python之R和Python的cov和cor的区别_编程设计

我经常使用 R，但我是 Python 的新手。在 R 中，计算给定矩阵的均值、cov 和 cor 的演示给出如下:

X = matrix(c(1,0.5,3,7,9,6,2,8,4), nrow=3, ncol=3, byrow=FALSE) 
X 
    # [,1] [,2] [,3] 
# [1,]  1.0    7    2 
# [2,]  0.5    9    8 
# [3,]  3.0    6    4 
M = colMeans(X) # apply(X,2,mean) 
M 
# [1] 1.500000 7.333333 4.666667 
S = cov(X) 
S 
    # [,1]      [,2]      [,3] 
# [1,]  1.75 -1.750000 -1.500000 
# [2,] -1.75  2.333333  3.666667 
# [3,] -1.50  3.666667  9.333333 
R = cor(X) 
R 
        # [,1]       [,2]       [,3] 
# [1,]  1.0000000 -0.8660254 -0.3711537 
# [2,] -0.8660254  1.0000000  0.7857143 
# [3,] -0.3711537  0.7857143  1.0000000

我想用 Python 重现上面的内容，我尝试:

import numpy as np 
X = np.array([1,0.5,3,7,9,6,2,8,4]).reshape(3, 3) 
X = np.transpose(X) # byrow=FALSE 
X 
# array([[ 1. ,  7. ,  2. ], 
    # [ 0.5,  9. ,  8. ], 
    # [ 3. ,  6. ,  4. ]]) 
 
M = X.mean(axis=0) # colMeans 
M 
# array([ 1.5       ,  7.33333333,  4.66666667]) 
S = np.cov(X) 
S 
# array([[ 10.33333333,  10.58333333,   4.83333333], 
    # [ 10.58333333,  21.58333333,   5.83333333], 
    # [  4.83333333,   5.83333333,   2.33333333]]) 
R = np.corrcoef(X) 
R 
# array([[ 1.        ,  0.70866828,  0.98432414], 
    # [ 0.70866828,  1.        ,  0.82199494], 
    # [ 0.98432414,  0.82199494,  1.        ]])

那么cov和cor的结果就不一样了。为什么？

请您参考如下方法:

这是因为 numpy 按行计算，R 按列计算。注释掉 X = np.transpose(X) # byrow=FALSE，或使用 np.cov(X, rowvar=False)。

np.cov(X, rowvar=False) 
array([[ 1.75      , -1.75      , -1.5       ], 
       [-1.75      ,  2.33333333,  3.66666667], 
       [-1.5       ,  3.66666667,  9.33333333]])

不同之处在各自的文档中有解释(重点是我的):

python :

help(np.cov)

rowvar : bool, optional If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.

回复:

?cov

var, cov and cor compute the variance of x and the covariance or correlation of x and y if these are vectors. If x and y are matrices then the covariances (or correlations) between the columns of x and the columns of y are computed.