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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
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Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
Chris@82 5
Chris@82 6 Copyright (C) 2003 Matteo Frigo.
Chris@82 7
Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@82 10 Permission is granted to make and distribute verbatim copies of this
Chris@82 11 manual provided the copyright notice and this permission notice are
Chris@82 12 preserved on all copies.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Complex DFTs</title>
Chris@82 26
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Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Complex-DFTs"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</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>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Complex-DFTs-1"></a>
Chris@82 78 <h4 class="subsection">4.3.1 Complex DFTs</h4>
Chris@82 79
Chris@82 80 <div class="example">
Chris@82 81 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
Chris@82 82 fftw_complex *in, fftw_complex *out,
Chris@82 83 int sign, unsigned flags);
Chris@82 84 fftw_plan fftw_plan_dft_2d(int n0, int n1,
Chris@82 85 fftw_complex *in, fftw_complex *out,
Chris@82 86 int sign, unsigned flags);
Chris@82 87 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
Chris@82 88 fftw_complex *in, fftw_complex *out,
Chris@82 89 int sign, unsigned flags);
Chris@82 90 fftw_plan fftw_plan_dft(int rank, const int *n,
Chris@82 91 fftw_complex *in, fftw_complex *out,
Chris@82 92 int sign, unsigned flags);
Chris@82 93 </pre></div>
Chris@82 94 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
Chris@82 95 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
Chris@82 96 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
Chris@82 97 <a name="index-fftw_005fplan_005fdft-1"></a>
Chris@82 98
Chris@82 99 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
Chris@82 100 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@82 101 </p>
Chris@82 102 <p>Once you have created a plan for a certain transform type and
Chris@82 103 parameters, then creating another plan of the same type and parameters,
Chris@82 104 but for different arrays, is fast and shares constant data with the
Chris@82 105 first plan (if it still exists).
Chris@82 106 </p>
Chris@82 107 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
Chris@82 108 standard FFTW distribution, the basic interface is guaranteed to return
Chris@82 109 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
Chris@82 110 using a customized FFTW configuration supporting a restricted set of
Chris@82 111 transforms.
Chris@82 112 </p>
Chris@82 113 <a name="Arguments"></a>
Chris@82 114 <h4 class="subsubheading">Arguments</h4>
Chris@82 115 <ul>
Chris@82 116 <li> <code>rank</code> is the rank of the transform (it should be the size of the
Chris@82 117 array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html#Complex-Multi_002dDimensional-DFTs">Complex Multi-Dimensional DFTs</a>, for the definition of &ldquo;rank&rdquo;.) The
Chris@82 118 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
Chris@82 119 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@82 120 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@82 121 copy of one number from input to output.
Chris@82 122
Chris@82 123 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
Chris@82 124 for each routine) specify the size of the transform dimensions. They
Chris@82 125 can be any positive integer.
Chris@82 126
Chris@82 127 <ul class="no-bullet">
Chris@82 128 <li>- <a name="index-row_002dmajor-1"></a>
Chris@82 129 Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@82 130 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@82 131 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@82 132 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@82 133 </li><li>- FFTW is best at handling sizes of the form
Chris@82 134 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@82 135 11<sup>e</sup> 13<sup>f</sup>,
Chris@82 136 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@82 137 are arbitrary. Other sizes are computed by means of a slow,
Chris@82 138 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
Chris@82 139 performance even for prime sizes). It is possible to customize FFTW
Chris@82 140 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
Chris@82 141 Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@82 142 </li></ul>
Chris@82 143
Chris@82 144 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@82 145 transform, which may be the same (yielding an in-place transform).
Chris@82 146 <a name="index-in_002dplace-2"></a>
Chris@82 147 These arrays are overwritten during planning, unless
Chris@82 148 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@82 149 initialized, but they must be allocated.)
Chris@82 150
Chris@82 151 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
Chris@82 152 array is overwritten. If <code>in != out</code>, the two arrays must
Chris@82 153 not overlap (but FFTW does not check for this condition).
Chris@82 154 </p>
Chris@82 155 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
Chris@82 156 <a name="index-FFTW_005fBACKWARD-2"></a>
Chris@82 157 <code>sign</code> is the sign of the exponent in the formula that defines the
Chris@82 158 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
Chris@82 159 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
Chris@82 160
Chris@82 161 </li><li> <a name="index-flags-2"></a>
Chris@82 162 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@82 163 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@82 164
Chris@82 165 </li></ul>
Chris@82 166
Chris@82 167 <p>FFTW computes an unnormalized transform: computing a forward followed by
Chris@82 168 a backward transform (or vice versa) will result in the original data
Chris@82 169 multiplied by the size of the transform (the product of the dimensions).
Chris@82 170 <a name="index-normalization-5"></a>
Chris@82 171 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
Chris@82 172 </p>
Chris@82 173 <hr>
Chris@82 174 <div class="header">
Chris@82 175 <p>
Chris@82 176 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</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>
Chris@82 177 </div>
Chris@82 178
Chris@82 179
Chris@82 180
Chris@82 181 </body>
Chris@82 182 </html>