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| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Tue, 18 Oct 2016 13:40:26 +0100 |
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| 126:4a7071416412 | 127:7867fa7e1b6b |
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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 3.3.5, 30 July 2016). | |
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| 6 Copyright (C) 2003 Matteo Frigo. | |
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| 8 Copyright (C) 2003 Massachusetts Institute of Technology. | |
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| 25 <title>FFTW 3.3.5: Transposed distributions</title> | |
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| 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> | |
| 72 <a name="Transposed-distributions"></a> | |
| 73 <div class="header"> | |
| 74 <p> | |
| 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> | |
| 76 </div> | |
| 77 <hr> | |
| 78 <a name="Transposed-distributions-1"></a> | |
| 79 <h4 class="subsection">6.4.3 Transposed distributions</h4> | |
| 80 | |
| 81 <p>Internally, FFTW’s MPI transform algorithms work by first computing | |
| 82 transforms of the data local to each process, then by globally | |
| 83 <em>transposing</em> the data in some fashion to redistribute the data | |
| 84 among the processes, transforming the new data local to each process, | |
| 85 and transposing back. For example, a two-dimensional <code>n0</code> by | |
| 86 <code>n1</code> array, distributed across the <code>n0</code> dimension, is | |
| 87 transformd by: (i) transforming the <code>n1</code> dimension, which are | |
| 88 local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code> | |
| 89 array, distributed across the <code>n1</code> dimension; (iii) transforming | |
| 90 the <code>n0</code> dimension, which is now local to each process; (iv) | |
| 91 transposing back. | |
| 92 <a name="index-transpose"></a> | |
| 93 </p> | |
| 94 | |
| 95 <p>However, in many applications it is acceptable to compute a | |
| 96 multidimensional DFT whose results are produced in transposed order | |
| 97 (e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a | |
| 98 significant performance advantage, because it means that the final | |
| 99 transposition step can be omitted. FFTW supports this optimization, | |
| 100 which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code> | |
| 101 to the planner routines. To compute the inverse transform of | |
| 102 transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell | |
| 103 it that the input is transposed. In this section, we explain how to | |
| 104 interpret the output format of such a transform. | |
| 105 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></a> | |
| 106 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></a> | |
| 107 </p> | |
| 108 | |
| 109 <p>Suppose you have are transforming multi-dimensional data with (at | |
| 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 | |
| 111 the first dimension n<sub>0</sub>. Now, if we compute its DFT with the | |
| 112 <code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored | |
| 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>, | |
| 114 distributed along the n<sub>1</sub> dimension. Conversely, if we take the | |
| 115 n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> data and transform it with the | |
| 116 <code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the | |
| 117 original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> array. | |
| 118 </p> | |
| 119 <p>There are two ways to find the portion of the transposed array that | |
| 120 resides on the current process. First, you can simply call the | |
| 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 | |
| 122 transposed dimensions). This would mean calling the ‘<samp>local_size</samp>’ | |
| 123 function twice, once for the transposed and once for the | |
| 124 non-transposed dimensions. Alternatively, you can call one of the | |
| 125 ‘<samp>local_size_transposed</samp>’ functions, which returns both the | |
| 126 non-transposed and transposed data distribution from a single call. | |
| 127 For example, for a 3d transform with transposed output (or input), you | |
| 128 might call: | |
| 129 </p> | |
| 130 <div class="example"> | |
| 131 <pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed( | |
| 132 ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm, | |
| 133 ptrdiff_t *local_n0, ptrdiff_t *local_0_start, | |
| 134 ptrdiff_t *local_n1, ptrdiff_t *local_1_start); | |
| 135 </pre></div> | |
| 136 <a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></a> | |
| 137 | |
| 138 <p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and | |
| 139 starting index of the <code>n0</code> dimension for the | |
| 140 <em>non</em>-transposed data, as in the previous sections. For | |
| 141 <em>transposed</em> data (e.g. the output for | |
| 142 <code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and | |
| 143 <code>local_1_start</code> give the size and starting index of the <code>n1</code> | |
| 144 dimension, which is the first dimension of the transposed data | |
| 145 (<code>n1</code> by <code>n0</code> by <code>n2</code>). | |
| 146 </p> | |
| 147 <p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to | |
| 148 performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two | |
| 149 dimensions to the planner in reverse order, or vice versa. If you | |
| 150 pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and | |
| 151 <code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the | |
| 152 first two dimensions passed to the planner and passing <em>neither</em> | |
| 153 flag.) | |
| 154 </p> | |
| 155 <hr> | |
| 156 <div class="header"> | |
| 157 <p> | |
| 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> | |
| 159 </div> | |
| 160 | |
| 161 | |
| 162 | |
| 163 </body> | |
| 164 </html> |