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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>Real-data DFTs (FFTW 3.3.10)</title>
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<meta name="description" content="Real-data DFTs (FFTW 3.3.10)">
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<meta name="keywords" content="Real-data 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="Basic-Interface.html" rel="up" title="Basic Interface">
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<link href="Real_002ddata-DFT-Array-Format.html" rel="next" title="Real-data DFT Array Format">
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<link href="Planner-Flags.html" rel="prev" title="Planner Flags">
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</style>
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</head>
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<body lang="en">
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<span id="Real_002ddata-DFTs"></span><div class="header">
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<p>
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Next: <a href="Real_002ddata-DFT-Array-Format.html" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html" accesskey="p" rel="prev">Planner Flags</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic 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="Real_002ddata-DFTs-1"></span><h4 class="subsection">4.3.3 Real-data DFTs</h4>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
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double *in, fftw_complex *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
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double *in, fftw_complex *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
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double *in, fftw_complex *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
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double *in, fftw_complex *out,
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unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005fr2c-1"></span>
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<span id="index-r2c-2"></span>
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<p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
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zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html">Using Plans</a>).
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</p>
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<p>Once you have created a plan for a certain transform type and
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parameters, then creating another plan of the same type and parameters,
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but for different arrays, is fast and shares constant data with the
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first plan (if it still exists).
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</p>
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<p>The planner returns <code>NULL</code> if the plan cannot be created. A
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non-<code>NULL</code> plan is always returned by the basic interface unless
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you are using a customized FFTW configuration supporting a restricted
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set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
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with a multi-dimensional out-of-place c2r transform (see below).
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</p>
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<span id="Arguments-1"></span><h4 class="subsubheading">Arguments</h4>
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<ul>
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<li> <code>rank</code> is the rank of the transform (it should be the size of the
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array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html">Complex Multi-Dimensional DFTs</a>, for the definition of “rank”.) The
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‘<samp>_1d</samp>’, ‘<samp>_2d</samp>’, and ‘<samp>_3d</samp>’ planners correspond to a
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<code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
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may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
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copy of one real number (with zero imaginary part) from input to output.
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</li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
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for each routine) specify the size of the transform dimensions. They
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can be any positive integer. This is different in general from the
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<em>physical</em> array dimensions, which are described in <a href="Real_002ddata-DFT-Array-Format.html">Real-data DFT Array Format</a>.
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<ul class="no-bullet">
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<li>- FFTW is best at handling sizes of the form
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2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
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11<sup>e</sup> 13<sup>f</sup>,
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where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
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are arbitrary. Other sizes are computed by means of a slow,
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general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
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performance even for prime sizes). (It is possible to customize FFTW
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for different array sizes; see <a href="Installation-and-Customization.html">Installation and Customization</a>.)
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Transforms whose sizes are powers of <em>2</em> are especially fast, and
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it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
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transform to be <em>even</em>.
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</li></ul>
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</li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
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transform, which may be the same (yielding an in-place transform).
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<span id="index-in_002dplace-3"></span>
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These arrays are overwritten during planning, unless
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<code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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initialized, but they must be allocated.) For an in-place transform, it
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is important to remember that the real array will require padding,
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described in <a href="Real_002ddata-DFT-Array-Format.html">Real-data DFT Array Format</a>.
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<span id="index-padding-2"></span>
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</li><li> <span id="index-flags-3"></span>
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<code>flags</code> is a bitwise OR (‘<samp>|</samp>’) of zero or more planner flags,
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as defined in <a href="Planner-Flags.html">Planner Flags</a>.
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</li></ul>
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<p>The inverse transforms, taking complex input (storing the non-redundant
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half of a logically Hermitian array) to real output, are given by:
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</p>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
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fftw_complex *in, double *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
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fftw_complex *in, double *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
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fftw_complex *in, double *out,
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unsigned flags);
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fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
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fftw_complex *in, double *out,
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unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005fc2r_005f2d"></span>
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<span id="index-fftw_005fplan_005fdft_005fc2r_005f3d"></span>
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<span id="index-fftw_005fplan_005fdft_005fc2r"></span>
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<span id="index-c2r-2"></span>
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<p>The arguments are the same as for the r2c transforms, except that the
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input and output data formats are reversed.
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</p>
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<p>FFTW computes an unnormalized transform: computing an r2c followed by a
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c2r transform (or vice versa) will result in the original data
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multiplied by the size of the transform (the product of the logical
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dimensions).
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<span id="index-normalization-6"></span>
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An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
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complex DFT of the same input, and a c2r transform is correspondingly
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equivalent to <code>FFTW_BACKWARD</code>. For more information, see <a href="What-FFTW-Really-Computes.html">What FFTW Really Computes</a>.
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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="Real_002ddata-DFT-Array-Format.html" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html" accesskey="p" rel="prev">Planner Flags</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic 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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