R: Compute Generalized Inverse of Input Matrix

Ginv {haplo.stats} | R Documentation

## 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

### 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).

### 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.

### 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

[Package haplo.stats version 1.7.9 Index]