lumethods  R Documentation 
Computes the pivoted LU factorization of an m \times n
real matrix A
, which has the general form
P_{1} A P_{2} = L U
or (equivalently)
A = P_{1}' L U P_{2}'
where
P_{1}
is an m \times m
permutation matrix,
P_{2}
is an n \times n
permutation matrix,
L
is an m \times \min(m,n)
unit lower trapezoidal matrix, and
U
is a \min(m,n) \times n
upper trapezoidal matrix.
Methods for denseMatrix
are built on
LAPACK routine dgetrf
, which does not permute columns,
so that P_{2}
is an identity matrix.
Methods for sparseMatrix
are built on
CXSparse routine cs_lu
, which requires m = n
,
so that L
and U
are triangular matrices.
lu(x, ...)
## S4 method for signature 'dgeMatrix'
lu(x, warnSing = TRUE, ...)
## S4 method for signature 'dgCMatrix'
lu(x, errSing = TRUE, order = NA_integer_,
tol = 1, ...)
## S4 method for signature 'dsyMatrix'
lu(x, cache = TRUE, ...)
## S4 method for signature 'dsCMatrix'
lu(x, cache = TRUE, ...)
## S4 method for signature 'matrix'
lu(x, ...)
x 
a finite matrix or

warnSing 
a logical indicating if a warning should
be signaled for singular 
errSing 
a logical indicating if an error should
be signaled for singular 
order 
an integer in 
tol 
a number. The original pivot element is used
if its absolute value exceeds 
cache 
a logical indicating if the result should be
cached in 
... 
further arguments passed to or from methods. 
What happens when x
is determined to be nearsingular
differs by method. The method for class dgeMatrix
completes the factorization, warning if warnSing = TRUE
and in any case returning a valid denseLU
object. Users of this method can detect singular x
with
a suitable warning handler; see tryCatch
.
In contrast, the method for class dgCMatrix
abandons further computation, throwing an error if errSing = TRUE
and otherwise returning NA
. Users of this method can
detect singular x
with an error handler or by setting
errSing = FALSE
and testing for a formal result with
is(., "sparseLU")
.
An object representing the factorization, inheriting from
virtual class LU
. The specific class
is denseLU
unless x
inherits
from virtual class sparseMatrix
,
in which case it is sparseLU
.
The LAPACK source code, including documentation; see https://netlib.org/lapack/double/dgetrf.f.
Davis, T. A. (2006). Direct methods for sparse linear systems. Society for Industrial and Applied Mathematics. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/1.9780898718881")}
Golub, G. H., & Van Loan, C. F. (2013). Matrix computations (4th ed.). Johns Hopkins University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.56021/9781421407944")}
Classes denseLU
and
sparseLU
and their methods.
Classes dgeMatrix
and
dgCMatrix
.
Generic functions expand1
and expand2
,
for constructing matrix factors from the result.
Generic functions Cholesky
, BunchKaufman
,
Schur
, and qr
,
for computing other factorizations.
showMethods("lu", inherited = FALSE)
set.seed(0)
##  Dense 
(A1 < Matrix(rnorm(9L), 3L, 3L))
(lu.A1 < lu(A1))
(A2 < round(10 * A1[, 3L]))
(lu.A2 < lu(A2))
## A ~ P1' L U in floating point
str(e.lu.A2 < expand2(lu.A2), max.level = 2L)
stopifnot(all.equal(A2, Reduce(`%*%`, e.lu.A2)))
##  Sparse 
A3 < as(readMM(system.file("external/pores_1.mtx", package = "Matrix")),
"CsparseMatrix")
(lu.A3 < lu(A3))
## A ~ P1' L U P2' in floating point
str(e.lu.A3 < expand2(lu.A3), max.level = 2L)
stopifnot(all.equal(A3, Reduce(`%*%`, e.lu.A3)))
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