
Last chance! 50% off unlimited learning
Sale ends in
Objects of this class contain the components of the LU decomposition of a sparse square matrix.
Objects can be created by calls of the form new("sparseLU",
...)
but are more commonly created by function lu()
applied to a sparse matrix, such as a matrix of class
dgCMatrix
.
L
:Object of class "dtCMatrix"
, the lower
triangular factor from the left.
U
:Object of class "dtCMatrix"
, the upper
triangular factor from the right.
p
:Object of class "integer"
, permutation
applied from the left.
q
:Object of class "integer"
, permutation
applied from the right.
Dim
:the dimension of the original matrix; inherited
from class MatrixFactorization
.
Class "LU"
, directly.
Class "MatrixFactorization"
, by class "LU"
.
signature(x = "sparseLU")
Returns a list with
components P
, L
, U
, and Q
,
where
lu
, solve
, dgCMatrix
## Extending the one in examples(lu), calling the matrix A,
## and confirming the factorization identities :
A <- as(readMM(system.file("external/pores_1.mtx",
package = "Matrix")),
"CsparseMatrix")
## with dimnames(.) - to see that they propagate to L, U :
dimnames(A) <- dnA <- list(paste0("r", seq_len(nrow(A))),
paste0("C", seq_len(ncol(A))))
str(luA <- lu(A)) # p is a 0-based permutation of the rows
# q is a 0-based permutation of the columns
xA <- expand(luA)
## which is simply doing
stopifnot(identical(xA$ L, luA@L),
identical(xA$ U, luA@U),
identical(xA$ P, as(luA@p +1L, "pMatrix")),
identical(xA$ Q, as(luA@q +1L, "pMatrix")))
P.LUQ <- with(xA, t(P) %*% L %*% U %*% Q)
stopifnot(all.equal(A, P.LUQ, tolerance = 1e-12),
identical(dimnames(P.LUQ), dnA))
## permute rows and columns of original matrix
pA <- A[luA@p + 1L, luA@q + 1L]
stopifnot(identical(pA, with(xA, P %*% A %*% t(Q))))
pLU <- drop0(luA@L %*% luA@U) # L %*% U -- dropping extra zeros
stopifnot(all.equal(pA, pLU, tolerance = 1e-12))
Run the code above in your browser using DataLab