NFFT - Nonequispaced FFT

Overview

NFFT is a software library, written in C, for computing non-equispaced fast
Fourier transforms and related variations. It implements the following
transforms:

Non-equispaced fast Fourier transform (NFFT)
- forward transform (NFFT), i.e. frequency to time/space domain
- adjoint transform (adjoint NFFT), i.e. time/space to frequency domain
Generalisations
- to arbitrary nodes in time and frequency domain (NNFFT)
- to real-valued data, i.e. (co)sine transforms, (NFCT, NFST)
- to the sphere S^2 (NFSFT)
- to the rotation group (NFSOFT)
- to the hyperbolic cross (NSFFT)
Generalised inverse transformations based on iterative methods, e.g. CGNR/CGNE

Some examples for application of these transforms are provided:

Medical imaging
- magnetic resonance imaging (mri)
- computerised tomography (radon)
Summation schemes
- fast summation (fastsum)
- fast Gauss transform (FGT)
- singular kernels
- zonal kernels
polar FFT, discrete Radon transform, ridgelet transform

Detailed API documentation in HTML format can be found in
doc/html/index.html, if you are working from a release tarball.
When working from a source repository, the documentation can be
generated with Doxygen (which requires the doxygen-latex and perl packages):

make doc

Building

The NFFT depends on the FFTW library, which is available for many Linux distros, Homebrew on macOS and MSYS2 on Windows. If you compile the FFTW yourself, it should be configured with the flag --enable-shared (and --enable-threads for the multi-threaded version). Building the NFFT requires make and a C compiler such as gcc.

When working from a source repository, you need to run libtoolize and autoreconf first. A bash script to do this is provided. This step requries the tools autoconf, automake and libtool.

./bootstrap.sh

The rest of the build process is standard.

./configure --enable-all --enable-openmp [add options as necessary, see below]

Alternatively, you might run the configure script for Matlab.

./configure --enable-all --enable-openmp --with-matlab=/path/to/matlab

Here are some useful optional flags for ./configure:

--enable-all specifies that all modules should be compiled,
--enable-openmp enables the multicore support and
--enable-julia specifies that the julia interface will be compiled.
--with-matlab=/path/to/matlab specifies the path of a Matlab installation, and
--with-octave=/path/to/octave does the same for GNU Octave.
For a list of all available options, run ./configure --help.

Build the software.

make

Optionally, unit tests may be run. Some of the unit tests require an installation of cunit.

make check

Optionally, install NFFT on your system.

make install

CodSpeed benchmarks

Optionally, NFFT can build benchmark programs using the CodSpeed C++ integration library.
CodSpeed is a continuous benchmarking service that can help with tracking performance
regressions and improvements.

While these benchmarks can run locally, they are actually only intended to run in CI. They also require a build of the CodSpeed integration library from source.

To enable building the benchmarks with the CodSpeed integration library, run ./configure --enable-benchmarks --with-codspeed=<path to codspeed-cpp source directory>.

After the build, the benchmrks can be found in the benchmarks directory.

Citing

The current general paper, the one that we recommend if you wish to cite NFFT, is Keiner, J., Kunis, S., and Potts, D.
''Using NFFT 3 - a software library for various nonequispaced fast Fourier transforms''
ACM Trans. Math. Software 36, Article 19, 1-30, 2009. BibTeX entry:

@article{KeKuPo09,
 author = {Jens Keiner and Stefan Kunis and Daniel Potts},
 title = {Using {NFFT3} - a Software Library for Various Nonequispaced Fast {Fourier} Transforms},
 journal = {{ACM} Trans. Math. Software},
 year = {2009},
 volume = {36},
 pages = {Article 19, 1--30},
 doi = {10.1145/1555386.1555388}}

Feedback

Your comments are welcome! This is the third version of the library and may
not be as robust or well documented as it should be. Please keep track of bugs
or missing/confusing instructions and report them in our issue tracker or directly to
Daniel Potts.
The postal address is

  Prof. Dr. Daniel Potts
  TU Chemnitz, Fakultaet fuer Mathematik
  Reichenhainer Str. 39
  09107 Chemnitz
  GERMANY

Alternatively, you might contact
Stefan Kunis
or
Jens Keiner.

If you find NFFT useful, we would be delighted to hear about what application
you are using NFFT for!

Legal Information & Credits

This software was written by Jens Keiner, Stefan Kunis and Daniel Potts.
It was developed at the Mathematical Institute, University of
Luebeck, and at the Faculty of Mathematics, Chemnitz University of Technology.

NFFT3 is free software. You can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version. If not stated otherwise, this applies to all files contained in this
package and its sub-directories.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

Directory structure

File/Folder	Purpose
3rdparty (dir)	Third-party source code
aclocal.m4	Macros for configure script
applications (dir)	Application programs (see 4) above)
AUTHORS	Information about the authors of NFFT
benchmarks (dir)	Benchmark programs
bootstrap.sh	Bootstrap shell script that call Autoconf and friends
ChangeLog	A short version history
config (dir)	Used by configure script
configure	Configure script (created by calling ./bootstrap.sh)
configure.ac	Autoconf configure script template
CONVENTIONS	Internal coding conventions
COPYING	Information about redistributing NFFT
doc (dir)	User and developer documentation
examples (dir)	Simple examples for using NFFT routines
include (dir)	Header files
INSTALL	Installation instructions
julia (dir)	Julia interface for nfft
kernel (dir)	Source code for core library routines
Makefile.am	Automake Makefile template
Makefile.in	Makefile template generated from Makefile.am, processed by configure script
matlab (dir)	Matlab MEX interfaces for nfft, nfsft, nfsoft, nfft
NEWS	New and noteworthy
README	This file
README.md	This file
tests (dir)	CUnit tests