[SciPy-User] soft limiter function

[Matthieu Brucher]

You can still modify the functions to have such derivative at the
origin (this is often used to model amps in audio processing). Just
use a scaling factor.

Cheers,

2015-03-10 15:30 GMT+00:00 Neal Becker <ndbecker2 at gmail.com>:
> Matt Newville wrote:
>
>> 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
>
> Thanks, but I also need the derivative near the origin to be 1 - cannot
> change the steepness near the origin
>
> --
> Those who fail to understand recursion are doomed to repeat it
>
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