This function approximates x^2*sgn(x), such that the derivative is non-zero in x=0.
| Function | Approximation | Range |
|---|---|---|
| y = regSquare(x) | y ~= x^2*sgn(x) | abs(x) >>delta |
| y = regSquare(x) | y ~= x*delta | abs(x) << delta |
With the default value of delta=0.01, the difference between x^2 and regSquare(x) is 41% around x=0.01, 0.4% around x=0.1 and 0.005% around x=1.
function regSquare extends Modelica.Icons.Function; input Real x; input Real delta = 0.01 "Range of significant deviation from x^2*sgn(x)"; output Real y; end regSquare;