mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-05 20:35:06 +00:00
173 lines
8.2 KiB
HTML
173 lines
8.2 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>Reversing array dimensions (FFTW 3.3.10)</title>
|
|
|
|
<meta name="description" content="Reversing array dimensions (FFTW 3.3.10)">
|
|
<meta name="keywords" content="Reversing array dimensions (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="Calling-FFTW-from-Modern-Fortran.html" rel="up" title="Calling FFTW from Modern Fortran">
|
|
<link href="FFTW-Fortran-type-reference.html" rel="next" title="FFTW Fortran type reference">
|
|
<link href="Extended-and-quadruple-precision-in-Fortran.html" rel="prev" title="Extended and quadruple precision in Fortran">
|
|
<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="Reversing-array-dimensions"></span><div class="header">
|
|
<p>
|
|
Next: <a href="FFTW-Fortran-type-reference.html" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html" accesskey="u" rel="up">Calling FFTW from Modern Fortran</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="Reversing-array-dimensions-1"></span><h3 class="section">7.2 Reversing array dimensions</h3>
|
|
|
|
<span id="index-row_002dmajor-6"></span>
|
|
<span id="index-column_002dmajor-1"></span>
|
|
<p>A minor annoyance in calling FFTW from Fortran is that FFTW’s array
|
|
dimensions are defined in the C convention (row-major order), while
|
|
Fortran’s array dimensions are the opposite convention (column-major
|
|
order). See <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>. This is just a
|
|
bookkeeping difference, with no effect on performance. The only
|
|
consequence of this is that, whenever you create an FFTW plan for a
|
|
multi-dimensional transform, you must always <em>reverse the
|
|
ordering of the dimensions</em>.
|
|
</p>
|
|
<p>For example, consider the three-dimensional (L × M × N
|
|
) arrays:
|
|
</p>
|
|
<div class="example">
|
|
<pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
|
|
</pre></div>
|
|
|
|
<p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
|
|
</p>
|
|
<span id="index-fftw_005fplan_005fdft_005f3d-2"></span>
|
|
<div class="example">
|
|
<pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
|
|
</pre></div>
|
|
|
|
<p>That is, from FFTW’s perspective this is a N × M × L
|
|
array.
|
|
<em>No data transposition need occur</em>, as this is <em>only
|
|
notation</em>. Similarly, to use the more generic routine
|
|
<code>fftw_plan_dft</code> with the same arrays, you could do:
|
|
</p>
|
|
<div class="example">
|
|
<pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
|
|
plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
|
|
</pre></div>
|
|
|
|
<p>Note, by the way, that this is different from the legacy Fortran
|
|
interface (see <a href="Fortran_002dinterface-routines.html">Fortran-interface routines</a>), which automatically
|
|
reverses the order of the array dimension for you. Here, you are
|
|
calling the C interface directly, so there is no “translation” layer.
|
|
</p>
|
|
<span id="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></span>
|
|
<p>An important thing to keep in mind is the implication of this for
|
|
multidimensional real-to-complex transforms (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html">Multi-Dimensional DFTs of Real Data</a>). In C, a multidimensional real-to-complex DFT
|
|
chops the last dimension roughly in half (N × M × L
|
|
real input
|
|
goes to N × M × L/2+1
|
|
complex output). In Fortran, because
|
|
the array dimension notation is reversed, the <em>first</em> dimension of
|
|
the complex data is chopped roughly in half. For example consider the
|
|
‘<samp>r2c</samp>’ transform of L × M × N
|
|
real input in Fortran:
|
|
</p>
|
|
<span id="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></span>
|
|
<span id="index-fftw_005fexecute_005fdft_005fr2c-1"></span>
|
|
<div class="example">
|
|
<pre class="example"> type(C_PTR) :: plan
|
|
real(C_DOUBLE), dimension(L,M,N) :: in
|
|
complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
|
|
plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
|
|
...
|
|
call fftw_execute_dft_r2c(plan, in, out)
|
|
</pre></div>
|
|
|
|
<span id="index-in_002dplace-9"></span>
|
|
<span id="index-padding-5"></span>
|
|
<p>Alternatively, for an in-place r2c transform, as described in the C
|
|
documentation we must <em>pad</em> the <em>first</em> dimension of the
|
|
real input with an extra two entries (which are ignored by FFTW) so as
|
|
to leave enough space for the complex output. The input is
|
|
<em>allocated</em> as a 2[L/2+1] × M × N
|
|
array, even though only
|
|
L × M × N
|
|
of it is actually used. In this example, we will
|
|
allocate the array as a pointer type, using ‘<samp>fftw_alloc</samp>’ to
|
|
ensure aligned memory for maximum performance (see <a href="Allocating-aligned-memory-in-Fortran.html">Allocating aligned memory in Fortran</a>); this also makes it easy to reference the
|
|
same memory as both a real array and a complex array.
|
|
</p>
|
|
<span id="index-fftw_005falloc_005fcomplex-4"></span>
|
|
<span id="index-c_005ff_005fpointer"></span>
|
|
<div class="example">
|
|
<pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
|
|
complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
|
|
type(C_PTR) :: plan, data
|
|
data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
|
|
call c_f_pointer(data, in, [2*(L/2+1),M,N])
|
|
call c_f_pointer(data, out, [L/2+1,M,N])
|
|
plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
|
|
...
|
|
call fftw_execute_dft_r2c(plan, in, out)
|
|
...
|
|
call fftw_destroy_plan(plan)
|
|
call fftw_free(data)
|
|
</pre></div>
|
|
|
|
<hr>
|
|
<div class="header">
|
|
<p>
|
|
Next: <a href="FFTW-Fortran-type-reference.html" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html" accesskey="u" rel="up">Calling FFTW from Modern Fortran</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>
|
|
|
|
|
|
|
|
</body>
|
|
</html>
|