Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.8/doc/html/Complex-Multi_002dDimensional-DFTs.html @ 82:d0c2a83c1364

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
date Tue, 19 Nov 2019 14:52:55 +0000
parents
children
rev   line source
Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
Chris@82 2 <html>
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.
Chris@82 9
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.
Chris@82 13
Chris@82 14 Permission is granted to copy and distribute modified versions of this
Chris@82 15 manual under the conditions for verbatim copying, provided that the
Chris@82 16 entire resulting derived work is distributed under the terms of a
Chris@82 17 permission notice identical to this one.
Chris@82 18
Chris@82 19 Permission is granted to copy and distribute translations of this manual
Chris@82 20 into another language, under the above conditions for modified versions,
Chris@82 21 except that this permission notice may be stated in a translation
Chris@82 22 approved by the Free Software Foundation. -->
Chris@82 23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Complex Multi-Dimensional DFTs</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Complex Multi-Dimensional DFTs">
Chris@82 28 <meta name="keywords" content="FFTW 3.3.8: Complex Multi-Dimensional DFTs">
Chris@82 29 <meta name="resource-type" content="document">
Chris@82 30 <meta name="distribution" content="global">
Chris@82 31 <meta name="Generator" content="makeinfo">
Chris@82 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
Chris@82 33 <link href="index.html#Top" rel="start" title="Top">
Chris@82 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="Tutorial.html#Tutorial" rel="up" title="Tutorial">
Chris@82 37 <link href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" rel="next" title="One-Dimensional DFTs of Real Data">
Chris@82 38 <link href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" rel="prev" title="Complex One-Dimensional DFTs">
Chris@82 39 <style type="text/css">
Chris@82 40 <!--
Chris@82 41 a.summary-letter {text-decoration: none}
Chris@82 42 blockquote.indentedblock {margin-right: 0em}
Chris@82 43 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
Chris@82 44 blockquote.smallquotation {font-size: smaller}
Chris@82 45 div.display {margin-left: 3.2em}
Chris@82 46 div.example {margin-left: 3.2em}
Chris@82 47 div.lisp {margin-left: 3.2em}
Chris@82 48 div.smalldisplay {margin-left: 3.2em}
Chris@82 49 div.smallexample {margin-left: 3.2em}
Chris@82 50 div.smalllisp {margin-left: 3.2em}
Chris@82 51 kbd {font-style: oblique}
Chris@82 52 pre.display {font-family: inherit}
Chris@82 53 pre.format {font-family: inherit}
Chris@82 54 pre.menu-comment {font-family: serif}
Chris@82 55 pre.menu-preformatted {font-family: serif}
Chris@82 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
Chris@82 57 pre.smallexample {font-size: smaller}
Chris@82 58 pre.smallformat {font-family: inherit; font-size: smaller}
Chris@82 59 pre.smalllisp {font-size: smaller}
Chris@82 60 span.nolinebreak {white-space: nowrap}
Chris@82 61 span.roman {font-family: initial; font-weight: normal}
Chris@82 62 span.sansserif {font-family: sans-serif; font-weight: normal}
Chris@82 63 ul.no-bullet {list-style: none}
Chris@82 64 -->
Chris@82 65 </style>
Chris@82 66
Chris@82 67
Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Complex-Multi_002dDimensional-DFTs"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" accesskey="p" rel="prev">Complex One-Dimensional DFTs</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>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Complex-Multi_002dDimensional-DFTs-1"></a>
Chris@82 78 <h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>
Chris@82 79
Chris@82 80 <p>Multi-dimensional transforms work much the same way as one-dimensional
Chris@82 81 transforms: you allocate arrays of <code>fftw_complex</code> (preferably
Chris@82 82 using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
Chris@82 83 many times as you want with <code>fftw_execute(plan)</code>, and clean up
Chris@82 84 with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>).
Chris@82 85 </p>
Chris@82 86 <p>FFTW provides two routines for creating plans for 2d and 3d transforms,
Chris@82 87 and one routine for creating plans of arbitrary dimensionality.
