haplo.stats (version 1.4.4)

Ginv: Compute Generalized Inverse of Input Matrix

Description

Singular value decomposition (svd) is used to compute a generalized inverse of input matrix.

Usage

Ginv(x, eps=1e-6)

Arguments

x

A matrix.

eps

minimum cutoff for singular values in svd of x

Value

• List with components:
• Ginv
  Generalized inverse of x.
• rank
  Rank of matrix x.

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.

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).

See Also

svd

Examples

# 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