kappa {base} | R Documentation |
An estimate of the condition number of a matrix or of the R matrix of a QR decomposition, perhaps of a linear fit. The condition number is defined as the ratio of the largest to the smallest non-zero singular value of the matrix.
kappa(z, ...) kappa.lm (z, ...) kappa.default(z, exact = FALSE) kappa.qr (z, ...) kappa.tri (z, exact = FALSE, ...)
z |
A matrix or a the result of qr or a fit from a class
inheriting from "lm" . |
exact |
Should the result be exact? |
If exact = FALSE
(the default) the condition number is estimated
by a cheap approximation. Following S, this uses the LINPACK routine
`dtrco.f'. However, in R (or S) the exact calculation is also
likely to be quick enough.
The condition number, kappa, or an approximation if
exact=FALSE
.
B.D. Ripley
svd
for the singular value decomposition and
qr
for the QR one.
kappa(x1 <- cbind(1,1:10))# 15.71 kappa(x1, exact=T) # 13.68 kappa(x2 <- cbind(x1,2:11))# high! [x2 is singular!] hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") } sv9 <- svd(h9 <- hilbert(9))$ d kappa(h9)# pretty high! kappa(h9, exact=TRUE) == max(sv9) / min(sv9) kappa(h9, exact=TRUE) / kappa(h9) # .677 (i.e. rel.error = 32%)