[SciPy-User] soft limiter function

[Matt Newville]

Neal,


On Tue, Mar 10, 2015 at 9:10 AM, Neal Becker <ndbecker2 at gmail.com> wrote:

> I'm looking for a parameterized set of functions, similar to logistic,
> where
> a parameter determines the 'sharpness' of the transition from the linear
> region to the flat region.  I need to keep all the same scaling and
> derivative near the origin - so like a family of logistic functions that
> would overlay near the origin, but would become increasingly sharp limiters
> as the parameter was varied.  In the limit, would approach the ideal
> limiter
>
>       x |x<1|
> y = { 1 x > 1
>      -1 x < -1
>

This might be too simplistic, but have you considered the "classic"
step-like functions (here, going from 0 to 1, but not necessarily at
x=+/-1):

    arctan:     y(a) = 0.5 + arctan(a) / pi
    error fcn:  y(a) = 0.5 * (1 + erf(a))
    logistic:   y(a) = 1.0 - 1.0 /(1.0 + exp(a))

 where a = (x-x0)/sigma ?     That gives you a knob (sigma) to control the
sharpness of the step.

--Matt
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