Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/Complex-Multi_002dDimensional-DFTs.html @ 167:bd3cc4d1df30
Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Tue, 19 Nov 2019 14:52:55 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.8/doc/html/Complex-Multi_002dDimensional-DFTs.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,177 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<html> +<!-- This manual is for FFTW +(version 3.3.8, 24 May 2018). + +Copyright (C) 2003 Matteo Frigo. + +Copyright (C) 2003 Massachusetts Institute of Technology. + +Permission is granted to make and distribute verbatim copies of this +manual provided the copyright notice and this permission notice are +preserved on all copies. + +Permission is granted to copy and distribute modified versions of this +manual under the conditions for verbatim copying, provided that the +entire resulting derived work is distributed under the terms of a +permission notice identical to this one. + +Permission is granted to copy and distribute translations of this manual +into another language, under the above conditions for modified versions, +except that this permission notice may be stated in a translation +approved by the Free Software Foundation. --> +<!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> +<head> +<title>FFTW 3.3.8: Complex Multi-Dimensional DFTs</title> + +<meta name="description" content="FFTW 3.3.8: Complex Multi-Dimensional DFTs"> +<meta name="keywords" content="FFTW 3.3.8: Complex Multi-Dimensional DFTs"> +<meta name="resource-type" content="document"> +<meta name="distribution" content="global"> +<meta name="Generator" content="makeinfo"> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> +<link href="index.html#Top" rel="start" title="Top"> +<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> +<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> +<link href="Tutorial.html#Tutorial" rel="up" title="Tutorial"> +<link href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" rel="next" title="One-Dimensional DFTs of Real Data"> +<link href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" rel="prev" title="Complex One-Dimensional DFTs"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.indentedblock {margin-right: 0em} +blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smalllisp {margin-left: 3.2em} +kbd {font-style: oblique} +pre.display {font-family: inherit} +pre.format {font-family: inherit} +pre.menu-comment {font-family: serif} +pre.menu-preformatted {font-family: serif} +pre.smalldisplay {font-family: inherit; font-size: smaller} +pre.smallexample {font-size: smaller} +pre.smallformat {font-family: inherit; font-size: smaller} +pre.smalllisp {font-size: smaller} +span.nolinebreak {white-space: nowrap} +span.roman {font-family: initial; font-weight: normal} +span.sansserif {font-family: sans-serif; font-weight: normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en"> +<a name="Complex-Multi_002dDimensional-DFTs"></a> +<div class="header"> +<p> +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> [<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> +</div> +<hr> +<a name="Complex-Multi_002dDimensional-DFTs-1"></a> +<h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3> + +<p>Multi-dimensional transforms work much the same way as one-dimensional +transforms: you allocate arrays of <code>fftw_complex</code> (preferably +using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as +many times as you want with <code>fftw_execute(plan)</code>, and clean up +with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>). +</p> +<p>FFTW provides two routines for creating plans for 2d and 3d transforms, +and one routine for creating plans of arbitrary dimensionality. +The 2d and 3d routines have the following signature: +</p><div class="example"> +<pre class="example">fftw_plan fftw_plan_dft_2d(int n0, int n1, + fftw_complex *in, fftw_complex *out, + int sign, unsigned flags); +fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2, + fftw_complex *in, fftw_complex *out, + int sign, unsigned flags); +</pre></div> +<a name="index-fftw_005fplan_005fdft_005f2d"></a> +<a name="index-fftw_005fplan_005fdft_005f3d"></a> + +<p>These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional +(2d) transforms and <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms, +respectively. All of these transforms operate on contiguous arrays in +the C-standard <em>row-major</em> order, so that the last dimension has the +fastest-varying index in the array. This layout is described further in +<a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. +</p> +<p>FFTW can also compute transforms of higher dimensionality. In order to +avoid confusion between the various meanings of the the word +“dimension”, we use the term <em>rank</em> +<a name="index-rank"></a> +to denote the number of independent indices in an array.<a name="DOCF2" href="#FOOT2"><sup>2</sup></a> For +example, we say that a 2d transform has rank 2, a 3d transform has +rank 3, and so on. You can plan transforms of arbitrary rank by +means of the following function: +</p> +<div class="example"> +<pre class="example">fftw_plan fftw_plan_dft(int rank, const int *n, + fftw_complex *in, fftw_complex *out, + int sign, unsigned flags); +</pre></div> +<a name="index-fftw_005fplan_005fdft"></a> + +<p>Here, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting an +<code>n[0]</code> by <code>n[1]</code> by … by <code>n[rank-1]</code> transform. +Thus, for example, the call +</p><div class="example"> +<pre class="example">fftw_plan_dft_2d(n0, n1, in, out, sign, flags); +</pre></div> +<p>is equivalent to the following code fragment: +</p><div class="example"> +<pre class="example">int n[2]; +n[0] = n0; +n[1] = n1; +fftw_plan_dft(2, n, in, out, sign, flags); +</pre></div> +<p><code>fftw_plan_dft</code> is not restricted to 2d and 3d transforms, +however, but it can plan transforms of arbitrary rank. +</p> +<p>You may have noticed that all the planner routines described so far +have overlapping functionality. For example, you can plan a 1d or 2d +transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code> +or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code> +and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This +pattern continues, and FFTW’s planning routines in general form a +“partial order,” sequences of +<a name="index-partial-order"></a> +interfaces with strictly increasing generality but correspondingly +greater complexity. +</p> +<p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we +describe in this tutorial, but there are also the advanced and guru interfaces, +<a name="index-advanced-interface-1"></a> +<a name="index-guru-interface-1"></a> +which allow one to efficiently combine multiple/strided transforms +into a single FFTW plan, transform a subset of a larger +multi-dimensional array, and/or to handle more general complex-number +formats. For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>. +</p> +<div class="footnote"> +<hr> +<h4 class="footnotes-heading">Footnotes</h4> + +<h3><a name="FOOT2" href="#DOCF2">(2)</a></h3> +<p>The +term “rank” is commonly used in the APL, FORTRAN, and Common Lisp +traditions, although it is not so common in the C world.</p> +</div> +<hr> +<div class="header"> +<p> +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> [<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> +</div> + + + +</body> +</html>