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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"> | |
| 2 <head> | |
| 3 <title>Multi-dimensional MPI DFTs of Real Data - FFTW 3.3.3</title> | |
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| 5 <meta name="description" content="FFTW 3.3.3"> | |
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| 10 <link rel="next" href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" title="Other Multi-dimensional Real-data MPI Transforms"> | |
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| 12 <!-- | |
| 13 This manual is for FFTW | |
| 14 (version 3.3.3, 25 November 2012). | |
| 15 | |
| 16 Copyright (C) 2003 Matteo Frigo. | |
| 17 | |
| 18 Copyright (C) 2003 Massachusetts Institute of Technology. | |
| 19 | |
| 20 Permission is granted to make and distribute verbatim copies of | |
| 21 this manual provided the copyright notice and this permission | |
| 22 notice are preserved on all copies. | |
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| 25 this manual under the conditions for verbatim copying, provided | |
| 26 that the entire resulting derived work is distributed under the | |
| 27 terms of a permission notice identical to this one. | |
| 28 | |
| 29 Permission is granted to copy and distribute translations of this | |
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| 48 <div class="node"> | |
| 49 <a name="Multi-dimensional-MPI-DFTs-of-Real-Data"></a> | |
| 50 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a> | |
| 51 <p> | |
| 52 Next: <a rel="next" accesskey="n" href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms">Other Multi-dimensional Real-data MPI Transforms</a>, | |
| 53 Previous: <a rel="previous" accesskey="p" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>, | |
| 54 Up: <a rel="up" accesskey="u" href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI">Distributed-memory FFTW with MPI</a> | |
| 55 <hr> | |
| 56 </div> | |
| 57 | |
| 58 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3> | |
| 59 | |
| 60 <p>FFTW's MPI interface also supports multi-dimensional DFTs of real | |
| 61 data, similar to the serial r2c and c2r interfaces. (Parallel | |
| 62 one-dimensional real-data DFTs are not currently supported; you must | |
| 63 use a complex transform and set the imaginary parts of the inputs to | |
| 64 zero.) | |
| 65 | |
| 66 <p>The key points to understand for r2c and c2r MPI transforms (compared | |
| 67 to the MPI complex DFTs or the serial r2c/c2r transforms), are: | |
| 68 | |
| 69 <ul> | |
| 70 <li>Just as for serial transforms, r2c/c2r DFTs transform n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> real | |
| 71 data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) complex data: the last dimension of the | |
| 72 complex data is cut in half (rounded down), plus one. As for the | |
| 73 serial transforms, the sizes you pass to the ‘<samp><span class="samp">plan_dft_r2c</span></samp>’ and | |
| 74 ‘<samp><span class="samp">plan_dft_c2r</span></samp>’ are the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> dimensions of the real data. | |
| 75 | |
| 76 <li><a name="index-padding-386"></a>Although the real data is <em>conceptually</em> n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>, it is | |
| 77 <em>physically</em> stored as an n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × [2 (n<sub>d-1</sub>/2 + 1)] array, where the last | |
| 78 dimension has been <em>padded</em> to make it the same size as the | |
| 79 complex output. This is much like the in-place serial r2c/c2r | |
| 80 interface (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data">Multi-Dimensional DFTs of Real Data</a>), except that | |
| 81 in MPI the padding is required even for out-of-place data. The extra | |
| 82 padding numbers are ignored by FFTW (they are <em>not</em> like | |
| 83 zero-padding the transform to a larger size); they are only used to | |
| 84 determine the data layout. | |
| 85 | |
| 86 <li><a name="index-data-distribution-387"></a>The data distribution in MPI for <em>both</em> the real and complex data | |
| 87 is determined by the shape of the <em>complex</em> data. That is, you | |
| 88 call the appropriate ‘<samp><span class="samp">local size</span></samp>’ function for the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) | |
| 89 | |
| 90 <p>complex data, and then use the <em>same</em> distribution for the real | |
| 91 data except that the last complex dimension is replaced by a (padded) | |
| 92 real dimension of twice the length. | |
| 93 | |
| 94 </ul> | |
| 95 | |
| 96 <p>For example suppose we are performing an out-of-place r2c transform of | |
| 97 L × M × N real data [padded to L × M × 2(N/2+1)], | |
| 98 resulting in L × M × N/2+1 complex data. Similar to the | |
| 99 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like: | |
| 100 | |
| 101 <pre class="example"> #include <fftw3-mpi.h> | |
| 102 | |
| 103 int main(int argc, char **argv) | |
| 104 { | |
| 105 const ptrdiff_t L = ..., M = ..., N = ...; | |
| 106 fftw_plan plan; | |
| 107 double *rin; | |
| 108 fftw_complex *cout; | |
| 109 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k; | |
| 110 | |
| 111 MPI_Init(&argc, &argv); | |
| 112 fftw_mpi_init(); | |
| 113 | |
| 114 /* <span class="roman">get local data size and allocate</span> */ | |
| 115 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD, | |
| 116 &local_n0, &local_0_start); | |
| 117 rin = fftw_alloc_real(2 * alloc_local); | |
| 118 cout = fftw_alloc_complex(alloc_local); | |
| 119 | |
| 120 /* <span class="roman">create plan for out-of-place r2c DFT</span> */ | |
| 121 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD, | |
| 122 FFTW_MEASURE); | |
| 123 | |
| 124 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */ | |
| 125 for (i = 0; i < local_n0; ++i) | |
| 126 for (j = 0; j < M; ++j) | |
| 127 for (k = 0; k < N; ++k) | |
| 128 rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k); | |
| 129 | |
| 130 /* <span class="roman">compute transforms as many times as desired</span> */ | |
| 131 fftw_execute(plan); | |
| 132 | |
| 133 fftw_destroy_plan(plan); | |
| 134 | |
| 135 MPI_Finalize(); | |
| 136 } | |
| 137 </pre> | |
| 138 <p><a name="index-fftw_005falloc_005freal-388"></a><a name="index-row_002dmajor-389"></a>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an | |
| 139 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the | |
| 140 number of <em>complex</em> values to allocate, the number of <em>real</em> | |
| 141 values is twice as many. The <code>rin</code> array is then | |
| 142 local_n0 × M × 2(N/2+1) in row-major order, so its | |
| 143 <code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) + | |
| 144 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>). | |
| 145 | |
| 146 <p><a name="index-transpose-390"></a><a name="index-FFTW_005fTRANSPOSED_005fOUT-391"></a><a name="index-FFTW_005fTRANSPOSED_005fIN-392"></a>As for the complex transforms, improved performance can be obtained by | |
| 147 specifying that the output is the transpose of the input or vice versa | |
| 148 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c | |
| 149 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that | |
| 150 the input would be a padded L × M × 2(N/2+1) real array | |
| 151 distributed over the <code>L</code> dimension, while the output would be a | |
| 152 M × L × N/2+1 complex array distributed over the <code>M</code> | |
| 153 dimension. To perform the inverse c2r transform with the same data | |
| 154 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag. | |
| 155 | |
| 156 <!-- --> | |
| 157 </body></html> | |
| 158 |