如何更快地找到两个多维数组的交集？

Question

there are two multidimensional boolean arrays with a different number of rows. I want to quickly find indexes of True values in common rows. I wrote the following code but it is too slow. Is there a faster way to do this?

a=np.random.choice(a=[False, True], size=(100,100))
b=np.random.choice(a=[False, True], size=(1000,100))

for i in a:
    for j in b:
        if np.array_equal(i, j):
          print(np.where(i))

Answer 1

Let's start with an edition to the question that makes sense and usually prints something:

a = np.random.choice(a=[False, True], size=(2, 2))
b = np.random.choice(a=[False, True], size=(4, 2))

print(f"a: \n {a}")
print(f"b: \n {b}")

matches = []
for i, x in enumerate(a):
    for j, y in enumerate(b):
        if np.array_equal(x, y):
            matches.append((i, j))

And the solution using scipy.cdist which compares all rows in a against all rows in b , using hamming distance for Boolean vector comparison:

import numpy as np
import scipy
from scipy import spatial

d = scipy.spatial.distance.cdist(a, b, metric='hamming')
cdist_matches = np.where(d == 0)
mathces_values = [(a[i], b[j]) for (i, j) in matches]
cdist_values = a[cdist_matches[0]], b[cdist_matches[1]]
print(f"matches_inds = \n{matches}")
print(f"matches = \n{mathces_values}")

print(f"cdist_inds = \n{cdist_matches}")
print(f"cdist_matches =\n {cdist_values}")

out:

a: 
 [[ True False]
 [False False]]
b: 
 [[ True  True]
 [ True False]
 [False False]
 [False  True]]
matches_inds = 
[(0, 1), (1, 2)]
matches = 
[(array([ True, False]), array([ True, False])), (array([False, False]), array([False, False]))]
cdist_inds = 
(array([0, 1], dtype=int64), array([1, 2], dtype=int64))
cdist_matches =
 (array([[ True, False],
       [False, False]]), array([[ True, False],
       [False, False]]))

---

See this for a pure numpy implementation if you don't want to import scipy

Answer 2

The comparision of each row of a to each row of b can be made by making the shape of a broadcastable to the shape of b with the use of np.newaxis and np.tile

import numpy as np

a=np.random.choice(a=[True, False], size=(2,5))
b=np.random.choice(a=[True, False], size=(10,5))
broadcastable_a = np.tile(a[:, np.newaxis, :], (1, b.shape[0], 1))
a_equal_b = np.equal(b, broadcastable_a)
indexes = np.where(a_equal_b)
indexes = np.stack(np.array(indexes[1:]), axis=1)

Answer 3

if you want to compare NDarrays element-wise, I would do something like that:

import numpy as np

# data
a = np.random.choice(a = [False, True], size = (100,100))
b = np.random.choice(a = [False, True], size = (1000,100))

# extract matching coordinates
match = np.where((a == b[:100,:]) == True)
match = list(zip(*match))

# first 20 coordinates match
print("Number of matches:", len(match))
print(match[:20])