Computes (generalized) triangular decompositions of square (sparse or dense) and non-square dense matrices.
lu(x, ...) ## S4 method for class 'matrix': lu((x, warnSing = TRUE, ...)) ## S4 method for class 'dgeMatrix': lu((x, warnSing = TRUE, ...)) ## S4 method for class 'dgCMatrix': lu((x, errSing = TRUE, order = TRUE, tol = 1, keep.dimnames = TRUE, ...))
- a dense or sparse matrix, in the latter case of square dimension. No missing values or IEEE special values are allowed.
"denseMatrix") logical specifying if a
warningshould be signalled when
"sparseMatrix") logical specifying if an error (see
stop) should be signalled when
xis singular. When
NAinstead of an LU decomposition. No warning is signalled and the useR should be careful in that case.
- logical or integer, used to choose which fill-reducing permutation technique will be used internally. Do not change unless you know what you are doing.
- positive number indicating the pivoting tolerance used in
cs_lu. Do only change with much care.
- logical indicating that
dimnamesshould be propagated to the result, i.e., “kept”. This was hardcoded to
FALSEin upto Matrix version 1.2-0. Setting to
FALSEmay gain some performance.
- further arguments passed to or from other methods.
The method for class
dgeMatrix (and all dense matrices) is based on LAPACK's
"dgetrf" subroutine. It returns a decomposition also for singular and non-square matrices.
The method for class
dgCMatrix (and all sparse matrices) is based on functions from the CSparse library. It signals an error (or returns
errSing = FALSE, see above) when the decomposition algorithm fails, as when
x is (too close to) singular.
An object of class
"denseLU" (see its separate help page), or
sparseLU; this is a representation of a triangular decomposition of
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
Timothy A. Davis (2006) Direct Methods for Sparse Linear Systems, SIAM Series “Fundamentals of Algorithms”.
Because the underlying algorithm differ entirely, in the dense case (class
denseLU), the decomposition is A = P L U, where as in the sparse case (class
sparseLU), it is A = P' L U Q.
##--- Dense ------------------------- x <- Matrix(rnorm(9), 3, 3) lu(x) dim(x2 <- round(10 * x[,-3]))# non-square expand(lu2 <- lu(x2)) ##--- Sparse (see more in ?"sparseLU-class")----- % ./sparseLU-class.Rd pm <- as(readMM(system.file("external/pores_1.mtx", package = "Matrix")), "CsparseMatrix") str(pmLU <- lu(pm)) # p is a 0-based permutation of the rows # q is a 0-based permutation of the columns ## permute rows and columns of original matrix ppm <- pm[pmLU@p + 1L, pmLU@q + 1L] pLU <- drop0(pmLU@L %*% pmLU@U) # L %*% U -- dropping extra zeros ## equal up to "rounding" ppm[1:14, 1:5] pLU[1:14, 1:5]
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