sv-dependency-builds: src/fftw-3.3.8/doc/html/Multi_002ddimensional-MPI-DFTs-of-Real-Data.html annotate

annotate src/fftw-3.3.8/doc/html/Multi_002ddimensional-MPI-DFTs-of-Real-Data.html @ 82:d0c2a83c1364

Add FFTW 3.3.8 source, and a Linux build

author	Chris Cannam
date	Tue, 19 Nov 2019 14:52:55 +0000
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rev	line source
Chris@82	1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@82	3 <!-- This manual is for FFTW
Chris@82	4 (version 3.3.8, 24 May 2018).
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Chris@82	6 Copyright (C) 2003 Matteo Frigo.
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Chris@82	24 <head>
Chris@82	25 <title>FFTW 3.3.8: Multi-dimensional MPI DFTs of Real Data</title>
Chris@82	26
Chris@82	27 <meta name="description" content="FFTW 3.3.8: Multi-dimensional MPI DFTs of Real Data">
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Chris@82	35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82	36 <link href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" rel="up" title="Distributed-memory FFTW with MPI">
Chris@82	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">
Chris@82	38 <link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="prev" title="One-dimensional distributions">
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Chris@82	68 </head>
Chris@82	69
Chris@82	70 <body lang="en">
Chris@82	71 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
Chris@82	72 <div class="header">
Chris@82	73 <p>
Chris@82	74 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@82	75 </div>
Chris@82	76 <hr>
Chris@82	77 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a>
Chris@82	78 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
Chris@82	79
Chris@82	80 <p>FFTW’s MPI interface also supports multi-dimensional DFTs of real
Chris@82	81 data, similar to the serial r2c and c2r interfaces. (Parallel
Chris@82	82 one-dimensional real-data DFTs are not currently supported; you must
Chris@82	83 use a complex transform and set the imaginary parts of the inputs to
Chris@82	84 zero.)
Chris@82	85 </p>
Chris@82	86 <p>The key points to understand for r2c and c2r MPI transforms (compared
Chris@82	87 to the MPI complex DFTs or the serial r2c/c2r transforms), are:
Chris@82	88 </p>
Chris@82	89 <ul>
Chris@82	90 <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>
Chris@82	91 real
Chris@82	92 data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1)
Chris@82	93 complex data: the last dimension of the
Chris@82	94 complex data is cut in half (rounded down), plus one. As for the
Chris@82	95 serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and
Chris@82	96 ‘<samp>plan_dft_c2r</samp>’ are the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
Chris@82	97 dimensions of the real data.
Chris@82	98
Chris@82	99 </li><li> <a name="index-padding-4"></a>
Chris@82	100 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>
Chris@82	101 , it is
Chris@82	102 <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)]
Chris@82	103 array, where the last
Chris@82	104 dimension has been <em>padded</em> to make it the same size as the
Chris@82	105 complex output. This is much like the in-place serial r2c/c2r
Chris@82	106 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@82	107 in MPI the padding is required even for out-of-place data. The extra
Chris@82	108 padding numbers are ignored by FFTW (they are <em>not</em> like
Chris@82	109 zero-padding the transform to a larger size); they are only used to
Chris@82	110 determine the data layout.
Chris@82	111
Chris@82	112 </li><li> <a name="index-data-distribution-3"></a>
Chris@82	113 The data distribution in MPI for <em>both</em> the real and complex data
Chris@82	114 is determined by the shape of the <em>complex</em> data. That is, you
Chris@82	115 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@82	116
Chris@82	117 complex data, and then use the <em>same</em> distribution for the real
Chris@82	118 data except that the last complex dimension is replaced by a (padded)
Chris@82	119 real dimension of twice the length.
Chris@82	120
Chris@82	121 </li></ul>
Chris@82	122
Chris@82	123 <p>For example suppose we are performing an out-of-place r2c transform of
Chris@82	124 L × M × N
Chris@82	125 real data [padded to L × M × 2(N/2+1)
Chris@82	126 ],
Chris@82	127 resulting in L × M × N/2+1
Chris@82	128 complex data. Similar to the
Chris@82	129 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like:
Chris@82	130 </p>
Chris@82	131 <div class="example">
Chris@82	132 <pre class="example">#include <fftw3-mpi.h>
Chris@82	133
Chris@82	134 int main(int argc, char **argv)
Chris@82	135 {
Chris@82	136 const ptrdiff_t L = ..., M = ..., N = ...;
Chris@82	137 fftw_plan plan;
Chris@82	138 double *rin;
Chris@82	139 fftw_complex *cout;
Chris@82	140 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
Chris@82	141
Chris@82	142 MPI_Init(&argc, &argv);
Chris@82	143 fftw_mpi_init();
Chris@82	144
Chris@82	145 /* <span class="roman">get local data size and allocate</span> */
Chris@82	146 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
Chris@82	147 &local_n0, &local_0_start);
Chris@82	148 rin = fftw_alloc_real(2 * alloc_local);
Chris@82	149 cout = fftw_alloc_complex(alloc_local);
Chris@82	150
Chris@82	151 /* <span class="roman">create plan for out-of-place r2c DFT</span> */
Chris@82	152 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
Chris@82	153 FFTW_MEASURE);
Chris@82	154
Chris@82	155 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
Chris@82	156 for (i = 0; i < local_n0; ++i)
Chris@82	157 for (j = 0; j < M; ++j)
Chris@82	158 for (k = 0; k < N; ++k)
Chris@82	159 rin[(iM + j) (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
Chris@82	160
Chris@82	161 /* <span class="roman">compute transforms as many times as desired</span> */
Chris@82	162 fftw_execute(plan);
Chris@82	163
Chris@82	164 fftw_destroy_plan(plan);
Chris@82	165
Chris@82	166 MPI_Finalize();
Chris@82	167 }
Chris@82	168 </pre></div>
Chris@82	169
Chris@82	170 <a name="index-fftw_005falloc_005freal-2"></a>
Chris@82	171 <a name="index-row_002dmajor-5"></a>
Chris@82	172 <p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
Chris@82	173 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
Chris@82	174 number of <em>complex</em> values to allocate, the number of <em>real</em>
Chris@82	175 values is twice as many. The <code>rin</code> array is then
Chris@82	176 local_n0 × M × 2(N/2+1)
Chris@82	177 in row-major order, so its
Chris@82	178 <code>(i,j,k)</code> element is at the index <code>(iM + j) (2*(N/2+1)) +
Chris@82	179 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
Chris@82	180 </p>
Chris@82	181 <a name="index-transpose-1"></a>
Chris@82	182 <a name="index-FFTW_005fTRANSPOSED_005fOUT"></a>
Chris@82	183 <a name="index-FFTW_005fTRANSPOSED_005fIN"></a>
Chris@82	184 <p>As for the complex transforms, improved performance can be obtained by
Chris@82	185 specifying that the output is the transpose of the input or vice versa
Chris@82	186 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N
Chris@82	187 r2c
Chris@82	188 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
Chris@82	189 the input would be a padded L × M × 2(N/2+1)
Chris@82	190 real array
Chris@82	191 distributed over the <code>L</code> dimension, while the output would be a
Chris@82	192 M × L × N/2+1
Chris@82	193 complex array distributed over the <code>M</code>
Chris@82	194 dimension. To perform the inverse c2r transform with the same data
Chris@82	195 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
Chris@82	196 </p>
Chris@82	197 <hr>
Chris@82	198 <div class="header">
Chris@82	199 <p>
Chris@82	200 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@82	201 </div>
Chris@82	202
Chris@82	203
Chris@82	204
Chris@82	205 </body>
Chris@82	206 </html>

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