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 <- runif(n*(p-1))
X <- matrix(c(x,x[1:n]),n,p)
qrx <- qr(X,LAPACK=TRUE)
Rrank(qr.R(qrx))
```

[Package

*mgcv*version 1.9-0 Index]