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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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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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into another language, under the above conditions for modified versions,
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>Advanced Complex DFTs (FFTW 3.3.10)</title>
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<meta name="description" content="Advanced Complex DFTs (FFTW 3.3.10)">
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<meta name="keywords" content="Advanced Complex DFTs (FFTW 3.3.10)">
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<meta name="resource-type" content="document">
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<meta name="distribution" content="global">
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<meta name="Generator" content="makeinfo">
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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="Advanced-Interface.html" rel="up" title="Advanced Interface">
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<link href="Advanced-Real_002ddata-DFTs.html" rel="next" title="Advanced Real-data DFTs">
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<link href="Advanced-Interface.html" rel="prev" title="Advanced Interface">
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a.summary-letter {text-decoration: none}
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-->
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</style>
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</head>
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<body lang="en">
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<span id="Advanced-Complex-DFTs"></span><div class="header">
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<p>
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Next: <a href="Advanced-Real_002ddata-DFTs.html" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html" accesskey="u" rel="up">Advanced Interface</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="Advanced-Complex-DFTs-1"></span><h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
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fftw_complex *in, const int *inembed,
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int istride, int idist,
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fftw_complex *out, const int *onembed,
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int ostride, int odist,
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int sign, unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fmany_005fdft"></span>
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<p>This routine plans multiple multidimensional complex DFTs, and it
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extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html">Complex DFTs</a>) to
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compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
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<code>n</code>. In addition, the transform data need not be contiguous, but
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it may be laid out in memory with an arbitrary stride. To account for
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these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
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<code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
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{<code>i</code>,<code>o</code>}<code>stride</code>, and
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{<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
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(see <a href="Complex-DFTs.html">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
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and 3, but the advanced interface handles only the general-rank
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case.
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</p>
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<p><code>howmany</code> is the (nonnegative) number of transforms to compute. The resulting
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plan computes <code>howmany</code> transforms, where the input of the
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<code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
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arithmetic), and its output is at location <code>out+k*odist</code>. Plans
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obtained in this way can often be faster than calling FFTW multiple
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times for the individual transforms. The basic <code>fftw_plan_dft</code>
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interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
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parameters are ignored).
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<span id="index-howmany-parameter"></span>
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<span id="index-dist"></span>
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</p>
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<p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
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<code>n</code>, as in the basic interface. In addition, the advanced
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interface allows the input and output arrays of each transform to be
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row-major subarrays of larger rank-<code>rank</code> arrays, described by
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<code>inembed</code> and <code>onembed</code> parameters, respectively.
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{<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
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and <code>n</code> should be elementwise less than or equal to
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{<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
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<code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
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physical and logical dimensions, as in the basic interface.)
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</p>
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<p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
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the input or output arrays is located at <code>j*istride</code> or
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<code>j*ostride</code>, respectively. (For a multi-dimensional array,
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<code>j</code> is the ordinary row-major index.) When combined with the
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<code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
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that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
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(The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
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<span id="index-stride-1"></span>
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</p>
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<p>For in-place transforms, the input and output <code>stride</code> and
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<code>dist</code> parameters should be the same; otherwise, the planner may
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return <code>NULL</code>.
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</p>
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<p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
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this function returns. You can safely free or reuse them.
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</p>
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<p><strong>Examples</strong>:
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One transform of one 5 by 6 array contiguous in memory:
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</p><div class="example">
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<pre class="example"> int rank = 2;
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int n[] = {5, 6};
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int howmany = 1;
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int idist = odist = 0; /* unused because howmany = 1 */
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int istride = ostride = 1; /* array is contiguous in memory */
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int *inembed = n, *onembed = n;
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</pre></div>
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<p>Transform of three 5 by 6 arrays, each contiguous in memory,
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stored in memory one after another:
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</p><div class="example">
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<pre class="example"> int rank = 2;
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int n[] = {5, 6};
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int howmany = 3;
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int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
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between the first element
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of the first array and the
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first element of the second array */
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int istride = ostride = 1; /* array is contiguous in memory */
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int *inembed = n, *onembed = n;
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</pre></div>
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<p>Transform each column of a 2d array with 10 rows and 3 columns:
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</p><div class="example">
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<pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
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int n[] = {10}; /* 1d transforms of length 10 */
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int howmany = 3;
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int idist = odist = 1;
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int istride = ostride = 3; /* distance between two elements in
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the same column */
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int *inembed = n, *onembed = n;
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</pre></div>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Advanced-Real_002ddata-DFTs.html" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html" accesskey="u" rel="up">Advanced Interface</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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