Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.8/doc/html/Complex-DFTs.html @ 167:bd3cc4d1df30

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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
parents
children
rev   line source
cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
cannam@167 2 <html>
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.
cannam@167 9
cannam@167 10 Permission is granted to make and distribute verbatim copies of this
cannam@167 11 manual provided the copyright notice and this permission notice are
cannam@167 12 preserved on all copies.
cannam@167 13
cannam@167 14 Permission is granted to copy and distribute modified versions of this
cannam@167 15 manual under the conditions for verbatim copying, provided that the
cannam@167 16 entire resulting derived work is distributed under the terms of a
cannam@167 17 permission notice identical to this one.
cannam@167 18
cannam@167 19 Permission is granted to copy and distribute translations of this manual
cannam@167 20 into another language, under the above conditions for modified versions,
cannam@167 21 except that this permission notice may be stated in a translation
cannam@167 22 approved by the Free Software Foundation. -->
cannam@167 23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: Complex DFTs</title>
cannam@167 26
cannam@167 27 <meta name="description" content="FFTW 3.3.8: Complex DFTs">
cannam@167 28 <meta name="keywords" content="FFTW 3.3.8: Complex DFTs">
cannam@167 29 <meta name="resource-type" content="document">
cannam@167 30 <meta name="distribution" content="global">
cannam@167 31 <meta name="Generator" content="makeinfo">
cannam@167 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
cannam@167 33 <link href="index.html#Top" rel="start" title="Top">
cannam@167 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
cannam@167 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@167 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
cannam@167 37 <link href="Planner-Flags.html#Planner-Flags" rel="next" title="Planner Flags">
cannam@167 38 <link href="Basic-Interface.html#Basic-Interface" rel="prev" title="Basic Interface">
cannam@167 39 <style type="text/css">
cannam@167 40 <!--
cannam@167 41 a.summary-letter {text-decoration: none}
cannam@167 42 blockquote.indentedblock {margin-right: 0em}
cannam@167 43 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
cannam@167 44 blockquote.smallquotation {font-size: smaller}
cannam@167 45 div.display {margin-left: 3.2em}
cannam@167 46 div.example {margin-left: 3.2em}
cannam@167 47 div.lisp {margin-left: 3.2em}
cannam@167 48 div.smalldisplay {margin-left: 3.2em}
cannam@167 49 div.smallexample {margin-left: 3.2em}
cannam@167 50 div.smalllisp {margin-left: 3.2em}
cannam@167 51 kbd {font-style: oblique}
cannam@167 52 pre.display {font-family: inherit}
cannam@167 53 pre.format {font-family: inherit}
cannam@167 54 pre.menu-comment {font-family: serif}
cannam@167 55 pre.menu-preformatted {font-family: serif}
cannam@167 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
cannam@167 57 pre.smallexample {font-size: smaller}
cannam@167 58 pre.smallformat {font-family: inherit; font-size: smaller}
cannam@167 59 pre.smalllisp {font-size: smaller}
cannam@167 60 span.nolinebreak {white-space: nowrap}
cannam@167 61 span.roman {font-family: initial; font-weight: normal}
cannam@167 62 span.sansserif {font-family: sans-serif; font-weight: normal}
cannam@167 63 ul.no-bullet {list-style: none}
cannam@167 64 -->
cannam@167 65 </style>
cannam@167 66
cannam@167 67
cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="Complex-DFTs"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 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>
cannam@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="Complex-DFTs-1"></a>
cannam@167 78 <h4 class="subsection">4.3.1 Complex DFTs</h4>
cannam@167 79
cannam@167 80 <div class="example">
cannam@167 81 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
cannam@167 82 fftw_complex *in, fftw_complex *out,
cannam@167 83 int sign, unsigned flags);
cannam@167 84 fftw_plan fftw_plan_dft_2d(int n0, int n1,
cannam@167 85 fftw_complex *in, fftw_complex *out,
cannam@167 86 int sign, unsigned flags);
cannam@167 87 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
cannam@167 88 fftw_complex *in, fftw_complex *out,
cannam@167 89 int sign, unsigned flags);
cannam@167 90 fftw_plan fftw_plan_dft(int rank, const int *n,
cannam@167 91 fftw_complex *in, fftw_complex *out,
cannam@167 92 int sign, unsigned flags);
cannam@167 93 </pre></div>
cannam@167 94 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
cannam@167 95 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
cannam@167 96 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
cannam@167 97 <a name="index-fftw_005fplan_005fdft-1"></a>
cannam@167 98
cannam@167 99 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
cannam@167 100 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@167 101 </p>
cannam@167 102 <p>Once you have created a plan for a certain transform type and
cannam@167 103 parameters, then creating another plan of the same type and parameters,
cannam@167 104 but for different arrays, is fast and shares constant data with the
cannam@167 105 first plan (if it still exists).
