mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-16 09:45:06 +00:00
166 lines
7.9 KiB
HTML
166 lines
7.9 KiB
HTML
<!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 3.3.10, 10 December 2020).
|
|
|
|
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 6.7, http://www.gnu.org/software/texinfo/ -->
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
|
<title>Complex Multi-Dimensional DFTs (FFTW 3.3.10)</title>
|
|
|
|
<meta name="description" content="Complex Multi-Dimensional DFTs (FFTW 3.3.10)">
|
|
<meta name="keywords" content="Complex Multi-Dimensional DFTs (FFTW 3.3.10)">
|
|
<meta name="resource-type" content="document">
|
|
<meta name="distribution" content="global">
|
|
<meta name="Generator" content="makeinfo">
|
|
<link href="index.html" rel="start" title="Top">
|
|
<link href="Concept-Index.html" rel="index" title="Concept Index">
|
|
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
|
|
<link href="Tutorial.html" rel="up" title="Tutorial">
|
|
<link href="One_002dDimensional-DFTs-of-Real-Data.html" rel="next" title="One-Dimensional DFTs of Real Data">
|
|
<link href="Complex-One_002dDimensional-DFTs.html" rel="prev" title="Complex One-Dimensional DFTs">
|
|
<style type="text/css">
|
|
<!--
|
|
a.summary-letter {text-decoration: none}
|
|
blockquote.indentedblock {margin-right: 0em}
|
|
div.display {margin-left: 3.2em}
|
|
div.example {margin-left: 3.2em}
|
|
div.lisp {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}
|
|
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">
|
|
<span id="Complex-Multi_002dDimensional-DFTs"></span><div class="header">
|
|
<p>
|
|
Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html" 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" title="Index" rel="index">Index</a>]</p>
|
|
</div>
|
|
<hr>
|
|
<span id="Complex-Multi_002dDimensional-DFTs-1"></span><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>
|
|
<span id="index-fftw_005fplan_005fdft_005f2d"></span>
|
|
<span id="index-fftw_005fplan_005fdft_005f3d"></span>
|
|
|
|
<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-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>
|
|
<span id="index-rank"></span>
|
|
to denote the number of independent indices in an array.<a id="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>
|
|
<span id="index-fftw_005fplan_005fdft"></span>
|
|
|
|
<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
|
|
<span id="index-partial-order"></span>
|
|
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,
|
|
<span id="index-advanced-interface-1"></span>
|
|
<span id="index-guru-interface-1"></span>
|
|
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</a>.
|
|
</p>
|
|
<div class="footnote">
|
|
<hr>
|
|
<h4 class="footnotes-heading">Footnotes</h4>
|
|
|
|
<h5><a id="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" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html" 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" title="Index" rel="index">Index</a>]</p>
|
|
</div>
|
|
|
|
|
|
|
|
</body>
|
|
</html>
|