lu {Matrix} | R Documentation |
Computes triangular decompositions of square matrices.
lu(x, ...)
x |
a matrix. No missing values or IEEE special values are allowed. |
... |
further arguments passed to or from other methods. |
This 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
is based on
LAPACK's "dgetrf"
subroutine.
The method for class dgCMatrix
of sparse matrices
is based on functions from the CSparse library.
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
.
x <- Matrix(rnorm(9), 3, 3) lu(x) 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 + 1:1, pmLU@q + 1:1] ppm[1:14, 1:5] (pmLU@L %*% pmLU@U)[1:14, 1:5] # product can have extra zeros