Fast way to find length and start index of repeated elements in array

Question

I have an array A:

import numpy as np
A = np.array( [0, 0, 1, 1, 1, 0, 1, 1, 0 ,0, 1, 0] )

The length of consecutive '1s' would be:

output: [3, 2, 1]

with the corresponding starting indices:

idx = [2, 6, 10]

The original arrays are huge and I prefer a solution with less for-loop.

Edit (Run time):

import numpy as np
import time

A = np.array( [0, 0, 1, 1, 1, 0, 1, 1, 0 ,0, 1, 0] )

def LoopVersion(A):
    l_A = len(A)
    size = []
    idx = []
    temp_idx = []
    temp_size = []
    for i in range(l_A):
        if A[i] == 1:
            temp_size.append(1)
            if not temp_idx:
                temp_idx = i
                idx.append(temp_idx)
        else:
            size.append( len(temp_size) )
            size = [i for i in size if i != 0]
            temp_size = []
            temp_idx = []
    return size, idx

Quang's solution:

def UniqueVersion(A):
    _, idx, counts = np.unique(np.cumsum(1-A)*A, return_index=True, return_counts=True)
    return idx, counts

Jacco's solution:

def ConcatVersion(A):
    A = np.concatenate(([0], A, [0]))  #  get rid of some edge cases
    starts = np.argwhere((A[:-1] + A[1:]) == 1).ravel()[::2]
    ends = np.argwhere((A[:-1] + A[1:]) == 1).ravel()[1::2]
    len_of_repeats = ends - starts
    return starts, len_of_repeats

Dan's solution (works with special cases as well):

def structure(A):
    ZA = np.concatenate(([0], A, [0]))
    indices = np.flatnonzero( ZA[1:] != ZA[:-1] )
    counts = indices[1:] - indices[:-1]
    return indices[::2], counts[::2]

Run time analysis with 10000 elements:

np.random.seed(1234)
B = np.random.randint(2, size=10000)


start = time.time()
size, idx = LoopVersion(B)
end = time.time()
print ( (end - start) )
# 0.32489800453186035 seconds

start = time.time()
idx, counts = UniqueVersion(B)
end = time.time()
print ( (end - start) )
# 0.008305072784423828 seconds

start = time.time()
idx, counts = ConcatVersion(B)
end = time.time()
print ( (end - start) )
# 0.0009801387786865234 seconds

start = time.time()
idx, counts = structure(B)
end = time.time()
print ( (end - start) )
# 0.000347137451171875 seconds

Answer 1

Let's try unique:

_, idx, counts = np.unique(np.cumsum(1-A)*A, return_index=True, return_counts=True)

# your expected output:
idx, counts

Output:

(array([ 2,  6, 10]), array([3, 2, 1]))

Answer 2

Here is a pedestrian try, solving the problem by programming the problem.

We prepend and also append a zero to A, getting a vector ZA, then detect the 1 islands, and the 0 islands coming in alternating manner in the ZA by comparing the shifted versions ZA[1:] and ZA[-1]. (In the constructed arrays we take the even places, corresponding to the ones in A.)

import numpy as np

def structure(A):
    ZA = np.concatenate(([0], A, [0]))
    indices = np.flatnonzero( ZA[1:] != ZA[:-1] )
    counts = indices[1:] - indices[:-1]
    return indices[::2], counts[::2]

Some sample runs:

In [71]: structure(np.array( [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0] ))
Out[71]: (array([ 2,  6, 10]), array([3, 2, 1]))

In [72]: structure(np.array( [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1] ))
Out[72]: (array([ 0,  5,  9, 13, 15]), array([3, 3, 2, 1, 1]))

In [73]: structure(np.array( [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0] ))
Out[73]: (array([0, 5, 9]), array([3, 3, 2]))

In [74]: structure(np.array( [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1] ))
Out[74]: (array([ 0,  2,  5,  7, 11, 14]), array([1, 2, 1, 3, 2, 3]))

Answer 3

You can use the fact that the indexes of '1s' provide all information you need. It's enough to find starts and ends of series of '1s'.

A = np.concatenate(([0], A, [0]))  #  get rid of some edge cases
diff = np.argwhere((A[:-1] + A[1:]) == 1).ravel()
starts = diff[::2]
ends = diff[1::2]
    
print(starts, ends - starts)