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Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
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Chris@10 1 <html lang="en">
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Chris@10 3 <title>Other Multi-dimensional Real-data MPI Transforms - FFTW 3.3.3</title>
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Chris@10 48 <div class="node">
Chris@10 49 <a name="Other-Multi-dimensional-Real-data-MPI-Transforms"></a>
Chris@10 50 <a name="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms"></a>
Chris@10 51 <p>
Chris@10 52 Next:&nbsp;<a rel="next" accesskey="n" href="FFTW-MPI-Transposes.html#FFTW-MPI-Transposes">FFTW MPI Transposes</a>,
Chris@10 53 Previous:&nbsp;<a rel="previous" accesskey="p" href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data">Multi-dimensional MPI DFTs of Real Data</a>,
Chris@10 54 Up:&nbsp;<a rel="up" accesskey="u" href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI">Distributed-memory FFTW with MPI</a>
Chris@10 55 <hr>
Chris@10 56 </div>
Chris@10 57
Chris@10 58 <h3 class="section">6.6 Other multi-dimensional Real-Data MPI Transforms</h3>
Chris@10 59
Chris@10 60 <p><a name="index-r2r-393"></a>FFTW's MPI interface also supports multi-dimensional &lsquo;<samp><span class="samp">r2r</span></samp>&rsquo;
Chris@10 61 transforms of all kinds supported by the serial interface
Chris@10 62 (e.g. discrete cosine and sine transforms, discrete Hartley
Chris@10 63 transforms, etc.). Only multi-dimensional &lsquo;<samp><span class="samp">r2r</span></samp>&rsquo; transforms, not
Chris@10 64 one-dimensional transforms, are currently parallelized.
Chris@10 65
Chris@10 66 <p><a name="index-fftw_005fr2r_005fkind-394"></a>These are used much like the multidimensional complex DFTs discussed
Chris@10 67 above, except that the data is real rather than complex, and one needs
Chris@10 68 to pass an r2r transform kind (<code>fftw_r2r_kind</code>) for each
Chris@10 69 dimension as in the serial FFTW (see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>).
Chris@10 70
Chris@10 71 <p>For example, one might perform a two-dimensional L&nbsp;&times;&nbsp;M that is
Chris@10 72 an REDFT10 (DCT-II) in the first dimension and an RODFT10 (DST-II) in
Chris@10 73 the second dimension with code like:
Chris@10 74
Chris@10 75 <pre class="example"> const ptrdiff_t L = ..., M = ...;
Chris@10 76 fftw_plan plan;
Chris@10 77 double *data;
Chris@10 78 ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
Chris@10 79
Chris@10 80 /* <span class="roman">get local data size and allocate</span> */
Chris@10 81 alloc_local = fftw_mpi_local_size_2d(L, M, MPI_COMM_WORLD,
Chris@10 82 &amp;local_n0, &amp;local_0_start);
Chris@10 83 data = fftw_alloc_real(alloc_local);
Chris@10 84
Chris@10 85 /* <span class="roman">create plan for in-place REDFT10 x RODFT10</span> */
Chris@10 86 plan = fftw_mpi_plan_r2r_2d(L, M, data, data, MPI_COMM_WORLD,
Chris@10 87 FFTW_REDFT10, FFTW_RODFT10, FFTW_MEASURE);
Chris@10 88
Chris@10 89 /* <span class="roman">initialize data to some function</span> my_function(x,y) */
Chris@10 90 for (i = 0; i &lt; local_n0; ++i) for (j = 0; j &lt; M; ++j)
Chris@10 91 data[i*M + j] = my_function(local_0_start + i, j);
Chris@10 92
Chris@10 93 /* <span class="roman">compute transforms, in-place, as many times as desired</span> */
Chris@10 94 fftw_execute(plan);
Chris@10 95
Chris@10 96 fftw_destroy_plan(plan);
Chris@10 97 </pre>
Chris@10 98 <p><a name="index-fftw_005falloc_005freal-395"></a>Notice that we use the same &lsquo;<samp><span class="samp">local_size</span></samp>&rsquo; functions as we did for
Chris@10 99 complex data, only now we interpret the sizes in terms of real rather
Chris@10 100 than complex values, and correspondingly use <code>fftw_alloc_real</code>.
Chris@10 101
Chris@10 102 <!-- -->
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Chris@10 104