Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/More-DFTs-of-Real-Data.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/More-DFTs-of-Real-Data.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,168 @@ +<!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: More DFTs of Real Data</title> + +<meta name="description" content="FFTW 3.3.8: More DFTs of Real Data"> +<meta name="keywords" content="FFTW 3.3.8: More DFTs of Real Data"> +<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="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT" rel="next" title="The Halfcomplex-format DFT"> +<link href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" rel="prev" title="Multi-Dimensional DFTs of Real Data"> +<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="More-DFTs-of-Real-Data"></a> +<div class="header"> +<p> +Previous: <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" accesskey="p" rel="prev">Multi-Dimensional DFTs of Real Data</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="More-DFTs-of-Real-Data-1"></a> +<h3 class="section">2.5 More DFTs of Real Data</h3> +<table class="menu" border="0" cellspacing="0"> +<tr><td align="left" valign="top">• <a href="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT" accesskey="1">The Halfcomplex-format DFT</a>:</td><td> </td><td align="left" valign="top"> +</td></tr> +<tr><td align="left" valign="top">• <a href="Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029.html#Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029" accesskey="2">Real even/odd DFTs (cosine/sine transforms)</a>:</td><td> </td><td align="left" valign="top"> +</td></tr> +<tr><td align="left" valign="top">• <a href="The-Discrete-Hartley-Transform.html#The-Discrete-Hartley-Transform" accesskey="3">The Discrete Hartley Transform</a>:</td><td> </td><td align="left" valign="top"> +</td></tr> +</table> + +<p>FFTW supports several other transform types via a unified <em>r2r</em> +(real-to-real) interface, +<a name="index-r2r"></a> +so called because it takes a real (<code>double</code>) array and outputs a +real array of the same size. These r2r transforms currently fall into +three categories: DFTs of real input and complex-Hermitian output in +halfcomplex format, DFTs of real input with even/odd symmetry +(a.k.a. discrete cosine/sine transforms, DCTs/DSTs), and discrete +Hartley transforms (DHTs), all described in more detail by the +following sections. +</p> +<p>The r2r transforms follow the by now familiar interface of creating an +<code>fftw_plan</code>, executing it with <code>fftw_execute(plan)</code>, and +destroying it with <code>fftw_destroy_plan(plan)</code>. Furthermore, all +r2r transforms share the same planner interface: +</p> +<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> +<a name="index-fftw_005fplan_005fr2r_005f1d"></a> +<a name="index-fftw_005fplan_005fr2r_005f2d"></a> +<a name="index-fftw_005fplan_005fr2r_005f3d"></a> +<a name="index-fftw_005fplan_005fr2r"></a> + +<p>Just as for the complex DFT, these plan 1d/2d/3d/multi-dimensional +transforms for contiguous arrays in row-major order, transforming (real) +input to output of the same size, where <code>n</code> specifies the +<em>physical</em> dimensions of the arrays. All positive <code>n</code> are +supported (with the exception of <code>n=1</code> for the <code>FFTW_REDFT00</code> +kind, noted in the real-even subsection below); products of small +factors are most efficient (factorizing <code>n-1</code> and <code>n+1</code> for +<code>FFTW_REDFT00</code> and <code>FFTW_RODFT00</code> kinds, described below), but +an <i>O</i>(<i>n</i> log <i>n</i>) + algorithm is used even for prime sizes. +</p> +<p>Each dimension has a <em>kind</em> parameter, of type +<code>fftw_r2r_kind</code>, specifying the kind of r2r transform to be used +for that dimension. +<a name="index-kind-_0028r2r_0029"></a> +<a name="index-fftw_005fr2r_005fkind"></a> +(In the case of <code>fftw_plan_r2r</code>, this is an array <code>kind[rank]</code> +where <code>kind[i]</code> is the transform kind for the dimension +<code>n[i]</code>.) The kind can be one of a set of predefined constants, +defined in the following subsections. +</p> +<p>In other words, FFTW computes the separable product of the specified +r2r transforms over each dimension, which can be used e.g. for partial +differential equations with mixed boundary conditions. (For some r2r +kinds, notably the halfcomplex DFT and the DHT, such a separable +product is somewhat problematic in more than one dimension, however, +as is described below.) +</p> +<p>In the current version of FFTW, all r2r transforms except for the +halfcomplex type are computed via pre- or post-processing of +halfcomplex transforms, and they are therefore not as fast as they +could be. Since most other general DCT/DST codes employ a similar +algorithm, however, FFTW’s implementation should provide at least +competitive performance. +</p> +<hr> +<div class="header"> +<p> +Previous: <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" accesskey="p" rel="prev">Multi-Dimensional DFTs of Real Data</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>