# 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