如何在不使用循环的情况下为给定矩阵计算所有列向量对之间的欧式距离？ （仅使用numpy）

Question

如标题所示，我需要在不使用循环且仅使用numpy的情况下，计算给定矩阵的所有可能的列向量对之间的欧式距离。

这将产生我正在寻找的输出（但带有循环）：

import numpy as np
def all_column_euclidean(x):
    output = np.zeros((len(x[0]),len(x[0])))
    for i in range(len(x[0])):
        for j in range(len(x[0])):
                   output[i][j] = np.sqrt(np.sum((x[:,i]-x[:,j])**2))
    return output                 

Answer 1

您可以使用numpy的广播功能来完成，这比python循环要快

import numpy as np
x = np.random.rand(10)
y = np.random.rand(10)

# calculate xi-xj for all i,j pair
xi_minus_xj = x - x.reshape(-1,1)

# calculate yi-yj for all i,j pair
yi_minus_yj = y - y.reshape(-1,1)

# calculate (xi-xj)**2 + (yi-yj)**2 for all i, j pair
distances = np.sqrt(xi_minus_xj**2 + yi_minus_yj**2)


# get distance between ith and jth item
print(distances[2,3])
print(distances[2,2])
print(distances[1,8])

Answer 2

S.Vengat是正确的，您将不得不以一种或另一种方式使用循环，但是有一个可以帮助您在1行中完成此操作的库：

import numpy as np
import scipy
data = np.array([[1,2,3],[4,5,6],[7,8,9]])
scipy.spatial.distance.cdist(data.T,data.T)

给出：

array([[0.        , 1.73205081, 3.46410162],
       [1.73205081, 0.        , 1.73205081],
       [3.46410162, 1.73205081, 0.        ]])

您的比较代码：

import numpy as np
def all_column_euclidean(x):
    output = np.zeros((len(x[0]),len(x[0])))
    for i in range(len(x[0])):
        for j in range(len(x[0])):
                   output[i][j] = np.sqrt(np.sum((x[:,i]-x[:,j])**2))
    return output    
data = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(all_column_euclidean(data))

输出：

[[0.         1.73205081 3.46410162]
 [1.73205081 0.         1.73205081]
 [3.46410162 1.73205081 0.        ]]

Answer 3

scipy.spatial.distance中有相应的功能：

import numpy as np
from scipy.spatial.distance import pdist,squareform

a = np.random.randint(0,10,(3,4))

# pairwise dist, compressed
pdist(a.T)
# array([ 8.60232527,  8.77496439, 10.29563014,  6.70820393,  8.1240384 ,
#         3.        ])

# same expanded to full table
squareform(pdist(a.T))
# array([[ 0.        ,  8.60232527,  8.77496439, 10.29563014],
#        [ 8.60232527,  0.        ,  6.70820393,  8.1240384 ],
#        [ 8.77496439,  6.70820393,  0.        ,  3.        ],
#        [10.29563014,  8.1240384 ,  3.        ,  0.        ]])