This function approximates sqrt(abs(x))*sgn(x), such that the derivative is finite and smooth in x=0.
| Function | Approximation | Range |
|---|---|---|
| y = regRoot(x) | y ~= sqrt(abs(x))*sgn(x) | abs(x) >>delta |
| y = regRoot(x) | y ~= x/sqrt(delta) | abs(x) << delta |
With the default value of delta=0.01, the difference between sqrt(x) and regRoot(x) is 16% around x=0.01, 0.25% around x=0.1 and 0.0025% around x=1.
function regRoot extends Modelica.Icons.Function; input Real x; input Real delta = 0.01 "Range of significant deviation from sqrt(abs(x))*sgn(x)"; output Real y; end regRoot;