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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
5
6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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24 <head>
25 <title>FFTW 3.3.8: MPI Data Distribution</title>
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27 <meta name="description" content="FFTW 3.3.8: MPI Data Distribution">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
36 <link href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" rel="up" title="Distributed-memory FFTW with MPI">
37 <link href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" rel="next" title="Basic and advanced distribution interfaces">
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70 <body lang="en">
71 <a name="MPI-Data-Distribution"></a>
72 <div class="header">
73 <p>
74 Next: <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data" accesskey="n" rel="next">Multi-dimensional MPI DFTs of Real Data</a>, Previous: <a href="2d-MPI-example.html#g_t2d-MPI-example" accesskey="p" rel="prev">2d MPI example</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> &nbsp; [<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>
75 </div>
76 <hr>
77 <a name="MPI-Data-Distribution-1"></a>
78 <h3 class="section">6.4 MPI Data Distribution</h3>
79 <a name="index-data-distribution-2"></a>
80
81 <p>The most important concept to understand in using FFTW&rsquo;s MPI interface
82 is the data distribution. With a serial or multithreaded FFT, all of
83 the inputs and outputs are stored as a single contiguous chunk of
84 memory. With a distributed-memory FFT, the inputs and outputs are
85 broken into disjoint blocks, one per process.
86 </p>
87 <p>In particular, FFTW uses a <em>1d block distribution</em> of the data,
88 distributed along the <em>first dimension</em>. For example, if you
89 want to perform a 100&nbsp;&times;&nbsp;200
90 complex DFT, distributed over 4
91 processes, each process will get a 25&nbsp;&times;&nbsp;200
92 slice of the data.
93 That is, process 0 will get rows 0 through 24, process 1 will get rows
94 25 through 49, process 2 will get rows 50 through 74, and process 3
95 will get rows 75 through 99. If you take the same array but
96 distribute it over 3 processes, then it is not evenly divisible so the
97 different processes will have unequal chunks. FFTW&rsquo;s default choice
98 in this case is to assign 34 rows to processes 0 and 1, and 32 rows to
99 process 2.
100 <a name="index-block-distribution"></a>
101 </p>
102
103 <p>FFTW provides several &lsquo;<samp>fftw_mpi_local_size</samp>&rsquo; routines that you can
104 call to find out what portion of an array is stored on the current
105 process. In most cases, you should use the default block sizes picked
106 by FFTW, but it is also possible to specify your own block size. For
107 example, with a 100&nbsp;&times;&nbsp;200
108 array on three processes, you can
109 tell FFTW to use a block size of 40, which would assign 40 rows to
110 processes 0 and 1, and 20 rows to process 2. FFTW&rsquo;s default is to
111 divide the data equally among the processes if possible, and as best
112 it can otherwise. The rows are always assigned in &ldquo;rank order,&rdquo;
113 i.e. process 0 gets the first block of rows, then process 1, and so
114 on. (You can change this by using <code>MPI_Comm_split</code> to create a
115 new communicator with re-ordered processes.) However, you should
116 always call the &lsquo;<samp>fftw_mpi_local_size</samp>&rsquo; routines, if possible,
117 rather than trying to predict FFTW&rsquo;s distribution choices.
118 </p>
119 <p>In particular, it is critical that you allocate the storage size that
120 is returned by &lsquo;<samp>fftw_mpi_local_size</samp>&rsquo;, which is <em>not</em>
121 necessarily the size of the local slice of the array. The reason is
122 that intermediate steps of FFTW&rsquo;s algorithms involve transposing the
123 array and redistributing the data, so at these intermediate steps FFTW
124 may require more local storage space (albeit always proportional to
125 the total size divided by the number of processes). The
126 &lsquo;<samp>fftw_mpi_local_size</samp>&rsquo; functions know how much storage is required
127 for these intermediate steps and tell you the correct amount to
128 allocate.
129 </p>
130 <table class="menu" border="0" cellspacing="0">
131 <tr><td align="left" valign="top">&bull; <a href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" accesskey="1">Basic and advanced distribution interfaces</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
132 </td></tr>
133 <tr><td align="left" valign="top">&bull; <a href="Load-balancing.html#Load-balancing" accesskey="2">Load balancing</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
134 </td></tr>
135 <tr><td align="left" valign="top">&bull; <a href="Transposed-distributions.html#Transposed-distributions" accesskey="3">Transposed distributions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
136 </td></tr>
137 <tr><td align="left" valign="top">&bull; <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="4">One-dimensional distributions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
138 </td></tr>
139 </table>
140
141 <hr>
142 <div class="header">
143 <p>
144 Next: <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data" accesskey="n" rel="next">Multi-dimensional MPI DFTs of Real Data</a>, Previous: <a href="2d-MPI-example.html#g_t2d-MPI-example" accesskey="p" rel="prev">2d MPI example</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> &nbsp; [<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>
145 </div>
146
147
148
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150 </html>