R: Find rank of upper triangular matrix

Rrank {mgcv} | R Documentation

## Find rank of upper triangular matrix

### Description

Finds rank of upper triangular matrix R, by estimating condition number of upper `rank` by `rank` block, and reducing `rank` until this is acceptably low. Assumes R has been computed by a method that uses pivoting, usually pivoted QR or Choleski.

### Usage

    Rrank(R,tol=.Machine$double.eps^.9)

### Arguments

`R` | An upper triangular matrix, obtained by pivoted QR or pivoted Choleski.
`tol` | the tolerance to use for judging rank.

### Details

The method is based on Cline et al. (1979) as described in Golub and van Loan (1996).

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Cline, A.K., C.B. Moler, G.W. Stewart and J.H. Wilkinson (1979) An estimate for the condition number of a matrix. SIAM J. Num. Anal. 16, 368-375

Golub, G.H, and C.F. van Loan (1996) Matrix Computations 3rd ed. Johns Hopkins University Press, Baltimore.

### Examples

      set.seed(0)
      n <- 10;p <- 5
      X <- matrix(runif(n*(p-1)),n,p)
      qrx <- qr(X,LAPACK=TRUE)
      Rrank(qr.R(qrx))

[Package mgcv version 1.8-3 Index]