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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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72 <a name="Load-balancing"></a>
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74 <p>
75 Next: <a href="Transposed-distributions.html#Transposed-distributions" accesskey="n" rel="next">Transposed distributions</a>, Previous: <a href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" accesskey="p" rel="prev">Basic and advanced distribution interfaces</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</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>
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78 <a name="Load-balancing-1"></a>
79 <h4 class="subsection">6.4.2 Load balancing</h4>
80 <a name="index-load-balancing"></a>
81
82 <p>Ideally, when you parallelize a transform over some <em>P</em>
83 processes, each process should end up with work that takes equal time.
84 Otherwise, all of the processes end up waiting on whichever process is
85 slowest. This goal is known as &ldquo;load balancing.&rdquo; In this section,
86 we describe the circumstances under which FFTW is able to load-balance
87 well, and in particular how you should choose your transform size in
88 order to load balance.
89 </p>
90 <p>Load balancing is especially difficult when you are parallelizing over
91 heterogeneous machines; for example, if one of your processors is a
92 old 486 and another is a Pentium IV, obviously you should give the
93 Pentium more work to do than the 486 since the latter is much slower.
94 FFTW does not deal with this problem, however&mdash;it assumes that your
95 processes run on hardware of comparable speed, and that the goal is
96 therefore to divide the problem as equally as possible.
97 </p>
98 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
99 equally among the processes if: (i) the <em>first</em> dimension
100 <code>n0</code> is divisible by <em>P</em>; and (ii), the <em>product</em> of
101 the subsequent dimensions is divisible by <em>P</em>. (For the advanced
102 interface, where you can specify multiple simultaneous transforms via
103 some &ldquo;vector&rdquo; length <code>howmany</code>, a factor of <code>howmany</code> is
104 included in the product of the subsequent dimensions.)
105 </p>
106 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
107 should be divisible by <em>P</em> <em>squared</em> to be able to divide
108 the problem equally among the processes.
109 </p>
110
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