WALSH
Walsh and Haar Transforms

WALSH is a FORTRAN90 library which implements versions of the Walsh and Haar transforms.

Note that the programs, as printed in the reference, had a few typographical errors. Several programs, in particular FHT and FRT, could not be made to perform as described in the text, and hence have been omitted.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

WALSH is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

FFTPACK5, a FORTRAN90 library which implements the Fast Fourier Transform by Paul Swarztrauber and Dick Valent;

HAAR, a FORTRAN90 library which computes the Haar transform of data.

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

SINE_TRANSFORM, a FORTRAN90 library which demonstrates some simple properties of the discrete sine transform.

WAVELET, a FORTRAN90 library which does some simple wavelet calculations;

Reference:

1. Ken Beauchamp,
   Walsh functions and their applications,
   Academic Press, 1975,
   ISBN: 0-12-084050-2,
   LC: QA404.5.B33.

Source Code:

• walsh.f90, the source code.

Examples and Tests:

• walsh_test.f90, a sample calling program.
• walsh_test.txt, the output file.

List of Routines:

• FFWT performs an in-place fast Walsh transform.
• FWT performs a fast Walsh transform.
• HAAR performs a Haar transform.
• HAARIN inverts a Haar transform.
• HNORM computes the normalization factors for a forward or inverse Haar transform.
• I4_LOG_2 returns the integer part of the logarithm base 2 of an I4.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• R8VEC_SHIFT_CIRCULAR performs a circular shift on an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• WALSH performs a fast Walsh transform.

You can go up one level to the FORTRAN90 source codes.