In SVD, is there any way to calculate only U and S, not V^T?

+1 vote
asked Feb 20 by hexagon (160 points)

Hello.

I'm trying to do HOTRG calculation for 2D Ising model.
As the system size (that I want to see) increases, computation time of SVD increases rapidly.
Actually, I don't need V^T in the process.
Is there any way to skip the calculation of V^T in SVD?

Best,
hexagon

1 Answer

0 votes
answered Feb 20 by miles (12,650 points)
selected Feb 21 by hexagon
 
Best answer

Good question: this is what the denmatDecomp function is for. There is more detailed info about it on this page:
http://itensor.org/docs.cgi?page=classes/decomp

Basically its interface works the same way as the svd function but you have to provide a "dir" argument (either Fromleft or Fromright) which in SVD language says whether you want U or V (the other tensor will be set equal to either SV or US where S is the singular value matrix).

Internally, denmatDecomp squares the tensor you are decomposing and then calls a Hermitian diagonalization routine on it to get just U or just V. So it is more efficient than doing a full SVD.

Miles

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