Python 协方差在numpy内部是如何实现的?
这是协方差矩阵的定义 矩阵中除主对角线外的每个元素(如果我没有错的话)简化为E(x{I}*x{j})-均值(I)*均值(j),其中I和j是协方差矩阵的行号和列号 从numpy文档中Python 协方差在numpy内部是如何实现的?,python,numpy,matrix,covariance,Python,Numpy,Matrix,Covariance,这是协方差矩阵的定义 矩阵中除主对角线外的每个元素(如果我没有错的话)简化为E(x{I}*x{j})-均值(I)*均值(j),其中I和j是协方差矩阵的行号和列号 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} 第二行即[2,1,0]对应于X_
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}
第二行即[2,1,0]对应于X_{1}
由于随机变量的分布未知,如何计算X_{0}*X_{1}的期望值
谢谢。只需检查代码即可。
\site packages\numpy\lib\function\u base.py中的cov
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.
可能完全重复!这是开源代码的一个主要优势:您可以查看实现。
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()