Matrix (version 1.5-1)

lu: (Generalized) Triangular Decomposition of a Matrix

Description

Computes (generalized) triangular decompositions of square (sparse or dense) and non-square dense matrices.

Usage

lu(x, ...)
# S4 method for matrix
lu(x, ...)
# S4 method for dgeMatrix
lu(x, warnSing = TRUE, ...)
# S4 method for dgCMatrix
lu(x, errSing = TRUE, order = TRUE, tol = 1,
   keep.dimnames = TRUE, ...)
# S4 method for dsyMatrix
lu(x, cache = TRUE, ...)
# S4 method for dsCMatrix
lu(x, cache = TRUE, ...)

Value

An object of class "LU", i.e., "denseLU"

(see its separate help page), or "sparseLU", see sparseLU; this is a representation of a triangular decomposition of x.

Arguments

x

a dense or sparse matrix, in the latter case of square dimension. No missing values or IEEE special values are allowed.

warnSing

(when x is a "denseMatrix") logical specifying if a warning should be signalled when x is singular.

errSing

(when x is a "sparseMatrix") logical specifying if an error (see stop) should be signalled when x is singular. When x is singular, lu(x, errSing=FALSE) returns NA instead of an LU decomposition. No warning is signalled and the useR should be careful in that case.

order

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.

tol

positive number indicating the pivoting tolerance used in cs_lu. Do only change with much care.

keep.dimnames

logical indicating that dimnames should be propagated to the result, i.e., “kept”. This was hardcoded to FALSE in upto Matrix version 1.2-0. Setting to FALSE may gain some performance.

cache

logical indicating if the result should be cached in x@factors; note that this argument is experimental and only available for certain classes inheriting from compMatrix.

...

further arguments passed to or from other methods.

Details

lu() is a generic function with special methods for different types of matrices. Use showMethods("lu") to list all the methods for the lu generic.

The method for class dgeMatrix (and all dense, non-triangular 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, non-triangular matrices) is based on functions from the CSparse library. It signals an error (or returns NA, when errSing = FALSE; see above) when the decomposition algorithm fails, as when x is (too close to) singular.

References

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”.

See Also

Class definitions denseLU and sparseLU and function expand; qr, chol.

Examples

##--- 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]