Finding first samples greater than a threshold value efficiently in Python (and MATLAB comparison)

Question

Instead of finding all the samples / data points within a list or an array which are greater than a particular threshold, I would like to find only the first samples where a signal becomes greater than a threshold. The signal might cross the threshold several times. For example if I have an example signal:

signal = [1, 2, 3, 4, 4, 3, 2, 1, 0, 3, 2, 1, 0, 0, 1, 1, 4, 8, 7, 6, 5, 0]

and a threshold = 2, then

signal = numpy.array(signal)
is_bigger_than_threshold = signal > threshold

would give me all values in signalwhich are greater than threshold. However, I would like to get only the first samples whenever signal becomes greater than threshold. Therefore, I am going through the whole list and make boolean comparisons like

first_bigger_than_threshold = list()
first_bigger_than_threshold.append(False)
for i in xrange(1, len(is_bigger_than_threshold)):
    if(is_bigger_than_threshold[i] == False):
        val = False
    elif(is_bigger_than_threshold[i]):
        if(is_bigger_than_threshold[i - 1] == False):
            val = True
        elif(is_bigger_than_threshold[i - 1] == True):
            val = False
    first_bigger_than_threshold.append(val)

This gives me the result I was looking for, namely

[False, False, True, False, False, False, False, False, False, True, False, False, False,   
False, False, False, True, False, False, False, False, False]

In MATLAB I would do similarily

for i = 2 : numel(is_bigger_than_threshold)
    if(is_bigger_than_threshold(i) == 0)
        val = 0;
    elseif(is_bigger_than_threshold(i))
        if(is_bigger_than_threshold(i - 1) == 0)
            val = 1;
        elseif(is_bigger_than_threshold(i - 1) == 1)
            val = 0;
        end
    end
    first_bigger_than_threshold(i) = val;
end % for

Is there a more efficient (faster) way to perform this calculation?

If I generate data in Python, e.g.

signal = [round(random.random() * 10) for i in xrange(0, 1000000)]

and time it, calculating these values took 4.45 seconds. If I generate data in MATLAB

signal = round(rand(1, 1000000) * 10);

and execute the program it takes only 0.92 seconds.

Why is MATLAB almost 5 times quicker than Python performing this task?

Thanks in advance for your comments!

Answer 1

The other answers give you positions of first Trues, if you want a bool array that marks the first True, you can do it faster:

import numpy as np

signal = np.random.rand(1000000)
th = signal > 0.5
th[1:][th[:-1] & th[1:]] = False

Answer 2

This post explains why your code is slower than Matlab.

Try this code

import numpy as np

threshold = 2
signal = np.array([1, 2, 3, 4, 4, 3, 2, 1, 0, 3, 2, 1, 0, 0, 1, 1, 4, 8, 7, 6, 5, 0])

indices_bigger_than_threshold = np.where(signal > threshold)[0] # get item
print indices_bigger_than_threshold
# [ 2  3  4  5  9 16 17 18 19 20]
non_consecutive = np.where(np.diff(indices_bigger_than_threshold) != 1)[0]+1 # +1 for selecting the next
print non_consecutive
# [4 5]
first_bigger_than_threshold1 = np.zeros_like(signal, dtype=np.bool)
first_bigger_than_threshold1[indices_bigger_than_threshold[0]] = True # retain the first
first_bigger_than_threshold1[indices_bigger_than_threshold[non_consecutive]] = True

np.where returns indices that match the condition.

The strategy is to get indices upper than threshold and remove the consecutive.

BTW, welcome to Python/Numpy world.

Answer 3

Based on the notion that the best way to speed things up is to pick the best algorithm, you can do this neatly with a simple edge detector:

import numpy

signal = numpy.array([1, 2, 3, 4, 4, 3, 2, 1, 0, 3, 2, 1, 0, 0, 1, 1, 4, 8, 7, 6, 5, 0])

thresholded_data = signal > threshold
threshold_edges = numpy.convolve([1, -1], thresholded_data, mode='same')

thresholded_edge_indices = numpy.where(threshold_edges==1)[0]

print(thresholded_edge_indices)

prints [2 9 16], the indices corresponding to first entry in a sequence greater than the threshold. This will make things faster in both Matlab and Python (with Numpy) - on my machine about 12ms to do what took you 4.5s.

Edit: As pointed out by @eickenberg, the convolution can be replaced with numpy.diff(thresholded_data), which is conceptually a bit simpler, though in that case the indices will be out by 1, so remember to add those back in, and also to convert thresholded_data to be an array of ints with thresholded_data.astype(int). There is no appreciable speed difference between the two methods.