How to find "grouped" or "uneaven" data? - numpy

Question

I need to find if thousands of arrays have data that are "grouped" into lower or higher that are adjacent(correct word to use?) values or not.
a is "uneaven" and b, c have grouped data. I need some way to separate the a:s from b and c:s. Maybe there are som statistical measurement to use? I thought about using the time it takes to sort the arrays to separate them but it feels uncertain.
import numpy as np
a = np.array([0,10,0,10,0,10,0,10]) #Very uneaven _'_'_'_'
b = np.array([0,0,0,0,10,10,10,10]) #two groups ____''''
c = np.array([0,0,10,10,10,10,0,0]) #three groups __''''__
import timeit
for name, arr in zip(['a','b','c'], [a,b,c]):
print(name, ' ', round(timeit.timeit(lambda: np.sort(a, axis=None), number=10000), 5))
#The most sorted array is the slowest to sort...
#a 0.01802
#b 0.01807
#c 0.01716
#This work if the array is sorted. But if I sort the arrays all become grouped... (also array "a")
for name, arr in zip(['a','b','c'], [a,b,c]):
if arr[:4].mean() == arr[4:].mean():
print(name, ' ', 'uneaven')
else:
print(name, ' ', 'grouped')
a uneaven
b grouped
c uneaven

Answer 1

As often, writing a question give you ideas..
I can calculate the sum of change/difference between all pair of values in each array:
for name, arr in zip(['a','b','c'], [a,b,c]):
sum_of_change = sum([abs(val1-val2) for val1,val2 in zip(arr,arr[1:])])
print(name, ' ', sum_of_change)
a 70 #A more unsorted array will have larger sum
b 10
c 20

Answer 2

A pattern in your data is the rate of change in consecutive numbers. The sensitivity is adjustable with the threshold argument.
import numpy as np
a = np.array([0,10,0,10,0,10,0,10])
b = np.array([0,0,0,0,10,10,10,10])
c = np.array([0,0,10,10,10,10,0,0])
d = np.array([0,0,0,0,0,0,0,0])
def classify(x, threshold = .2):
t = (x[1:] != x[:-1]).sum() / (len(x)-1)
return 'grouped' if t < threshold else 'uneven'
for i in [a,b,c,d]:
print(classify(i))
Output
uneven
grouped
uneven
grouped