| 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, ...) ## S3 method for class 'lm': kappa(z, ...) ## Default S3 method: kappa(z, exact = FALSE, ...) ## S3 method for class 'qr': kappa(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 |
logical. Should the result be exact? |
... |
further arguments passed to or from other methods. |
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.
kappa.tri is an internal function called by kappa.qr.
The condition number, kappa, or an approximation if
exact = FALSE.
The design was inspired by (but differs considerably from) the S function of the same name described in Chambers (1992).
Chambers, J. M. (1992) Linear models. Chapter 4 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
svd for the singular value decomposition and
qr for the QR one.
kappa(x1 <- cbind(1,1:10))# 15.71
kappa(x1, exact = TRUE) # 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%)