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| author | Chris Cannam <cannam@all-day-breakfast.com> |
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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/Reversing-array-dimensions.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,132 @@ +<html lang="en"> +<head> +<title>Reversing array dimensions - 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="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" title="Calling FFTW from Modern Fortran"> +<link rel="prev" href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" title="Overview of Fortran interface"> +<link rel="next" href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" title="FFTW Fortran type reference"> +<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="Reversing-array-dimensions"></a> +<p> +Next: <a rel="next" accesskey="n" href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference">FFTW Fortran type reference</a>, +Previous: <a rel="previous" accesskey="p" href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface">Overview of Fortran interface</a>, +Up: <a rel="up" accesskey="u" href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran">Calling FFTW from Modern Fortran</a> +<hr> +</div> + +<h3 class="section">7.2 Reversing array dimensions</h3> + +<p><a name="index-row_002dmajor-517"></a><a name="index-column_002dmajor-518"></a>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>For example, consider the three-dimensional (L × M × N) arrays: + +<pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out +</pre> + <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-519"></a> +<pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE) +</pre> + <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: + +<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> + <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-520"></a>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><span class="samp">r2c</span></samp>’ transform of L × M × N real input in Fortran: + + <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-521"></a><a name="index-fftw_005fexecute_005fdft_005fr2c-522"></a> +<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> + <p><a name="index-in_002dplace-523"></a><a name="index-padding-524"></a>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><span class="samp">fftw_alloc</span></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-525"></a><a name="index-c_005ff_005fpointer-526"></a> +<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> + <!-- --> + </body></html> +