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author	Chris Cannam
date	Wed, 07 Sep 2016 10:40:32 +0100
parents	26056e866c29
children

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Chris@19	3 <title>Multi-dimensional MPI DFTs of Real Data - FFTW 3.3.4</title>
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Chris@19	13 This manual is for FFTW
Chris@19	14 (version 3.3.4, 20 September 2013).
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Chris@19	49 <a name="Multi-dimensional-MPI-DFTs-of-Real-Data"></a>
Chris@19	50 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
Chris@19	51 <p>
Chris@19	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>,
Chris@19	53 Previous: <a rel="previous" accesskey="p" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>,
Chris@19	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>
Chris@19	55 <hr>
Chris@19	56 </div>
Chris@19	57
Chris@19	58 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
Chris@19	59
Chris@19	60 <p>FFTW's MPI interface also supports multi-dimensional DFTs of real
Chris@19	61 data, similar to the serial r2c and c2r interfaces. (Parallel
Chris@19	62 one-dimensional real-data DFTs are not currently supported; you must
Chris@19	63 use a complex transform and set the imaginary parts of the inputs to
Chris@19	64 zero.)
Chris@19	65
Chris@19	66 <p>The key points to understand for r2c and c2r MPI transforms (compared
Chris@19	67 to the MPI complex DFTs or the serial r2c/c2r transforms), are:
Chris@19	68
Chris@19	69 <ul>
Chris@19	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
Chris@19	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
Chris@19	72 complex data is cut in half (rounded down), plus one. As for the
Chris@19	73 serial transforms, the sizes you pass to the ‘<samp><span class="samp">plan_dft_r2c</span></samp>’ and
Chris@19	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.
Chris@19	75
Chris@19	76 <li><a name="index-padding-389"></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
Chris@19	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
Chris@19	78 dimension has been <em>padded</em> to make it the same size as the
Chris@19	79 complex output. This is much like the in-place serial r2c/c2r
Chris@19	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
Chris@19	81 in MPI the padding is required even for out-of-place data. The extra
Chris@19	82 padding numbers are ignored by FFTW (they are <em>not</em> like
Chris@19	83 zero-padding the transform to a larger size); they are only used to
Chris@19	84 determine the data layout.
Chris@19	85
Chris@19	86 <li><a name="index-data-distribution-390"></a>The data distribution in MPI for <em>both</em> the real and complex data
Chris@19	87 is determined by the shape of the <em>complex</em> data. That is, you
Chris@19	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)
Chris@19	89
Chris@19	90 <p>complex data, and then use the <em>same</em> distribution for the real
Chris@19	91 data except that the last complex dimension is replaced by a (padded)
Chris@19	92 real dimension of twice the length.
Chris@19	93
Chris@19	94 </ul>
Chris@19	95
Chris@19	96 <p>For example suppose we are performing an out-of-place r2c transform of
Chris@19	97 L × M × N real data [padded to L × M × 2(N/2+1)],
Chris@19	98 resulting in L × M × N/2+1 complex data. Similar to the
Chris@19	99 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like:
Chris@19	100
Chris@19	101 <pre class="example"> #include <fftw3-mpi.h>
Chris@19	102
Chris@19	103 int main(int argc, char **argv)
Chris@19	104 {
Chris@19	105 const ptrdiff_t L = ..., M = ..., N = ...;
Chris@19	106 fftw_plan plan;
Chris@19	107 double *rin;
Chris@19	108 fftw_complex *cout;
Chris@19	109 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
Chris@19	110
Chris@19	111 MPI_Init(&argc, &argv);
Chris@19	112 fftw_mpi_init();
Chris@19	113
Chris@19	114 /* <span class="roman">get local data size and allocate</span> */
Chris@19	115 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
Chris@19	116 &local_n0, &local_0_start);
Chris@19	117 rin = fftw_alloc_real(2 * alloc_local);
Chris@19	118 cout = fftw_alloc_complex(alloc_local);
Chris@19	119
Chris@19	120 /* <span class="roman">create plan for out-of-place r2c DFT</span> */
Chris@19	121 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
Chris@19	122 FFTW_MEASURE);
Chris@19	123
Chris@19	124 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
Chris@19	125 for (i = 0; i < local_n0; ++i)
Chris@19	126 for (j = 0; j < M; ++j)
Chris@19	127 for (k = 0; k < N; ++k)
Chris@19	128 rin[(iM + j) (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
Chris@19	129
Chris@19	130 /* <span class="roman">compute transforms as many times as desired</span> */
Chris@19	131 fftw_execute(plan);
Chris@19	132
Chris@19	133 fftw_destroy_plan(plan);
Chris@19	134
Chris@19	135 MPI_Finalize();
Chris@19	136 }
Chris@19	137 </pre>
Chris@19	138 <p><a name="index-fftw_005falloc_005freal-391"></a><a name="index-row_002dmajor-392"></a>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
Chris@19	139 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
Chris@19	140 number of <em>complex</em> values to allocate, the number of <em>real</em>
Chris@19	141 values is twice as many. The <code>rin</code> array is then
Chris@19	142 local_n0 × M × 2(N/2+1) in row-major order, so its
Chris@19	143 <code>(i,j,k)</code> element is at the index <code>(iM + j) (2*(N/2+1)) +
Chris@19	144 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
Chris@19	145
Chris@19	146 <p><a name="index-transpose-393"></a><a name="index-FFTW_005fTRANSPOSED_005fOUT-394"></a><a name="index-FFTW_005fTRANSPOSED_005fIN-395"></a>As for the complex transforms, improved performance can be obtained by
Chris@19	147 specifying that the output is the transpose of the input or vice versa
Chris@19	148 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c
Chris@19	149 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
Chris@19	150 the input would be a padded L × M × 2(N/2+1) real array
Chris@19	151 distributed over the <code>L</code> dimension, while the output would be a
Chris@19	152 M × L × N/2+1 complex array distributed over the <code>M</code>
Chris@19	153 dimension. To perform the inverse c2r transform with the same data
Chris@19	154 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
Chris@19	155
Chris@19	156 <!-- -->
Chris@19	157 </body></html>
Chris@19	158

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