Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/Multi_002ddimensional-MPI-DFTs-of-Real-Data.html @ 167:bd3cc4d1df30
Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Tue, 19 Nov 2019 14:52:55 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.8/doc/html/Multi_002ddimensional-MPI-DFTs-of-Real-Data.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,206 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<html> +<!-- This manual is for FFTW +(version 3.3.8, 24 May 2018). + +Copyright (C) 2003 Matteo Frigo. + +Copyright (C) 2003 Massachusetts Institute of Technology. + +Permission is granted to make and distribute verbatim copies of this +manual provided the copyright notice and this permission notice are +preserved on all copies. + +Permission is granted to copy and distribute modified versions of this +manual under the conditions for verbatim copying, provided that the +entire resulting derived work is distributed under the terms of a +permission notice identical to this one. + +Permission is granted to copy and distribute translations of this manual +into another language, under the above conditions for modified versions, +except that this permission notice may be stated in a translation +approved by the Free Software Foundation. --> +<!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> +<head> +<title>FFTW 3.3.8: Multi-dimensional MPI DFTs of Real Data</title> + +<meta name="description" content="FFTW 3.3.8: Multi-dimensional MPI DFTs of Real Data"> +<meta name="keywords" content="FFTW 3.3.8: Multi-dimensional MPI DFTs of Real Data"> +<meta name="resource-type" content="document"> +<meta name="distribution" content="global"> +<meta name="Generator" content="makeinfo"> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> +<link href="index.html#Top" rel="start" title="Top"> +<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> +<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> +<link href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" rel="up" title="Distributed-memory FFTW with MPI"> +<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"> +<link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="prev" title="One-dimensional distributions"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.indentedblock {margin-right: 0em} +blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smalllisp {margin-left: 3.2em} +kbd {font-style: oblique} +pre.display {font-family: inherit} +pre.format {font-family: inherit} +pre.menu-comment {font-family: serif} +pre.menu-preformatted {font-family: serif} +pre.smalldisplay {font-family: inherit; font-size: smaller} +pre.smallexample {font-size: smaller} +pre.smallformat {font-family: inherit; font-size: smaller} +pre.smalllisp {font-size: smaller} +span.nolinebreak {white-space: nowrap} +span.roman {font-family: initial; font-weight: normal} +span.sansserif {font-family: sans-serif; font-weight: normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en"> +<a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a> +<div class="header"> +<p> +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> +</div> +<hr> +<a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a> +<h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3> + +<p>FFTW’s MPI interface also supports multi-dimensional DFTs of real +data, similar to the serial r2c and c2r interfaces. (Parallel +one-dimensional real-data DFTs are not currently supported; you must +use a complex transform and set the imaginary parts of the inputs to +zero.) +</p> +<p>The key points to understand for r2c and c2r MPI transforms (compared +to the MPI complex DFTs or the serial r2c/c2r transforms), are: +</p> +<ul> +<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 +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 +complex data is cut in half (rounded down), plus one. As for the +serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and +‘<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. + +</li><li> <a name="index-padding-4"></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 +<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 +dimension has been <em>padded</em> to make it the same size as the +complex output. This is much like the in-place serial r2c/c2r +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 +in MPI the padding is required even for out-of-place data. The extra +padding numbers are ignored by FFTW (they are <em>not</em> like +zero-padding the transform to a larger size); they are only used to +determine the data layout. + +</li><li> <a name="index-data-distribution-3"></a> +The data distribution in MPI for <em>both</em> the real and complex data +is determined by the shape of the <em>complex</em> data. That is, you +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) + +complex data, and then use the <em>same</em> distribution for the real +data except that the last complex dimension is replaced by a (padded) +real dimension of twice the length. + +</li></ul> + +<p>For example suppose we are performing an out-of-place r2c transform of +L × M × N + real data [padded to L × M × 2(N/2+1) +], +resulting in L × M × N/2+1 + complex data. Similar to the +example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like: +</p> +<div class="example"> +<pre class="example">#include <fftw3-mpi.h> + +int main(int argc, char **argv) +{ + const ptrdiff_t L = ..., M = ..., N = ...; + fftw_plan plan; + double *rin; + fftw_complex *cout; + ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k; + + MPI_Init(&argc, &argv); + fftw_mpi_init(); + + /* <span class="roman">get local data size and allocate</span> */ + alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD, + &local_n0, &local_0_start); + rin = fftw_alloc_real(2 * alloc_local); + cout = fftw_alloc_complex(alloc_local); + + /* <span class="roman">create plan for out-of-place r2c DFT</span> */ + plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD, + FFTW_MEASURE); + + /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */ + for (i = 0; i < local_n0; ++i) + for (j = 0; j < M; ++j) + for (k = 0; k < N; ++k) + rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k); + + /* <span class="roman">compute transforms as many times as desired</span> */ + fftw_execute(plan); + + fftw_destroy_plan(plan); + + MPI_Finalize(); +} +</pre></div> + +<a name="index-fftw_005falloc_005freal-2"></a> +<a name="index-row_002dmajor-5"></a> +<p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an +argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the +number of <em>complex</em> values to allocate, the number of <em>real</em> +values is twice as many. The <code>rin</code> array is then +local_n0 × M × 2(N/2+1) + in row-major order, so its +<code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) + +k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>). +</p> +<a name="index-transpose-1"></a> +<a name="index-FFTW_005fTRANSPOSED_005fOUT"></a> +<a name="index-FFTW_005fTRANSPOSED_005fIN"></a> +<p>As for the complex transforms, improved performance can be obtained by +specifying that the output is the transpose of the input or vice versa +(see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N + r2c +example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that +the input would be a padded L × M × 2(N/2+1) + real array +distributed over the <code>L</code> dimension, while the output would be a +M × L × N/2+1 + complex array distributed over the <code>M</code> +dimension. To perform the inverse c2r transform with the same data +distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag. +</p> +<hr> +<div class="header"> +<p> +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> +</div> + + + +</body> +</html>