"LU" class is the virtual class of LU decompositions of real matrices.
"denseLU" the class of LU decompositions of dense real matrices.
The decomposition is of the form A = P L U where typically all matrices are of size n by n, and the matrix P is a permutation matrix, L is lower triangular and U is upper triangular (both of class
Note that the dense decomposition is also implemented for a m by n matrix A, when m != n.
If m < n (“wide case”), U is m by n, and hence not triangular.
If m > n (“long case”), L is m by n, and hence not triangular.
Objects from the Class
Objects can be created by calls of the form
new("denseLU", ...). More commonly the objects are created explicitly from calls of the form
mm is an object that inherits from the
"dgeMatrix" class or as a side-effect of other functions applied to
"LU" directly extends the virtual class
"denseLU" directly extends
- object of class
"L"(unit lower triangular) and
"U"(upper triangular) factors of the original matrix. These are stored in a packed format described in the Lapack manual, and can retrieved by the
expand()method, see below.
- Object of class
"integer"- a vector of length
min(Dim)that describes the permutation applied to the rows of the original matrix. The contents of this vector are described in the Lapack manual.
- the dimension of the original matrix; inherited from class
Documentation reproduced from package Matrix, version 1.2-3. License: GPL (>= 2)