symmetry of terms for multi-species descriptor about dscribe

[gabor1]

Thanks. I haven't explicitly said, but perhaps should, that I am a keen supporter of other implementations of SOAP (especially ones like dscribe with improved radial basis), the quippy one is just for reference.

[lauri-codes]

Now fixed in 0.4.0. Thanks again @gabor1!

[lauri-codes]

Hi Gabor!

Thanks for reporting this. I think I understand your point. I will have to check our implementation to see if we are truly misusing symmetry here. If so, this should be fixed ASAP.

[gabor1]

Thanks. A direct test would be to compute the elements I am talking about and to see if they match with the ones you think they match with… If they do, then we need to fix quip!

…

-- Gábor Gábor Csányi Professor of Molecular Modelling Engineering Laboratory, University of Cambridge Pembroke College Cambridge Pembroke College supports CARA. A Lifeline to Academics at Risk. http://www.cara.ngo/

On 28 Apr 2020, at 21:37, Lauri Himanen ***@***.***> wrote: Hi Gabor! Thanks for reporting this. I think I understand your point. I will have to check our implementation to see if we are truly misusing symmetry here. If so, this should be fixed ASAP. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[gabor1]

it's a funny terminology to label this "enhancement" ...

[lauri-codes]

I looked at this briefly, and indeed it seems to be a bug on our side. Now labeled correctly. Now I just need to find the time to fix it.

[lauri-codes]

Great, your input is very much appreciated!

[lauri-codes]

This is more of a note for future reference:

The individual terms in the multi-species power spectrum are of the form:

So the question is, what terms are redundant due to symmetry? One way to analyze the symmetries is by taking the complex conjugate of the power spectrum (taking the complex conjugate doesn't affect the result as the power spectrum terms are real numbers):

This shows that swapping both n and Z simultaneously creates identical output:

As @gabor1 already mentioned, this symmetry can be very neatly taken into account by using combined indices (Z,n) and (Z',n') and adding only values for which (Z',n') >= (Z,n). The combined indices can be represented directly as python tuples as they have a suitable comparison operator.

[gabor1]

great, thanks!