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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
5
6 Copyright (C) 2003 Matteo Frigo.
7
8 Copyright (C) 2003 Massachusetts Institute of Technology.
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11 manual provided the copyright notice and this permission notice are
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24 <head>
25 <title>FFTW 3.3.8: More DFTs of Real Data</title>
26
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
36 <link href="Tutorial.html#Tutorial" rel="up" title="Tutorial">
37 <link href="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT" rel="next" title="The Halfcomplex-format DFT">
38 <link href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" rel="prev" title="Multi-Dimensional DFTs of Real Data">
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71 <a name="More-DFTs-of-Real-Data"></a>
72 <div class="header">
73 <p>
74 Previous: <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" accesskey="p" rel="prev">Multi-Dimensional DFTs of Real Data</a>, Up: <a href="Tutorial.html#Tutorial" accesskey="u" rel="up">Tutorial</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
75 </div>
76 <hr>
77 <a name="More-DFTs-of-Real-Data-1"></a>
78 <h3 class="section">2.5 More DFTs of Real Data</h3>
79 <table class="menu" border="0" cellspacing="0">
80 <tr><td align="left" valign="top">&bull; <a href="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT" accesskey="1">The Halfcomplex-format DFT</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
81 </td></tr>
82 <tr><td align="left" valign="top">&bull; <a href="Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029.html#Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029" accesskey="2">Real even/odd DFTs (cosine/sine transforms)</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
83 </td></tr>
84 <tr><td align="left" valign="top">&bull; <a href="The-Discrete-Hartley-Transform.html#The-Discrete-Hartley-Transform" accesskey="3">The Discrete Hartley Transform</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
85 </td></tr>
86 </table>
87
88 <p>FFTW supports several other transform types via a unified <em>r2r</em>
89 (real-to-real) interface,
90 <a name="index-r2r"></a>
91 so called because it takes a real (<code>double</code>) array and outputs a
92 real array of the same size. These r2r transforms currently fall into
93 three categories: DFTs of real input and complex-Hermitian output in
94 halfcomplex format, DFTs of real input with even/odd symmetry
95 (a.k.a. discrete cosine/sine transforms, DCTs/DSTs), and discrete
96 Hartley transforms (DHTs), all described in more detail by the
97 following sections.
98 </p>
99 <p>The r2r transforms follow the by now familiar interface of creating an
100 <code>fftw_plan</code>, executing it with <code>fftw_execute(plan)</code>, and
101 destroying it with <code>fftw_destroy_plan(plan)</code>. Furthermore, all
102 r2r transforms share the same planner interface:
103 </p>
104 <div class="example">
105 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
106 fftw_r2r_kind kind, unsigned flags);
107 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
108 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
109 unsigned flags);
110 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
111 double *in, double *out,
112 fftw_r2r_kind kind0,
113 fftw_r2r_kind kind1,
114 fftw_r2r_kind kind2,
115 unsigned flags);
116 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
117 const fftw_r2r_kind *kind, unsigned flags);
118 </pre></div>
119 <a name="index-fftw_005fplan_005fr2r_005f1d"></a>
120 <a name="index-fftw_005fplan_005fr2r_005f2d"></a>
121 <a name="index-fftw_005fplan_005fr2r_005f3d"></a>
122 <a name="index-fftw_005fplan_005fr2r"></a>
123
124 <p>Just as for the complex DFT, these plan 1d/2d/3d/multi-dimensional
125 transforms for contiguous arrays in row-major order, transforming (real)
126 input to output of the same size, where <code>n</code> specifies the
127 <em>physical</em> dimensions of the arrays. All positive <code>n</code> are
128 supported (with the exception of <code>n=1</code> for the <code>FFTW_REDFT00</code>
129 kind, noted in the real-even subsection below); products of small
130 factors are most efficient (factorizing <code>n-1</code> and <code>n+1</code> for
131 <code>FFTW_REDFT00</code> and <code>FFTW_RODFT00</code> kinds, described below), but
132 an <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
133 algorithm is used even for prime sizes.
134 </p>
135 <p>Each dimension has a <em>kind</em> parameter, of type
136 <code>fftw_r2r_kind</code>, specifying the kind of r2r transform to be used
137 for that dimension.
138 <a name="index-kind-_0028r2r_0029"></a>
139 <a name="index-fftw_005fr2r_005fkind"></a>
140 (In the case of <code>fftw_plan_r2r</code>, this is an array <code>kind[rank]</code>
141 where <code>kind[i]</code> is the transform kind for the dimension
142 <code>n[i]</code>.) The kind can be one of a set of predefined constants,
143 defined in the following subsections.
144 </p>
145 <p>In other words, FFTW computes the separable product of the specified
146 r2r transforms over each dimension, which can be used e.g. for partial
147 differential equations with mixed boundary conditions. (For some r2r
148 kinds, notably the halfcomplex DFT and the DHT, such a separable
149 product is somewhat problematic in more than one dimension, however,
150 as is described below.)
151 </p>
152 <p>In the current version of FFTW, all r2r transforms except for the
153 halfcomplex type are computed via pre- or post-processing of
154 halfcomplex transforms, and they are therefore not as fast as they
155 could be. Since most other general DCT/DST codes employ a similar
156 algorithm, however, FFTW&rsquo;s implementation should provide at least
157 competitive performance.
158 </p>
159 <hr>
160 <div class="header">
161 <p>
162 Previous: <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" accesskey="p" rel="prev">Multi-Dimensional DFTs of Real Data</a>, Up: <a href="Tutorial.html#Tutorial" accesskey="u" rel="up">Tutorial</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
163 </div>
164
165
166
167 </body>
168 </html>