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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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<head>
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<title>Multi-dimensional MPI DFTs of Real Data (FFTW 3.3.10)</title>
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<meta name="description" content="Multi-dimensional MPI DFTs of Real Data (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Distributed_002dmemory-FFTW-with-MPI.html" rel="up" title="Distributed-memory FFTW with MPI">
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<link href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" rel="next" title="Other Multi-dimensional Real-data MPI Transforms">
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<link href="One_002ddimensional-distributions.html" rel="prev" title="One-dimensional distributions">
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</head>
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<body lang="en">
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<span id="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></span><div class="header">
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<p>
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Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></span><h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
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<p>FFTW’s MPI interface also supports multi-dimensional DFTs of real
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data, similar to the serial r2c and c2r interfaces. (Parallel
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one-dimensional real-data DFTs are not currently supported; you must
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use a complex transform and set the imaginary parts of the inputs to
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zero.)
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</p>
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<p>The key points to understand for r2c and c2r MPI transforms (compared
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to the MPI complex DFTs or the serial r2c/c2r transforms), are:
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</p>
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<ul>
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<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>
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real
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data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1)
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complex data: the last dimension of the
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complex data is cut in half (rounded down), plus one. As for the
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serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and
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‘<samp>plan_dft_c2r</samp>’ are the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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dimensions of the real data.
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</li><li> <span id="index-padding-4"></span>
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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>
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, it is
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<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)]
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array, where the last
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dimension has been <em>padded</em> to make it the same size as the
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complex output. This is much like the in-place serial r2c/c2r
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interface (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html">Multi-Dimensional DFTs of Real Data</a>), except that
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in MPI the padding is required even for out-of-place data. The extra
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padding numbers are ignored by FFTW (they are <em>not</em> like
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zero-padding the transform to a larger size); they are only used to
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determine the data layout.
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</li><li> <span id="index-data-distribution-3"></span>
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The data distribution in MPI for <em>both</em> the real and complex data
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is determined by the shape of the <em>complex</em> data. That is, you
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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)
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complex data, and then use the <em>same</em> distribution for the real
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data except that the last complex dimension is replaced by a (padded)
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real dimension of twice the length.
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</li></ul>
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<p>For example suppose we are performing an out-of-place r2c transform of
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L × M × N
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real data [padded to L × M × 2(N/2+1)
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],
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resulting in L × M × N/2+1
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complex data. Similar to the
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example in <a href="2d-MPI-example.html">2d MPI example</a>, we might do something like:
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</p>
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<div class="example">
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<pre class="example">#include <fftw3-mpi.h>
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int main(int argc, char **argv)
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{
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const ptrdiff_t L = ..., M = ..., N = ...;
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fftw_plan plan;
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double *rin;
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fftw_complex *cout;
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ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
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MPI_Init(&argc, &argv);
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fftw_mpi_init();
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/* <span class="roman">get local data size and allocate</span> */
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alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
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&local_n0, &local_0_start);
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rin = fftw_alloc_real(2 * alloc_local);
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cout = fftw_alloc_complex(alloc_local);
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/* <span class="roman">create plan for out-of-place r2c DFT</span> */
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plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
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FFTW_MEASURE);
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/* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
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for (i = 0; i < local_n0; ++i)
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for (j = 0; j < M; ++j)
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for (k = 0; k < N; ++k)
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rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
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/* <span class="roman">compute transforms as many times as desired</span> */
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fftw_execute(plan);
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fftw_destroy_plan(plan);
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MPI_Finalize();
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}
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</pre></div>
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<span id="index-fftw_005falloc_005freal-2"></span>
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<span id="index-row_002dmajor-5"></span>
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<p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
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argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
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number of <em>complex</em> values to allocate, the number of <em>real</em>
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values is twice as many. The <code>rin</code> array is then
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local_n0 × M × 2(N/2+1)
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in row-major order, so its
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<code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) +
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k</code> (see <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>).
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</p>
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<span id="index-transpose-1"></span>
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<span id="index-FFTW_005fTRANSPOSED_005fOUT"></span>
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<span id="index-FFTW_005fTRANSPOSED_005fIN"></span>
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<p>As for the complex transforms, improved performance can be obtained by
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specifying that the output is the transpose of the input or vice versa
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(see <a href="Transposed-distributions.html">Transposed distributions</a>). In our L × M × N
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r2c
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example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
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the input would be a padded L × M × 2(N/2+1)
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real array
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distributed over the <code>L</code> dimension, while the output would be a
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M × L × N/2+1
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complex array distributed over the <code>M</code>
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dimension. To perform the inverse c2r transform with the same data
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distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
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</p>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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