Change SVD type in pod.py

[annaivagnes]

Only replaced the torch.svd_lowrank method with torch.svd: the reason is that torch.svd_lowrank is randomized and may give different results in different runs (as specified in the documentation: https://pytorch.org/docs/stable/generated/torch.svd_lowrank.html)

[dario-coscia]

Thanks @annaivagnes ! Maybe we can add in the init a boolean kwarg called 'randomizedwhich if true usestorch.svd_lowrankotherwisetorch.svd. Like this we can use both, I think torch.svd_lowrank` it is a bit faster in CUDA

[dario-coscia]

So here would be something like:

        if X.device.type == "mps":  #  svd_lowrank not arailable for mps
            self._basis = torch.svd(X.T)[0].T
        else:
            self._basis = self.svd(X.T, q=X.shape[0])[0].T

We should put a warning on the doc for MPS users maybe?

[annaivagnes]

Thank you for reviewing!

In my opinion, if we want to keep the svd_lowrank to speed up the computations, then we should set up a seed or give a Warning saying that the method is randomized and that the computation of the discretized basis may differ in different runs. Also what you suggested with the randomized kwarg is ok (I would include the Warning anyway, maybe).

Then, maybe for MPS users the Warning can be The POD is computed using the standard SVD approach and this may slow down the computation

[dario-coscia]

Ok, then let's do it like this. We can put a warning at initialization, and if an mps user is using the layer we raise another waning like the one you described :)

[dario-coscia]

Thanks Anna!