mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-01 18:42:40 +00:00
168 lines
8.4 KiB
HTML
168 lines
8.4 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>Real-to-Real Transforms (FFTW 3.3.10)</title>
|
|
|
|
<meta name="description" content="Real-to-Real Transforms (FFTW 3.3.10)">
|
|
<meta name="keywords" content="Real-to-Real Transforms (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="Basic-Interface.html" rel="up" title="Basic Interface">
|
|
<link href="Real_002dto_002dReal-Transform-Kinds.html" rel="next" title="Real-to-Real Transform Kinds">
|
|
<link href="Real_002ddata-DFT-Array-Format.html" rel="prev" title="Real-data DFT Array Format">
|
|
<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="Real_002dto_002dReal-Transforms"></span><div class="header">
|
|
<p>
|
|
Next: <a href="Real_002dto_002dReal-Transform-Kinds.html" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic Interface</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="Real_002dto_002dReal-Transforms-1"></span><h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
|
|
<span id="index-r2r-1"></span>
|
|
|
|
<div class="example">
|
|
<pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
|
|
fftw_r2r_kind kind, unsigned flags);
|
|
fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
|
|
fftw_r2r_kind kind0, fftw_r2r_kind kind1,
|
|
unsigned flags);
|
|
fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
|
|
double *in, double *out,
|
|
fftw_r2r_kind kind0,
|
|
fftw_r2r_kind kind1,
|
|
fftw_r2r_kind kind2,
|
|
unsigned flags);
|
|
fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
|
|
const fftw_r2r_kind *kind, unsigned flags);
|
|
</pre></div>
|
|
<span id="index-fftw_005fplan_005fr2r_005f1d-1"></span>
|
|
<span id="index-fftw_005fplan_005fr2r_005f2d-1"></span>
|
|
<span id="index-fftw_005fplan_005fr2r_005f3d-1"></span>
|
|
<span id="index-fftw_005fplan_005fr2r-1"></span>
|
|
|
|
<p>Plan a real input/output (r2r) transform of various kinds in zero or
|
|
more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html">Using Plans</a>).
|
|
</p>
|
|
<p>Once you have created a plan for a certain transform type and
|
|
parameters, then creating another plan of the same type and parameters,
|
|
but for different arrays, is fast and shares constant data with the
|
|
first plan (if it still exists).
|
|
</p>
|
|
<p>The planner returns <code>NULL</code> if the plan cannot be created. A
|
|
non-<code>NULL</code> plan is always returned by the basic interface unless
|
|
you are using a customized FFTW configuration supporting a restricted
|
|
set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
|
|
not defined).
|
|
<span id="index-FFTW_005fREDFT00-1"></span>
|
|
</p>
|
|
<span id="Arguments-2"></span><h4 class="subsubheading">Arguments</h4>
|
|
<ul>
|
|
<li> <code>rank</code> is the dimensionality of the transform (it should be the
|
|
size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
|
|
non-negative integer. The ‘<samp>_1d</samp>’, ‘<samp>_2d</samp>’, and ‘<samp>_3d</samp>’
|
|
planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
|
|
<code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
|
|
of one number from input to output.
|
|
|
|
</li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
|
|
respectively, gives the (physical) size of the transform dimensions.
|
|
They can be any positive integer.
|
|
|
|
<ul class="no-bullet">
|
|
<li>- <span id="index-row_002dmajor-2"></span>
|
|
Multi-dimensional arrays are stored in row-major order with dimensions:
|
|
<code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
|
|
<code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
|
|
See <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>.
|
|
</li><li>- FFTW is generally best at handling sizes of the form
|
|
2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
|
|
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
|
|
are arbitrary. Other sizes are computed by means of a slow,
|
|
general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
|
|
performance even for prime sizes). (It is possible to customize FFTW
|
|
for different array sizes; see <a href="Installation-and-Customization.html">Installation and Customization</a>.)
|
|
Transforms whose sizes are powers of <em>2</em> are especially fast.
|
|
</li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
|
|
size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
|
|
should be factorizable in the above form.
|
|
</li></ul>
|
|
|
|
</li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
|
|
transform, which may be the same (yielding an in-place transform).
|
|
<span id="index-in_002dplace-5"></span>
|
|
These arrays are overwritten during planning, unless
|
|
<code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
|
|
initialized, but they must be allocated.)
|
|
|
|
</li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
|
|
<code>kind[rank]</code>, is the kind of r2r transform used for the
|
|
corresponding dimension. The valid kind constants are described in
|
|
<a href="Real_002dto_002dReal-Transform-Kinds.html">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
|
|
what is computed is the separable product formed by taking each
|
|
transform kind along the corresponding dimension, one dimension after
|
|
another.
|
|
|
|
</li><li> <span id="index-flags-4"></span>
|
|
<code>flags</code> is a bitwise OR (‘<samp>|</samp>’) of zero or more planner flags,
|
|
as defined in <a href="Planner-Flags.html">Planner Flags</a>.
|
|
|
|
</li></ul>
|
|
|
|
<hr>
|
|
<div class="header">
|
|
<p>
|
|
Next: <a href="Real_002dto_002dReal-Transform-Kinds.html" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic Interface</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>
|