Banded Matrix

Description

The templated class banded_matrix<T, F, A> is the base container adaptor for banded matrices. For a (m x n)-dimensional banded matrix with l lower and u upper diagonals and 0 < = i < m, 0 < = j < n holds b_i,j = 0, if i > j + l or i < j - u. The storage of banded matrices is packed.

Example

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

int main () {
    using namespace boost::numeric::ublas;
    banded_matrix<double> m (3, 3, 1, 1);
    for (signed i = 0; i < signed (m.size1 ()); ++ i)
        for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (m.size2 ())); ++ j)
            m (i, j) = 3 * i + j;
    std::cout << m << std::endl;
}

Definition

Defined in the header banded.hpp.

Template parameters

Parameter Description Default

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>`

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_container<banded_matrix<T, F, A> >

Members

Member Description

Member	Description
`banded_matrix ()`	Allocates an uninitialized `banded_matrix` that holds zero rows of zero elements.
`banded_matrix (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0)`	Allocates an uninitialized `banded_matrix` that holds `(lower + 1 + upper)` diagonals around the main diagonal of a matrix with `size1` rows of `size2` elements.
`banded_matrix (const banded_matrix &m)`	The copy constructor.
`template<class AE> banded_matrix (const matrix_expression<AE> &ae)`	The extended copy constructor.
`void resize (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0, bool preserve = true)`	Reallocates a `banded_matrix` to hold `(lower + 1 + upper)` diagonals around the main diagonal of a matrix with `size1` rows of `size2` elements. The existing elements of the `banded_matrix` are preseved when specified.
`size_type size1 () const`	Returns the number of rows.
`size_type size2 () const`	Returns the number of columns.
`size_type lower () const`	Returns the number of diagonals below the main diagonal.
`size_type upper () const`	Returns the number of diagonals above the main diagonal.
`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.
`banded_matrix &operator = (const banded_matrix &m)`	The assignment operator.
`banded_matrix &assign_temporary (banded_matrix &m)`	Assigns a temporary. May change the banded matrix `m` .
`template<class AE> banded_matrix &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> banded_matrix &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the banded matrix. Left and right hand side of the assignment should be independent.
`template<class AE> banded_matrix &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the banded matrix.
`template<class AE> banded_matrix &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the banded matrix. Left and right hand side of the assignment should be independent.
`template<class AE> banded_matrix &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the banded matrix.
`template<class AE> banded_matrix &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the banded matrix. Left and right hand side of the assignment should be independent.
`template<class AT> banded_matrix &operator *= (const AT &at)`	A computed assignment operator. Multiplies the banded matrix with a scalar.
`template<class AT> banded_matrix &operator /= (const AT &at)`	A computed assignment operator. Divides the banded matrix through a scalar.
`void swap (banded_matrix &m)`	Swaps the contents of the banded 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 elemenst of the `i`-th row.
`void clear ()`	Clears the matrix.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `banded_matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `banded_matrix`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `banded_matrix`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `banded_matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `banded_matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `banded_matrix`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `banded_matrix`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `banded_matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `banded_matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `banded_matrix`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `banded_matrix`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `banded_matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `banded_matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `banded_matrix`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `banded_matrix`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `banded_matrix`.

banded_matrix ()

Allocates an uninitialized banded_matrix that holds zero rows of zero elements.

banded_matrix (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0)

Allocates an uninitialized banded_matrix that holds (lower + 1 + upper) diagonals around the main diagonal of a matrix with size1 rows of size2 elements.

banded_matrix (const banded_matrix &m)

The copy constructor.

template<class AE> banded_matrix (const matrix_expression<AE> &ae)

The extended copy constructor.

void resize (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0, bool preserve = true)

Reallocates a banded_matrix to hold (lower + 1 + upper) diagonals around the main diagonal of a matrix with size1 rows of size2 elements. The existing elements of the banded_matrix are preseved when specified.

size_type size1 () const

Returns the number of rows.

size_type size2 () const

Returns the number of columns.

size_type lower () const

Returns the number of diagonals below the main diagonal.

size_type upper () const

Returns the number of diagonals above the main diagonal.

