;
index_array_type &index1_data ();
const index_array_type &index2_data () const;
index_array_type &index2_data ();
const value_array_type &value_data () const;
value_array_type &value_data ();
// Resizing
void resize (size_type size1, size_type size2, size_type non_zeros = 0);
// Element access
const_reference operator () (size_type i, size_type j) const;
reference operator () (size_type i, size_type j);
// Assignment
compressed_matrix &operator = (const compressed_matrix &m);
compressed_matrix &assign_temporary (compressed_matrix &m);
template<class AE>
compressed_matrix &operator = (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix &reset (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix &assign (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix& operator += (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix &plus_assign (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix& operator -= (const matrix_expression<AE> &ae);
template<class AE>
compressed_matrix &minus_assign (const matrix_expression<AE> &ae);
template<class AT>
compressed_matrix& operator *= (const AT &at);
template<class AT>
compressed_matrix& operator /= (const AT &at);
// Swapping
void swap (compressed_matrix &m);
friend void swap (compressed_matrix &m1, compressed_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<compressed_matrix>,
public bidirectional_iterator_base<const_iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename compressed_matrix::difference_type difference_type;
typedef typename compressed_matrix::value_type value_type;
typedef typename compressed_matrix::const_reference reference;
typedef typename compressed_matrix::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const compressed_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator1 (const iterator1 &it);
// 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;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class iterator1:
public container_reference<compressed_matrix>,
public bidirectional_iterator_base<iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename compressed_matrix::difference_type difference_type;
typedef typename compressed_matrix::value_type value_type;
typedef typename compressed_matrix::reference reference;
typedef typename compressed_matrix::pointer pointer;
typedef iterator2 dual_iterator_type;
typedef reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
iterator1 ();
iterator1 (compressed_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator1 &operator ++ ();
iterator1 &operator -- ();
// 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;
};
iterator1 begin1 ();
iterator1 end1 ();
class const_iterator2:
public container_const_reference<compressed_matrix>,
public bidirectional_iterator_base<const_iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename compressed_matrix::difference_type difference_type;
typedef typename compressed_matrix::value_type value_type;
typedef typename compressed_matrix::const_reference reference;
typedef typename compressed_matrix::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const compressed_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator2 (const iterator2 &it);
// 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 &operato
r = (const const_iterator2 &it);
// Comparison
bool operator == (const const_iterator2 &it) const;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
class iterator2:
public container_reference<compressed_matrix>,
public bidirectional_iterator_base<iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename compressed_matrix::difference_type difference_type;
typedef typename compressed_matrix::value_type value_type;
typedef typename compressed_matrix::reference reference;
typedef typename compressed_matrix::pointer pointer;
typedef iterator1 dual_iterator_type;
typedef reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
iterator2 ();
iterator2 (compressed_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator2 &operator ++ ();
iterator2 &operator -- ();
// 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;
};
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 ();
};
The templated class coordinate_matrix<T, F, IB, IA, TA>
is the base container adaptor for compressed matrices. For a (m x n
)-dimensional sorted coordinate matrix and 0 <= i < m,
0 <= j < n the non-zero elements mi, j
are mapped via (i x n + j) for row major orientation or via
(i + j x m) for column major orientation to consecutive elements of
the index and value containers, i.e. for elements k = m
i1,j
1 and k + 1 = mi
2,j2
of the container holds i1 <
i2 or (i1 = i
2 and j1 < j
2) with row major orientation or j1
< j2 or (j1
= j2 and i1 <
i2) with column major orientation.
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
coordinate_matrix<double> m (3, 3, 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;
}
Defined in the header matrix_sparse.hpp.
Parameter | Description | Default |
---|---|---|
T |
The type of object stored in the coordinate matrix. | |
F |
Functor describing the storage organization. [1] | row_major |
IB |
The index base of the coordinate vector. [2] | 0 |
IA |
The type of the adapted array for indices. [3] | unbounded_array<std::size_t> |
TA |
The type of the adapted array for values. [3] | unbounded_array<T> |
Matrix .
None, except for those imposed by the requirements of Matrix .
matrix_expression<coordinate_matrix<T, F, IB, IA, TA> >
Member | Description |
---|---|
coordinate_matrix () |
Allocates a coordinate_matrix that holds
at most zero rows of zero elements. |
coordinate_matrix (size_type size1, size_type2,
size_type non_zeros) |
Allocates a coordinate_matrix that holds
at most size1 rows of size2 elements. |
coordinate_matrix (const coordinate_matrix &m) |
The copy constructor. |
template<class AE> |
The extended copy constructor. |
void resize (size_type size1, size_type size2,
size_type non_zeros) |
Reallocates a coordinate_matrix to hold
at most size1 rows of size2 elements.
The content of the coordinate_matrix is 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 the value 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. |
coordinate_matrix &operator = (const coordinate_matrix
&m) |
The assignment operator. |
coordinate_matrix &assign_temporary (coordinate_matrix
&m) |
Assigns a temporary. May change the coordinate matrix
m . |
template<class AE> |
The extended assignment operator. |
template<class AE> |
Assigns a matrix expression to the coordinate matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Adds the matrix expression to the coordinate matrix. |
template<class AE> |
Adds a matrix expression to the coordinate matrix. Left and right hand side of the assignment should be independent. |
template<class AE> |
A computed assignment operator. Subtracts the matrix expression from the coordinate matrix. |
template<class AE> |
Subtracts a matrix expression from the coordinate matrix. Left and right hand side of the assignment should be independent. |
template<class AT> |
A computed assignment operator. Multiplies the coordinate matrix with a scalar. |
template<class AT> |
A computed assignment operator. Divides the coordinate matrix through a scalar. |
void swap (coordinate_matrix &m) |
Swaps the contents of the coordinate 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 coordinate matrix. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the coordinate_matrix . |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the
end of the coordinate_matrix . |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning
of the coordinate_matrix . |
iterator1 end1 () |
Returns a iterator1 pointing to the end
of the coordinate_matrix . |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the coordinate_matrix . |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the
end of the coordinate_matrix . |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning
of the coordinate_matrix . |
iterator2 end2 () |
Returns a iterator2 pointing to the end
of the coordinate_matrix . |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing
to the beginning of the reversed coordinate_matrix .
