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<h1><a name="label-0" id="label-0">module NumRu::FFTW3</a></h1><!-- RDLabel: "module NumRu::FFTW3" -->
<p>Fast Fourier Transforms by using <a href="http://www.fftw.org">FFTW</a> Ver.3.</p>
<p>Takeshi Horinouchi</p>
<p>(C) Takeshi Horinouchi / GFD Dennou Club,
2003</p>
<p>NO WARRANTY</p>
<h2><a name="label-1" id="label-1">Features</a></h2><!-- RDLabel: "Features" -->
<ul>
<li>Uses <a href="http://www.ruby-lang.org/en/raa-list.rhtml?name=NArray">NArray</a>.</li>
<li>Multi-dimensional complex FFT. (Real data are coerced to complex).</li>
<li>Supports both double and single float transforms.</li>
<li>Not normalized as in FFTW</li>
</ul>
<h2><a name="label-2" id="label-2">Features yet to be introduced</a></h2><!-- RDLabel: "Features yet to be introduced" -->
<ul>
<li>Sine / cosine transforms</li>
<li>User choice of optimization levels (i.e., FFTW_MEASURE etc in
addition to FFTW_ESTIMATE).</li>
<li>Multi-threaded FFT3 support -- don't know whether it's really feasible.</li>
</ul>
<h2><a name="label-3" id="label-3">Installation</a></h2><!-- RDLabel: "Installation" -->
<ul>
<li>Install <a href="http://www.fftw.org">FFTW</a> Ver.3.
<ul>
<li>NOTE:
To activate the single-float transform, you have to install FFTW3 with
the single-float compilation, in addition to the default double-float
version. This can be done by configuring FFTW3 with
the --enable-float option, and install it again. The single-float
version will coexist with the double-float version.
If you do not install the single-float version, FFT is always done
with the double precision, which is not bad if you are not time- and
memory-conscious.</li>
</ul></li>
<li>Install <a href="http://www.ruby-lang.org/en/raa-list.rhtml?name=NArray">NArray</a>.</li>
<li><p>Then, install this library as follows (replace "version" with
the actual version number):</p>
<pre>% tar xvzf fftw3-version.tar.gz
% cd fftw3-version
% ruby extconf.rb
% make
% make site-install</pre>
<p>Or</p>
<pre>% make install</pre>
<p>(If you are using Ruby 1.8, make install is the same make site-install.)</p></li>
</ul>
<h2><a name="label-4" id="label-4">How to use</a></h2><!-- RDLabel: "How to use" -->
<p>See the following peice of code. (Install this library and copy and
paste the following to the interactive shell irb).</p>
<pre>require "numru/fftw3"
include NumRu
na = NArray.float(8,6) # float -> will be corced to complex
na[1,1]=1
# <example 1>
fc = FFTW3.fft(na, -1)/na.length # forward 2D FFT and normalization
nc = FFTW3.fft(fc, 1) # backward 2D FFT (complex) -->
nb = nc.real # should be equal to na except round errors
# <example 2>
fc = FFTW3.fft(na, -1, 0) / na.shape[0] # forward FFT with the first dim
# <example 3>
fc = FFTW3.fft(na, -1, 1) / na.shape[1] # forward FFT with the second dim</pre>
<h2><a name="label-5" id="label-5">API Reference</a></h2><!-- RDLabel: "API Reference" -->
<h3><a name="label-6" id="label-6">Module methods</a></h3><!-- RDLabel: "Module methods" -->
<dl>
<dt><a name="label-7" id="label-7"><code>fft(<var>narray</var>, <var>dir</var> [,<var>dim</var>,<var>dim</var>,...])</code></a></dt><!-- RDLabel: "fft" -->
<dd>
<p>Complex FFT.</p>
<p>The 3rd, 4th,... arguments are optional.</p>
<p>ARGUMENTS</p>
<ul>
<li>narray (NArray or NArray-compatible Array) : array to be
transformed. If real, coerced to complex before transformation.
If narray is single-precision and the single-precision
version of FFTW3 is installed (before installing this module),
this method does a single-precision transform.
Otherwise, a double-precision transform is used.</li>
<li>dir (-1 or 1) : forward transform if -1; backward transform if 1.</li>
<li>optional 3rd, 4th,... arguments (Integer) : Specifies dimensions
to apply FFT. For example, if 0, the first dimension is
transformed (1D FFT); If -1, the last dimension is used (1D FFT);
If 0,2,4, the first, third, and fifth dimensions
are transformed (3D FFT); If entirely omitted, ALL DIMENSIONS
ARE SUBJECT TO FFT, so 3D FFT is done with a 3D array.</li>
</ul>
<p>RETURN VALUE</p>
<ul>
<li>a complex NArray</li>
</ul>
<p>NOTE</p>
<ul>
<li>As in FFTW, return value is NOT normalized. Thus, a consecutive
forward and backward transform would multiply the size of
data used for transform. You can normalize, for example,
the forward transform FFTW.fft(narray, -1, 0, 1)
(FFT regarding the first (dim 0) & second (dim 1) dimensions) by
dividing with (narray.shape[0]*narray.shape[1]). Likewise,
the result of FFTW.fft(narray, -1) (FFT for all dimensions)
can be normalized by narray.length.</li>
</ul></dd>
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