如何在numpy内部实现协方差? [英] How is covariance implemented internally in numpy?
问题描述
这是协方差矩阵的定义. http://en.wikipedia.org/wiki/Covariance_matrix#Definition
This is the definition of a covariance matrix. http://en.wikipedia.org/wiki/Covariance_matrix#Definition
矩阵中除主对角线上的每个元素(如果我没记错的话)都简化为E(x_ {i} * x_ {j})-mean(i)* mean(j),其中i和j是协方差矩阵的行数和列数.
Each element in the matrix, except in the principal diagonal, (if I am not wrong) simplifies to E(x_{i} * x_{j}) - mean(i)*mean(j) where i and j are the row number and column number of the covariance matrix.
从numpy文档中,
x = np.array([[0, 2], [1, 1], [2, 0]]).T
x
array([[0, 1, 2], [2, 1, 0]])
np.cov(x)
array([[ 1., -1.],
[-1., 1.]])
第一行,即[0,1,2]对应于X_ {0} 第二行[2,1,0]对应于X_ {1} 由于不知道随机变量的分布,如何计算X_ {0} * X_ {1}的期望值?
The first row i.e [0, 1, 2] corresponds to X_{0} and the second row i.e [2, 1, 0] corresponds to X_{1} How is expectation of X_{0}*X_{1} calculated, since the distributions of the random variables are not knowno?
谢谢.
推荐答案
只需检查代码.
\site-packages\numpy\lib\function_base.py
def cov(m, y=None, rowvar=1, bias=0, ddof=None):
"""
Estimate a covariance matrix, given data.
Covariance indicates the level to which two variables vary together.
If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
then the covariance matrix element :math:`C_{ij}` is the covariance of
:math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
of :math:`x_i`.
Parameters
----------
m : array_like
A 1-D or 2-D array containing multiple variables and observations.
Each row of `m` represents a variable, and each column a single
observation of all those variables. Also see `rowvar` below.
...
if y is not None:
y = array(y, copy=False, ndmin=2, dtype=float)
X = concatenate((X,y), axis)
X -= X.mean(axis=1-axis)[tup]
if rowvar:
N = X.shape[1]
else:
N = X.shape[0]
if ddof is None:
if bias == 0:
ddof = 1
else:
ddof = 0
fact = float(N - ddof)
if not rowvar:
return (dot(X.T, X.conj()) / fact).squeeze()
else:
return (dot(X, X.T.conj()) / fact).squeeze()
这篇关于如何在numpy内部实现协方差?的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持IT屋!