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| author | Chris Cannam |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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| 1 <html lang="en"> | |
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| 3 <title>Transposed distributions - FFTW 3.3.3</title> | |
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| 12 <!-- | |
| 13 This manual is for FFTW | |
| 14 (version 3.3.3, 25 November 2012). | |
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| 16 Copyright (C) 2003 Matteo Frigo. | |
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| 18 Copyright (C) 2003 Massachusetts Institute of Technology. | |
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| 49 <a name="Transposed-distributions"></a> | |
| 50 <p> | |
| 51 Next: <a rel="next" accesskey="n" href="One_002ddimensional-distributions.html#One_002ddimensional-distributions">One-dimensional distributions</a>, | |
| 52 Previous: <a rel="previous" accesskey="p" href="Load-balancing.html#Load-balancing">Load balancing</a>, | |
| 53 Up: <a rel="up" accesskey="u" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a> | |
| 54 <hr> | |
| 55 </div> | |
| 56 | |
| 57 <h4 class="subsection">6.4.3 Transposed distributions</h4> | |
| 58 | |
| 59 <p>Internally, FFTW's MPI transform algorithms work by first computing | |
| 60 transforms of the data local to each process, then by globally | |
| 61 <em>transposing</em> the data in some fashion to redistribute the data | |
| 62 among the processes, transforming the new data local to each process, | |
| 63 and transposing back. For example, a two-dimensional <code>n0</code> by | |
| 64 <code>n1</code> array, distributed across the <code>n0</code> dimension, is | |
| 65 transformd by: (i) transforming the <code>n1</code> dimension, which are | |
| 66 local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code> | |
| 67 array, distributed across the <code>n1</code> dimension; (iii) transforming | |
| 68 the <code>n0</code> dimension, which is now local to each process; (iv) | |
| 69 transposing back. | |
| 70 <a name="index-transpose-379"></a> | |
| 71 | |
| 72 <p>However, in many applications it is acceptable to compute a | |
| 73 multidimensional DFT whose results are produced in transposed order | |
| 74 (e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a | |
| 75 significant performance advantage, because it means that the final | |
| 76 transposition step can be omitted. FFTW supports this optimization, | |
| 77 which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code> | |
| 78 to the planner routines. To compute the inverse transform of | |
| 79 transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell | |
| 80 it that the input is transposed. In this section, we explain how to | |
| 81 interpret the output format of such a transform. | |
| 82 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT-380"></a><a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN-381"></a> | |
| 83 | |
| 84 <p>Suppose you have are transforming multi-dimensional data with (at | |
| 85 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 | |
| 86 the first dimension n<sub>0</sub>. Now, if we compute its DFT with the | |
| 87 <code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored | |
| 88 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>, | |
| 89 distributed along the n<sub>1</sub> dimension. Conversely, if we take the | |
| 90 n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> data and transform it with the | |
| 91 <code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the | |
| 92 original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> array. | |
| 93 | |
| 94 <p>There are two ways to find the portion of the transposed array that | |
| 95 resides on the current process. First, you can simply call the | |
| 96 appropriate ‘<samp><span class="samp">local_size</span></samp>’ function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> (the | |
| 97 transposed dimensions). This would mean calling the ‘<samp><span class="samp">local_size</span></samp>’ | |
| 98 function twice, once for the transposed and once for the | |
| 99 non-transposed dimensions. Alternatively, you can call one of the | |
| 100 ‘<samp><span class="samp">local_size_transposed</span></samp>’ functions, which returns both the | |
| 101 non-transposed and transposed data distribution from a single call. | |
| 102 For example, for a 3d transform with transposed output (or input), you | |
| 103 might call: | |
| 104 | |
| 105 <pre class="example"> ptrdiff_t fftw_mpi_local_size_3d_transposed( | |
| 106 ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm, | |
| 107 ptrdiff_t *local_n0, ptrdiff_t *local_0_start, | |
| 108 ptrdiff_t *local_n1, ptrdiff_t *local_1_start); | |
| 109 </pre> | |
| 110 <p><a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed-382"></a> | |
| 111 Here, <code>local_n0</code> and <code>local_0_start</code> give the size and | |
| 112 starting index of the <code>n0</code> dimension for the | |
| 113 <em>non</em>-transposed data, as in the previous sections. For | |
| 114 <em>transposed</em> data (e.g. the output for | |
| 115 <code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and | |
| 116 <code>local_1_start</code> give the size and starting index of the <code>n1</code> | |
| 117 dimension, which is the first dimension of the transposed data | |
| 118 (<code>n1</code> by <code>n0</code> by <code>n2</code>). | |
| 119 | |
| 120 <p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to | |
| 121 performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two | |
| 122 dimensions to the planner in reverse order, or vice versa. If you | |
| 123 pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and | |
| 124 <code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the | |
| 125 first two dimensions passed to the planner and passing <em>neither</em> | |
| 126 flag.) | |
| 127 | |
| 128 </body></html> | |
| 129 |