|
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing
to the end of the reversed coordinate_matrix . |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to
the beginning of the reversed coordinate_matrix . |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to
the end of the reversed coordinate_matrix . |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing
to the beginning of the reversed coordinate_matrix .
|
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing
to the end of the reversed coordinate_matrix . |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to
the beginning of the reversed coordinate_matrix . |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to
the end of the reversed coordinate_matrix . |
[1]
Supported parameters for the storage organization are row_major
and column_major
.
[2]
Supported parameters for the index base are 0
and 1
at least.
[3]
Supported parameters for the adapted array are unbounded_array<>
, bounded_array<>
and std::vector<>
.
// Array based sparse matrix class
template<class T, class F, std::size_t IB, class IA, class TA>
class coordinate_matrix:
public matrix_expression<coordinate_matrix<T, F, IB, IA, TA> > {
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 IA index_array_type;
typedef TA value_array_type;
typedef const coordinate_matrix<T, F, IB, IA, TA> const_self_type;
typedef coordinate_matrix<T, F, IB, IA, TA> 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 sparse_tag storage_category;
typedef typename F::orientation_category orientation_category;
// Construction and destruction
coordinate_matrix ();
coordinate_matrix (size_type size1, size_type size2, size_type non_zeros = 0);
coordinate_matrix (const coordinate_matrix &m);
template<class AE>
coordinate_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);
// Accessors
size_type size1 () const;
size_type size2 () const;
size_type non_zeros () const;
static size_type index_base ();
const index_array_type &index1_data () const;
index_array_type &index1_data ();
const index_array_type &index2_data () const;
index_array_type &index2_data ();
const value_array_type &value_data () const;
value_array_type &value_data ();
// Resizing
void resize (size_type size1, size_type size2, size_type non_zeros = 0);
// Element access
const_reference operator () (size_type i, size_type j) const;
reference operator () (size_type i, size_type j);
// Assignment
coordinate_matrix &operator = (const coordinate_matrix &m);
coordinate_matrix &assign_temporary (coordinate_matrix &m);
template<class AE>
coordinate_matrix &operator = (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix &reset (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix &assign (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix& operator += (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix &plus_assign (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix& operator -= (const matrix_expression<AE> &ae);
template<class AE>
coordinate_matrix &minus_assign (const matrix_expression<AE> &ae);
template<class AT>
coordinate_matrix& operator *= (const AT &at);
template<class AT>
coordinate_matrix& operator /= (const AT &at);
// Swapping
void swap (coordinate_matrix &m);
friend void swap (coordinate_matrix &m1, coordinate_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<coordinate_matrix>,
public bidirectional_iterator_base<const_iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename coordinate_matrix::difference_type difference_type;
typedef typename coordinate_matrix::value_type value_type;
typedef typename coordinate_matrix::const_reference reference;
typedef typename coordinate_matrix::const_pointer pointer;
typedef const_iterator2 dual_iterator_type;
typedef const_reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
const_iterator1 ();
const_iterator1 (const coordinate_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator1 (const iterator1 &it);
// 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;
};
const_iterator1 begin1 () const;
const_iterator1 end1 () const;
class iterator1:
public container_reference<coordinate_matrix>,
public bidirectional_iterator_base<iterator1, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename coordinate_matrix::difference_type difference_type;
typedef typename coordinate_matrix::value_type value_type;
typedef typename coordinate_matrix::reference reference;
typedef typename coordinate_matrix::pointer pointer;
typedef iterator2 dual_iterator_type;
typedef reverse_iterator2 dual_reverse_iterator_type;
typedef typename functor_type::functor1_type functor1_type;
// Construction and destruction
iterator1 ();
iterator1 (coordinate_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator1 &operator ++ ();
iterator1 &operator -- ();
// 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;
};
iterator1 begin1 ();<
br> iterator1 end1 ();
class const_iterator2:
public container_const_reference<coordinate_matrix>,
public bidirectional_iterator_base<const_iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename coordinate_matrix::difference_type difference_type;
typedef typename coordinate_matrix::value_type value_type;
typedef typename coordinate_matrix::const_reference reference;
typedef typename coordinate_matrix::const_pointer pointer;
typedef const_iterator1 dual_iterator_type;
typedef const_reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
const_iterator2 ();
const_iterator2 (const coordinate_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
const_iterator2 (const iterator2 &it);
// 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;
};
const_iterator2 begin2 () const;
const_iterator2 end2 () const;
class iterator2:
public container_reference<coordinate_matrix>,
public bidirectional_iterator_base<iterator2, value_type> {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename coordinate_matrix::difference_type difference_type;
typedef typename coordinate_matrix::value_type value_type;
typedef typename coordinate_matrix::reference reference;
typedef typename coordinate_matrix::pointer pointer;
typedef iterator1 dual_iterator_type;
typedef reverse_iterator1 dual_reverse_iterator_type;
typedef typename functor_type::functor2_type functor2_type;
// Construction and destruction
iterator2 ();
iterator2 (coordinate_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
// Arithmetic
iterator2 &operator ++ ();
iterator2 &operator -- ();
// 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;
};
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