Singular value decomposition (svd) is used to compute a
generalized inverse of input matrix.
Usage
Ginv(x, eps=1e-6)
Value
List with components:
Ginv
Generalized inverse of x.
rank
Rank of matrix x.
Arguments
x
A matrix.
eps
minimum cutoff for singular values in svd of x
Details
The svd function uses the LAPACK standard library to compute the
singular values of the input matrix, and the rank of the matrix is
determined by the number of singular values that are at least as
large as max(svd)*eps, where eps is a small value.
For S-PLUS, the Matrix library is required (Ginv loads Matrix if not already
done so).
References
Press WH, Teukolsky SA, Vetterling WT, Flannery BP.
Numerical recipes in C. The art of scientific computing.
2nd ed. Cambridge University Press, Cambridge.1992. page
61.
Anderson, E., et al. (1994). LAPACK User's Guide,
2nd edition, SIAM, Philadelphia.
# for matrix x, extract the generalized inverse and # rank of x as follows x <- matrix(c(1,2,1,2,3,2),ncol=3)
save <- Ginv(x)
ginv.x <- save$Ginv
rank.x <- save$rank