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Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam |
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| date | Tue, 19 Nov 2019 14:52:55 +0000 |
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<!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>