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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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cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
cannam@167 5
cannam@167 6 Copyright (C) 2003 Matteo Frigo.
cannam@167 7
cannam@167 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@167 10 Permission is granted to make and distribute verbatim copies of this
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cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: More DFTs of Real Data</title>
cannam@167 26
cannam@167 27 <meta name="description" content="FFTW 3.3.8: More DFTs of Real Data">
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cannam@167 37 <link href="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT" rel="next" title="The Halfcomplex-format DFT">
cannam@167 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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cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="More-DFTs-of-Real-Data"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 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>
cannam@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="More-DFTs-of-Real-Data-1"></a>
cannam@167 78 <h3 class="section">2.5 More DFTs of Real Data</h3>
cannam@167 79 <table class="menu" border="0" cellspacing="0">
cannam@167 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">
cannam@167 81 </td></tr>
cannam@167 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">
cannam@167 83 </td></tr>
cannam@167 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">
cannam@167 85 </td></tr>
cannam@167 86 </table>
cannam@167 87
cannam@167 88 <p>FFTW supports several other transform types via a unified <em>r2r</em>
cannam@167 89 (real-to-real) interface,
cannam@167 90 <a name="index-r2r"></a>
cannam@167 91 so called because it takes a real (<code>double</code>) array and outputs a
cannam@167 92 real array of the same size. These r2r transforms currently fall into
cannam@167 93 three categories: DFTs of real input and complex-Hermitian output in
cannam@167 94 halfcomplex format, DFTs of real input with even/odd symmetry
cannam@167 95 (a.k.a. discrete cosine/sine transforms, DCTs/DSTs), and discrete
cannam@167 96 Hartley transforms (DHTs), all described in more detail by the
cannam@167 97 following sections.
cannam@167 98 </p>
cannam@167 99 <p>The r2r transforms follow the by now familiar interface of creating an
cannam@167 100 <code>fftw_plan</code>, executing it with <code>fftw_execute(plan)</code>, and
cannam@167 101 destroying it with <code>fftw_destroy_plan(plan)</code>. Furthermore, all
cannam@167 102 r2r transforms share the same planner interface:
cannam@167 103 </p>
cannam@167 104 <div class="example">
cannam@167 105 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
cannam@167 106 fftw_r2r_kind kind, unsigned flags);
cannam@167 107 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
cannam@167 108 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
cannam@167 109 unsigned flags);
cannam@167 110 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
cannam@167 111 double *in, double *out,
cannam@167 112 fftw_r2r_kind kind0,
cannam@167 113 fftw_r2r_kind kind1,
cannam@167 114 fftw_r2r_kind kind2,
cannam@167 115 unsigned flags);
cannam@167 116 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
cannam@167 117 const fftw_r2r_kind *kind, unsigned flags);
cannam@167 118 </pre></div>
cannam@167 119 <a name="index-fftw_005fplan_005fr2r_005f1d"></a>
cannam@167 120 <a name="index-fftw_005fplan_005fr2r_005f2d"></a>
cannam@167 121 <a name="index-fftw_005fplan_005fr2r_005f3d"></a>
cannam@167 122 <a name="index-fftw_005fplan_005fr2r"></a>
cannam@167 123
cannam@167 124 <p>Just as for the complex DFT, these plan 1d/2d/3d/multi-dimensional
cannam@167 125 transforms for contiguous arrays in row-major order, transforming (real)
cannam@167 126 input to output of the same size, where <code>n</code> specifies the
cannam@167 127 <em>physical</em> dimensions of the arrays. All positive <code>n</code> are
cannam@167 128 supported (with the exception of <code>n=1</code> for the <code>FFTW_REDFT00</code>
cannam@167 129 kind, noted in the real-even subsection below); products of small
cannam@167 130 factors are most efficient (factorizing <code>n-1</code> and <code>n+1</code> for
cannam@167 131 <code>FFTW_REDFT00</code> and <code>FFTW_RODFT00</code> kinds, described below), but
cannam@167 132 an <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
cannam@167 133 algorithm is used even for prime sizes.
cannam@167 134 </p>
cannam@167 135 <p>Each dimension has a <em>kind</em> parameter, of type
cannam@167 136 <code>fftw_r2r_kind</code>, specifying the kind of r2r transform to be used
cannam@167 137 for that dimension.
cannam@167 138 <a name="index-kind-_0028r2r_0029"></a>
cannam@167 139 <a name="index-fftw_005fr2r_005fkind"></a>
cannam@167 140 (In the case of <code>fftw_plan_r2r</code>, this is an array <code>kind[rank]</code>
cannam@167 141 where <code>kind[i]</code> is the transform kind for the dimension
cannam@167 142 <code>n[i]</code>.) The kind can be one of a set of predefined constants,
cannam@167 143 defined in the following subsections.
cannam@167 144 </p>
cannam@167 145 <p>In other words, FFTW computes the separable product of the specified
cannam@167 146 r2r transforms over each dimension, which can be used e.g. for partial
cannam@167 147 differential equations with mixed boundary conditions. (For some r2r
cannam@167 148 kinds, notably the halfcomplex DFT and the DHT, such a separable
cannam@167 149 product is somewhat problematic in more than one dimension, however,
cannam@167 150 as is described below.)
cannam@167 151 </p>
cannam@167 152 <p>In the current version of FFTW, all r2r transforms except for the
cannam@167 153 halfcomplex type are computed via pre- or post-processing of
cannam@167 154 halfcomplex transforms, and they are therefore not as fast as they
cannam@167 155 could be. Since most other general DCT/DST codes employ a similar
cannam@167 156 algorithm, however, FFTW&rsquo;s implementation should provide at least
cannam@167 157 competitive performance.
cannam@167 158 </p>
cannam@167 159 <hr>
cannam@167 160 <div class="header">
cannam@167 161 <p>
cannam@167 162 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>
cannam@167 163 </div>
cannam@167 164
cannam@167 165
cannam@167 166
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cannam@167 168 </html>