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 multi-D data
COSQ1I	COSQ1F	COSQ1B	Even function 1D quarter-cosine FFT
COSQMI	COSQMF	COSQMB	Even function 1D quarter-cosine 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 multi-D data
SINQ1I	SINQ1F	SINQ1B	Even function 1D quarter-sine FFT
SINQMI	SINQMF	SINQMB	Even function 1D quarter-sine 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) 1995-2004, 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:

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 Library,
   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. FFTPACK 5.0 Reference manual
10. http://www.cisl.ucar.edu/css/software/fftpack5 the home page for the original FORTRAN77 version of FFTPACK5.

Source Code:

• fftpack5.f, the source code.
• fftpack5.sh, commands to compile the source code.

Examples and Tests:

• fftpack5_prb.f, a sample calling program.
• fftpack5_prb.sh, commands to compile and run the sample program.
• fftpack5_prb_output.txt, the output from a run of the sample program.

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.

• cost_test.f, the sample calling program.
• cost_test.sh, commands to compile and run the sample program.
• cost_test_output.txt, the output from a run of the sample program.

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.

• sint_test.f, the sample calling program.
• sint_test.sh, commands to compile and run the sample program.
• sint_test_output.txt, the output from a run of the sample program.

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.