# fullRank: Remove Columns (or Rows) From a Matrix to Make It Full Rank In robustbase: Basic Robust Statistics

 fullRank R Documentation

## Remove Columns (or Rows) From a Matrix to Make It Full Rank

### Description

From the QR decomposition with pivoting, (qr(x, tol) if n \ge p), if the matrix is not of full rank, the corresponding columns (n \ge p) or rows (n < p) are omitted to form a full rank matrix.

### Usage


fullRank(x, tol = 1e-7, qrx = qr(x, tol=tol))


### Arguments

 x a numeric matrix of dimension n \times p, or a similar object for which qr() works. tol tolerance for determining rank (deficiency). Currently is simply passed to qr. qrx optionally may be used to pass a qr(x, ..); only used when p <= n.

### Value

a version of the matrix x, with less columns or rows if x's rank was smaller than min(n,p).

If x is of full rank, it is returned unchanged.

### Note

This is useful for robustness algorithms that rely on X matrices of full rank, e.g., adjOutlyingness.

This also works for numeric data frames and whenever qr() works correctly.

### Author(s)

Martin Maechler

qr; for more sophisticated rank determination, rankMatrix from package Matrix.

### Examples

stopifnot(identical(fullRank(wood), wood))

## More sophisticated and delicate
dim(T <- tcrossprod(data.matrix(toxicity))) # 38 x 38
dim(T. <- fullRank(T)) # 38 x 10
if(requireNamespace("Matrix")) {
rMmeths <- eval(formals(Matrix::rankMatrix)$method) rT. <- sapply(rMmeths, function(.m.) Matrix::rankMatrix(T., method = .m.)) print(rT.) # "qr" (= "qrLinpack"): 13, others rather 10 } dim(T.2 <- fullRank(T, tol = 1e-15))# 38 x 18 dim(T.3 <- fullRank(T, tol = 1e-12))# 38 x 13 dim(T.3 <- fullRank(T, tol = 1e-10))# 38 x 13 dim(T.3 <- fullRank(T, tol = 1e-8 ))# 38 x 12 dim(T.) # default from above 38 x 10 dim(T.3 <- fullRank(T, tol = 1e-5 ))# 38 x 10 -- still plot(svd(T, 0,0)$d, log="y", main = "singular values of T", yaxt="n")
axis(2, at=10^(-14:5), las=1)
## pretty clearly indicates that  rank 10  is "correct" here.


robustbase documentation built on July 10, 2023, 2:01 a.m.