matlab里面的求协方差函数
一：matlab里面关于方差和协方差的几点需要注意的
求均值的函数：mean
求方差的函数：var
标准差：
方差：
求协方差的函数：cov
1 如果a,b是向量，则：
cov(a,b)相当于是[D(a),cov(a,b);cov(b,a),D(b)]，其中D(a)和D(b)分别代表了a,b的方差。cov(a,b)和cov(b,a)分别代表了两者之间的协方差
举例：
>> a=[1.1 2.2 3 4.5 0.8]
a =
1.1000 2.2000 3.0000 4.5000 0.8000
>> b=[1.3 2.4 2.1 5 3.3]
b =
1.3000 2.4000 2.1000 5.0000 3.3000
>> cov(a,b)
ans =
2.2570 1.3595
1.3595 1.9970
其中，对角线的值是两个向量的方差，斜对角线的是两个向量之间的协方差
2 如果a,b是矩阵，则：
cov(a,b)相当于是cov(a(:),b(:))，举例说明：
>> a=randn(4);
>> a
a =
-0.4326 -1.1465 0.3273 -0.5883
-1.6656 1.1909 0.1746 2.1832
0.1253 1.1892 -0.1867 -0.1364
0.2877 -0.0376 0.7258 0.1139
>> b=randn(4);
>> b
b =
1.0668 0.2944 -0.6918 -1.4410
0.0593 -1.3362 0.8580 0.5711
-0.0956 0.7143 1.2540 -0.3999
-0.8323 1.6236 -1.5937 0.6900
>> cov(a,b)
ans =
0.8513 -0.0860
-0.0860 1.0129
/////////////////////////////////////////////////////////////////////////////
>> a(:)
ans =
-0.4326
-1.6656
0.1253
0.2877
-1.1465
1.1909
1.1892
-0.0376
0.3273
0.1746
-0.1867
0.7258
-0.5883
2.1832
-0.1364
0.1139
>> b(:)
ans =
1.0668
0.0593
-0.0956
-0.8323
0.2944
-1.3362
0.7143
1.6236
-0.6918
0.8580
1.2540
-1.5937
-1.4410
0.5711
-0.3999
0.6900
>> cov(a(:),b(:))
ans =
0.8513 -0.0860
-0.0860 1.0129
另外，matlab里面关于cov函数的说明解释的很详细：
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).
其使用示例可见：http://www.mathworks.cn/cn/help/matlab/ref/cov.html?searchHighlight=cov
参考：
http://pinkyjie.com/2010/08/31/covariance/
http://www.cnblogs.com/cvlabs/archive/2010/05/08/1730319.html
http://blog.csdn.net/faceRec/article/details/1697362
http://blog.csdn.net/ybdesire/article/details/6270328