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Banded Matrix

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

Model of

Matrix .

Type requirements

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

Public base classes

matrix_expression<banded_matrix<T, F, A> >

Members

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.

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
banded_adaptor () Constructs a banded_adaptor that holds zero rows of zero elements.
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
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