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I would like to fit a diffusion coefficient as function of e.g. salt, pH etc. If I use a linear combination of all variables, I will have to apply constraints because the model fails, if the diffusion coefficient will get too large or negative.

I was wondering if there exists a function that behaves similar to the logistic function (asymptotic between 0 and a certain limit) but instead it asymptotically reaches -1 and +1. In this way I would avoid constraints and bounds. At the same time, negative parameters would mean that the corresponding variables do decrease diffusion and vice versa.

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Tangens Hyperbolicus behaves as you want.

Tanh formula

Tanh Graph

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