Ленточная матрица

Описание

Шаблонный класс banded_matrix<T, F, A> является базовым контейнером-адаптером для ленточных матриц. Для (m x n)-размерной ленточной матрицы с l нижней и u верхней диагоналями и 0 <= i < m, 0 <= j < n элементами являются b_{i, j} = 0, если i > j + l или i < j - u. Хранилище (storage) ленточных матриц сжато.

Пример

#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;
}

Будет выведено на экран:

[3,3]((0,1,0),(3,4,5),(0,7,8))

Определение

Определено в заголовочном файле banded.hpp.

Параметры шаблона

Параметр	Описание	Значение по-умолчанию
`T`	Тип объектов, размещаемых в матрице.
`F`	Функция, определяющая организацию хранения. [1]	`row_major`
`A`	Тип приспособленного (adapted) массива. [2]	`unbounded_array<T>`

Является моделью

матрицы (matrix) .

Требования к типам данных

Для которых базовый класс матрица (matrix) .

Базовый класс

matrix_container<banded_matrix<T, F, A> >

Функции-члены

Приведенные ниже функции-члены в основном аналогичны функциям, перевод которым дан в разделе матрица. Характерные только для banded_matrix функции-члены переведены в таблице ниже.

Функция-член	Описание
`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)`	Создает неинициализированную `banded_matrix`, которая содержит `(lower + 1 + upper)` диагоналей вокруг главной диагонали матрицы с `size1` строками и `size2` столбцами.
`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)`	Изменяет размер `banded_matrix` до содержащей `(lower + 1 + upper)` диагоналей вокруг главной диагонали матрицы с `size1` строками и `size2` столбцами. Существующие элементы `banded_matrix` сохраняются.
`size_type size1 () const`	Returns the number of rows.
`size_type size2 () const`	Returns the number of columns.
`size_type lower () const`	Возвращает число диагоналей под главной диагональю.
`size_type upper () const`	Возвращает число диагоналей над главной диагональю.
`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`.

Примечание

[1] Поддерживаемые параметры организации хранения: row_major и column_major.

[2] Поддерживаемые параметры для приспособленного (adapted) массива unbounded_array<T> , bounded_array<T> и std::vector<T> .

Ленточный адаптер

Описание

Шаблонный класс banded_adaptor<M> является ленточным адаптером для других матриц.

Пример

#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;
}

Будет выведено на экран:

[3,3]((0,1,0),(3,4,5),(0,7,8))

Определение

Определено в заголовочном файле banded.hpp.

Параметры шаблона

Параметр	Описание	Значение по-умолчанию
`M`	Тип приспособленной (adapted) матрицы.

Является моделью

матричного выражения (matrix expression) .

Требования к типам данных

Для которых базовый класс матричное выражение (matrix expression) .

Базовый класс

matrix_expression<banded_adaptor<M> >

Функции-члены

Функция-член	Описание
`banded_adaptor (matrix_type &data, size_type lower = 0, size_type upper = 0)`	Создает `banded_adaptor`, которая содержит `(lower + 1 + upper)` диагоналей вокруг главной диагонали матрицы .
`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`	Возвращает число диагоналей под главной диагональю.
`size_type upper () const`	Возвращает число диагоналей над главной диагональю.
`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.

Перевод с оригинала: Кулиш. В. И. 2006 год.