文章目录
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:
- 引入numpy模块
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/90cebeec08fa513d1aee8d9f3e6d55fbb3fbd9e8.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/507c389759ee3d6d6a82668a40166d224e4adee8.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/c87c6ecf3bc79f3d34aa0571b9a1cd11738b29ed.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/d019d2bf6c81800aafae684fb23533fa838b47ed.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/cdfe7281800a19d80b48654430fa828ba71e46ed.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/ac0acf1373f08202a0e7707e48fbfbedab641b3f.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/808a27dbb6fd5266375edd55a818972bd407363f.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/c28fddfdfc0392450efe004e8494a4c27c1e25ed.jpg)
- 求得标准差矩阵
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/a75fb6d3fd1f4134287ce43f261f95cad0c85eed.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/020e66f0f736afc37a78de24b019ebc4b745123f.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/e78c65899e510fb3fe6c96d6da33c895d1430c3f.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/ea85a94543a98226c5b5ca668982b9014a90eb38.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](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/a6c7d7177f3e6709014ba4be38c79f3df9dc55ed.jpg)
![python 线性代数:[15]从协方差阵计算相关阵](/2016/08/15/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B15%5D%E4%BB%8E%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5%E8%AE%A1%E7%AE%97%E7%9B%B8%E5%85%B3%E9%98%B5/0fb505d5ad6eddc4b3ac55ba3adbb6fd536633ed.jpg)
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