R: Rank of a Matrix

rankMatrix {Matrix}

R Documentation

Rank of a Matrix

Description

Compute the rank of matrix, a well-defined functional in theory, somewhat ambigous in practice. We provide several methods, the default corresponding to Matlab's definition.

Usage

rankMatrix(x, tol = NULL,
           method = c("tolNorm2", "qrLINPACK", "useGrad", "maybeGrad"),
           sval = svd(x, 0, 0)$d)

Arguments

`x`	numeric matrix, of dimension n x m, say.
`tol`	nonnegative number specifying a tolerance for “practically zero” with specific meaning depending on `method`; by default, `max(dim(x)) * .Machine$double.eps * abs(max(sval))` is according to Matlab's default (for its only `method` "tolNorm2").
`method`	a character string specifying the computational method, can be abbreviated: tolNorm2 the number of singular values `>= tol`; qrLINPACK = `qr(x, tol, LAPACK=FALSE)$rank`; this used to be the recommended way to compute a matrix rank for a while in the past. For this method, `sval` are not used (nor computed). useGrad considering the “gradient” of the (decreasing) singular values, the index of the smallest gap. maybeGrad choosing method `"useGrad"` only when that seems reasonable; otherwise using `"tolNorm2"`.
`sval`	numeric vector of non-increasing singular values of `x`; typically unspecified and computed from `x`.

Value

positive integer in 1:min(dim(x)), with attributes detailing the method used.

Author(s)

Martin Maechler; for the "*Grad" methods, building on suggestions by Ravi Varadhan.

Examples

rankMatrix(cbind(1, 0, 1:3)) # 2

(meths <- eval(formals(rankMatrix)$method))

## a "border" case:
H12 <- Hilbert(12)
rankMatrix(H12, tol = 1e-20) # 12;  but  11  with default method & tol.
sapply(meths, function(.m.) rankMatrix(H12, method = .m.))
## tolNorm2 qrLINPACK   useGrad maybeGrad
##       11        12        11        11

[Package Matrix version 0.999375-29 Index]