matlab cov函数

原理：

cov(x), if x is a vector, returns the variance of x. For matrix input X, where each row is an observation, and each column is a variable, cov(X) is the covariance matrix. diag(cov(X)) is a vector of variances for each column, and sqrt(diag(cov(X))) is a vector of standard deviations. cov(X,Y), where X and Y are matrices with the same number of elements, is equivalent to cov([X(:) Y(:)]).

cov(x) or cov(x,y) normalizes by N – 1, if N > 1, where N is the number of observations. This makes cov(X) the best unbiased estimate of the covariance matrix if the observations are from a normal distribution. For N = 1, cov normalizes by N.

cov(x,1) or cov(x,y,1) normalizes by N and produces the second moment matrix of the observations about their mean. cov(X,Y,0) is the same as cov(X,Y) and cov(X,0) is the same as cov(X).

代码：

clc;
clear all;


OriginMatrix = [2,3,2; 4,5,3; 6,4,2; 4,5,3];
[M,N]=size(OriginMatrix);


MeanArray = mean( OriginMatrix );
MeanMatrix = ones( M, 1 ) * MeanArray;

% 得到每列减去每列均值的的矩阵
OriginSubMean = OriginMatrix - MeanMatrix;

% 计算出相关矩阵
if M == 1
    CovMatrixComputed = OriginSubMean' * OriginSubMean / M;
else
    CovMatrixComputed = OriginSubMean' * OriginSubMean / ( M-1 );
end

 

Result:

2.6667 0.6667 0

0.6667 0.9167 0.5000

0 0.5000 0.3333

matlab 自带的函数

CovMatrix = cov( OriginMatrix );

Result:

2.6667 0.6667 0

0.6667 0.9167 0.5000

0 0.5000 0.3333

OK 现在理解了没？？

最后找了一张公式附上：

概率的基础，可以看看的  不难的，很简单的。。。。。

好了 该回宿舍了。。。。。