Boost C++ Libraries

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Sparse Matrix

Sparse Matrix

Description

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 ,j1and k + 1 = mi2 ,j2of the container holds i1 < i2 or (i1 = i2 and j1 < j2) with row major orientation or j1 < j2 or (j1 = j2 and i1 < i2) with column major orientation.

Example

#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;
}

Definition

Defined in the header matrix_sparse.hpp.

Template parameters

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_std<std::size_t, T>

Model of

Matrix .

Type requirements

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

Public base classes

matrix_expression<sparse_matrix<T, F, A> >

Members

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 = 0) 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>
sparse_matrix (size_type non_zeros, const matrix_expression<AE> &ae)
The extended copy constructor.
void resize (size_type size1, size_type size2, bool preserve = true) Reallocates a sparse_matrix to hold at most size1 rows of size2 elements. The existing elements of the sparse_matrix are preseved when specified.
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>
sparse_matrix &operator = (const matrix_expression<AE> &ae)
The extended assignment operator.
template<class AE>
sparse_matrix &assign (const matrix_expression<AE> &ae)
Assigns a matrix expression to the sparse matrix. Left and right hand side of the assignment should be independent.
template<class AE>
sparse_matrix &operator += (const matrix_expression<AE> &ae)
A computed assignment operator. Adds the matrix expression to the sparse matrix.
template<class AE>
sparse_matrix &plus_assign (const matrix_expression<AE> &ae)
Adds a matrix expression to the sparse matrix. Left and right hand side of the assignment should be independent.
template<class AE>
sparse_matrix &operator -= (const matrix_expression<AE> &ae)
A computed assignment operator. Subtracts the matrix expression from the sparse matrix.
template<class AE>
sparse_matrix &minus_assign (const matrix_expression<AE> &ae)
Subtracts a matrix expression from the sparse matrix. Left and right hand side of the assignment should be independent.
template<class AT>
sparse_matrix &operator *= (const AT &at)
A computed assignment operator. Multiplies the sparse matrix with a scalar.
template<class AT>
sparse_matrix &operator /= (const AT &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.

Notes

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

[1] Supported parameters for the adapted array are map_array<std::size_t, T> and map_std<std::size_t, T>. The latter is equivalent to std::map<std::size_t, T>.

Compressed Matrix

Description

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 = mi1 ,j1and k + 1 = mi2 ,j2of the container holds i1 < i2 or (i1 = i2 and j1 < j2) with row major orientation or j1 < j2 or (j1 = j2 and i1 < i2) with column major orientation.

Example

#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;
}

Definition

Defined in the header matrix_sparse.hpp.

Template parameters

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>

Model of

Matrix .

Type requirements

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

Public base classes

matrix_expression<compressed_matrix<T, F, IB, IA, TA> >

Members

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 = 0) 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>
compressed_matrix (size_type non_zeros, const matrix_expression<AE> &ae)
The extended copy constructor.
void resize (size_type size1, size_type size2, bool preserve = true) Reallocates a compressed_matrix to hold at most size1 rows of size2 elements. The existing elements of the compressed_matrix are preseved when specified.
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>
compressed_matrix &operator = (const matrix_expression<AE> &ae)
The extended assignment operator.
template<class AE>
compressed_matrix &assign (const matrix_expression<AE> &ae)
Assigns a matrix expression to the compressed matrix. Left and right hand side of the assignment should be independent.
template<class AE>
compressed_matrix &operator += (const matrix_expression<AE> &ae)
A computed assignment operator. Adds the matrix expression to the compressed matrix.
template<class AE>
compressed_matrix &plus_assign (const matrix_expression<AE> &ae)
Adds a matrix expression to the compressed matrix. Left and right hand side of the assignment should be independent.
template<class AE>
compressed_matrix &operator -= (const matrix_expression<AE> &ae)
A computed assignment operator. Subtracts the matrix expression from the compressed matrix.
template<class AE>
compressed_matrix &minus_assign (const matrix_expression<AE> &ae)
Subtracts a matrix expression from the compressed matrix. Left and right hand side of the assignment should be independent.
template<class AT>
compressed_matrix &operator *= (const AT &at)
A computed assignment operator. Multiplies the compressed matrix with a scalar.
template<class AT>
compressed_matrix &operator /= (const AT &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.

Notes

[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<> .

Coordinate Matrix

Description

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 = mi1 ,j1and k + 1 = mi2 ,j2of the container holds i1 < i2 or (i1 = i2 and j1 < j2) with row major orientation or j1 < j2 or (j1 = j2 and i1 < i2) with column major orientation.

Example

#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;
}

Definition

Defined in the header matrix_sparse.hpp.

Template parameters

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>

Model of

Matrix .

Type requirements

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

Public base classes

matrix_expression<coordinate_matrix<T, F, IB, IA, TA> >

Members

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 = 0) 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>
coordinate_matrix (size_type non_zeros, const matrix_expression<AE> &ae)
The extended copy constructor.
void resize (size_type size1, size_type size2, bool preserve = true) Reallocates a coordinate_matrix to hold at most size1 rows of size2 elements. The existing elements of the coordinate_matrix are preseved when specified.
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>
coordinate_matrix &operator = (const matrix_expression<AE> &ae)
The extended assignment operator.
template<class AE>
coordinate_matrix &assign (const matrix_expression<AE> &ae)
Assigns a matrix expression to the coordinate matrix. Left and right hand side of the assignment should be independent.
template<class AE>
coordinate_matrix &operator += (const matrix_expression<AE> &ae)
A computed assignment operator. Adds the matrix expression to the coordinate matrix.
template<class AE>
coordinate_matrix &plus_assign (const matrix_expression<AE> &ae)
Adds a matrix expression to the coordinate matrix. Left and right hand side of the assignment should be independent.
template<class AE>
coordinate_matrix &operator -= (const matrix_expression<AE> &ae)
A computed assignment operator. Subtracts the matrix expression from the coordinate matrix.
template<class AE>
coordinate_matrix &minus_assign (const matrix_expression<AE> &ae)
Subtracts a matrix expression from the coordinate matrix. Left and right hand side of the assignment should be independent.
template<class AT>
coordinate_matrix &operator *= (const AT &at)
A computed assignment operator. Multiplies the coordinate matrix with a scalar.
template<class AT>
coordinate_matrix &operator /= (const AT &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.

Notes

[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<> .


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