fftpack5

fftpack5, a FORTRAN90 code which computes Fast Fourier Transforms, by Paul Swarztrauber and Dick Valent;

Note: An apparent indexing problem in the 2D complex codes CFFT2B/CFFT2F/CFFT2I and ZFFT2B/ZFFT2F/ZFFT2I was reported on 10 May 2010. A partial fix was inserted, the authors have been noted, and a proper fix has been promised...

Special features include:

• real or complex data can be handled;
• separate routines for forward analysis (data => Fourier coefficients) and backward analysis (Fourier coefficients => data);
• sine and cosine transform routines;
• quarter wave sine and cosine transform routines;
• the amount of data is NOT required to be a power of 2.

Routines in the code come in groups of three:

• an initialization routine;
• the forward computational routine (data to FFT coefficients);
• the backward computational routine (FFT coefficients to data).

The following table groups the routines:

Initialization	Forward	Backward	Purpose
CFFT1I	CFFT1F	CFFT1B	FFT for complex single precision 1D data
CFFT2I	CFFT2F	CFFT2B	FFT for complex single precision 2D data
CFFTMI	CFFTMF	CFFTMB	FFT for complex single precision multi-D data
COSQ1I	COSQ1F	COSQ1B	Even function 1D quarter-cosine FFT for real single precision data
DCOSQ1I	DCOSQ1F	DCOSQ1B	Even function 1D quarter-cosine FFT for real double precision data
COSQMI	COSQMF	COSQMB	Even function 1D quarter-cosine FFT for real single precision data
COST1I	COST1F	COST1B	Even function 1D cosine FFT for real single precision data
DCOST1I	DCOST1F	DCOST1B	Even function 1D cosine FFT for real double precision data
COSTMI	COSTMF	COSTMB	Even function 1D cosine FFT for real single precision data
RFFT1I	RFFT1F	RFFT1B	FFT for real single precision 1D data
DFFT1I	DFFT1F	DFFT1B	FFT for real double precision 1D data
RFFT2I	RFFT2F	RFFT2B	FFT for real single precision 2D data
RFFTMI	RFFTMF	RFFTMB	FFT for real single precision multi-D data
SINQ1I	SINQ1F	SINQ1B	Even function 1D quarter-sine FFT for real single precision data
SINQMI	SINQMF	SINQMB	Even function 1D quarter-sine FFT for real single precision data
SINT1I	SINT1F	SINT1B	Even function 1D sine FFT for real single precision data
DSINT1I	DSINT1F	DSINT1B	Even function 1D sine FFT for real double precision data
SINTMI	SINTMF	SINTMB	Even function 1D sine FFT for real single precision data
ZFFT1I	ZFFT1F	ZFFT1B	FFT for complex double precision 1D data
ZFFT2I	ZFFT2F	ZFFT2B	FFT for complex double precision 2D data
ZFFTMI	ZFFTMF	ZFFTMB	FFT for complex double precision multi-D data

Licensing:

Licensed under the GNU General Public License (GPL).
Copyright (C) 1995-2004, Scientific Computing Division,
University Corporation for Atmospheric Research.

Languages:

fftpack5 is available in a FORTRAN90 version.

Related Data and codes:

fftpack5_test

FFTPACK51, a FORTRAN90 code which implements the Fast Fourier Transform by Paul Swarztrauber and Dick Valent;

fftw_test, FORTRAN90 codes which illustrate the use of the FFTW3 code for Fast Fourier Transforms, by Matteo Frigo and Steven Johnson.

nms, a FORTRAN90 code which includes a number of FFT routines.

sftpack, a FORTRAN90 code which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

xerror, a FORTRAN90 code which is designed to report and handle errors detected during code execution.

Author:

The original Fortran77 version of this code was written by Dick Valent and Paul Swarztrauber, of the National Center for Atmospheric Research (NCAR).

Modifications and additions were made by John Burkardt to convert the code to FORTRAN90 format, and to add real and complex double precision routines.

Reference:

1. William Briggs, Van Emden Henson,
   The DFT: An Owner's Manual for the Discrete Fourier Transform,
   SIAM, 1995,
   ISBN13: 978-0-898713-42-8,
   LC: QA403.5.B75.
2. Elbert Brigham,
   The Fast Fourier Transform and Its Applications,
   Prentice-Hall, 1988,
   ISBN: 0133075052,
   LC: QA403.B74.
3. Bill Buzbee,
   The SLATEC Common Math code,
   in Sources and Development of Mathematical Software,
   edited by Wayne Cowell,
   Prentice-Hall, 1984,
   ISBN: 0-13-823501-5,
   LC: QA76.95.S68.
4. Eleanor Chu, Alan George,
   Inside the FFT Black Box,
   CRC Press,
   ISBN: 0849302706,
   LC: QA403.5C5.
5. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.
6. Paul Swarztrauber,
   Symmetric FFT's,
   Mathematics of Computation,
   Volume 47, Number 175, July 1986, pages 323-346.
7. Paul Swarztrauber,
   Vectorizing the Fast Fourier Transforms,
   in Parallel Computations,
   edited by Garry Rodrigue,
   Academic Press, 1982,
   ISBN: 0125921012,
   LC: QA76.6.P348.
8. Paul Swarztrauber,
   Fast Fourier Transform Algorithms for Vector Computers,
   Parallel Computing,
   Volume 1, Number 1, August 1984, pages 45-63.
9. https://www.cisl.ucar.edu/css/software/fftpack5 the home page for the original FORTRAN77 version of FFTPACK5.

Source Code:

• fftpack5.f90, the source code.
• fftpack5.sh, compiles the source code.