其实Python的numpy包有可以直接计算相关矩阵/协方差矩阵的方法,但是这篇文章是教大家如何理解他俩之间的关系的,所以我们给出协方差矩阵,求相关矩阵。利用公式:
p=((V**0.5)**-1)∑((V**0.5)**-1)
引入numpy模块![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/d04eec260d9a310ef880ea9f31b842406bfea2b2.jpg)
创建一个协方差矩阵
这个矩阵为:![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/3931cb413a8ca608b6159749db8c9bcec6f8feb2.jpg)
我们先求得协方差矩阵的尺寸![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/3201a8f39187031cbcdaac496a86242fa972ecb2.jpg)
生成一个与sigma同大小的单位矩阵:e
输出为:![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/d47cb624d8e9ccd2f17c52ec0e40102a05e2c9b2.jpg)
计算方差矩阵,其实就是利用单位矩阵消除协方差矩阵中的非对角线元素![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/18aebc5f0c14c27b8898853c2a46b7b1eff939b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/c8373cbc7dc5cf674045d6f38e96b814f5d026b3.jpg)
求得标准差矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/340e4eb8b43ea8db2c50f987189c2cf7deb216b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/125ed0ecd3d9697578deef2cd243040149fe09b3.jpg)
求得标准差的逆矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/059057299a8839137dffef5b26bcbe2f46707cb3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/92174dbbf82064fb321132948e6104a354e96fb3.jpg)
根据公式就求得了相关系数矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/1570c1b6326c57662bd501e6a4632385e13661b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/31097f43d7d44831c6f1f512d40f822b75ee51b3.jpg)
其实Python的numpy包有可以直接计算相关矩阵/协方差矩阵的方法,但是这篇文章是教大家如何理解他俩之间的关系的,所以我们给出协方差矩阵,求相关矩阵。利用公式:
p=((V**0.5)**-1)∑((V**0.5)**-1)
引入numpy模块![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/d04eec260d9a310ef880ea9f31b842406bfea2b2.jpg)
创建一个协方差矩阵
这个矩阵为:![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/3931cb413a8ca608b6159749db8c9bcec6f8feb2.jpg)
我们先求得协方差矩阵的尺寸![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/3201a8f39187031cbcdaac496a86242fa972ecb2.jpg)
生成一个与sigma同大小的单位矩阵:e
输出为:![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/d47cb624d8e9ccd2f17c52ec0e40102a05e2c9b2.jpg)
计算方差矩阵,其实就是利用单位矩阵消除协方差矩阵中的非对角线元素![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/18aebc5f0c14c27b8898853c2a46b7b1eff939b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/c8373cbc7dc5cf674045d6f38e96b814f5d026b3.jpg)
求得标准差矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/340e4eb8b43ea8db2c50f987189c2cf7deb216b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/125ed0ecd3d9697578deef2cd243040149fe09b3.jpg)
求得标准差的逆矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/059057299a8839137dffef5b26bcbe2f46707cb3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/92174dbbf82064fb321132948e6104a354e96fb3.jpg)
根据公式就求得了相关系数矩阵![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/1570c1b6326c57662bd501e6a4632385e13661b3.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](https://exp-picture.cdn.bcebos.com/31097f43d7d44831c6f1f512d40f822b75ee51b3.jpg)