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Current fftw source
| author | Chris Cannam |
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| date | Tue, 18 Oct 2016 13:40:26 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.5/doc/html/Real_002dto_002dReal-Transforms.html Tue Oct 18 13:40:26 2016 +0100 @@ -0,0 +1,179 @@ +<!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 3.3.5, 30 July 2016). + +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 5.2, http://www.gnu.org/software/texinfo/ --> +<head> +<title>FFTW 3.3.5: Real-to-Real Transforms</title> + +<meta name="description" content="FFTW 3.3.5: Real-to-Real Transforms"> +<meta name="keywords" content="FFTW 3.3.5: Real-to-Real Transforms"> +<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="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface"> +<link href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" rel="next" title="Real-to-Real Transform Kinds"> +<link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="prev" title="Real-data DFT Array Format"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.indentedblock {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smallindentedblock {margin-left: 3.2em; font-size: smaller} +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.nocodebreak {white-space:nowrap} +span.nolinebreak {white-space:nowrap} +span.roman {font-family:serif; font-weight:normal} +span.sansserif {font-family:sans-serif; font-weight:normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> +<a name="Real_002dto_002dReal-Transforms"></a> +<div class="header"> +<p> +Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> +</div> +<hr> +<a name="Real_002dto_002dReal-Transforms-1"></a> +<h4 class="subsection">4.3.5 Real-to-Real Transforms</h4> +<a name="index-r2r-1"></a> + +<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-1"></a> +<a name="index-fftw_005fplan_005fr2r_005f2d-1"></a> +<a name="index-fftw_005fplan_005fr2r_005f3d-1"></a> +<a name="index-fftw_005fplan_005fr2r-1"></a> + +<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">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). +<a name="index-FFTW_005fREDFT00-1"></a> +</p> +<a name="Arguments-2"></a> +<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>- <a name="index-row_002dmajor-2"></a> +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_002ddimensional-Array-Format">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">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). +<a name="index-in_002dplace-5"></a> +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_002dto_002dReal-Transform-Kinds">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> <a name="index-flags-4"></a> +<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">Planner Flags</a>. + +</li></ul> + +<hr> +<div class="header"> +<p> +Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> +</div> + + + +</body> +</html>