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<html>
<head>
<title>
SFTPACK - "Slow" Fourier Transforms
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SFTPACK <br> "Slow" Fourier Transforms
</h1>
<hr>
<p>
<b>SFTPACK</b>
is a C++ library which
carries out some "slow" Fourier transforms, that is, Fourier
transforms without the techniques that allow for very fast
computation.
</p>
<p>
The intention is to make the underlying calculation clear,
and to provide a simple check and comparison of timing and usage
for the fast calculations.
</p>
<p>
The fast Fourier transform is a highly efficient procedure. However,
the coding of the algorithm, and the conventions for indexing, ordering,
and normalization, can make it quite difficult to understand what is
being done, or even to see how to use the software correctly. This
means that a coding error or mistaken use can be undetected.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SFTPACK</b> is available in
<a href = "../../c_src/sftpack/sftpack.html">a C version</a> and
<a href = "../../cpp_src/sftpack/sftpack.html">a C++ version</a> and
<a href = "../../f77_src/sftpack/sftpack.html">a FORTRAN77 version</a> and
<a href = "../../f_src/sftpack/sftpack.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sftpack/sftpack.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/c4lib/c4lib.html">
C4LIB</a>,
a C++ library which
implements certain elementary functions for single precision complex variables;
</p>
<p>
<a href = "../../cpp_src/c8lib/c8lib.html">
C8LIB</a>,
a C++ library which
implements certain elementary functions for double precision complex variables;
</p>
<p>
<a href = "../../cpp_src/complex_numbers/complex_numbers.html">
COMPLEX_NUMBERS</a>,
a C++ program which
demonstrates some simple features involved in the use of
complex numbers in C programming.
</p>
<p>
<a href = "../../cpp_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a C++ program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../f_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for implementing an OpenMP parallel version.
</p>
<p>
<a href = "../../f_src/fftpack5/fftpack5.html">
FFTPACK5</a>,
a FORTRAN90 library which
implements the Fast Fourier Transform
by Paul Swarztrauber and Dick Valent;
</p>
<p>
<a href = "../../cpp_src/haar/haar.html">
HAAR</a>,
a C++ library which
computes the Haar transform of data.
</p>
<p>
<a href = "../../cpp_src/sine_transform/sine_transform.html">
SINE_TRANSFORM</a>,
a C++ library which
demonstrates some simple properties of the discrete sine transform.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
William Briggs, Van Emden Henson,<br>
The DFT: An Owner's Manual for the Discrete Fourier Transform,<br>
SIAM, 1995,<br>
ISBN13: 978-0-898713-42-8,<br>
LC: QA403.5.B75.
</li>
<li>
Ralph Hartley,<br>
A More Symmetrical Fourier Analysis Applied to Transmission
Problems,<br>
Proceedings of the Institute of Radio Engineers,<br>
Volume 30, 1942, pages 144-150.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sftpack.cpp">sftpack.cpp</a>, the source code;
</li>
<li>
<a href = "sftpack.hpp">sftpack.hpp</a>, the include file;
</li>
<li>
<a href = "sftpack.sh">sftpack.sh</a>, commands to compile the code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sftpack_prb.cpp">sftpack_prb.cpp</a>, the calling program;
</li>
<li>
<a href = "sftpack_prb.sh">sftpack_prb.sh</a>, commands to
compile, link and run the sample problem;
</li>
<li>
<a href = "sftpack_prb_output.txt">sftpack_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4MAT_PRINT_SOME</b> prints some of a C4MAT.
</li>
<li>
<b>C4MAT_SFTB</b> computes a "slow" backward Fourier transform of a C4MAT.
</li>
<li>
<b>C4MAT_SFTF</b> computes a "slow" forward Fourier transform of a C4MAT.
</li>
<li>
<b>C4MAT_UNIFORM_01_NEW</b> returns a new unit pseudorandom C4MAT.
