|
Chris@82
|
1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
|
|
Chris@82
|
2 <html>
|
|
Chris@82
|
3 <!-- This manual is for FFTW
|
|
Chris@82
|
4 (version 3.3.8, 24 May 2018).
|
|
Chris@82
|
5
|
|
Chris@82
|
6 Copyright (C) 2003 Matteo Frigo.
|
|
Chris@82
|
7
|
|
Chris@82
|
8 Copyright (C) 2003 Massachusetts Institute of Technology.
|
|
Chris@82
|
9
|
|
Chris@82
|
10 Permission is granted to make and distribute verbatim copies of this
|
|
Chris@82
|
11 manual provided the copyright notice and this permission notice are
|
|
Chris@82
|
12 preserved on all copies.
|
|
Chris@82
|
13
|
|
Chris@82
|
14 Permission is granted to copy and distribute modified versions of this
|
|
Chris@82
|
15 manual under the conditions for verbatim copying, provided that the
|
|
Chris@82
|
16 entire resulting derived work is distributed under the terms of a
|
|
Chris@82
|
17 permission notice identical to this one.
|
|
Chris@82
|
18
|
|
Chris@82
|
19 Permission is granted to copy and distribute translations of this manual
|
|
Chris@82
|
20 into another language, under the above conditions for modified versions,
|
|
Chris@82
|
21 except that this permission notice may be stated in a translation
|
|
Chris@82
|
22 approved by the Free Software Foundation. -->
|
|
Chris@82
|
23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
|
|
Chris@82
|
24 <head>
|
|
Chris@82
|
25 <title>FFTW 3.3.8: Load balancing</title>
|
|
Chris@82
|
26
|
|
Chris@82
|
27 <meta name="description" content="FFTW 3.3.8: Load balancing">
|
|
Chris@82
|
28 <meta name="keywords" content="FFTW 3.3.8: Load balancing">
|
|
Chris@82
|
29 <meta name="resource-type" content="document">
|
|
Chris@82
|
30 <meta name="distribution" content="global">
|
|
Chris@82
|
31 <meta name="Generator" content="makeinfo">
|
|
Chris@82
|
32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
|
Chris@82
|
33 <link href="index.html#Top" rel="start" title="Top">
|
|
Chris@82
|
34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
|
|
Chris@82
|
35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
|
|
Chris@82
|
36 <link href="MPI-Data-Distribution.html#MPI-Data-Distribution" rel="up" title="MPI Data Distribution">
|
|
Chris@82
|
37 <link href="Transposed-distributions.html#Transposed-distributions" rel="next" title="Transposed distributions">
|
|
Chris@82
|
38 <link href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" rel="prev" title="Basic and advanced distribution interfaces">
|
|
Chris@82
|
39 <style type="text/css">
|
|
Chris@82
|
40 <!--
|
|
Chris@82
|
41 a.summary-letter {text-decoration: none}
|
|
Chris@82
|
42 blockquote.indentedblock {margin-right: 0em}
|
|
Chris@82
|
43 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
|
|
Chris@82
|
44 blockquote.smallquotation {font-size: smaller}
|
|
Chris@82
|
45 div.display {margin-left: 3.2em}
|
|
Chris@82
|
46 div.example {margin-left: 3.2em}
|
|
Chris@82
|
47 div.lisp {margin-left: 3.2em}
|
|
Chris@82
|
48 div.smalldisplay {margin-left: 3.2em}
|
|
Chris@82
|
49 div.smallexample {margin-left: 3.2em}
|
|
Chris@82
|
50 div.smalllisp {margin-left: 3.2em}
|
|
Chris@82
|
51 kbd {font-style: oblique}
|
|
Chris@82
|
52 pre.display {font-family: inherit}
|
|
Chris@82
|
53 pre.format {font-family: inherit}
|
|
Chris@82
|
54 pre.menu-comment {font-family: serif}
|
|
Chris@82
|
55 pre.menu-preformatted {font-family: serif}
