Is there a function to sort eigenvectors in by decreasing eigenvalues

1

Having computed eigenvectors and eigenvalues of a matrix with pytorch,
w, lamb = torch.eig(matrix,eigenvectors=True)

Is there a function to sort the eigenvectors in the decreasing order of the eigenvalues?

2

You can use .sort() on the eigenvalues and use the indices to get the same sorting in the eigenvectors.

3

@albanD, is the following right? Especially the dim?

sortedEig, indices=torch.sort(w, dim=0, descending=True, out=None)
lambSort = lamb.gather(dim=1, index=indices)
4

You don’t need to specify out=None.

This looks good according to the doc yes.

5

Thanks for your help, lambSort is a N x 2 tensor instead of N x N tensor which lamb actually is. How do I fix this?

6

Ho sorry I misread, I think you want index_select() instead of gather here.

7

OK! Since the first element/column of the eigenvalue tensor is the real part and the second element is the imaginary part, is it safe to use/take just the first element(real part) for sorting? Or do I need to combine them? If yes, is there a way to combine them?

8

If yes, is there a way to combine them?

That depends on your application ! Do you want to only consider the real part? Or the norm of the complex number?

9

I am actually implementing PCA so I guess I dabble ignore the complex elements.