[SciPy-Dev] Function for finding relative maxima of a 1d array

[Jacob Silterra]

Hello all,

I posted an idea for a simple function for finding relative maxima of 1D
data in the numpy mailing list; the general consensus seemed to be that it
was useless but more advanced algorithm would be useful in scipy.  Since
this is an addition of new functionality, I thought (re: was told in the
case of numpy) it'd be best to discuss it over the mailing list before
issuing a pull request. Full code available at
https://github.com/jsilter/scipy/tree/find_peaks.  The method is named
find_peaks, located in optimize.py in the optimize module.

Copied from the docstring:
    The algorithm is as follows:
    1. Perform a continuous wavelet transform on `vector`, for the supplied
    `widths`. This is a convolution of `vector` with `wavelet(width)` for
    each width in `widths`. See scipy.signals.cwt (pending).
    2. Identify "ridge lines" in the cwt matrix. These are relative maxima
    at each row, connected across adjacent rows. See identify_ridge_lines
(in optimize.py)
    3. Filter the ridge_lines using filter_ridge_lines (in optimize.py) by
length and signal to noise ratio.

This algorithm requires several parameters be specified, I chose what I
thought were reasonable values to be defaults. This method was designed for
use in mass-spectrogram analysis, which typically have large,sharp peaks on
top of a flat and noisy baseline. With proper parameter selection, I believe
it would function well for a wide class of peaks. The default wavelet for
step 1 is a ricker
<http://en.wikipedia.org/wiki/Mexican_hat_wavelet>wavelet, which is
added in scipy.signal.wavelets.

This is implemented in pure python, which is appropriate for steps 1 and 3.
Step 2 involves a lot of looping, that may be better in C, but it's Python
at the moment.

I used my best judgement on placing functions in appropriate modules, which
led to some circular dependencies. As a temporary fix, the imports are
within each function rather than at the top of each module. Once it's
decided where each function should actually live that can be resolved.

Thoughts?

-Jacob

PS There's a good comparison different algorithms available
here<http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2631518/>
.

PPS I have Eclipse configured to use PEP8 standards for spacing after
commas, assignment operators, and so forth. This ended up changing a lot of
code which may make this specific function hard to review (sorry). I put the
new functions close to the bottom of each file.
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