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Current fftw source

author	Chris Cannam
date	Tue, 18 Oct 2016 13:40:26 +0100
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Chris@42	25 <title>FFTW 3.3.5: Multi-dimensional MPI DFTs of Real Data</title>
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Chris@42	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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Chris@42	70
Chris@42	71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42	72 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
Chris@42	73 <div class="header">
Chris@42	74 <p>
Chris@42	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>
Chris@42	76 </div>
Chris@42	77 <hr>
Chris@42	78 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a>
Chris@42	79 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
Chris@42	80
Chris@42	81 <p>FFTW’s MPI interface also supports multi-dimensional DFTs of real
Chris@42	82 data, similar to the serial r2c and c2r interfaces. (Parallel
Chris@42	83 one-dimensional real-data DFTs are not currently supported; you must
Chris@42	84 use a complex transform and set the imaginary parts of the inputs to
Chris@42	85 zero.)
Chris@42	86 </p>
Chris@42	87 <p>The key points to understand for r2c and c2r MPI transforms (compared
Chris@42	88 to the MPI complex DFTs or the serial r2c/c2r transforms), are:
Chris@42	89 </p>
Chris@42	90 <ul>
Chris@42	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
Chris@42	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
Chris@42	93 complex data is cut in half (rounded down), plus one. As for the
Chris@42	94 serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and
Chris@42	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.
Chris@42	96
Chris@42	97 </li><li> <a name="index-padding-4"></a>
Chris@42	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
Chris@42	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
Chris@42	100 dimension has been <em>padded</em> to make it the same size as the
Chris@42	101 complex output. This is much like the in-place serial r2c/c2r
Chris@42	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
Chris@42	103 in MPI the padding is required even for out-of-place data. The extra
Chris@42	104 padding numbers are ignored by FFTW (they are <em>not</em> like
Chris@42	105 zero-padding the transform to a larger size); they are only used to
Chris@42	106 determine the data layout.
Chris@42	107
Chris@42	108 </li><li> <a name="index-data-distribution-3"></a>
Chris@42	109 The data distribution in MPI for <em>both</em> the real and complex data
Chris@42	110 is determined by the shape of the <em>complex</em> data. That is, you
Chris@42	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)
Chris@42	112 complex data, and then use the <em>same</em> distribution for the real
Chris@42	113 data except that the last complex dimension is replaced by a (padded)
Chris@42	114 real dimension of twice the length.
Chris@42	115
Chris@42	116 </li></ul>
Chris@42	117
Chris@42	118 <p>For example suppose we are performing an out-of-place r2c transform of
Chris@42	119 L × M × N real data [padded to L × M × 2(N/2+1)],
Chris@42	120 resulting in L × M × N/2+1 complex data. Similar to the
Chris@42	121 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like:
Chris@42	122 </p>
Chris@42	123 <div class="example">
Chris@42	124 <pre class="example">#include <fftw3-mpi.h>
Chris@42	125
Chris@42	126 int main(int argc, char **argv)
Chris@42	127 {
Chris@42	128 const ptrdiff_t L = ..., M = ..., N = ...;
Chris@42	129 fftw_plan plan;
Chris@42	130 double *rin;
Chris@42	131 fftw_complex *cout;
Chris@42	132 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
Chris@42	133
Chris@42	134 MPI_Init(&argc, &argv);
Chris@42	135 fftw_mpi_init();
Chris@42	136
Chris@42	137 /* <span class="roman">get local data size and allocate</span> */
Chris@42	138 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
Chris@42	139 &local_n0, &local_0_start);
Chris@42	140 rin = fftw_alloc_real(2 * alloc_local);
Chris@42	141 cout = fftw_alloc_complex(alloc_local);
Chris@42	142
Chris@42	143 /* <span class="roman">create plan for out-of-place r2c DFT</span> */
Chris@42	144 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
Chris@42	145 FFTW_MEASURE);
Chris@42	146
Chris@42	147 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
Chris@42	148 for (i = 0; i < local_n0; ++i)
Chris@42	149 for (j = 0; j < M; ++j)
Chris@42	150 for (k = 0; k < N; ++k)
Chris@42	151 rin[(iM + j) (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
Chris@42	152
Chris@42	153 /* <span class="roman">compute transforms as many times as desired</span> */
Chris@42	154 fftw_execute(plan);
Chris@42	155
Chris@42	156 fftw_destroy_plan(plan);
Chris@42	157
Chris@42	158 MPI_Finalize();
Chris@42	159 }
Chris@42	160 </pre></div>
Chris@42	161
Chris@42	162 <a name="index-fftw_005falloc_005freal-2"></a>
Chris@42	163 <a name="index-row_002dmajor-5"></a>
Chris@42	164 <p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
Chris@42	165 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
Chris@42	166 number of <em>complex</em> values to allocate, the number of <em>real</em>
Chris@42	167 values is twice as many. The <code>rin</code> array is then
Chris@42	168 local_n0 × M × 2(N/2+1) in row-major order, so its
Chris@42	169 <code>(i,j,k)</code> element is at the index <code>(iM + j) (2*(N/2+1)) +
Chris@42	170 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
Chris@42	171 </p>
Chris@42	172 <a name="index-transpose-1"></a>
Chris@42	173 <a name="index-FFTW_005fTRANSPOSED_005fOUT"></a>
Chris@42	174 <a name="index-FFTW_005fTRANSPOSED_005fIN"></a>
Chris@42	175 <p>As for the complex transforms, improved performance can be obtained by
Chris@42	176 specifying that the output is the transpose of the input or vice versa
Chris@42	177 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c
Chris@42	178 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
Chris@42	179 the input would be a padded L × M × 2(N/2+1) real array
Chris@42	180 distributed over the <code>L</code> dimension, while the output would be a
Chris@42	181 M × L × N/2+1 complex array distributed over the <code>M</code>
Chris@42	182 dimension. To perform the inverse c2r transform with the same data
Chris@42	183 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
Chris@42	184 </p>
Chris@42	185 <hr>
Chris@42	186 <div class="header">
Chris@42	187 <p>
Chris@42	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>
Chris@42	189 </div>
Chris@42	190
Chris@42	191
Chris@42	192
Chris@42	193 </body>
Chris@42	194 </html>

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