Question: data dimension limit

[PatrickSteinmueller]

Hi,

I am interested in using your library in a quantum computing context. We have a large body of data in a high dimensional space, that is not sampled in an equidistant grid (sobol sequences). However, most libraries for adjoint NFFTs seem to have a technical limit of only allowing three dimensional data.

As far as your publications go, I have not seen any limit described. Is there a technical limitation with regards to the dimension?

Kind Regards

Patrick Steinmüller

[michaelquellmalz]

Hi, the NFFT usually works well for dimensions up to d=5. I know of a practical application with d=4.

There is no strict technical limit of the dimension (although the Matlab interface currently allows only d<=5). However, for higher dimensions the memory requirements become much bigger so that it seems usually not practical anymore (e.g. the number of Fourier coefficients is N^d).

For higher dimensions, one could work on different grids, for example rank-one lattices.

[PatrickSteinmueller]

Hi Michael, thanks for your answer. In our use case (Parametrized Quantum Circuit) the number of acceptable Fourier coefficients is restricted and usually much smaller than N^d. I will have a look at the paper. Kind Regards Patrick Steinmüller From: Michael Quellmalz ***@***.***> Sent: Montag, 7. Juni 2021 13:00 To: NFFT/nfft ***@***.***> Cc: Steinmueller, Patrick ***@***.***>; Author ***@***.***> Subject: Re: [NFFT/nfft] Question: data dimension limit (#117) Hi, the NFFT usually works well for dimensions up to d=5. I know of a practical application with d=4. There is no strict technical limit of the dimension (although the Matlab interface currently allows only d<=5). However, for higher dimensions the memory requirements become much bigger so that it seems usually not practical anymore (e.g. the number of Fourier coefficients is N^d). For higher dimensions, one could work on different grids, for example rank-one lattices<https://www-user.tu-chemnitz.de/~potts/paper/reco_indexset_incr.pdf>. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<#117 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ATOVB2NFRN23JJ5YSAK6R7TTRSRDVANCNFSM46DM7RDQ>. Please do not print this document unless it is necessary, consider the environment. d-fine GmbH: Sitz der Gesellschaft: An der Hauptwache 7, 60313 Frankfurt am Main; Amtsgericht Frankfurt am Main: HRB Nr. 48 103; Geschaeftsfuehrer: Christoph Belafi, Dr. Christoph Bennemann, Dr. Oliver Bohr, Dr. Christoph Burmester, Dr. Ashot Davtyan, Todor Dobrikov, Dr. Arndt Dombert, Dr. Uwe Doerr, Dr. Andreas Geyer, Nadine Gottschalk, Dr. Oliver Hein, Dr. Stefan Heinrichs, Dr. Bodo Huckestein, Dr. Sascha Huegle, Dr. Tilman Huhne, Jens Itzenhaeuser, Ulf Henning Jacobs, Dr. Jan Jureit, Dr. Andreas Keese, Dr. Florian Merz, Dr. Jochen Meyer, Dr. Karsten Meyer, Dr. Mathias Michel, Dr. Cornelius Mund, Dr. Christian Oehler, Wolfgang Pleyer, Dr. Joern Rank, Dr. Christian Romeike, Markus von Rothkirch, Alexander Schalk, Dr. Egbert Schark, Dr. Christoph Schneggenburger, Nadja Schuster, Dr. Markus Seifert, Dr. Constantin Sobiella, Artur Steiner, Dr. Roland Uhlig, Dr. Hans Peter Waechter, Dr. Andreas Werner, Dr. Magnus Wobben This e-mail communication (and any attachment/s) is confidential and intended only for the individual(s) or entity named above and to others who have been specifically authorized to receive it. If you are not the intended recipient, please do not read, copy, use or disclose the contents of this communication to others. Please notify the sender that you have received this e-mail in error, and delete the e-mail (including any attachment/s) subsequently. This information may be subject to professional secrecy (e. g. of auditor, tax or legal advisor), other privilege or otherwise be protected by work product immunity or other legal rules. For more information about how and why we use personal information and who to contact with any queries about this, please consult our Data Privacy Policy on https://www.d-fine.com/en_DE/privacy-policy/. Thank you.