Sparse Matricies

Mapped Matrix

Description

The templated class mapped_matrix<T, F, A> is the base container adaptor for sparse matricies using element maps. For a (m xn)-dimensional sparse matrix and 0 <= i < m, 0 <= j < n the non-zero elements m_{i, 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 = m_i_₁_,j_₁and k + 1 = m_i_₂_,j_₂of 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;
    mapped_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 mapped 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_container<mapped_matrix<T, F, A> >

Members

Member	Description
`mapped_matrix ()`	Allocates a `mapped_matrix` that holds at most zero rows of zero elements.
`mapped_matrix (size_type size1, size_type2, size_type non_zeros = 0)`	Allocates a `mapped_matrix` that holds at most `size1` rows of `size2` elements.
`mapped_matrix (const mapped_matrix &m)`	The copy constructor.
`template<class AE> mapped_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 `mapped_matrix` to hold at most `size1` rows of `size2` elements. The existing elements of the `mapped_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.
`mapped_matrix &operator = (const mapped_matrix &m)`	The assignment operator.
`mapped_matrix &assign_temporary (mapped_matrix &m)`	Assigns a temporary. May change the mapped matrix `m` .
`template<class AE> mapped_matrix &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> mapped_matrix &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the mapped matrix. Left and right hand side of the assignment should be independent.
`template<class AE> mapped_matrix &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the mapped matrix.
`template<class AE> mapped_matrix &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the mapped matrix. Left and right hand side of the assignment should be independent.
`template<class AE> mapped_matrix &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the mapped matrix.
`template<class AE> mapped_matrix &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the mapped matrix. Left and right hand side of the assignment should be independent.
`template<class AT> mapped_matrix &operator *= (const AT &at)`	A computed assignment operator. Multiplies the mapped matrix with a scalar.
`template<class AT> mapped_matrix &operator /= (const AT &at)`	A computed assignment operator. Divides the mapped matrix through a scalar.
`void swap (mapped_matrix &m)`	Swaps the contents of the mapped matrices.
`true_refrence insert_element (size_type i, size_type j, const_reference t)`	Inserts the value `t` at the `j`-th element of the `i`-th row. Duplicates elements are not allowed.
`void erase_element (size_type i, size_type j)`	Erases the value at the `j`-th element of the `i`-th row.
`void clear ()`	Clears the mapped matrix.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `mapped_matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `mapped_matrix`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `mapped_matrix`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `mapped_matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `mapped_matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `mapped_matrix`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `mapped_matrix`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `mapped_matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `mapped_matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `mapped_matrix`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `mapped_matrix`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `mapped_matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `mapped_matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `mapped_matrix`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `mapped_matrix`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `mapped_matrix`.

Notes

[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 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 m_{i, 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_i_₁_,j_₁and k + 1 = m_i_₂_,j_₂of 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_container<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.
`true_reference insert_element (size_type i, size_type j, const_reference t)`	Inserts the value `t` at the `j`-th element of the `i`-th row. Duplicates elements are not allowed.
`void erase_element (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 m_{i, 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_i_₁_,j_₁and k + 1 = m_i_₂_,j_₂of 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_container<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.
`true_reference insert_element (size_type i, size_type j, const_reference t)`	Inserts the value `t` at the `j`-th element of the `i`-th row. Duplicates elements are not allowed.
`void append_element (size_type i, size_type j, const_reference t)`	Appends the value `t` at the `j`-th element of the `i`-th row. Duplicate elements can be appended to a `coordinate_matrix`. They are merged into a single arithmetically summed element by the `sort` function.
`void erase_element (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.