equilibrate {fastmatrix}

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)