NFFT
I'm a maintainer and contributor of the NFFT (Nonequispaced fast Fourier transform) software library. The source code is available at the NFFT GitHub repository. Precompiled Octave, MATLAB, and Julia interfaces can be found here.multilayer-SSL-NFFT-Examples
Code examples for semi-supervised learning using multilayer graphs and NFFT-based fast summation.For further details, please read
- Kai Bergermann, Martin Stoll, Toni Volkmer.
Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products.
ArXiv e-prints, 2020, arXiv:2007.05239 [math.NA]. (pdf).
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multilayer-SSL-NFFT-Examples.tar.gzSublinearizedCoSaMPv2
The code for all experiments in Section 5 of- Bosu Choi, Mark Iwen, Toni Volkmer.
Sparse Harmonic Transforms II: Best s-Term Approximation Guarantees for Bounded Orthonormal Product Bases in Sublinear-Time.
ArXiv e-prints, 2019; arXiv:1909.09564 [math.NA]. (pdf).
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SublinearizedCoSaMPv2.zipsparseFFTrandomR1L
sparseFFTr1l is a collection of MATLAB routines for computing the sparse fast Fourier transform based on random rank-1 lattices in a dimension incremental way.For further details, please read
- Kämmerer, L., Krahmer, F., Volkmer, T.
A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions.
ArXiv e-prints, 2020, arXiv:2006.13053 [math.NA]. (pdf).
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sparseFFTrandomR1L-0.1.0.tar.gz is the first version of the software.sparseFFTr1l
sparseFFTr1l is a collection of MATLAB routines for computing the sparse fast Fourier transform based on reconstructing rank-1 lattices in a dimension incremental way.For further details, please read
- Potts, D., Volkmer, T.
Sparse high-dimensional FFT based on rank-1 lattice sampling.
Appl. Comput. Harm. Anal. 41, 713 – 748, 2016. (pdf, DOI).
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sparseFFTr1l-0.1.5.tar.gz is the updated version of the software with bugfixes and Octave support.prony_sparseFFT_iterative
prony_sparseFFT_iterative is a collection of MATLAB routines for computing the sparse fast Fourier transform in an iterative way based on Prony's method via MUSIC or ESPRIT. There exists a one-dimensional version as well as a multi-dimensional version based on rank-1 lattice techniques.For further details, please read
- Potts, D., Tasche, M., Volkmer, T.
Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT.
Front. Appl. Math. Stat. 2, 2016. (pdf, DOI).
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prony_sparseFFT_iterative-0.1.0.tar.gz is the first version of the software.nonperiodicR1L
nonperiodicR1L is a collection of MATLAB routines for computing Chebyshev coefficients based on samples along reconstructing rank-1 Chebyshev lattices.For further details, please read
- Potts, D., Volkmer, T.
Fast and exact reconstruction of arbitrary multivariate algebraic polynomials in Chebyshev form.
Proceedings of the 11th International Conference on Sampling Theory and Applications, 392–396, 2015. (pdf, DOI). - Potts, D., Volkmer, T.
Sparse high-dimensional FFT based on rank-1 lattice sampling.
Appl. Comput. Harm. Anal. 41, 713 – 748, 2016. (pdf, DOI).
Download
nonperiodicR1L-0.1.1.tar.gz is the updated version of the software with minor bugfixes.taylorR1Lnfft
taylorR1Lnfft is a collection of MATLAB routines for computing approximated Fourier coefficients based on samples along perturbed nodes of reconstructing rank-1 lattices.For further details, please read
- Volkmer, T.
Taylor and rank-1 lattice based nonequispaced fast Fourier transform.
In 10th international conference on Sampling Theory and Applications (SampTA 2013), pages 576–579, Bremen, Germany, July 2013. (pdf). - Kämmerer, L., Potts, D., Volkmer, T.
Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling.
J. Complexity 31, 543–576, 2015. (pdf).