点之间的向量/线性代数距离?

假设我有一组点,

import numpy as np
pts = np.random.rand(100,3)  # 1000 points, X, Y, Z along second dimension

计算每个点组合之间的距离的幼稚方法涉及一个双for循环,对于大量的点来说速度会非常慢。

def euclidian_distance(p1, p2):
    d = p2 - p1
    return np.sqrt(d**2).sum()

out = np.empty((pts.shape[0], pts.shape[0]))
pts_swapped = pts.swapaxes(0,1)
for idx, point in enumerate(pts_swapped):
    for idx2, point_inner in enumerate(pts_swapped):
        out[idx,idx2] = euclidian_distance(point, point_inner)

如何将此计算向量化?