(Generalized) Triangular Decomposition of a Matrix
Computes (generalized) triangular decompositions of square (sparse or dense) and non-square dense matrices.
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a dense or sparse matrix, in the latter case of square dimension. No missing values or IEEE special values are allowed.
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
logical indicating that
further arguments passed to or from other methods.
lu() is a generic function with special methods for different types
of matrices. Use
showMethods("lu") to list all the 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
(too close to) singular.
An object of class
(see its separate help page),
sparseLU; this is
a representation of a triangular decomposition of
Because the underlying algorithm differ entirely,
in the dense case (class
A = P L U,
where as in the sparse case (class
sparseLU), it is
A = P' L U Q.
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”.
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##--- 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]