| LU-class {Matrix} | R Documentation |
The "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
dtrMatrix).
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 can be created by calls of the form new("denseLU", ...).
More commonly the objects are created explicitly from calls of the form
lu(mm) where mm is an object that inherits from the
"dgeMatrix" class or as a side-effect of other functions applied
to "dgeMatrix" objects.
"LU" directly extends the virtual class
"MatrixFactorization".
"denseLU" directly extends "LU".
x:object of class "numeric". The "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.
perm: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.
Dim:the dimension of the original matrix; inherited
from class MatrixFactorization .
signature(x = "denseLU"): Produce the "L" and
"U" (and "P") factors as a named list of matrices,
see also the example below.
signature(a = "denseLU", b = "missing"): Compute
the inverse of A, A^(-1), solve(A) using the LU
decomposition.
class sparseLU for LU decompositions of
sparse matrices;
further, class dgeMatrix and functions lu,
expand.
set.seed(1)
mm <- Matrix(round(rnorm(9),2), nrow = 3)
mm
str(lum <- lu(mm))
elu <- expand(lum)
elu # three components: "L", "U", and "P", the permutation
elu$L %*% elu$U
(m2 <- with(elu, P %*% L %*% U)) # the same as 'mm'
stopifnot(all.equal(as(mm, "matrix"),
as(m2, "matrix")))