Counting Peaks in a Time Series
Question:
I am counting the number of peaks and troughs in a numpy array.
I have a numpy array like so:
stack = np.array([0,0,5,4,1,1,1,5,1,1,5,1,1,1,5,1,1,5,1,1,5,1,1,5,1,1,5,1,1])
Plotted, this data looks like something like this:
I am looking to find the number of peaks in this time series:
This is my code, which works well for an example like this where there are clear peaks and troughs in the time series representation. My code returns the indexes of the array where peaks have been found.
#example
import numpy as np
from scipy.signal import argrelextrema
stack =
np.array([0,0,5,4,1,1,1,5,1,1,5,1,1,1,5,1,1,5,1,1,5,1,1,5,1,1,5,1,1])
# for local maxima
y = argrelextrema(stack, np.greater)
print(y)
Result:
(array([ 2, 7, 10, 14, 17, 20, 23, 26]),)
There are 8 clear peaks that have been found and can be correctly counted.
My solution does not appear to work well with data that is less clear cut and more messy.
An array below does not work well and does not find the peaks that I need:
array([ 0. , 5.70371806, 5.21210157, 3.71144767, 3.9020162 ,
3.87735984, 3.89030171, 6.00879918, 4.91964227, 4.37756275,
4.03048542, 4.26943028, 4.02080471, 7.54749062, 3.9150576 ,
4.08933851, 4.01794766, 4.13217794, 4.15081972, 8.11213474,
4.6561735 , 4.54128693, 3.63831552, 4.3415324 , 4.15944019,
8.55171441, 4.86579459, 4.13221943, 4.487663 , 3.95297979,
4.35334706, 9.91524674, 4.44738182, 4.32562141, 4.420753 ,
3.54525697, 4.07070637, 9.21055852, 4.87767969, 4.04429321,
4.50863677, 3.38154581, 3.73663523, 3.83690315, 6.95321174,
5.11325128, 4.50351938, 4.38070175, 3.20891173, 3.51142661,
7.80429569, 3.98677631, 3.89820773, 4.15614576, 3.47369797,
3.73355768, 8.85240649, 6.0876192 , 3.57292324, 4.43599135,
3.77887259, 3.62302175, 7.03985076, 4.91916556, 4.22246518,
3.48080777, 3.26199699, 2.89680969, 3.19251448])
Plotted, this data looks like:
And the same code returns:
(array([ 1, 4, 7, 11, 13, 15, 19, 23, 25, 28, 31, 34, 37, 40, 44, 50, 53,
56, 59, 62]),)
This output incorrectly counts data points as peaks.
Ideal Output
The ideal output should return the number of clear peaks, 11 in this case which are located at indexes:
[1,7,13,19,25,31,37,44,50,56,62]
I believe my problem comes about because of the aggregated nature of the argrelextrema function.
Answers:
It looks like argrelextrema gets you most of the way. It has all the peaks that you want, but it also has some extra ones. You need to come up with a criteria that suits your case and filter out the peaks you don’t want.
For example, if you don’t want peaks that are less than 5, you could do this:
In [17]: result = argrelextrema(a, np.greater)
In [18]: result
Out[18]:
(array([ 1, 4, 7, 11, 13, 15, 19, 23, 25, 28, 31, 34, 37, 40, 44, 50, 53,
56, 59, 62]),)
In [19]: result[0][a[result[0]] > 5]
Out[19]: array([ 1, 7, 13, 19, 25, 31, 37, 44, 50, 56, 62])
You can use some treshold to find peaks:
prev = stack[0] or 0.001
threshold = 0.5
peaks = []
for num, i in enumerate(stack[1:], 1):
if (i - prev) / prev > threshold:
peaks.append(num)
prev = i or 0.001
print(peaks)
# [1, 7, 13, 19, 25, 31, 37, 44, 50, 56, 62]
You should try find_peaks in the scipy.signal module
Example with your data
import numpy as np
from scipy.signal import find_peaks
import matplotlib.pyplot as plt
a = np.array([ 0. , 5.70371806, 5.21210157, 3.71144767, 3.9020162 , 3.87735984, 3.89030171, 6.00879918, 4.91964227, 4.37756275,
4.03048542, 4.26943028, 4.02080471, 7.54749062, 3.9150576 ,
4.08933851, 4.01794766, 4.13217794, 4.15081972, 8.11213474,
4.6561735 , 4.54128693, 3.63831552, 4.3415324 , 4.15944019,
8.55171441, 4.86579459, 4.13221943, 4.487663 , 3.95297979,
4.35334706, 9.91524674, 4.44738182, 4.32562141, 4.420753 ,
3.54525697, 4.07070637, 9.21055852, 4.87767969, 4.04429321,
4.50863677, 3.38154581, 3.73663523, 3.83690315, 6.95321174,
5.11325128, 4.50351938, 4.38070175, 3.20891173, 3.51142661,
7.80429569, 3.98677631, 3.89820773, 4.15614576, 3.47369797,
3.73355768, 8.85240649, 6.0876192 , 3.57292324, 4.43599135,
3.77887259, 3.62302175, 7.03985076, 4.91916556, 4.22246518,
3.48080777, 3.26199699, 2.89680969, 3.19251448])
# Here you should fine tune parameters to get what you want
peaks = find_peaks(a, prominence=1.5)
print("Peaks position:", peaks[0])
# Plotting
plt.plot(a)
plt.title("Finding Peaks")
[plt.axvline(p, c='C3', linewidth=0.3) for p in peaks[0]]
plt.show()
Plot
Output
# Peaks position: [ 1 7 13 19 25 31 37 44 50 56 62]
I am counting the number of peaks and troughs in a numpy array.
