R: Matrix Rank

mat.rank {mixOmics} | R Documentation

## 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.

### 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`.

### Value

The returned value is a list with components:

`rank` | a integer value, the matrix rank.
`tol` | the tolerance used for singular values.

### Author(s)

Sébastien Déjean and Ignacio González.

### 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)

[Package mixOmics version 6.3.2 Index]