mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-23 21:15:11 +00:00
108 lines
5 KiB
HTML
108 lines
5 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>Row-major Format (FFTW 3.3.10)</title>
|
||
|
|
|
||
|
|
<meta name="description" content="Row-major Format (FFTW 3.3.10)">
|
||
|
|
<meta name="keywords" content="Row-major Format (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="Multi_002ddimensional-Array-Format.html" rel="up" title="Multi-dimensional Array Format">
|
||
|
|
<link href="Column_002dmajor-Format.html" rel="next" title="Column-major Format">
|
||
|
|
<link href="Multi_002ddimensional-Array-Format.html" rel="prev" title="Multi-dimensional 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="Row_002dmajor-Format"></span><div class="header">
|
||
|
|
<p>
|
||
|
|
Next: <a href="Column_002dmajor-Format.html" accesskey="n" rel="next">Column-major Format</a>, Previous: <a href="Multi_002ddimensional-Array-Format.html" accesskey="p" rel="prev">Multi-dimensional Array Format</a>, Up: <a href="Multi_002ddimensional-Array-Format.html" accesskey="u" rel="up">Multi-dimensional Array Format</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="Row_002dmajor-Format-1"></span><h4 class="subsection">3.2.1 Row-major Format</h4>
|
||
|
|
<span id="index-row_002dmajor"></span>
|
||
|
|
|
||
|
|
<p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
|
||
|
|
are expected to be stored as a single contiguous block in
|
||
|
|
<em>row-major</em> order (sometimes called “C order”). Basically, this
|
||
|
|
means that as you step through adjacent memory locations, the first
|
||
|
|
dimension’s index varies most slowly and the last dimension’s index
|
||
|
|
varies most quickly.
|
||
|
|
</p>
|
||
|
|
<p>To be more explicit, let us consider an array of rank <em>d</em> whose
|
||
|
|
dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
|
||
|
|
. Now, we specify a location in the array by a
|
||
|
|
sequence of <em>d</em> (zero-based) indices, one for each dimension:
|
||
|
|
(i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>).
|
||
|
|
If the array is stored in row-major
|
||
|
|
order, then this element is located at the position
|
||
|
|
i<sub>d-1</sub> + n<sub>d-1</sub> * (i<sub>d-2</sub> + n<sub>d-2</sub> * (... + n<sub>1</sub> * i<sub>0</sub>)).
|
||
|
|
</p>
|
||
|
|
<p>Note that, for the ordinary complex DFT, each element of the array
|
||
|
|
must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
|
||
|
|
(double-precision) numbers.
|
||
|
|
</p>
|
||
|
|
<p>In the advanced FFTW interface, the physical dimensions <em>n</em> from
|
||
|
|
which the indices are computed can be different from (larger than)
|
||
|
|
the logical dimensions of the transform to be computed, in order to
|
||
|
|
transform a subset of a larger array.
|
||
|
|
<span id="index-advanced-interface-2"></span>
|
||
|
|
Note also that, in the advanced interface, the expression above is
|
||
|
|
multiplied by a <em>stride</em> to get the actual array index—this is
|
||
|
|
useful in situations where each element of the multi-dimensional array
|
||
|
|
is actually a data structure (or another array), and you just want to
|
||
|
|
transform a single field. In the basic interface, however, the stride
|
||
|
|
is 1.
|
||
|
|
<span id="index-stride"></span>
|
||
|
|
</p>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|