A possible subtle mistake related to code implementation of nplr

[MichaelY310]

In s4/src/models/hippo/hippo.py line 240

W_im, V = torch.linalg.eigh(AP*-1j) # (..., N) (..., N, N)

to calculate the complex part of the eigenvalue and eigenvectors, instead of AP, the skew symmetric part, which is AP - torch.diag(torch.diag(AP)), should be eigendecomposed. So I think this line should be replaced by

W_im, V = torch.linalg.eigh((AP-torch.diag(torch.diag(AP)))*-1j)

However, the mistake is very subtle here since the diagonal value -0.5 is very small comparing to other entries in AP. The revision only decreases the reconstruction error of A by about 0.00001 if I set cdtype to torch.complex128. And there is no difference at all if I use the default setting torch.complex64. But if the mistake indeed present, it may cause greater errors when methods other than LegS with matrices having small matrix norms are used.