|
|
Chris@82
|
56 pre.smalldisplay {font-family: inherit; font-size: smaller}
|
|
Chris@82
|
57 pre.smallexample {font-size: smaller}
|
|
Chris@82
|
58 pre.smallformat {font-family: inherit; font-size: smaller}
|
|
Chris@82
|
59 pre.smalllisp {font-size: smaller}
|
|
Chris@82
|
60 span.nolinebreak {white-space: nowrap}
|
|
Chris@82
|
61 span.roman {font-family: initial; font-weight: normal}
|
|
Chris@82
|
62 span.sansserif {font-family: sans-serif; font-weight: normal}
|
|
Chris@82
|
63 ul.no-bullet {list-style: none}
|
|
Chris@82
|
64 -->
|
|
Chris@82
|
65 </style>
|
|
Chris@82
|
66
|
|
Chris@82
|
67
|
|
Chris@82
|
68 </head>
|
|
Chris@82
|
69
|
|
Chris@82
|
70 <body lang="en">
|
|
Chris@82
|
71 <a name="Load-balancing"></a>
|
|
Chris@82
|
72 <div class="header">
|
|
Chris@82
|
73 <p>
|
|
Chris@82
|
74 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> [<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>
|
|
Chris@82
|
75 </div>
|
|
Chris@82
|
76 <hr>
|
|
Chris@82
|
77 <a name="Load-balancing-1"></a>
|
|
Chris@82
|
78 <h4 class="subsection">6.4.2 Load balancing</h4>
|
|
Chris@82
|
79 <a name="index-load-balancing"></a>
|
|
Chris@82
|
80
|
|
Chris@82
|
81 <p>Ideally, when you parallelize a transform over some <em>P</em>
|
|
Chris@82
|
82 processes, each process should end up with work that takes equal time.
|
|
Chris@82
|
83 Otherwise, all of the processes end up waiting on whichever process is
|
|
Chris@82
|
84 slowest. This goal is known as “load balancing.” In this section,
|
|
Chris@82
|
85 we describe the circumstances under which FFTW is able to load-balance
|
|
Chris@82
|
86 well, and in particular how you should choose your transform size in
|
|
Chris@82
|
87 order to load balance.
|
|
Chris@82
|
88 </p>
|
|
Chris@82
|
89 <p>Load balancing is especially difficult when you are parallelizing over
|
|
Chris@82
|
90 heterogeneous machines; for example, if one of your processors is a
|
|
Chris@82
|
91 old 486 and another is a Pentium IV, obviously you should give the
|
|
Chris@82
|
92 Pentium more work to do than the 486 since the latter is much slower.
|
|
Chris@82
|
93 FFTW does not deal with this problem, however—it assumes that your
|
|
Chris@82
|
94 processes run on hardware of comparable speed, and that the goal is
|
|
Chris@82
|
95 therefore to divide the problem as equally as possible.
|
|
Chris@82
|
96 </p>
|
|
Chris@82
|
97 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
|
|
Chris@82
|
98 equally among the processes if: (i) the <em>first</em> dimension
|
|
Chris@82
|
99 <code>n0</code> is divisible by <em>P</em>; and (ii), the <em>product</em> of
|
|
Chris@82
|
100 the subsequent dimensions is divisible by <em>P</em>. (For the advanced
|
|
Chris@82
|
101 interface, where you can specify multiple simultaneous transforms via
|
|
Chris@82
|
102 some “vector” length <code>howmany</code>, a factor of <code>howmany</code> is
|
|
Chris@82
|
103 included in the product of the subsequent dimensions.)
|
|
Chris@82
|
104 </p>
|
|
Chris@82
|
105 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
|
|
Chris@82
|
106 should be divisible by <em>P</em> <em>squared</em> to be able to divide
|
|
Chris@82
|
107 the problem equally among the processes.
|
|
Chris@82
|
108 </p>
|
|
Chris@82
|
109
|
|
Chris@82
|
110
|
|
Chris@82
|
111
|
|
Chris@82
|
112 </body>
|
|
Chris@82
|
113 </html>
|
