FFTPACK5
Fast Fourier Transform
FFTPACK5
is a FORTRAN77 library which
computes the Fast Fourier Transform,
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 to
the authors on 10 May 2010. A 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 library 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 shows how the names of the routines in each group:
Initialization  Forward  Backward  Purpose 
CFFT1I  CFFT1F  CFFT1B  FFT for complex 1D data 
CFFT2I  CFFT2F  CFFT2B  FFT for complex 2D data 
CFFTMI  CFFTMF  CFFTMB  FFT for complex multiD data 
COSQ1I  COSQ1F  COSQ1B  Even function 1D quartercosine FFT 
COSQMI  COSQMF  COSQMB  Even function 1D quartercosine FFT 
COST1I  COST1F  COST1B  Even function 1D cosine FFT 
COSTMI  COSTMF  COSTMB  Even function 1D cosine FFT 
RFFT1I  RFFT1F  RFFT1B  FFT for real 1D data 
RFFT2I  RFFT2F  RFFT2B  FFT for real 2D data 
RFFTMI  RFFTMF  RFFTMB  FFT for real multiD data 
SINQ1I  SINQ1F  SINQ1B  Even function 1D quartersine FFT 
SINQMI  SINQMF  SINQMB  Even function 1D quartersine FFT 
SINT1I  SINT1F  SINT1B  Even function 1D sine FFT 
SINTMI  SINTMF  SINTMB  Even function 1D sine FFT 
Licensing:
Licensed under the GNU General Public License (GPL).
Copyright (C) 19952004, Scientific Computing Division,
University Corporation for Atmospheric Research.
Languages:
FFTPACK5 is available in
a FORTRAN77 version and
a FORTRAN90 version.
Related Programs:
FFTPACK5.1,
a FORTRAN77 library which
implements the Fast Fourier Transform
by Swarztrauber and Valent;
FFTW3,
FORTRAN77 programs which
illustrate the use of the FFTW3 library for Fast Fourier Transforms,
by Matteo Frigo and Steven Johnson.
SFTPACK,
a FORTRAN77 library which
implements the "slow" Fourier transform, intended as a teaching
tool and comparison with the fast Fourier transform.
WALSH,
a FORTRAN77 library which
implements versions of the Walsh and Haar transforms.
WAVELET,
a FORTRAN77 library which
does some simple calculations with wavelet transforms;
XERROR,
a FORTRAN77 library which
is used for error reporting by FFTPACK5.
Author:
The original Fortran77 version of this code was written by Dick Valent and
Paul Swarztrauber, of the National Center for Atmospheric Research (NCAR).
Reference:

William Briggs, Van Emden Henson,
The DFT: An Owner's Manual for the Discrete Fourier Transform,
SIAM, 1995,
ISBN13: 9780898713428,
LC: QA403.5.B75.

Elbert Brigham,
The Fast Fourier Transform and Its Applications,
PrenticeHall, 1988,
ISBN: 0133075052,
LC: QA403.B74.

Bill Buzbee,
The SLATEC Common Math Library,
in Sources and Development of Mathematical Software,
edited by Wayne Cowell,
PrenticeHall, 1984,
ISBN: 0138235015,
LC: QA76.95.S68.

Eleanor Chu, Alan George,
Inside the FFT Black Box,
CRC Press,
ISBN: 0849302706,
LC: QA403.5C5.

David Kahaner, Cleve Moler, Steven Nash,
Numerical Methods and Software,
Prentice Hall, 1989,
ISBN: 0136272584,
LC: TA345.K34.

Paul Swarztrauber,
Symmetric FFT's,
Mathematics of Computation,
Volume 47, Number 175, July 1986, pages 323346.

Paul Swarztrauber,
Vectorizing the Fast Fourier Transforms,
in Parallel Computations,
edited by Garry Rodrigue,
Academic Press, 1982,
ISBN: 0125921012,
LC: QA76.6.P348.

Paul Swarztrauber,
Fast Fourier Transform Algorithms for Vector Computers,
Parallel Computing,
Volume 1, Number 1, August 1984, pages 4563.

FFTPACK 5.0 Reference manual

http://www.cisl.ucar.edu/css/software/fftpack5
the home page for the original FORTRAN77 version of FFTPACK5.
Source Code:
Examples and Tests:
A discrepancy seems to have shown up in the COST1* routines.
Calling COST1F followed by COST1B does not reproduce the original
data. This discrepancy disappears if double precision is used.
A discrepancy seems to have shown up in the SINT1* routines.
Calling SINT1F followed by SINT1B does not reproduce the original
data. This discrepancy disappears if double precision is used.
List of Routines:

CFFT1B: complex backward fast Fourier transform, 1D.

CFFT1F: complex forward fast Fourier transform, 1D.

CFFT1I: initialization for CFFT1B and CFFT1F.

CFFT2B: complex backward fast Fourier transform, 2D.

CFFT2F: complex forward fast Fourier transform, 2D.

CFFT2I: initialization for CFFT2B and CFFT2F.

CFFTMB: complex backward fast Fourier transform, 1D, multiple vectors.

CFFTMF: complex forward fast Fourier transform, 1D, multiple vectors.

CFFTMI: initialization for CFFTMB and CFFTMF.

COSQ1B: complex backward cosine quarter wave transform, 1D.

COSQ1F: complex forward cosine quarter wave transform, 1D.

COSQ1I: initialization for COSQ1B and COSQ1F.

COSQMB: complex backward cosine quarter wave transform, multiple vectors.

COSQMF: complex forward cosine quarter wave transform, multiple vectors.

COSQMI: initialization for COSQMB and COSQMF.

COST1B: complex backward cosine transform, 1D.

COST1F: complex forward cosine transform, 1D.

COST1I: initialization for COST1B and COST1F.

COSTMB: complex backward cosine transform, multiple vectors.

COSTMF: complex forward cosine transform, multiple vectors.

COSTMI: initialization for COSTMB and COSTMF.

FACTOR determines the factors of an integer.

RFFT1B: real backward fast Fourier transform, 1D.

RFFT1F: real forward fast Fourier transform, 1D.

RFFT1I: initialization for RFFT1B and RFFT1F.

RFFT2B: real backward fast Fourier transform, 2D.

RFFT2F: real forward fast Fourier transform, 2D.

RFFT2I: initialization for RFFT2B and RFFT2F.

RFFTMB: real backward fast Fourier transform, 1D, multiple vectors.

RFFTMF: real forward fast Fourier transform, 1D, multiple vectors.

RFFTMI: initialization for RFFTMB and RFFTMF.

SINQ1B: complex backward sine quarter wave transform, 1D.

SINQ1F: complex forward sine quarter wave transform, 1D.

SINQ1I: initialization for SINQ1B and SINQ1F.

SINQMB: complex backward sine quarter wave transform, multiple vectors.

SINQMF: complex forward sine quarter wave transform, multiple vectors.

SINQMI: initialization for SINQMB and SINQMF.

SINT1B: complex backward sine transform, 1D.

SINT1F: complex forward sine transform, 1D.

SINT1I: initialization for SINT1B and SINT1F.

SINTMB: complex backward sine transform, multiple vectors.

SINTMF: complex forward sine transform, multiple vectors.

SINTMI: initialization for SINTMB and SINTMF.

TABLES computes trigonometric tables needed by the FFT routines.

XERCON checks INC, JUMP, N and LOT for consistency.

XERFFT is an error handler for the FFTPACK routines.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 28 November 2005.