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Add FFTW3
| author | Chris Cannam |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.3/doc/html/Complex-Multi_002dDimensional-DFTs.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,138 @@ +<html lang="en"> +<head> +<title>Complex Multi-Dimensional DFTs - FFTW 3.3.3</title> +<meta http-equiv="Content-Type" content="text/html"> +<meta name="description" content="FFTW 3.3.3"> +<meta name="generator" content="makeinfo 4.13"> +<link title="Top" rel="start" href="index.html#Top"> +<link rel="up" href="Tutorial.html#Tutorial" title="Tutorial"> +<link rel="prev" href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" title="Complex One-Dimensional DFTs"> +<link rel="next" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" title="One-Dimensional DFTs of Real Data"> +<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> +<!-- +This manual is for FFTW +(version 3.3.3, 25 November 2012). + +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. + --> +<meta http-equiv="Content-Style-Type" content="text/css"> +<style type="text/css"><!-- + pre.display { font-family:inherit } + pre.format { font-family:inherit } + pre.smalldisplay { font-family:inherit; font-size:smaller } + pre.smallformat { font-family:inherit; font-size:smaller } + pre.smallexample { font-size:smaller } + pre.smalllisp { font-size:smaller } + span.sc { font-variant:small-caps } + span.roman { font-family:serif; font-weight:normal; } + span.sansserif { font-family:sans-serif; font-weight:normal; } +--></style> +</head> +<body> +<div class="node"> +<a name="Complex-Multi-Dimensional-DFTs"></a> +<a name="Complex-Multi_002dDimensional-DFTs"></a> +<p> +Next: <a rel="next" accesskey="n" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data">One-Dimensional DFTs of Real Data</a>, +Previous: <a rel="previous" accesskey="p" href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs">Complex One-Dimensional DFTs</a>, +Up: <a rel="up" accesskey="u" href="Tutorial.html#Tutorial">Tutorial</a> +<hr> +</div> + +<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>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: +<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> + <p><a name="index-fftw_005fplan_005fdft_005f2d-39"></a><a name="index-fftw_005fplan_005fdft_005f3d-40"></a> +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 <dfn>row-major</dfn> 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_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. + + <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> +<a name="index-rank-41"></a>to denote the number of independent indices in an array.<a rel="footnote" href="#fn-1" name="fnd-1"><sup>1</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: + +<pre class="example"> fftw_plan fftw_plan_dft(int rank, const int *n, + fftw_complex *in, fftw_complex *out, + int sign, unsigned flags); +</pre> + <p><a name="index-fftw_005fplan_005fdft-42"></a> +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 <small class="dots">...</small> by <code>n[rank-1]</code> transform. +Thus, for example, the call +<pre class="example"> fftw_plan_dft_2d(n0, n1, in, out, sign, flags); +</pre> + <p>is equivalent to the following code fragment: +<pre class="example"> int n[2]; + n[0] = n0; + n[1] = n1; + fftw_plan_dft(2, n, in, out, sign, flags); +</pre> + <p><code>fftw_plan_dft</code> is not restricted to 2d and 3d transforms, +however, but it can plan transforms of arbitrary rank. + + <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 +<a name="index-partial-order-43"></a>interfaces with strictly increasing generality but correspondingly +greater complexity. + + <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, +<a name="index-advanced-interface-44"></a><a name="index-guru-interface-45"></a>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">FFTW Reference</a>. + +<!-- --> + <div class="footnote"> +<hr> +<h4>Footnotes</h4><p class="footnote"><small>[<a name="fn-1" href="#fnd-1">1</a>]</small> 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> + + <hr></div> + + </body></html> +