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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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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>Real-to-Real Transforms (FFTW 3.3.10)</title>
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<meta name="description" content="Real-to-Real Transforms (FFTW 3.3.10)">
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<meta name="keywords" content="Real-to-Real Transforms (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="Basic-Interface.html" rel="up" title="Basic Interface">
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<link href="Real_002dto_002dReal-Transform-Kinds.html" rel="next" title="Real-to-Real Transform Kinds">
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<link href="Real_002ddata-DFT-Array-Format.html" rel="prev" title="Real-data DFT Array Format">
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</head>
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<body lang="en">
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<span id="Real_002dto_002dReal-Transforms"></span><div class="header">
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<p>
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Next: <a href="Real_002dto_002dReal-Transform-Kinds.html" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html" accesskey="p" rel="prev">Real-data DFT Array Format</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_002dto_002dReal-Transforms-1"></span><h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
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<span id="index-r2r-1"></span>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
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fftw_r2r_kind kind, unsigned flags);
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fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
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fftw_r2r_kind kind0, fftw_r2r_kind kind1,
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unsigned flags);
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fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
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double *in, double *out,
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fftw_r2r_kind kind0,
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fftw_r2r_kind kind1,
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fftw_r2r_kind kind2,
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unsigned flags);
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fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
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const fftw_r2r_kind *kind, unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fr2r_005f1d-1"></span>
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<span id="index-fftw_005fplan_005fr2r_005f2d-1"></span>
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<span id="index-fftw_005fplan_005fr2r_005f3d-1"></span>
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<span id="index-fftw_005fplan_005fr2r-1"></span>
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<p>Plan a real input/output (r2r) transform of various kinds in zero or
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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 for size-1 <code>FFTW_REDFT00</code> kinds (which are
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not defined).
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<span id="index-FFTW_005fREDFT00-1"></span>
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</p>
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<span id="Arguments-2"></span><h4 class="subsubheading">Arguments</h4>
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<ul>
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<li> <code>rank</code> is the dimensionality of the transform (it should be the
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size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
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non-negative integer. The ‘<samp>_1d</samp>’, ‘<samp>_2d</samp>’, and ‘<samp>_3d</samp>’
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planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
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<code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
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of one number from input to output.
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</li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
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respectively, gives the (physical) size of the transform dimensions.
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They can be any positive integer.
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<ul class="no-bullet">
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<li>- <span id="index-row_002dmajor-2"></span>
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Multi-dimensional arrays are stored in row-major order with dimensions:
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<code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
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<code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
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See <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>.
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</li><li>- FFTW is generally 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.
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</li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
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size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
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should be factorizable in the above form.
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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-5"></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.)
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</li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
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<code>kind[rank]</code>, is the kind of r2r transform used for the
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corresponding dimension. The valid kind constants are described in
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<a href="Real_002dto_002dReal-Transform-Kinds.html">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
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what is computed is the separable product formed by taking each
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transform kind along the corresponding dimension, one dimension after
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another.
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</li><li> <span id="index-flags-4"></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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<hr>
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<div class="header">
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<p>
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Next: <a href="Real_002dto_002dReal-Transform-Kinds.html" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html" accesskey="p" rel="prev">Real-data DFT Array Format</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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