Smooth approximation to the absolute value function

Smooth approximation to the absolute value function

Usage

abs_smooth(x, epsilon = 1e-06)

Arguments

x

vector of evaluation points

epsilon

smoothing constant

Value

Smooth absolute value of x.

Details

We approximate the absolute value here as $$\vert x \vert \approx \sqrt{x^2 + \epsilon}$$

Examples

abs(0)
#> [1] 0
abs_smooth(0, 1e-4)
#> [1] 0.01