Rrank {mgcv} | R Documentation |
Find rank of upper triangular matrix
Description
Finds rank of upper triangular matrix R, by estimating condition
number of upper rank
by rank
block, and reducing rank
until this is acceptably low. Assumes R has been computed by a method that uses
pivoting, usually pivoted QR or Choleski.
Usage
Rrank(R,tol=.Machine$double.eps^.9)
Arguments
R |
An upper triangular matrix, obtained by pivoted QR or pivoted Choleski. |
tol |
the tolerance to use for judging rank. |
Details
The method is based on Cline et al. (1979) as described in Golub and van Loan (1996).
Author(s)
Simon N. Wood simon.wood@r-project.org
References
Cline, A.K., C.B. Moler, G.W. Stewart and J.H. Wilkinson (1979) An estimate for the condition number of a matrix. SIAM J. Num. Anal. 16, 368-375
Golub, G.H, and C.F. van Loan (1996) Matrix Computations 3rd ed. Johns Hopkins University Press, Baltimore.
Examples
set.seed(0)
n <- 10;p <- 5
x <- runif(n*(p-1))
X <- matrix(c(x,x[1:n]),n,p)
qrx <- qr(X,LAPACK=TRUE)
Rrank(qr.R(qrx))
[Package mgcv version 1.9-1 Index]