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.

banded_matrix &operator = (const banded_matrix &m)

The assignment operator.

banded_matrix &assign_temporary (banded_matrix &m)

Assigns a temporary. May change the banded matrix m .

template<class AE> banded_matrix &operator = (const matrix_expression<AE> &ae)

The extended assignment operator.

template<class AE> banded_matrix &assign (const matrix_expression<AE> &ae)

Assigns a matrix expression to the banded matrix. Left and right hand side of the assignment should be independent.

template<class AE> banded_matrix &operator += (const matrix_expression<AE> &ae)

A computed assignment operator. Adds the matrix expression to the banded matrix.

template<class AE> banded_matrix &plus_assign (const matrix_expression<AE> &ae)

Adds a matrix expression to the banded matrix. Left and right hand side of the assignment should be independent.

template<class AE> banded_matrix &operator -= (const matrix_expression<AE> &ae)

A computed assignment operator. Subtracts the matrix expression from the banded matrix.

template<class AE> banded_matrix &minus_assign (const matrix_expression<AE> &ae)

Subtracts a matrix expression from the banded matrix. Left and right hand side of the assignment should be independent.

template<class AT> banded_matrix &operator *= (const AT &at)

A computed assignment operator. Multiplies the banded matrix with a scalar.

template<class AT> banded_matrix &operator /= (const AT &at)

A computed assignment operator. Divides the banded matrix through a scalar.

void swap (banded_matrix &m)

Swaps the contents of the banded 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 elemenst of the i-th row.

void clear ()

Clears the matrix.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the banded_matrix.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the banded_matrix.

iterator1 begin1 ()

Returns a iterator1 pointing to the beginning of the banded_matrix.

iterator1 end1 ()

Returns a iterator1 pointing to the end of the banded_matrix.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the banded_matrix.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the banded_matrix.

iterator2 begin2 ()

Returns a iterator2 pointing to the beginning of the banded_matrix.

iterator2 end2 ()

Returns a iterator2 pointing to the end of the banded_matrix.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed banded_matrix.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed banded_matrix.

reverse_iterator1 rbegin1 ()

Returns a reverse_iterator1 pointing to the beginning of the reversed banded_matrix.

reverse_iterator1 rend1 ()

Returns a reverse_iterator1 pointing to the end of the reversed banded_matrix.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed banded_matrix.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed banded_matrix.

reverse_iterator2 rbegin2 ()

Returns a reverse_iterator2 pointing to the beginning of the reversed banded_matrix.

reverse_iterator2 rend2 ()

Returns a reverse_iterator2 pointing to the end of the reversed banded_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> .

Banded Adaptor

Description

The templated class banded_adaptor<M> is a banded matrix adaptor for other matrices.

Example

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

int main () {
    using namespace boost::numeric::ublas;
    matrix<double> m (3, 3);
    banded_adaptor<matrix<double> > ba (m, 1, 1);
    for (signed i = 0; i < signed (ba.size1 ()); ++ i)
        for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (ba.size2 ())); ++ j)
            ba (i, j) = 3 * i + j;
    std::cout << ba << std::endl;
}

Definition

Defined in the header banded.hpp.

Template parameters

Parameter

Description

Default

M

The type of the adapted matrix.

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<banded_adaptor<M> >

Members

Member Description

Member	Description
`banded_adaptor (matrix_type &data, size_type lower = 0, size_type upper = 0)`	Constructs a `banded_adaptor` that holds `(lower + 1 + upper)` diagonals around the main diagonal of a matrix.
`banded_adaptor (const banded_adaptor &m)`	The copy constructor.
`template<class AE> banded_adaptor (const matrix_expression<AE> &ae)`	The extended copy constructor.
`size_type size1 () const`	Returns the number of rows.
`size_type size2 () const`	Returns the number of columns.
`size_type lower () const`	Returns the number of diagonals below the main diagonal.
`size_type upper () const`	Returns the number of diagonals above the main diagonal.
`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.
`banded_adaptor &operator = (const banded_adaptor &m)`	The assignment operator.
`banded_adaptor &assign_temporary (banded_adaptor &m)`	Assigns a temporary. May change the banded adaptor `m` .
`template<class AE> banded_adaptor &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> banded_adaptor &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the banded adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> banded_adaptor &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the banded adaptor.
`template<class AE> banded_adaptor &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the banded adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> banded_adaptor &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the banded adaptor.
`template<class AE> banded_adaptor &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the banded adaptor. Left and right hand side of the assignment should be independent.
`template<class AT> banded_adaptor &operator *= (const AT &at)`	A computed assignment operator. Multiplies the banded adaptor with a scalar.
`template<class AT> banded_adaptor &operator /= (const AT &at)`	A computed assignment operator. Divides the banded adaptor through a scalar.
`void swap (banded_adaptor &m)`	Swaps the contents of the banded adaptors.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `banded_adaptor`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `banded_adaptor`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `banded_adaptor`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `banded_adaptor`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `banded_adaptor`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `banded_adaptor`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `banded_adaptor`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `banded_adaptor`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `banded_adaptor`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `banded_adaptor`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `banded_adaptor`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `banded_adaptor`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `banded_adaptor`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `banded_adaptor`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `banded_adaptor`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `banded_adaptor`.

