|
Chris@42
|
1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
|
|
Chris@42
|
2 <html>
|
|
Chris@42
|
3 <!-- This manual is for FFTW
|
|
Chris@42
|
4 (version 3.3.5, 30 July 2016).
|
|
Chris@42
|
5
|
|
Chris@42
|
6 Copyright (C) 2003 Matteo Frigo.
|
|
Chris@42
|
7
|
|
Chris@42
|
8 Copyright (C) 2003 Massachusetts Institute of Technology.
|
|
Chris@42
|
9
|
|
Chris@42
|
10 Permission is granted to make and distribute verbatim copies of this
|
|
Chris@42
|
11 manual provided the copyright notice and this permission notice are
|
|
Chris@42
|
12 preserved on all copies.
|
|
Chris@42
|
13
|
|
Chris@42
|
14 Permission is granted to copy and distribute modified versions of this
|
|
Chris@42
|
15 manual under the conditions for verbatim copying, provided that the
|
|
Chris@42
|
16 entire resulting derived work is distributed under the terms of a
|
|
Chris@42
|
17 permission notice identical to this one.
|
|
Chris@42
|
18
|
|
Chris@42
|
19 Permission is granted to copy and distribute translations of this manual
|
|
Chris@42
|
20 into another language, under the above conditions for modified versions,
|
|
Chris@42
|
21 except that this permission notice may be stated in a translation
|
|
Chris@42
|
22 approved by the Free Software Foundation. -->
|
|
Chris@42
|
23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
|
|
Chris@42
|
24 <head>
|
|
Chris@42
|
25 <title>FFTW 3.3.5: Transposed distributions</title>
|
|
Chris@42
|
26
|
|
Chris@42
|
27 <meta name="description" content="FFTW 3.3.5: Transposed distributions">
|
|
Chris@42
|
28 <meta name="keywords" content="FFTW 3.3.5: Transposed distributions">
|
|
Chris@42
|
29 <meta name="resource-type" content="document">
|
|
Chris@42
|
30 <meta name="distribution" content="global">
|
|
Chris@42
|
31 <meta name="Generator" content="makeinfo">
|
|
Chris@42
|
32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
|
Chris@42
|
33 <link href="index.html#Top" rel="start" title="Top">
|
|
Chris@42
|
34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
|
|
Chris@42
|
35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
|
|
Chris@42
|
36 <link href="MPI-Data-Distribution.html#MPI-Data-Distribution" rel="up" title="MPI Data Distribution">
|
|
Chris@42
|
37 <link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="next" title="One-dimensional distributions">
|
|
Chris@42
|
38 <link href="Load-balancing.html#Load-balancing" rel="prev" title="Load balancing">
|
|
Chris@42
|
39 <style type="text/css">
|
|
Chris@42
|
40 <!--
|
|
Chris@42
|
41 a.summary-letter {text-decoration: none}
|
|
Chris@42
|
42 blockquote.smallquotation {font-size: smaller}
|
|
Chris@42
|
43 div.display {margin-left: 3.2em}
|
|
Chris@42
|
44 div.example {margin-left: 3.2em}
|
|
Chris@42
|
45 div.indentedblock {margin-left: 3.2em}
|
|
Chris@42
|
46 div.lisp {margin-left: 3.2em}
|
|
Chris@42
|
47 div.smalldisplay {margin-left: 3.2em}
|
|
Chris@42
|
48 div.smallexample {margin-left: 3.2em}
|
|
Chris@42
|
49 div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
|
|
Chris@42
|
50 div.smalllisp {margin-left: 3.2em}
|
|
Chris@42
|
51 kbd {font-style:oblique}
|
|
Chris@42
|
52 pre.display {font-family: inherit}
|
|
Chris@42
|
53 pre.format {font-family: inherit}
|
|
Chris@42
|
54 pre.menu-comment {font-family: serif}
|
|
Chris@42
|
55 pre.menu-preformatted {font-family: serif}
|
|
Chris@42
|
56 pre.smalldisplay {font-family: inherit; font-size: smaller}
|
|
Chris@42
|
57 pre.smallexample {font-size: smaller}
|
|
Chris@42
|
58 pre.smallformat {font-family: inherit; font-size: smaller}
|
|
Chris@42
|
59 pre.smalllisp {font-size: smaller}
|
|
Chris@42
|
60 span.nocodebreak {white-space:nowrap}
|
|
Chris@42
|
61 span.nolinebreak {white-space:nowrap}
|
|
Chris@42
|
62 span.roman {font-family:serif; font-weight:normal}
|
|
Chris@42
|
63 span.sansserif {font-family:sans-serif; font-weight:normal}
|
|
Chris@42
|
64 ul.no-bullet {list-style: none}
|
|
Chris@42
|
65 -->
|
|
Chris@42
|
66 </style>
|
|
Chris@42
|
67
|
|
Chris@42
|
68
|
|
Chris@42
|
69 </head>
|
|
Chris@42
|
70
|
|
Chris@42
|
71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
|
|
Chris@42
|
72 <a name="Transposed-distributions"></a>
|
|
Chris@42
|
73 <div class="header">
|
|
Chris@42
|
74 <p>
|
|
Chris@42
|
75 Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</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@42
|
76 </div>
|
|
Chris@42
|
77 <hr>
|
|
Chris@42
|
78 <a name="Transposed-distributions-1"></a>
|
|
Chris@42
|
79 <h4 class="subsection">6.4.3 Transposed distributions</h4>
|
|
Chris@42
|
80
|
|
Chris@42
|
81 <p>Internally, FFTW’s MPI transform algorithms work by first computing
|
|
Chris@42
|
82 transforms of the data local to each process, then by globally
|
|
Chris@42
|
83 <em>transposing</em> the data in some fashion to redistribute the data
|
|
Chris@42
|
84 among the processes, transforming the new data local to each process,
|
|
Chris@42
|
85 and transposing back. For example, a two-dimensional <code>n0</code> by
|
|
Chris@42
|
86 <code>n1</code> array, distributed across the <code>n0</code> dimension, is
|
|
Chris@42
|
87 transformd by: (i) transforming the <code>n1</code> dimension, which are
|
|
Chris@42
|
88 local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code>
|
|
Chris@42
|
89 array, distributed across the <code>n1</code> dimension; (iii) transforming
|
|
Chris@42
|
90 the <code>n0</code> dimension, which is now local to each process; (iv)
|
|
Chris@42
|
91 transposing back.
