How to fit with case differentiation

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Niklas Kurz
Niklas Kurz 2020-7-4
I guess this is a really tricky question and might solved with a good amount of mathmatical knowledge. But first things first:
I want to execute a fit with a custom equation in cftool. The problem remains in the fact that the function consist of case differentation:
  • atan((2*d*w)/(v^2-w^2)) for w < v
  • π/2 for w = v
  • π/2 + atan((2*d*w)/(v^2-w^2)) for w > v
with w being 'x'
Actually I got handed the solution: fitting with :
acos((v^2 - w^2)/sqrt((2*d*w)^2 + (v^2 - w^2)^2)).
But how you hade have approached that problem?

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