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Cytnx-dev / Cytnx

Project Cytnx, A Cross-section of Python & C++,Tensor network library
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cytnx.linalg.ExpM always returns complex UniTensor #493

Closed chiamin closed 1 month ago

chiamin commented 1 month ago

cytnx.linalg.ExpM(T) returns a complex UniTensor even if the input tensor is real. It can be demonstrated as follows.

T = cytnx.UniTensor.uniform([2,2], low=0., high=1.)
Q = cytnx.linalg.ExpM(T)
print(T.dtype_str())
print(Q.dtype_str())
kaihsin commented 1 month ago

ExpM rely on diagonalization, which eigenvalues is not always real right? ExpH is the the one that can always guarantee that

chiamin commented 1 month ago

You are right! I will close this issue.

ianmccul commented 1 month ago

Well, you should be careful, that if the matrix doesn't have a complete set of real eigenvalues then diagonalization is a really terrible way of calculating the exponential! There are much better ways of calculating the matrix exponential; I use https://www.maths.uq.edu.au/expokit/ that uses a Pade approximation. Scipy also uses Pade.

kaihsin commented 1 month ago

Yes. There are also other approximation methods via iteration.

On Sat, Oct 19, 2024, 05:26 Ian McCulloch @.***> wrote:

Well, you should be careful, that if the matrix doesn't have a complete set of real eigenvalues then diagonalization is a really terrible way of calculating the exponential! There are much better ways of calculating the matrix exponential; I use https://www.maths.uq.edu.au/expokit/ that uses a Pade approximation. Scipy also uses Pade.

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