optimization - Find minimum distance between points of two lists in Python

Question

I have two lists of coordinates:

s1 = [(0,0), (0,1), (1,0), (1,1)]
s2 = [(3,2), (1,9)]

I want to calculate the minimum distance of each point in s1 to any point in s2. e.g. the results should be as follows.

result = [3.60, 3.16, 2.82, 2.23]

Question: What is the most optimized way in terms of execution time, to achieve this result?

So far I've tried this but the execution time is not promising:

import math
def nearestDistance(boundary, p):
    minDistList = map(lambda b: (b[0] - p[0])**2 + (b[1] - p[1])**2, boundary)
    minDist2 = min(minDistList)
    return math.sqrt(float(minDist2))

d = []
for p in s1:
    d.append(nearestDistance(s2, p))

Should I change the structure of s1 and s2 (instead of points use 2d arrays for example)?

Answer 1

The easiest way is probably to use scipy.spatial.distance.cdist:

import numpy as np
from scipy.spatial import distance

s1 = np.array([(0,0), (0,1), (1,0), (1,1)])
s2 = np.array([(3,2), (1,9)])
print(distance.cdist(s1,s2).min(axis=1))
# array([3.60555128, 3.16227766, 2.82842712, 2.23606798])

Some more speed might be gained by directly outputting 0 for any point from s1 that is also in s2.