R: Equilibration of a rectangular or symmetric matrix

equilibrate {fastmatrix} | R Documentation

## Equilibration of a rectangular or symmetric matrix

### Description

Equilibrate a rectangular or symmetric matrix using 2-norm.

### Usage

    equilibrate(x, scale = TRUE)

### Arguments

`x` | a numeric matrix.
`scale` | a logical value, `x` must be scaled to norm unity?

### Value

For `scale = TRUE`, the equilibrated matrix. The scalings and an approximation of the condition number, are returned as attributes `"scales"` and `"condition"`. If `x` is a rectangular matrix, only the columns are equilibrated.

### Examples

    x <- matrix(c(1, 1, 1,
                  1, 2, 1,
                  1, 3, 1,
                  1, 1,-1,
                  1, 2,-1,
                  1, 3,-1), ncol = 3, byrow = TRUE)
    z <- equilibrate(x)
    apply(z, 2, function(x) sum(x^2)) # all 1

    xx <- crossprod(x)
    equilibrate(xx)

[Package fastmatrix version 0.4 Index]