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Rows provide views on a specific row of a dense or sparse matrix. As such, rows act as a reference to a specific row. This reference is valid and can be used in every way any other row vector can be used as long as the matrix containing the row is not resized or entirely destroyed. The row also acts as an alias to the row elements: Changes made to the elements (e.g. modifying values, inserting or erasing elements) are immediately visible in the matrix and changes made via the matrix are immediately visible in the row.
The blaze::Row class template represents a reference to a specific row of a dense or sparse matrix primitive. It can be included via the header file
The type of the matrix is specified via template parameter:
MT
specifies the type of the matrix primitive. Row can be used with every matrix primitive, but does not work with any matrix expression type.
A reference to a dense or sparse row can be created very conveniently via the row()
function. This reference can be treated as any other row vector, i.e. it can be assigned to, it can be copied from, and it can be used in arithmetic operations. The reference can also be used on both sides of an assignment: The row can either be used as an alias to grant write access to a specific row of a matrix primitive on the left-hand side of an assignment or to grant read-access to a specific row of a matrix primitive or expression on the right-hand side of an assignment. The following two examples demonstrate this for dense and sparse matrices:
The row()
function can be used on any dense or sparse matrix, including expressions, as illustrated by the source code example. However, rows cannot be instantiated for expression types, but only for matrix primitives, respectively, i.e. for matrix types that offer write access.
A row view can be used like any other row vector. For instance, the current number of elements can be obtained via the size()
function, the current capacity via the capacity()
function, and the number of non-zero elements via the nonZeros()
function. However, since rows are references to specific rows of a matrix, several operations are not possible on views, such as resizing and swapping. The following example shows this by means of a dense row view:
The elements of the row can be directly accessed with the subscript operator. The numbering of the row elements is
where N is the number of columns of the referenced matrix. Alternatively, the elements of a row can be traversed via iterators. Just as with vectors, in case of non-const rows, begin()
and end()
return an Iterator, which allows a manipulation of the non-zero value, in case of a constant row a ConstIterator is returned:
Inserting/accessing elements in a sparse row can be done by several alternative functions. The following example demonstrates all options:
Both dense and sparse rows can be used in all arithmetic operations that any other dense or sparse row vector can be used in. The following example gives an impression of the use of dense rows within arithmetic operations. All operations (addition, subtraction, multiplication, scaling, ...) can be performed on all possible combinations of dense and sparse rows with fitting element types:
Especially noteworthy is that row views can be created for both row-major and column-major matrices. Whereas the interface of a row-major matrix only allows to traverse a row directly and the interface of a column-major matrix only allows to traverse a column, via views it is possible to traverse a row of a column-major matrix or a column of a row-major matrix. For instance:
However, please note that creating a row view on a matrix stored in a column-major fashion can result in a considerable performance decrease in comparison to a view on a matrix with a fitting storage orientation. This is due to the non-contiguous storage of the matrix elements. Therefore care has to be taken in the choice of the most suitable storage order:
Although Blaze performs the resulting vector/matrix multiplication as efficiently as possible using a row-major storage order for matrix A would result in a more efficient evaluation.
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