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author | Chris Cannam |
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date | Tue, 18 Oct 2016 13:40:26 +0100 |
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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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25 <title>FFTW 3.3.5: Multi-dimensional MPI DFTs of Real Data</title> | |
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37 <link href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" rel="next" title="Other Multi-dimensional Real-data MPI Transforms"> | |
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71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> | |
72 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a> | |
73 <div class="header"> | |
74 <p> | |
75 Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a> | |
79 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3> | |
80 | |
81 <p>FFTW’s MPI interface also supports multi-dimensional DFTs of real | |
82 data, similar to the serial r2c and c2r interfaces. (Parallel | |
83 one-dimensional real-data DFTs are not currently supported; you must | |
84 use a complex transform and set the imaginary parts of the inputs to | |
85 zero.) | |
86 </p> | |
87 <p>The key points to understand for r2c and c2r MPI transforms (compared | |
88 to the MPI complex DFTs or the serial r2c/c2r transforms), are: | |
89 </p> | |
90 <ul> | |
91 <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 | |
92 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 | |
93 complex data is cut in half (rounded down), plus one. As for the | |
94 serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and | |
95 ‘<samp>plan_dft_c2r</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. | |
96 | |
97 </li><li> <a name="index-padding-4"></a> | |
98 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 | |
99 <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 | |
100 dimension has been <em>padded</em> to make it the same size as the | |
101 complex output. This is much like the in-place serial r2c/c2r | |
102 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 | |
103 in MPI the padding is required even for out-of-place data. The extra | |
104 padding numbers are ignored by FFTW (they are <em>not</em> like | |
105 zero-padding the transform to a larger size); they are only used to | |
106 determine the data layout. | |
107 | |
108 </li><li> <a name="index-data-distribution-3"></a> | |
109 The data distribution in MPI for <em>both</em> the real and complex data | |
110 is determined by the shape of the <em>complex</em> data. That is, you | |
111 call the appropriate ‘<samp>local size</samp>’ function for the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) | |
112 complex data, and then use the <em>same</em> distribution for the real | |
113 data except that the last complex dimension is replaced by a (padded) | |
114 real dimension of twice the length. | |
115 | |
116 </li></ul> | |
117 | |
118 <p>For example suppose we are performing an out-of-place r2c transform of | |
119 L × M × N real data [padded to L × M × 2(N/2+1)], | |
120 resulting in L × M × N/2+1 complex data. Similar to the | |
121 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like: | |
122 </p> | |
123 <div class="example"> | |
124 <pre class="example">#include <fftw3-mpi.h> | |
125 | |
126 int main(int argc, char **argv) | |
127 { | |
128 const ptrdiff_t L = ..., M = ..., N = ...; | |
129 fftw_plan plan; | |
130 double *rin; | |
131 fftw_complex *cout; | |
132 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k; | |
133 | |
134 MPI_Init(&argc, &argv); | |
135 fftw_mpi_init(); | |
136 | |
137 /* <span class="roman">get local data size and allocate</span> */ | |
138 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD, | |
139 &local_n0, &local_0_start); | |
140 rin = fftw_alloc_real(2 * alloc_local); | |
141 cout = fftw_alloc_complex(alloc_local); | |
142 | |
143 /* <span class="roman">create plan for out-of-place r2c DFT</span> */ | |
144 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD, | |
145 FFTW_MEASURE); | |
146 | |
147 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */ | |
148 for (i = 0; i < local_n0; ++i) | |
149 for (j = 0; j < M; ++j) | |
150 for (k = 0; k < N; ++k) | |
151 rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k); | |
152 | |
153 /* <span class="roman">compute transforms as many times as desired</span> */ | |
154 fftw_execute(plan); | |
155 | |
156 fftw_destroy_plan(plan); | |
157 | |
158 MPI_Finalize(); | |
159 } | |
160 </pre></div> | |
161 | |
162 <a name="index-fftw_005falloc_005freal-2"></a> | |
163 <a name="index-row_002dmajor-5"></a> | |
164 <p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an | |
165 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the | |
166 number of <em>complex</em> values to allocate, the number of <em>real</em> | |
167 values is twice as many. The <code>rin</code> array is then | |
168 local_n0 × M × 2(N/2+1) in row-major order, so its | |
169 <code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) + | |
170 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>). | |
171 </p> | |
172 <a name="index-transpose-1"></a> | |
173 <a name="index-FFTW_005fTRANSPOSED_005fOUT"></a> | |
174 <a name="index-FFTW_005fTRANSPOSED_005fIN"></a> | |
175 <p>As for the complex transforms, improved performance can be obtained by | |
176 specifying that the output is the transpose of the input or vice versa | |
177 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c | |
178 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that | |
179 the input would be a padded L × M × 2(N/2+1) real array | |
180 distributed over the <code>L</code> dimension, while the output would be a | |
181 M × L × N/2+1 complex array distributed over the <code>M</code> | |
182 dimension. To perform the inverse c2r transform with the same data | |
183 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag. | |
184 </p> | |
185 <hr> | |
186 <div class="header"> | |
187 <p> | |
188 Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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> | |
189 </div> | |
190 | |
191 | |
192 | |
193 </body> | |
194 </html> |