</li>
<li>
<b>C4VEC_PRINT_PART</b> prints "part" of a C4VEC.
</li>
<li>
<b>C4VEC_SFTB</b> computes a "slow" backward Fourier transform of a C4VEC.
</li>
<li>
<b>C4VEC_SFTF</b> computes a "slow" forward Fourier transform of a C4VEC.
</li>
<li>
<b>C4VEC_UNIFORM_01_NEW</b> returns a unit pseudorandom C4VEC.
</li>
<li>
<b>C8MAT_PRINT_SOME</b> prints some of a C8MAT.
</li>
<li>
<b>C8MAT_SFTB</b> computes a "slow" backward Fourier transform of a C8MAT.
</li>
<li>
<b>C8MAT_SFTF</b> computes a "slow" forward Fourier transform of a C8MAT.
</li>
<li>
<b>C8MAT_UNIFORM_01_NEW</b> returns a new unit pseudorandom C8MAT.
</li>
<li>
<b>C8VEC_PRINT_PART</b> prints "part" of a C8VEC.
</li>
<li>
<b>C8VEC_SFTB</b> computes a "slow" backward Fourier transform of a C8VEC.
</li>
<li>
<b>C8VEC_SFTF</b> computes a "slow" forward Fourier transform of a C8VEC.
</li>
<li>
<b>C8VEC_UNIFORM_01_NEW</b> returns a unit pseudorandom C8VEC.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>R4VEC_PRINT_PART</b> prints "part" of an R4VEC.
</li>
<li>
<b>R4VEC_SCT</b> computes a "slow" cosine transform of an R4VEC.
</li>
<li>
<b>R4VEC_SFTB</b> computes a "slow" backward Fourier transform of an R4VEC.
</li>
<li>
<b>R4VEC_SFTF</b> computes a "slow" forward Fourier transform of an R4VEC.
</li>
<li>
<b>R4VEC_SHT</b> computes a "slow" Hartley transform of an R4VEC.
</li>
<li>
<b>R4VEC_SQCTB</b> computes a "slow" quarter cosine transform backward of an R4VEC.
</li>
<li>
<b>R4VEC_SQCTF</b> computes a "slow" quarter cosine transform forward of an R4VEC.
</li>
<li>
<b>R4VEC_SQSTB</b> computes a "slow" quarter sine transform backward of an R4VEC.
</li>
<li>
<b>R4VEC_SQSTF</b> computes a "slow" quarter sine transform forward of an R4VEC.
</li>
<li>
<b>R4VEC_SST</b> computes a "slow" sine transform of an R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_NEW</b> returns a scaled pseudorandom R4VEC.
</li>
<li>
<b>R8VEC_PRINT_PART</b> prints "part" of an R8VEC.
</li>
<li>
<b>R8VEC_SCT</b> computes a "slow" cosine transform of an R8VEC.
</li>
<li>
<b>R8VEC_SFTB</b> computes a "slow" backward Fourier transform of an R8VEC.
</li>
<li>
<b>R8VEC_SFTF</b> computes a "slow" forward Fourier transform of an R8VEC.
</li>
<li>
<b>R8VEC_SHT</b> computes a "slow" Hartley transform of an R8VEC.
</li>
<li>
<b>R8VEC_SQCTB</b> computes a "slow" quarter cosine transform backward of an R8VEC.
</li>
<li>
<b>R8VEC_SQCTF</b> computes a "slow" quarter cosine transform forward of an R8VEC.
</li>
<li>
<b>R8VEC_SQSTB</b> computes a "slow" quarter sine transform backward of an R8VEC.
</li>
<li>
<b>R8VEC_SQSTF</b> computes a "slow" quarter sine transform forward of an R8VEC.
</li>
<li>
<b>R8VEC_SST</b> computes a "slow" sine transform of an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_NEW</b> returns a scaled pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 22 June 2010.
</i>
<!-- John Burkardt -->
</body>
</html>