cannam@167 106 </p>
cannam@167 107 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
cannam@167 108 standard FFTW distribution, the basic interface is guaranteed to return
cannam@167 109 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
cannam@167 110 using a customized FFTW configuration supporting a restricted set of
cannam@167 111 transforms.
cannam@167 112 </p>
cannam@167 113 <a name="Arguments"></a>
cannam@167 114 <h4 class="subsubheading">Arguments</h4>
cannam@167 115 <ul>
cannam@167 116 <li> <code>rank</code> is the rank of the transform (it should be the size of the
cannam@167 117 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
cannam@167 118 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
cannam@167 119 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
cannam@167 120 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
cannam@167 121 copy of one number from input to output.
cannam@167 122
cannam@167 123 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
cannam@167 124 for each routine) specify the size of the transform dimensions. They
cannam@167 125 can be any positive integer.
cannam@167 126
cannam@167 127 <ul class="no-bullet">
cannam@167 128 <li>- <a name="index-row_002dmajor-1"></a>
cannam@167 129 Multi-dimensional arrays are stored in row-major order with dimensions:
cannam@167 130 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
cannam@167 131 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
cannam@167 132 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
cannam@167 133 </li><li>- FFTW is best at handling sizes of the form
cannam@167 134 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@167 135 11<sup>e</sup> 13<sup>f</sup>,
cannam@167 136 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
cannam@167 137 are arbitrary. Other sizes are computed by means of a slow,
cannam@167 138 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
cannam@167 139 performance even for prime sizes). It is possible to customize FFTW
cannam@167 140 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
cannam@167 141 Transforms whose sizes are powers of <em>2</em> are especially fast.
cannam@167 142 </li></ul>
cannam@167 143
cannam@167 144 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@167 145 transform, which may be the same (yielding an in-place transform).
cannam@167 146 <a name="index-in_002dplace-2"></a>
cannam@167 147 These arrays are overwritten during planning, unless
cannam@167 148 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@167 149 initialized, but they must be allocated.)
cannam@167 150
cannam@167 151 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
cannam@167 152 array is overwritten. If <code>in != out</code>, the two arrays must
cannam@167 153 not overlap (but FFTW does not check for this condition).
cannam@167 154 </p>
cannam@167 155 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
cannam@167 156 <a name="index-FFTW_005fBACKWARD-2"></a>
cannam@167 157 <code>sign</code> is the sign of the exponent in the formula that defines the
cannam@167 158 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
cannam@167 159 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
cannam@167 160
cannam@167 161 </li><li> <a name="index-flags-2"></a>
cannam@167 162 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
cannam@167 163 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@167 164
cannam@167 165 </li></ul>
cannam@167 166
cannam@167 167 <p>FFTW computes an unnormalized transform: computing a forward followed by
cannam@167 168 a backward transform (or vice versa) will result in the original data
cannam@167 169 multiplied by the size of the transform (the product of the dimensions).
cannam@167 170 <a name="index-normalization-5"></a>
cannam@167 171 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
cannam@167 172 </p>
cannam@167 173 <hr>
cannam@167 174 <div class="header">
cannam@167 175 <p>
cannam@167 176 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>
cannam@167 177 </div>
cannam@167 178
cannam@167 179
cannam@167 180
cannam@167 181 </body>
cannam@167 182 </html>