Numpy 的广播机制高效计算矩阵之间两两距离

利用numpy可以很方便的计算两个二维数组之间的距离。二维数组之间的距离定义为：X的维度为(a,c),Y的维度为(b,c),Z为X到Y的距离数组,维度为(a,b)。且Z[0,0]是X[0]到Y[0]的距离。Z(m,n)为X[m]到Y[n]的距离。

例如： 计算 m*2 的矩阵 与  n * 2 的矩阵中，m*2 的每一行到  n*2 的两两之间欧氏距离。 

#computer the distance between text point x and train point x_train
import numpy as np
X = np.random.random((3,2))
X_train = np.random.random((5,2))
print('X:')
print(X)
print('X_train:')
print(X_train)

dist = np.zeros((X.shape[0],X_train.shape[0]))
print('--------------------')
#way 1:use two loops ，使用两层循环
for i in range(X.shape[0]):
    for j in range(X_train.shape[0]):
        dist[i,j] = np.sum((X[i,:]-X_train[j,:])**2)
print('way 1 result:')
print(dist)

#way 2:use one loops ，使用一层循环
for i in range(X.shape[0]):
    dist[i,:] = np.sum((X_train-X[i,:])**2,axis=1)
print('--------------------')
print('way 2 result:')
print(dist)

#way 3:use no loops，不使用循环
dist = np.reshape(np.sum(X**2,axis=1),(X.shape[0],1))+ np.sum(X_train**2,axis=1)-2*X.dot(X_train.T)
print('--------------------')
print('way 3 result:')
print(dist)