| lu {Matrix} | R Documentation |
Computes triangular decompositions of square matrices.
lu(x, ...) ## S4 method for signature 'dgeMatrix': lu(x, warnSing = TRUE, ...)
x |
a matrix 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. |
... |
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
for the lu generic.
The method for class dgeMatrix (and all dense
matrices) is based on LAPACK's "dgetrf" subroutine. It returns
a decomposition also for singular matrices.
The method for class dgCMatrix (and all sparse
matrices) is based on functions from the CSparse library. It signals
an error when the decomposition algorithm fails, as when x is
(too close to) singular.
An object of class "LU", i.e., "denseLU"
or "sparseLU", see sparseLU; this is
a representation of a triangular decomposition of x.
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
Tim Davis (2005) http://www.cise.ufl.edu/research/sparse/CSparse/
Timothy A. Davis (2006) Direct Methods for Sparse Linear Systems, SIAM Series “Fundamentals of Algorithms”.
Class definitions LU and sparseLU
and function expand;
qr, chol.
##--- Dense -------------------------
x <- Matrix(rnorm(9), 3, 3)
lu(x)
##--- Sparse ------------------------
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 <- pmLU@L %*% pmLU@U
## equal up to "rounding"
ppm[1:14, 1:5]
pLU[1:14, 1:5] # product can have extra zeros
## "prove" consistency (up to rounding):
i0 <- ppm != pLU & ppm == 0
iN <- ppm != pLU & ppm != 0
stopifnot(all(abs((ppm - pLU)[i0]) < 1e-7), # absolute error for true 0
all(abs((ppm - pLU)[iN]/ppm[iN]) < 1e-9)) # relative error