问题描述
我从R来到Python，并尝试重现使用Python在R中做过的许多事情. R的Matrix库具有一个非常漂亮的函数，称为nearPD()，可找到与给定矩阵最接近的正半定(PSD)矩阵.尽管我可以编写一些东西，但是对于Python/Numpy来说是新手，如果已经有了一些东西，我对重新发明轮子并不感到兴奋.关于Python现有实现的任何提示?
I'm coming to Python from R and trying to reproduce a number of things that I'm used to doing in R using Python. The Matrix library for R has a very nifty function called nearPD() which finds the closest positive semi-definite (PSD) matrix to a given matrix. While I could code something up, being new to Python/Numpy I don't feel too excited about reinventing the wheel if something is already out there. Any tips on an existing implementation in Python?
推荐答案
我不认为有一个库可以返回您想要的矩阵，但是这里是近东正半定矩阵的只是为了好玩"编码Higham(2000)的算法
I don't think there is a library which returns the matrix you want, but here is a "just for fun" coding of neareast positive semi-definite matrix algorithm from Higham (2000)
import numpy as np,numpy.linalg
def _getAplus(A):
eigval, eigvec = np.linalg.eig(A)
Q = np.matrix(eigvec)
xdiag = np.matrix(np.diag(np.maximum(eigval, 0)))
return Q*xdiag*Q.T
def _getPs(A, W=None):
W05 = np.matrix(W**.5)
return W05.I * _getAplus(W05 * A * W05) * W05.I
def _getPu(A, W=None):
Aret = np.array(A.copy())
Aret[W > 0] = np.array(W)[W > 0]
return np.matrix(Aret)
def nearPD(A, nit=10):
n = A.shape[0]
W = np.identity(n)
# W is the matrix used for the norm (assumed to be Identity matrix here)
# the algorithm should work for any diagonal W
deltaS = 0
Yk = A.copy()
for k in range(nit):
Rk = Yk - deltaS
Xk = _getPs(Rk, W=W)
deltaS = Xk - Rk
Yk = _getPu(Xk, W=W)
return Yk
在对本文示例进行测试时，它会返回正确答案
When tested on the example from the paper, it returns the correct answer
print nearPD(np.matrix([[2,-1,0,0],[-1,2,-1,0],[0,-1,2,-1],[0,0,-1,2]]),nit=10)
[[ 1. -0.80842467 0.19157533 0.10677227]
[-0.80842467 1. -0.65626745 0.19157533]
[ 0.19157533 -0.65626745 1. -0.80842467]
[ 0.10677227 0.19157533 -0.80842467 1. ]]
这篇关于如何计算最近的正半定矩阵?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！