Chris@82 88 The 2d and 3d routines have the following signature:
Chris@82 89 </p><div class="example">
Chris@82 90 <pre class="example">fftw_plan fftw_plan_dft_2d(int n0, int n1,
Chris@82 91 fftw_complex *in, fftw_complex *out,
Chris@82 92 int sign, unsigned flags);
Chris@82 93 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
Chris@82 94 fftw_complex *in, fftw_complex *out,
Chris@82 95 int sign, unsigned flags);
Chris@82 96 </pre></div>
Chris@82 97 <a name="index-fftw_005fplan_005fdft_005f2d"></a>
Chris@82 98 <a name="index-fftw_005fplan_005fdft_005f3d"></a>
Chris@82 99
Chris@82 100 <p>These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
Chris@82 101 (2d) transforms and <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
Chris@82 102 respectively. All of these transforms operate on contiguous arrays in
Chris@82 103 the C-standard <em>row-major</em> order, so that the last dimension has the
Chris@82 104 fastest-varying index in the array. This layout is described further in
Chris@82 105 <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@82 106 </p>
Chris@82 107 <p>FFTW can also compute transforms of higher dimensionality. In order to
Chris@82 108 avoid confusion between the various meanings of the the word
Chris@82 109 &ldquo;dimension&rdquo;, we use the term <em>rank</em>
Chris@82 110 <a name="index-rank"></a>
Chris@82 111 to denote the number of independent indices in an array.<a name="DOCF2" href="#FOOT2"><sup>2</sup></a> For
Chris@82 112 example, we say that a 2d transform has rank&nbsp;2, a 3d transform has
Chris@82 113 rank&nbsp;3, and so on. You can plan transforms of arbitrary rank by
Chris@82 114 means of the following function:
Chris@82 115 </p>
Chris@82 116 <div class="example">
Chris@82 117 <pre class="example">fftw_plan fftw_plan_dft(int rank, const int *n,
Chris@82 118 fftw_complex *in, fftw_complex *out,
Chris@82 119 int sign, unsigned flags);
Chris@82 120 </pre></div>
Chris@82 121 <a name="index-fftw_005fplan_005fdft"></a>
Chris@82 122
Chris@82 123 <p>Here, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting an
Chris@82 124 <code>n[0]</code> by <code>n[1]</code> by &hellip; by <code>n[rank-1]</code> transform.
Chris@82 125 Thus, for example, the call
Chris@82 126 </p><div class="example">
Chris@82 127 <pre class="example">fftw_plan_dft_2d(n0, n1, in, out, sign, flags);
Chris@82 128 </pre></div>
Chris@82 129 <p>is equivalent to the following code fragment:
Chris@82 130 </p><div class="example">
Chris@82 131 <pre class="example">int n[2];
Chris@82 132 n[0] = n0;
Chris@82 133 n[1] = n1;
Chris@82 134 fftw_plan_dft(2, n, in, out, sign, flags);
Chris@82 135 </pre></div>
Chris@82 136 <p><code>fftw_plan_dft</code> is not restricted to 2d and 3d transforms,
Chris@82 137 however, but it can plan transforms of arbitrary rank.
Chris@82 138 </p>
Chris@82 139 <p>You may have noticed that all the planner routines described so far
Chris@82 140 have overlapping functionality. For example, you can plan a 1d or 2d
Chris@82 141 transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
Chris@82 142 or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
Chris@82 143 and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This
Chris@82 144 pattern continues, and FFTW&rsquo;s planning routines in general form a
Chris@82 145 &ldquo;partial order,&rdquo; sequences of
Chris@82 146 <a name="index-partial-order"></a>
Chris@82 147 interfaces with strictly increasing generality but correspondingly
Chris@82 148 greater complexity.
Chris@82 149 </p>
Chris@82 150 <p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
Chris@82 151 describe in this tutorial, but there are also the advanced and guru interfaces,
Chris@82 152 <a name="index-advanced-interface-1"></a>
Chris@82 153 <a name="index-guru-interface-1"></a>
Chris@82 154 which allow one to efficiently combine multiple/strided transforms
Chris@82 155 into a single FFTW plan, transform a subset of a larger
Chris@82 156 multi-dimensional array, and/or to handle more general complex-number
Chris@82 157 formats. For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>.
Chris@82 158 </p>
Chris@82 159 <div class="footnote">
Chris@82 160 <hr>
Chris@82 161 <h4 class="footnotes-heading">Footnotes</h4>
Chris@82 162
Chris@82 163 <h3><a name="FOOT2" href="#DOCF2">(2)</a></h3>
Chris@82 164 <p>The
Chris@82 165 term &ldquo;rank&rdquo; is commonly used in the APL, FORTRAN, and Common Lisp
Chris@82 166 traditions, although it is not so common in the C&nbsp;world.</p>
Chris@82 167 </div>
Chris@82 168 <hr>
Chris@82 169 <div class="header">
Chris@82 170 <p>
Chris@82 171 Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" accesskey="p" rel="prev">Complex One-Dimensional DFTs</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>
Chris@82 172 </div>
Chris@82 173
Chris@82 174
Chris@82 175
Chris@82 176 </body>
Chris@82 177 </html>