mixOmics (version 5.0-4)

mat.rank: Matrix Rank

Description

This function estimate the rank of a matrix.

Usage

mat.rank(mat, tol)

Arguments

mat

a numeric matrix or data frame that can contain missing values.

tol

positive real, the tolerance for singular values, only those with values larger than tol are considered non-zero.

Value

• The returned value is a list with components:
• rank
  a integer value, the matrix rank.
• tol
  the tolerance used for singular values.

encoding

latin1

Details

mat.rank estimate the rank of a matrix by computing its singular values $d[i]$ (using nipals). The rank of the matrix can be defined as the number of singular values $d[i] > 0$.

If tol is missing, it is given by tol=max(dim(mat))*max(d)*.Machine$double.eps.

See Also

nipals

Examples

## Hilbert matrix
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
mat <- hilbert(16)
mat.rank(mat)

## Hilbert matrix with missing data
idx.na <- matrix(sample(c(0, 1, 1, 1, 1), 36, replace = TRUE), ncol = 6)
m.na <- m <- hilbert(9)[, 1:6]
m.na[idx.na == 0] <- NA
mat.rank(m)
mat.rank(m.na)