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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents 2cd0e3b3e1fd
children
rev   line source
Chris@42 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
Chris@42 5
Chris@42 6 Copyright (C) 2003 Matteo Frigo.
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Chris@42 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@42 10 Permission is granted to make and distribute verbatim copies of this
Chris@42 11 manual provided the copyright notice and this permission notice are
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Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: Complex DFTs</title>
Chris@42 26
Chris@42 27 <meta name="description" content="FFTW 3.3.5: Complex DFTs">
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Chris@42 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
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Chris@42 69 </head>
Chris@42 70
Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Complex-DFTs"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 75 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@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Complex-DFTs-1"></a>
Chris@42 79 <h4 class="subsection">4.3.1 Complex DFTs</h4>
Chris@42 80
Chris@42 81 <div class="example">
Chris@42 82 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
Chris@42 83 fftw_complex *in, fftw_complex *out,
Chris@42 84 int sign, unsigned flags);
Chris@42 85 fftw_plan fftw_plan_dft_2d(int n0, int n1,
Chris@42 86 fftw_complex *in, fftw_complex *out,
Chris@42 87 int sign, unsigned flags);
Chris@42 88 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
Chris@42 89 fftw_complex *in, fftw_complex *out,
Chris@42 90 int sign, unsigned flags);
Chris@42 91 fftw_plan fftw_plan_dft(int rank, const int *n,
Chris@42 92 fftw_complex *in, fftw_complex *out,
Chris@42 93 int sign, unsigned flags);
Chris@42 94 </pre></div>
Chris@42 95 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
Chris@42 96 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
Chris@42 97 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
Chris@42 98 <a name="index-fftw_005fplan_005fdft-1"></a>
Chris@42 99
Chris@42 100 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
Chris@42 101 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@42 102 </p>
Chris@42 103 <p>Once you have created a plan for a certain transform type and
Chris@42 104 parameters, then creating another plan of the same type and parameters,
Chris@42 105 but for different arrays, is fast and shares constant data with the
Chris@42 106 first plan (if it still exists).
Chris@42 107 </p>
Chris@42 108 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
Chris@42 109 standard FFTW distribution, the basic interface is guaranteed to return
Chris@42 110 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
Chris@42 111 using a customized FFTW configuration supporting a restricted set of
Chris@42 112 transforms.
Chris@42 113 </p>
Chris@42 114 <a name="Arguments"></a>
Chris@42 115 <h4 class="subsubheading">Arguments</h4>
Chris@42 116 <ul>
Chris@42 117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
Chris@42 118 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@42 119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
Chris@42 120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@42 121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@42 122 copy of one number from input to output.
Chris@42 123
Chris@42 124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
Chris@42 125 for each routine) specify the size of the transform dimensions. They
Chris@42 126 can be any positive integer.
Chris@42 127
Chris@42 128 <ul class="no-bullet">
Chris@42 129 <li>- <a name="index-row_002dmajor-1"></a>
Chris@42 130 Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@42 131 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@42 132 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@42 133 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@42 134 </li><li>- FFTW is best at handling sizes of the form
Chris@42 135 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@42 136 11<sup>e</sup> 13<sup>f</sup>,where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@42 137 are arbitrary. Other sizes are computed by means of a slow,
Chris@42 138 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) performance even for prime sizes). It is possible to customize FFTW
Chris@42 139 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
Chris@42 140 Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@42 141 </li></ul>
Chris@42 142
Chris@42 143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@42 144 transform, which may be the same (yielding an in-place transform).
Chris@42 145 <a name="index-in_002dplace-2"></a>
Chris@42 146 These arrays are overwritten during planning, unless
Chris@42 147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@42 148 initialized, but they must be allocated.)
Chris@42 149
Chris@42 150 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
Chris@42 151 array is overwritten. If <code>in != out</code>, the two arrays must
Chris@42 152 not overlap (but FFTW does not check for this condition).
Chris@42 153 </p>
Chris@42 154 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
Chris@42 155 <a name="index-FFTW_005fBACKWARD-2"></a>
Chris@42 156 <code>sign</code> is the sign of the exponent in the formula that defines the
Chris@42 157 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
Chris@42 158 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
Chris@42 159
Chris@42 160 </li><li> <a name="index-flags-2"></a>
Chris@42 161 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@42 162 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@42 163
Chris@42 164 </li></ul>
Chris@42 165
Chris@42 166 <p>FFTW computes an unnormalized transform: computing a forward followed by
Chris@42 167 a backward transform (or vice versa) will result in the original data
Chris@42 168 multiplied by the size of the transform (the product of the dimensions).
Chris@42 169 <a name="index-normalization-5"></a>
Chris@42 170 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
Chris@42 171 </p>
Chris@42 172 <hr>
Chris@42 173 <div class="header">
Chris@42 174 <p>
Chris@42 175 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@42 176 </div>
Chris@42 177
Chris@42 178
Chris@42 179
Chris@42 180 </body>
Chris@42 181 </html>