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