How do I identify sequences of values in a boolean array?

Question

I have a long boolean array:

bool_array = [ True, True, True, True, True, False, False, False, False, False, True, True, True, False, False, True, True, True, True, False, False, False, False, False, False, False ]

I need to figure out where the values flips, i.e., the addresses where sequences of True and False begin. In this particular case, I would want to get

index = [0, 5, 10, 13, 15, 19, 26]

Is there an easy way to do without manually looping to check every ith element with the (i+1)th?

Answer 1

As a more efficient approach for large datasets, in python 3.X you can use accumulate and groupby function from itertools module.

>>> from itertools import accumulate, groupby
>>> [0] + list(accumulate(sum(1 for _ in g) for _,g in groupby(bool_array)))
[0, 5, 10, 13, 15, 19, 26]

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The logic behind the code:

This code, categorizes the sequential duplicate items using groupby() function, then loops over the iterator returned by groupby() which is contains pairs of keys (that we escaped it using under line instead of a throw away variable) and these categorized iterators.

>>> [list(g) for _, g in groupby(bool_array)]
[[True, True, True, True, True], [False, False, False, False, False], [True, True, True], [False, False], [True, True, True, True], [False, False, False, False, False, False, False]]

So all we need is calculating the length of these iterators and sum each length with its previous length, in order to get the index of first item which is exactly where the item is changed, that is exactly what that accumulate() function is for.

In Numpy you can use the following approach:

In [19]: np.where(arr[1:] - arr[:-1])[0] + 1
Out[19]: array([ 5, 10, 13, 15, 19])
# With leading and trailing indices
In [22]: np.concatenate(([0], np.where(arr[1:] - arr[:-1])[0] + 1, [arr.size]))
Out[22]: array([ 0,  5, 10, 13, 15, 19, 26])

Answer 2

This will tell you where:

>>> import numpy as np
>>> np.argwhere(np.diff(bool_array)).squeeze()
array([ 4,  9, 12, 14, 18])

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np.diff calculates the difference between each element and the next. For booleans, it essentially interprets the values as integers (0: False, non-zero: True), so differences appear as +1 or -1 values, which then get mapped back to booleans (True when there is a change).

The np.argwhere function then tells you where the values are True --- which are now the changes.