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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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into another language, under the above conditions for modified versions,
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>MPI Data Distribution (FFTW 3.3.10)</title>
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<meta name="description" content="MPI Data Distribution (FFTW 3.3.10)">
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<meta name="keywords" content="MPI Data Distribution (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Distributed_002dmemory-FFTW-with-MPI.html" rel="up" title="Distributed-memory FFTW with MPI">
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<link href="Basic-and-advanced-distribution-interfaces.html" rel="next" title="Basic and advanced distribution interfaces">
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<link href="2d-MPI-example.html" rel="prev" title="2d MPI example">
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</head>
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<body lang="en">
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<span id="MPI-Data-Distribution"></span><div class="header">
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<p>
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Next: <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html" accesskey="n" rel="next">Multi-dimensional MPI DFTs of Real Data</a>, Previous: <a href="2d-MPI-example.html" accesskey="p" rel="prev">2d MPI example</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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>
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</div>
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<hr>
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<span id="MPI-Data-Distribution-1"></span><h3 class="section">6.4 MPI Data Distribution</h3>
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<span id="index-data-distribution-2"></span>
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<p>The most important concept to understand in using FFTW’s MPI interface
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is the data distribution. With a serial or multithreaded FFT, all of
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the inputs and outputs are stored as a single contiguous chunk of
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memory. With a distributed-memory FFT, the inputs and outputs are
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broken into disjoint blocks, one per process.
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</p>
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<p>In particular, FFTW uses a <em>1d block distribution</em> of the data,
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distributed along the <em>first dimension</em>. For example, if you
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want to perform a 100 × 200
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complex DFT, distributed over 4
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processes, each process will get a 25 × 200
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slice of the data.
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That is, process 0 will get rows 0 through 24, process 1 will get rows
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25 through 49, process 2 will get rows 50 through 74, and process 3
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will get rows 75 through 99. If you take the same array but
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distribute it over 3 processes, then it is not evenly divisible so the
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different processes will have unequal chunks. FFTW’s default choice
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in this case is to assign 34 rows to processes 0 and 1, and 32 rows to
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process 2.
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<span id="index-block-distribution"></span>
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</p>
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<p>FFTW provides several ‘<samp>fftw_mpi_local_size</samp>’ routines that you can
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call to find out what portion of an array is stored on the current
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process. In most cases, you should use the default block sizes picked
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by FFTW, but it is also possible to specify your own block size. For
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example, with a 100 × 200
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array on three processes, you can
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tell FFTW to use a block size of 40, which would assign 40 rows to
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processes 0 and 1, and 20 rows to process 2. FFTW’s default is to
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divide the data equally among the processes if possible, and as best
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it can otherwise. The rows are always assigned in “rank order,”
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i.e. process 0 gets the first block of rows, then process 1, and so
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on. (You can change this by using <code>MPI_Comm_split</code> to create a
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new communicator with re-ordered processes.) However, you should
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always call the ‘<samp>fftw_mpi_local_size</samp>’ routines, if possible,
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rather than trying to predict FFTW’s distribution choices.
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</p>
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<p>In particular, it is critical that you allocate the storage size that
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is returned by ‘<samp>fftw_mpi_local_size</samp>’, which is <em>not</em>
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necessarily the size of the local slice of the array. The reason is
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that intermediate steps of FFTW’s algorithms involve transposing the
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array and redistributing the data, so at these intermediate steps FFTW
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may require more local storage space (albeit always proportional to
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the total size divided by the number of processes). The
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‘<samp>fftw_mpi_local_size</samp>’ functions know how much storage is required
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for these intermediate steps and tell you the correct amount to
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allocate.
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</p>
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<table class="menu" border="0" cellspacing="0">
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<tr><td align="left" valign="top">• <a href="Basic-and-advanced-distribution-interfaces.html" accesskey="1">Basic and advanced distribution interfaces</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Load-balancing.html" accesskey="2">Load balancing</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Transposed-distributions.html" accesskey="3">Transposed distributions</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="One_002ddimensional-distributions.html" accesskey="4">One-dimensional distributions</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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</table>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html" accesskey="n" rel="next">Multi-dimensional MPI DFTs of Real Data</a>, Previous: <a href="2d-MPI-example.html" accesskey="p" rel="prev">2d MPI example</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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>
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</div>
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</body>
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</html>
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