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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>MPI Data Distribution - FFTW 3.3.3</title>
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16 Copyright (C) 2003 Matteo Frigo.
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49 <a name="MPI-Data-Distribution"></a>
50 <p>
51 Next:&nbsp;<a rel="next" accesskey="n" href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data">Multi-dimensional MPI DFTs of Real Data</a>,
52 Previous:&nbsp;<a rel="previous" accesskey="p" href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>,
53 Up:&nbsp;<a rel="up" accesskey="u" href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI">Distributed-memory FFTW with MPI</a>
54 <hr>
55 </div>
56
57 <h3 class="section">6.4 MPI Data Distribution</h3>
58
59 <p><a name="index-data-distribution-368"></a>
60 The most important concept to understand in using FFTW's MPI interface
61 is the data distribution. With a serial or multithreaded FFT, all of
62 the inputs and outputs are stored as a single contiguous chunk of
63 memory. With a distributed-memory FFT, the inputs and outputs are
64 broken into disjoint blocks, one per process.
65
66 <p>In particular, FFTW uses a <em>1d block distribution</em> of the data,
67 distributed along the <em>first dimension</em>. For example, if you
68 want to perform a 100&nbsp;&times;&nbsp;200 complex DFT, distributed over 4
69 processes, each process will get a 25&nbsp;&times;&nbsp;200 slice of the data.
70 That is, process 0 will get rows 0 through 24, process 1 will get rows
71 25 through 49, process 2 will get rows 50 through 74, and process 3
72 will get rows 75 through 99. If you take the same array but
73 distribute it over 3 processes, then it is not evenly divisible so the
74 different processes will have unequal chunks. FFTW's default choice
75 in this case is to assign 34 rows to processes 0 and 1, and 32 rows to
76 process 2.
77 <a name="index-block-distribution-369"></a>
78
79 <p>FFTW provides several &lsquo;<samp><span class="samp">fftw_mpi_local_size</span></samp>&rsquo; routines that you can
80 call to find out what portion of an array is stored on the current
81 process. In most cases, you should use the default block sizes picked
82 by FFTW, but it is also possible to specify your own block size. For
83 example, with a 100&nbsp;&times;&nbsp;200 array on three processes, you can
84 tell FFTW to use a block size of 40, which would assign 40 rows to
85 processes 0 and 1, and 20 rows to process 2. FFTW's default is to
86 divide the data equally among the processes if possible, and as best
87 it can otherwise. The rows are always assigned in &ldquo;rank order,&rdquo;
88 i.e. process 0 gets the first block of rows, then process 1, and so
89 on. (You can change this by using <code>MPI_Comm_split</code> to create a
90 new communicator with re-ordered processes.) However, you should
91 always call the &lsquo;<samp><span class="samp">fftw_mpi_local_size</span></samp>&rsquo; routines, if possible,
92 rather than trying to predict FFTW's distribution choices.
93
94 <p>In particular, it is critical that you allocate the storage size that
95 is returned by &lsquo;<samp><span class="samp">fftw_mpi_local_size</span></samp>&rsquo;, which is <em>not</em>
96 necessarily the size of the local slice of the array. The reason is
97 that intermediate steps of FFTW's algorithms involve transposing the
98 array and redistributing the data, so at these intermediate steps FFTW
99 may require more local storage space (albeit always proportional to
100 the total size divided by the number of processes). The
101 &lsquo;<samp><span class="samp">fftw_mpi_local_size</span></samp>&rsquo; functions know how much storage is required
102 for these intermediate steps and tell you the correct amount to
103 allocate.
104
105 <ul class="menu">
106 <li><a accesskey="1" href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces">Basic and advanced distribution interfaces</a>
107 <li><a accesskey="2" href="Load-balancing.html#Load-balancing">Load balancing</a>
108 <li><a accesskey="3" href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>
109 <li><a accesskey="4" href="One_002ddimensional-distributions.html#One_002ddimensional-distributions">One-dimensional distributions</a>
110 </ul>
111
112 </body></html>
113