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https://github.com/NFFT/nfft

The official NFFT library repository
https://github.com/NFFT/nfft

c fftw fourier-transform julia matlab nfft

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The official NFFT library repository

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README 

        
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:



1. 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



2. 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)*



3. Generalised inverse transformations based on iterative methods, e.g. CGNR/CGNE



Some examples for application of these transforms are provided:



1. Medical imaging

    - magnetic resonance imaging (mri)

    - computerised tomography (radon)



2. Summation schemes

    - fast summation (fastsum)

    - fast Gauss transform (FGT)

    - singular kernels

    - zonal kernels



3. 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](https://fftw.org) 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](http://cunit.sourceforge.net).

```

make check

```



Optionally, install NFFT on your system.

```

make install

```



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](mailto:[email protected]).

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](mailto:[email protected])

or

[Jens Keiner](mailto:[email protected]).



If you find NFFT useful, we would be delighted to hear about what application

you are using NFFT for!



Legal Information & Credits

---------------------------

Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts



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

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