我要说的第一件事是不要eigh用于测试正定性，因为eigh假定输入为hermitian。这可能就是为什么您认为引用的答案不起作用的原因。
我不喜欢那个答案，因为它有一个迭代（而且我不明白它的例子），也没有那里的另一个答案，它不能保证为您提供最佳 的正定矩阵，即最接近正定矩阵的矩阵。以Frobenius范数（元素的平方和）表示的输入。（我完全不知道问题中的代码应该做什么。）
我喜欢Higham 1988年 论文的Matlab实现：https ://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd，所以我将其移植到了Python：
from numpy import linalg as la
def nearestPD(A):
"""Find the nearest positive-definite matrix to input
A Python/Numpy port of John D'Errico's `nearestSPD` MATLAB code [1], which
credits [2].
[1] https://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd
[2] N.J. Higham, "Computing a nearest symmetric positive semidefinite
matrix" (1988): https://doi.org/10.1016/0024-3795(88)90223-6
"""
B = (A + A.T) / 2
_, s, V = la.svd(B)
H = np.dot(V.T, np.dot(np.diag(s), V))
A2 = (B + H) / 2
A3 = (A2 + A2.T) / 2
if isPD(A3):
return A3
spacing = np.spacing(la.norm(A))
# The above is different from [1]. It appears that MATLAB's `chol` Cholesky
# decomposition will accept matrixes with exactly 0-eigenvalue, whereas
# Numpy's will not. So where [1] uses `eps(mineig)` (where `eps` is Matlab
# for `np.spacing`), we use the above deFinition. CAVEAT: our `spacing`
# will be much larger than [1]'s `eps(mineig)`, since `mineig` is usually on
# the order of 1e-16, and `eps(1e-16)` is on the order of 1e-34, whereas
# `spacing` will, for Gaussian random matrixes of small dimension, be on
# othe order of 1e-16. In practice, both ways converge, as the unit test
# below suggests.
I = np.eye(A.shape[0])
k = 1
while not isPD(A3):
mineig = np.min(np.real(la.eigvals(A3)))
A3 += I * (-mineig * k**2 + spacing)
k += 1
return A3
def isPD(B):
"""Returns true when input is positive-definite, via Cholesky"""
try:
_ = la.cholesky(B)
return True
except la.LinAlgError:
return False
if __name__ == '__main__':
import numpy as np
for i in xrange(10):
for j in xrange(2, 100):
A = np.random.randn(j, j)
B = nearestPD(A)
assert(isPD(B))
print('unit test passed!')
除了只查找最接近的正定矩阵外，上述库还包括isPD使用Cholesky分解确定矩阵是否为正定矩阵。这样，您就不需要任何公差- 任何需要正定的函数都可以在其上运行Cholesky，因此，这是确定正定的绝对最佳方法。
最后，它还具有基于Monte Carlo的单元测试。如果将其放入posdef.py并运行python posdef.py，它将在我的笔记本电脑上运行约一秒钟的单元测试。然后可以在代码中import posdef调用posdef.nearestPD或posdef.isPD。
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