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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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+<html lang="en">
+<head>
+<title>One-dimensional distributions - FFTW 3.3.3</title>
+<meta http-equiv="Content-Type" content="text/html">
+<meta name="description" content="FFTW 3.3.3">
+<meta name="generator" content="makeinfo 4.13">
+<link title="Top" rel="start" href="index.html#Top">
+<link rel="up" href="MPI-Data-Distribution.html#MPI-Data-Distribution" title="MPI Data Distribution">
+<link rel="prev" href="Transposed-distributions.html#Transposed-distributions" title="Transposed distributions">
+<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
+<!--
+This manual is for FFTW
+(version 3.3.3, 25 November 2012).
+
+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.
+   -->
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+<style type="text/css"><!--
+  pre.display { font-family:inherit }
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+--></style>
+</head>
+<body>
+<div class="node">
+<a name="One-dimensional-distributions"></a>
+<a name="One_002ddimensional-distributions"></a>
+<p>
+Previous:&nbsp;<a rel="previous" accesskey="p" href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>,
+Up:&nbsp;<a rel="up" accesskey="u" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>
+<hr>
+</div>
+
+<h4 class="subsection">6.4.4 One-dimensional distributions</h4>
+
+<p>For one-dimensional distributed DFTs using FFTW, matters are slightly
+more complicated because the data distribution is more closely tied to
+how the algorithm works.  In particular, you can no longer pass an
+arbitrary block size and must accept FFTW's default; also, the block
+sizes may be different for input and output.  Also, the data
+distribution depends on the flags and transform direction, in order
+for forward and backward transforms to work correctly.
+
+<pre class="example">     ptrdiff_t fftw_mpi_local_size_1d(ptrdiff_t n0, MPI_Comm comm,
+                     int sign, unsigned flags,
+                     ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
+                     ptrdiff_t *local_no, ptrdiff_t *local_o_start);
+</pre>
+   <p><a name="index-fftw_005fmpi_005flocal_005fsize_005f1d-383"></a>
+This function computes the data distribution for a 1d transform of
+size <code>n0</code> with the given transform <code>sign</code> and <code>flags</code>. 
+Both input and output data use block distributions.  The input on the
+current process will consist of <code>local_ni</code> numbers starting at
+index <code>local_i_start</code>; e.g. if only a single process is used,
+then <code>local_ni</code> will be <code>n0</code> and <code>local_i_start</code> will
+be <code>0</code>.  Similarly for the output, with <code>local_no</code> numbers
+starting at index <code>local_o_start</code>.  The return value of
+<code>fftw_mpi_local_size_1d</code> will be the total number of elements to
+allocate on the current process (which might be slightly larger than
+the local size due to intermediate steps in the algorithm).
+
+   <p>As mentioned above (see <a href="Load-balancing.html#Load-balancing">Load balancing</a>), the data will be divided
+equally among the processes if <code>n0</code> is divisible by the
+<em>square</em> of the number of processes.  In this case,
+<code>local_ni</code> will equal <code>local_no</code>.  Otherwise, they may be
+different.
+
+   <p>For some applications, such as convolutions, the order of the output
+data is irrelevant.  In this case, performance can be improved by
+specifying that the output data be stored in an FFTW-defined
+&ldquo;scrambled&rdquo; format.  (In particular, this is the analogue of
+transposed output in the multidimensional case: scrambled output saves
+a communications step.)  If you pass <code>FFTW_MPI_SCRAMBLED_OUT</code> in
+the flags, then the output is stored in this (undocumented) scrambled
+order.  Conversely, to perform the inverse transform of data in
+scrambled order, pass the <code>FFTW_MPI_SCRAMBLED_IN</code> flag. 
+<a name="index-FFTW_005fMPI_005fSCRAMBLED_005fOUT-384"></a><a name="index-FFTW_005fMPI_005fSCRAMBLED_005fIN-385"></a>
+
+   <p>In MPI FFTW, only composite sizes <code>n0</code> can be parallelized; we
+have not yet implemented a parallel algorithm for large prime sizes.
+
+<!--  -->
+   </body></html>
+