banded_adaptor (matrix_type &data, size_type lower = 0, size_type upper = 0)

Constructs a banded_adaptor that holds (lower + 1 + upper) diagonals around the main diagonal of a matrix.

banded_adaptor (const banded_adaptor &m)

The copy constructor.

template<class AE> banded_adaptor (const matrix_expression<AE> &ae)

The extended copy constructor.

size_type size1 () const

Returns the number of rows.

size_type size2 () const

Returns the number of columns.

size_type lower () const

Returns the number of diagonals below the main diagonal.

size_type upper () const

Returns the number of diagonals above the main diagonal.

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.

banded_adaptor &operator = (const banded_adaptor &m)

The assignment operator.

banded_adaptor &assign_temporary (banded_adaptor &m)

Assigns a temporary. May change the banded adaptor m .

template<class AE> banded_adaptor &operator = (const matrix_expression<AE> &ae)

The extended assignment operator.

template<class AE> banded_adaptor &assign (const matrix_expression<AE> &ae)

Assigns a matrix expression to the banded adaptor. Left and right hand side of the assignment should be independent.

template<class AE> banded_adaptor &operator += (const matrix_expression<AE> &ae)

A computed assignment operator. Adds the matrix expression to the banded adaptor.

template<class AE> banded_adaptor &plus_assign (const matrix_expression<AE> &ae)

Adds a matrix expression to the banded adaptor. Left and right hand side of the assignment should be independent.

template<class AE> banded_adaptor &operator -= (const matrix_expression<AE> &ae)

A computed assignment operator. Subtracts the matrix expression from the banded adaptor.

template<class AE> banded_adaptor &minus_assign (const matrix_expression<AE> &ae)

Subtracts a matrix expression from the banded adaptor. Left and right hand side of the assignment should be independent.

template<class AT> banded_adaptor &operator *= (const AT &at)

A computed assignment operator. Multiplies the banded adaptor with a scalar.

template<class AT> banded_adaptor &operator /= (const AT &at)

A computed assignment operator. Divides the banded adaptor through a scalar.

void swap (banded_adaptor &m)

Swaps the contents of the banded adaptors.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the banded_adaptor.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the banded_adaptor.

iterator1 begin1 ()

Returns a iterator1 pointing to the beginning of the banded_adaptor.

iterator1 end1 ()

Returns a iterator1 pointing to the end of the banded_adaptor.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the banded_adaptor.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the banded_adaptor.

iterator2 begin2 ()

Returns a iterator2 pointing to the beginning of the banded_adaptor.

iterator2 end2 ()

Returns a iterator2 pointing to the end of the banded_adaptor.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed banded_adaptor.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed banded_adaptor.

reverse_iterator1 rbegin1 ()

Returns a reverse_iterator1 pointing to the beginning of the reversed banded_adaptor.

reverse_iterator1 rend1 ()

Returns a reverse_iterator1 pointing to the end of the reversed banded_adaptor.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed banded_adaptor.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed banded_adaptor.

reverse_iterator2 rbegin2 ()

Returns a reverse_iterator2 pointing to the beginning of the reversed banded_adaptor.

reverse_iterator2 rend2 ()

Returns a reverse_iterator2 pointing to the end of the reversed banded_adaptor.

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Copyright (©) 2021 Shikhar Vashistha
Use, modification and distribution are subject to the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt).