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Current fftw source
| author | Chris Cannam |
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| date | Tue, 18 Oct 2016 13:40:26 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.5/doc/html/Transposed-distributions.html Tue Oct 18 13:40:26 2016 +0100 @@ -0,0 +1,164 @@ +<!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 3.3.5, 30 July 2016). + +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 5.2, http://www.gnu.org/software/texinfo/ --> +<head> +<title>FFTW 3.3.5: Transposed distributions</title> + +<meta name="description" content="FFTW 3.3.5: Transposed distributions"> +<meta name="keywords" content="FFTW 3.3.5: Transposed distributions"> +<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="MPI-Data-Distribution.html#MPI-Data-Distribution" rel="up" title="MPI Data Distribution"> +<link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="next" title="One-dimensional distributions"> +<link href="Load-balancing.html#Load-balancing" rel="prev" title="Load balancing"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.indentedblock {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smallindentedblock {margin-left: 3.2em; font-size: smaller} +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.nocodebreak {white-space:nowrap} +span.nolinebreak {white-space:nowrap} +span.roman {font-family:serif; font-weight:normal} +span.sansserif {font-family:sans-serif; font-weight:normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> +<a name="Transposed-distributions"></a> +<div class="header"> +<p> +Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</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="Transposed-distributions-1"></a> +<h4 class="subsection">6.4.3 Transposed distributions</h4> + +<p>Internally, FFTW’s MPI transform algorithms work by first computing +transforms of the data local to each process, then by globally +<em>transposing</em> the data in some fashion to redistribute the data +among the processes, transforming the new data local to each process, +and transposing back. For example, a two-dimensional <code>n0</code> by +<code>n1</code> array, distributed across the <code>n0</code> dimension, is +transformd by: (i) transforming the <code>n1</code> dimension, which are +local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code> +array, distributed across the <code>n1</code> dimension; (iii) transforming +the <code>n0</code> dimension, which is now local to each process; (iv) +transposing back. +<a name="index-transpose"></a> +</p> + +<p>However, in many applications it is acceptable to compute a +multidimensional DFT whose results are produced in transposed order +(e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a +significant performance advantage, because it means that the final +transposition step can be omitted. FFTW supports this optimization, +which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code> +to the planner routines. To compute the inverse transform of +transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell +it that the input is transposed. In this section, we explain how to +interpret the output format of such a transform. +<a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></a> +<a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></a> +</p> + +<p>Suppose you have are transforming multi-dimensional data with (at +least two) dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>. As always, it is distributed along +the first dimension n<sub>0</sub>. Now, if we compute its DFT with the +<code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored +with the first <em>two</em> dimensions transposed: n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>, +distributed along the n<sub>1</sub> dimension. Conversely, if we take the +n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> data and transform it with the +<code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the +original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> array. +</p> +<p>There are two ways to find the portion of the transposed array that +resides on the current process. First, you can simply call the +appropriate ‘<samp>local_size</samp>’ function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> (the +transposed dimensions). This would mean calling the ‘<samp>local_size</samp>’ +function twice, once for the transposed and once for the +non-transposed dimensions. Alternatively, you can call one of the +‘<samp>local_size_transposed</samp>’ functions, which returns both the +non-transposed and transposed data distribution from a single call. +For example, for a 3d transform with transposed output (or input), you +might call: +</p> +<div class="example"> +<pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed( + ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm, + ptrdiff_t *local_n0, ptrdiff_t *local_0_start, + ptrdiff_t *local_n1, ptrdiff_t *local_1_start); +</pre></div> +<a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></a> + +<p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and +starting index of the <code>n0</code> dimension for the +<em>non</em>-transposed data, as in the previous sections. For +<em>transposed</em> data (e.g. the output for +<code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and +<code>local_1_start</code> give the size and starting index of the <code>n1</code> +dimension, which is the first dimension of the transposed data +(<code>n1</code> by <code>n0</code> by <code>n2</code>). +</p> +<p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to +performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two +dimensions to the planner in reverse order, or vice versa. If you +pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and +<code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the +first two dimensions passed to the planner and passing <em>neither</em> +flag.) +</p> +<hr> +<div class="header"> +<p> +Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</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>