FFTPACK5.1
Fast Fourier Transform
FFTPACK5.1
is a FORTRAN77 library which
computes the Fast Fourier Transform,
by Paul Swarztrauber and Dick Valent;
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 
Bugfixes from FFTPACK 5.0 to FFTPACK 5.1
The functionality of FFTPACK 5.1 is identical with the previous version 5.0.
The following bugfixes have been applied:

Corrected index error for highlevel routines [CR]FFT[12][BFI] requiring
WSAVE array, and all dependent routines to which LWSAVE is passed.
Namely, in LWSAV = L + LOG(REAL(INT(L))) + 4 definitions, the summand term
LOG(REAL(INT(L))) has been corrected to LOG(REAL(INT(L)/LOG(2.)).

Corrected index error in routime C1FM1F at label 56, where array offset
was declared 1 that should have been 2. This resulted in C1FFTF transforms
of length N calculated incorrectly, where N is any prime .GT. 5, or N=7*M,
M .GE. 6.

Corrected RFFT2x routines by rewriting them. The backward transform
followed by forward now returns identity. Input argument LENSAV must be
be at least
L + 3*M + INT(LOG(REAL(L))/LOG(2.)) + 2*INT(LOG(REAL(M))/LOG(2.)) +12.
Previously, the required value was smaller.
Licensing:
Licensed under the GNU General Public License (GPL).
Copyright (C) 19952004, Scientific Computing Division,
University Corporation for Atmospheric Research.
Languages:
FFTPACK5.1 is available in
a FORTRAN77 version and
a FORTRAN90 version.
Related Programs:
FFTPACK5,
a FORTRAN77 library which
implements the Fast Fourier Transform.
FFTW3,
FORTRAN77 programs which
illustrate the use of the FFTW3 library for Fast Fourier Transforms,
by Matteo Frigo and Steven Johnson.
GSL,
a C++ library which
embodies the "GNU Scientific Library", and includes FFT routines.
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.
XERROR,
a FORTRAN77 library which
is used for error reporting.
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.

fftpack5.1_reference.html,
the FFTPACK5.1 online reference.

fftpack5.1_readme.txt,
the FFTPACK5.1 "readme" file.

Makefile,
the FFTPACK5.1 makefile.
Source Code:
Examples and Tests:
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 29 March 2011.