Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/Real_002ddata-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/Real_002ddata-DFTs.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,203 @@ +<!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: Real-data DFTs</title> + +<meta name="description" content="FFTW 3.3.8: Real-data DFTs"> +<meta name="keywords" content="FFTW 3.3.8: Real-data 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="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface"> +<link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="next" title="Real-data DFT Array Format"> +<link href="Planner-Flags.html#Planner-Flags" rel="prev" title="Planner Flags"> +<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="Real_002ddata-DFTs"></a> +<div class="header"> +<p> +Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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_002ddata-DFTs-1"></a> +<h4 class="subsection">4.3.3 Real-data DFTs</h4> + +<div class="example"> +<pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0, + double *in, fftw_complex *out, + unsigned flags); +fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1, + double *in, fftw_complex *out, + unsigned flags); +fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2, + double *in, fftw_complex *out, + unsigned flags); +fftw_plan fftw_plan_dft_r2c(int rank, const int *n, + double *in, fftw_complex *out, + unsigned flags); +</pre></div> +<a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a> +<a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a> +<a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a> +<a name="index-fftw_005fplan_005fdft_005fr2c-1"></a> +<a name="index-r2c-2"></a> + +<p>Plan a real-input/complex-output discrete Fourier transform (DFT) 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 if you use the <code>FFTW_PRESERVE_INPUT</code> flag +with a multi-dimensional out-of-place c2r transform (see below). +</p> +<a name="Arguments-1"></a> +<h4 class="subsubheading">Arguments</h4> +<ul> +<li> <code>rank</code> is the rank of the transform (it should be the size of the +array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html#Complex-Multi_002dDimensional-DFTs">Complex Multi-Dimensional DFTs</a>, for the definition of “rank”.) 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. The rank +may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a +copy of one real number (with zero imaginary part) from input to output. + +</li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate +for each routine) specify the size of the transform dimensions. They +can be any positive integer. This is different in general from the +<em>physical</em> array dimensions, which are described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>. + +<ul class="no-bullet"> +<li>- FFTW is 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, and +it is generally beneficial for the <em>last</em> dimension of an r2c/c2r +transform to be <em>even</em>. +</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-3"></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.) For an in-place transform, it +is important to remember that the real array will require padding, +described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>. +<a name="index-padding-2"></a> + +</li><li> <a name="index-flags-3"></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> + +<p>The inverse transforms, taking complex input (storing the non-redundant +half of a logically Hermitian array) to real output, are given by: +</p> +<div class="example"> +<pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0, + fftw_complex *in, double *out, + unsigned flags); +fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1, + fftw_complex *in, double *out, + unsigned flags); +fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2, + fftw_complex *in, double *out, + unsigned flags); +fftw_plan fftw_plan_dft_c2r(int rank, const int *n, + fftw_complex *in, double *out, + unsigned flags); +</pre></div> +<a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a> +<a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a> +<a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a> +<a name="index-fftw_005fplan_005fdft_005fc2r"></a> +<a name="index-c2r-2"></a> + +<p>The arguments are the same as for the r2c transforms, except that the +input and output data formats are reversed. +</p> +<p>FFTW computes an unnormalized transform: computing an r2c followed by a +c2r transform (or vice versa) will result in the original data +multiplied by the size of the transform (the product of the logical +dimensions). +<a name="index-normalization-6"></a> +An r2c transform produces the same output as a <code>FFTW_FORWARD</code> +complex DFT of the same input, and a c2r transform is correspondingly +equivalent to <code>FFTW_BACKWARD</code>. For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. +</p> +<hr> +<div class="header"> +<p> +Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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>