|
|
Chris@42
|
92 <a name="index-transpose"></a>
|
|
Chris@42
|
93 </p>
|
|
Chris@42
|
94
|
|
Chris@42
|
95 <p>However, in many applications it is acceptable to compute a
|
|
Chris@42
|
96 multidimensional DFT whose results are produced in transposed order
|
|
Chris@42
|
97 (e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a
|
|
Chris@42
|
98 significant performance advantage, because it means that the final
|
|
Chris@42
|
99 transposition step can be omitted. FFTW supports this optimization,
|
|
Chris@42
|
100 which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code>
|
|
Chris@42
|
101 to the planner routines. To compute the inverse transform of
|
|
Chris@42
|
102 transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell
|
|
Chris@42
|
103 it that the input is transposed. In this section, we explain how to
|
|
Chris@42
|
104 interpret the output format of such a transform.
|
|
Chris@42
|
105 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></a>
|
|
Chris@42
|
106 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></a>
|
|
Chris@42
|
107 </p>
|
|
Chris@42
|
108
|
|
Chris@42
|
109 <p>Suppose you have are transforming multi-dimensional data with (at
|
|
Chris@42
|
110 least two) dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>. As always, it is distributed along
|
|
Chris@42
|
111 the first dimension n<sub>0</sub>. Now, if we compute its DFT with the
|
|
Chris@42
|
112 <code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored
|
|
Chris@42
|
113 with the first <em>two</em> dimensions transposed: n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>,
|
|
Chris@42
|
114 distributed along the n<sub>1</sub> dimension. Conversely, if we take the
|
|
Chris@42
|
115 n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> data and transform it with the
|
|
Chris@42
|
116 <code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the
|
|
Chris@42
|
117 original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> array.
|
|
Chris@42
|
118 </p>
|
|
Chris@42
|
119 <p>There are two ways to find the portion of the transposed array that
|
|
Chris@42
|
120 resides on the current process. First, you can simply call the
|
|
Chris@42
|
121 appropriate ‘<samp>local_size</samp>’ function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> (the
|
|
Chris@42
|
122 transposed dimensions). This would mean calling the ‘<samp>local_size</samp>’
|
|
Chris@42
|
123 function twice, once for the transposed and once for the
|
|
Chris@42
|
124 non-transposed dimensions. Alternatively, you can call one of the
|
|
Chris@42
|
125 ‘<samp>local_size_transposed</samp>’ functions, which returns both the
|
|
Chris@42
|
126 non-transposed and transposed data distribution from a single call.
|
|
Chris@42
|
127 For example, for a 3d transform with transposed output (or input), you
|
|
Chris@42
|
128 might call:
|
|
Chris@42
|
129 </p>
|
|
Chris@42
|
130 <div class="example">
|
|
Chris@42
|
131 <pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed(
|
|
Chris@42
|
132 ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
|
|
Chris@42
|
133 ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
|
|
Chris@42
|
134 ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
|
|
Chris@42
|
135 </pre></div>
|
|
Chris@42
|
136 <a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></a>
|
|
Chris@42
|
137
|
|
Chris@42
|
138 <p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and
|
|
Chris@42
|
139 starting index of the <code>n0</code> dimension for the
|
|
Chris@42
|
140 <em>non</em>-transposed data, as in the previous sections. For
|
|
Chris@42
|
141 <em>transposed</em> data (e.g. the output for
|
|
Chris@42
|
142 <code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and
|
|
Chris@42
|
143 <code>local_1_start</code> give the size and starting index of the <code>n1</code>
|
|
Chris@42
|
144 dimension, which is the first dimension of the transposed data
|
|
Chris@42
|
145 (<code>n1</code> by <code>n0</code> by <code>n2</code>).
|
|
Chris@42
|
146 </p>
|
|
Chris@42
|
147 <p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to
|
|
Chris@42
|
148 performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two
|
|
Chris@42
|
149 dimensions to the planner in reverse order, or vice versa. If you
|
|
Chris@42
|
150 pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and
|
|
Chris@42
|
151 <code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the
|
|
Chris@42
|
152 first two dimensions passed to the planner and passing <em>neither</em>
|
|
Chris@42
|
153 flag.)
|
|
Chris@42
|
154 </p>
|
|
Chris@42
|
155 <hr>
|
|
Chris@42
|
156 <div class="header">
|
|
Chris@42
|
157 <p>
|
|
Chris@42
|
158 Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</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@42
|
159 </div>
|
|
Chris@42
|
160
|
|
Chris@42
|
161
|
|
Chris@42
|
162
|
|
Chris@42
|
163 </body>
|
|
Chris@42
|
164 </html>
|