I have a numpy array like so:
stack = np.array([0,0,5,4,1,1,1,5,1,1,5,1,1,1,5,1,1,5,1,1,5,1,1,5,1,1,5,1,1])
Plotted, this data looks like something like this:
I am looking to find the number of peaks in this time series:
This is my code, which works well for an example like this where there are clear peaks and troughs in the time series representation. My code returns the indexes of the array where peaks have been found.
#example
import numpy as np
from scipy.signal import argrelextrema
stack =
np.array([0,0,5,4,1,1,1,5,1,1,5,1,1,1,5,1,1,5,1,1,5,1,1,5,1,1,5,1,1])
# for local maxima
y = argrelextrema(stack, np.greater)
print(y)
Result:
(array([ 2, 7, 10, 14, 17, 20, 23, 26]),)
There are 8 clear peaks that have been found and can be correctly counted.
My solution does not appear to work well with data that is less clear cut and more messy.
An array below does not work well and does not find the peaks that I need:
array([ 0. , 5.70371806, 5.21210157, 3.71144767, 3.9020162 ,
3.87735984, 3.89030171, 6.00879918, 4.91964227, 4.37756275,
4.03048542, 4.26943028, 4.02080471, 7.54749062, 3.9150576 ,
4.08933851, 4.01794766, 4.13217794, 4.15081972, 8.11213474,
4.6561735 , 4.54128693, 3.63831552, 4.3415324 , 4.15944019,
8.55171441, 4.86579459, 4.13221943, 4.487663 , 3.95297979,
4.35334706, 9.91524674, 4.44738182, 4.32562141, 4.420753 ,
3.54525697, 4.07070637, 9.21055852, 4.87767969, 4.04429321,
4.50863677, 3.38154581, 3.73663523, 3.83690315, 6.95321174,
5.11325128, 4.50351938, 4.38070175, 3.20891173, 3.51142661,
7.80429569, 3.98677631, 3.89820773, 4.15614576, 3.47369797,
3.73355768, 8.85240649, 6.0876192 , 3.57292324, 4.43599135,
3.77887259, 3.62302175, 7.03985076, 4.91916556, 4.22246518,
3.48080777, 3.26199699, 2.89680969, 3.19251448])
Plotted, this data looks like:
And the same code returns:
(array([ 1, 4, 7, 11, 13, 15, 19, 23, 25, 28, 31, 34, 37, 40, 44, 50, 53,
56, 59, 62]),)
This output incorrectly counts data points as peaks.
Ideal Output
The ideal output should return the number of clear peaks, 11 in this case which are located at indexes:
[1,7,13,19,25,31,37,44,50,56,62]
I believe my problem comes about because of the aggregated nature of the argrelextrema function.
It looks like argrelextrema gets you most of the way. It has all the peaks that you want, but it also has some extra ones. You need to come up with a criteria that suits your case and filter out the peaks you don’t want.
For example, if you don’t want peaks that are less than 5, you could do this:
In [17]: result = argrelextrema(a, np.greater)
In [18]: result
Out[18]:
(array([ 1, 4, 7, 11, 13, 15, 19, 23, 25, 28, 31, 34, 37, 40, 44, 50, 53,
56, 59, 62]),)
In [19]: result[0][a[result[0]] > 5]
Out[19]: array([ 1, 7, 13, 19, 25, 31, 37, 44, 50, 56, 62])
You can use some treshold to find peaks:
prev = stack[0] or 0.001
threshold = 0.5
peaks = []
for num, i in enumerate(stack[1:], 1):
if (i - prev) / prev > threshold:
peaks.append(num)
prev = i or 0.001
print(peaks)
# [1, 7, 13, 19, 25, 31, 37, 44, 50, 56, 62]
You should try find_peaks in the scipy.signal module
Example with your data
import numpy as np
from scipy.signal import find_peaks
import matplotlib.pyplot as plt
a = np.array([ 0. , 5.70371806, 5.21210157, 3.71144767, 3.9020162 , 3.87735984, 3.89030171, 6.00879918, 4.91964227, 4.37756275,
4.03048542, 4.26943028, 4.02080471, 7.54749062, 3.9150576 ,
4.08933851, 4.01794766, 4.13217794, 4.15081972, 8.11213474,
4.6561735 , 4.54128693, 3.63831552, 4.3415324 , 4.15944019,
8.55171441, 4.86579459, 4.13221943, 4.487663 , 3.95297979,
4.35334706, 9.91524674, 4.44738182, 4.32562141, 4.420753 ,
3.54525697, 4.07070637, 9.21055852, 4.87767969, 4.04429321,
4.50863677, 3.38154581, 3.73663523, 3.83690315, 6.95321174,
5.11325128, 4.50351938, 4.38070175, 3.20891173, 3.51142661,
7.80429569, 3.98677631, 3.89820773, 4.15614576, 3.47369797,
3.73355768, 8.85240649, 6.0876192 , 3.57292324, 4.43599135,
3.77887259, 3.62302175, 7.03985076, 4.91916556, 4.22246518,
3.48080777, 3.26199699, 2.89680969, 3.19251448])
# Here you should fine tune parameters to get what you want
peaks = find_peaks(a, prominence=1.5)
print("Peaks position:", peaks[0])
# Plotting
plt.plot(a)
plt.title("Finding Peaks")
[plt.axvline(p, c='C3', linewidth=0.3) for p in peaks[0]]
plt.show()
Plot
Output
# Peaks position: [ 1 7 13 19 25 31 37 44 50 56 62]