Nathan Thomas February 2016

Find local maximums in numpy array

I am looking to find the peaks in some gaussian smoothed data that I have. I have looked at some of the peak detection methods available but they require an input range over which to search and I want this to be more automated than that. These methods are also designed for non-smoothed data. As my data is already smoothed I require a much more simple way of retrieving the peaks. My raw and smoothed data is in the graph below.

enter image description here

Essentially, is there a pythonic way of retrieving the max values from the array of smoothed data such that an array like

    a = [1,2,3,4,5,4,3,2,1,2,3,2,1,2,3,4,5,6,5,4,3,2,1]

would return:

    r = [5,3,6]

Answers


MSeifert February 2016

If you can exclude maxima at the edges of the arrays you can always check if one elements is bigger than each of it's neighbors by checking:

import numpy as np
array = np.array([1,2,3,4,5,4,3,2,1,2,3,2,1,2,3,4,5,6,5,4,3,2,1])
# Check that it is bigger than either of it's neighbors exluding edges:
max = (array[1:-1] > array[:-2]) & (array[1:-1] > array[2:])
# Print these values
print(array[1:-1][max])
# Locations of the maxima
print(np.arange(1, array.size-1)[max])


ebarr February 2016

If your original data is noisy, then using statistical methods is preferable, as not all peaks are going to be significant. For your a array, a possible solution is to use double differentials:

peaks = a[1:-1][np.diff(np.diff(a)) < 0]
# peaks = array([5, 3, 6])


Cleb February 2016

There exists a bulit-in function argrelextrema that gets this task done:

import numpy as np
from scipy.signal import argrelextrema

a = np.array([1,2,3,4,5,4,3,2,1,2,3,2,1,2,3,4,5,6,5,4,3,2,1])

# determine the indices of the local maxima
maxInd = argrelextrema(a, np.greater)

# get the actual values using these indices
r = a[maxInd]  # array([5, 3, 6])

That gives you the desired output for r.

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