Euclidean distance in Python

Question

I have two 3000x3 vectors and I'd like to compute 1-to-1 Euclidean distance between them. For example, vec1 is

1 1 1  
2 2 2    
3 3 3  
4 4 4  
...

The vec2 is

2 2 2
3 3 3  
4 4 4  
5 5 5  
...

I'd like to get the results as

1.73205081  
1.73205081
1.73205081
1.73205081
...

I tried scipy.spatial.distance.cdist(vec1,vec2) , and it returns a 3000x3000 matrix whereas I only need the main diagonal. I also tried np.sqrt(np.sum((vec1-vec2)**2 for vec1,vec2 in zip(vec1,vec2))) and it didn't work for my purpose. Is there any way to compute the distances please? I'd appreciate any comments.

Answer 1

cdist gives you back a 3000 x 3000 array because it computes the distance between every pair of row vectors in your two input arrays.

To compute only the distances between corresponding row indices, you could use np.linalg.norm :

a = np.repeat((np.arange(3000) + 1)[:, None], 3, 1)
b = a + 1

dist = np.linalg.norm(a - b, axis=1)

Or using standard vectorized array operations:

dist = np.sqrt(((a - b) ** 2).sum(1))

Answer 2

Here's another way that works. It still utilizes the np.linalg.norm function but it processes the data, if that is something you needed.

import numpy as np
vec1='''1 1 1
    2 2 2
    3 3 3
    4 4 4'''
vec2='''2 2 2
    3 3 3
    4 4 4
    5 5 5'''

process_vec1 = np.array([])
process_vec2 = np.array([])

for line in vec1:
    process_vec1 = np.append( process_vec1, map(float,line.split()) )
for line in vec2:
    process_vec2 = np.append( process_vec2, map(float,line.split()) )

process_vec1 = process_vec1.reshape( (len(process_vec1)/3, 3) )
process_vec2 = process_vec2.reshape( (len(process_vec2)/3, 3) )

dist = np.linalg.norm( process_vec1 - process_vec2 , axis = 1 )

print dist

[1.7320508075688772 1.7320508075688772 1.7320508075688772 1.7320508075688772]