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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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approved by the Free Software Foundation. -->
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<title>Transposed distributions (FFTW 3.3.10)</title>
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<meta name="description" content="Transposed distributions (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="MPI-Data-Distribution.html" rel="up" title="MPI Data Distribution">
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<link href="One_002ddimensional-distributions.html" rel="next" title="One-dimensional distributions">
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<link href="Load-balancing.html" rel="prev" title="Load balancing">
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</head>
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<body lang="en">
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<span id="Transposed-distributions"></span><div class="header">
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<p>
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Next: <a href="One_002ddimensional-distributions.html" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html" accesskey="u" rel="up">MPI Data Distribution</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Transposed-distributions-1"></span><h4 class="subsection">6.4.3 Transposed distributions</h4>
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<p>Internally, FFTW’s MPI transform algorithms work by first computing
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transforms of the data local to each process, then by globally
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<em>transposing</em> the data in some fashion to redistribute the data
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among the processes, transforming the new data local to each process,
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and transposing back. For example, a two-dimensional <code>n0</code> by
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<code>n1</code> array, distributed across the <code>n0</code> dimension, is
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transformd by: (i) transforming the <code>n1</code> dimension, which are
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local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code>
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array, distributed across the <code>n1</code> dimension; (iii) transforming
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the <code>n0</code> dimension, which is now local to each process; (iv)
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transposing back.
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<span id="index-transpose"></span>
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</p>
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<p>However, in many applications it is acceptable to compute a
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multidimensional DFT whose results are produced in transposed order
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(e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a
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significant performance advantage, because it means that the final
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transposition step can be omitted. FFTW supports this optimization,
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which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code>
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to the planner routines. To compute the inverse transform of
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transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell
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it that the input is transposed. In this section, we explain how to
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interpret the output format of such a transform.
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<span id="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></span>
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<span id="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></span>
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</p>
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<p>Suppose you have are transforming multi-dimensional data with (at
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least two) dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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. As always, it is distributed along
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the first dimension n<sub>0</sub>
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. Now, if we compute its DFT with the
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<code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored
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with the first <em>two</em> dimensions transposed: n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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,
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distributed along the n<sub>1</sub>
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dimension. Conversely, if we take the
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n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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data and transform it with the
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<code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the
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original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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array.
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</p>
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<p>There are two ways to find the portion of the transposed array that
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resides on the current process. First, you can simply call the
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appropriate ‘<samp>local_size</samp>’ function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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(the
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transposed dimensions). This would mean calling the ‘<samp>local_size</samp>’
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function twice, once for the transposed and once for the
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non-transposed dimensions. Alternatively, you can call one of the
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‘<samp>local_size_transposed</samp>’ functions, which returns both the
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non-transposed and transposed data distribution from a single call.
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For example, for a 3d transform with transposed output (or input), you
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might call:
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</p>
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<div class="example">
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<pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed(
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ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
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ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
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ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
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</pre></div>
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<span id="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></span>
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<p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and
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starting index of the <code>n0</code> dimension for the
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<em>non</em>-transposed data, as in the previous sections. For
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<em>transposed</em> data (e.g. the output for
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<code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and
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<code>local_1_start</code> give the size and starting index of the <code>n1</code>
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dimension, which is the first dimension of the transposed data
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(<code>n1</code> by <code>n0</code> by <code>n2</code>).
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</p>
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<p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to
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performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two
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dimensions to the planner in reverse order, or vice versa. If you
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pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and
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<code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the
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first two dimensions passed to the planner and passing <em>neither</em>
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flag.)
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</p>
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<hr>
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<div class="header">
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<p>
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Next: <a href="One_002ddimensional-distributions.html" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html" accesskey="u" rel="up">MPI Data Distribution</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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