[SciPy-Dev] ENH: Extend peak finding capabilities in scipy.signal (#8264)

[Lars G.]

On 26.01.2018 20:59, Eric Larson wrote:
>> - argrelmax doesn't catch peaks that are wider than one sample. Decide
>> how to deal with this. I have implemented an alternative here which may
>> even be faster. But I plan to make a performance comparison to confirm
>> this. I have a feeling this should be addressed (if wanted) in a new
>> pull request.
> 
> Another PR is fine, but we should merge that one before this find_peaks
> PR to avoid creating backward compatibility problems. 

Actually I have changed my mind about submitting the alternative in
another PR. My current solution
http://nbviewer.jupyter.org/urls/gitlab.com/snippets/1695752/raw#Proposed-solution-2:-Cython
compares to `argrelmax` as follows:

- It is measurably faster than `argrelmax` for all
  supported cases I could think of.
- It can find flat maxima / peaks which is my main
  gripe with `argrelmax`.
- It uses Cython with all its implications. I have a
  feeling that Python is preferred over creating
  another file to compile but I think usage of
  Cython is well-founded here. Dealing with flat peaks
  was really costly in my pure-Python experiments.
- It only supports 1D arrays (which honestly is the
  main use case for the signal module).

Because this function will be wrapped by find_peaks (or however choose
to name it) it doesn't really need to be exposed to the user
`find_peaks(x)` would be equivalent to `_maxima1D(x)`.

If nobody has any objections I'll include this as part of my original PR.

Regards, Lars