Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/Reversing-array-dimensions.html @ 82:d0c2a83c1364
Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam |
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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/Reversing-array-dimensions.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,184 @@ +<!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: Reversing array dimensions</title> + +<meta name="description" content="FFTW 3.3.8: Reversing array dimensions"> +<meta name="keywords" content="FFTW 3.3.8: Reversing array dimensions"> +<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="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" rel="up" title="Calling FFTW from Modern Fortran"> +<link href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" rel="next" title="FFTW Fortran type reference"> +<link href="Extended-and-quadruple-precision-in-Fortran.html#Extended-and-quadruple-precision-in-Fortran" rel="prev" title="Extended and quadruple precision in Fortran"> +<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="Reversing-array-dimensions"></a> +<div class="header"> +<p> +Next: <a href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> +</div> +<hr> +<a name="Reversing-array-dimensions-1"></a> +<h3 class="section">7.2 Reversing array dimensions</h3> + +<a name="index-row_002dmajor-6"></a> +<a name="index-column_002dmajor-1"></a> +<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_002ddimensional-Array-Format">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> +<a name="index-fftw_005fplan_005fdft_005f3d-2"></a> +<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_002dinterface-routines">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> +<a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a> +<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_002dDimensional-DFTs-of-Real-Data">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> +<a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a> +<a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a> +<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> + +<a name="index-in_002dplace-9"></a> +<a name="index-padding-5"></a> +<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">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> +<a name="index-fftw_005falloc_005fcomplex-4"></a> +<a name="index-c_005ff_005fpointer"></a> +<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#FFTW-Fortran-type-reference" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> +</div> + + + +</body> +</html>