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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents d0c2a83c1364
children
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Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
Chris@82 2 <html>
Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
Chris@82 5
Chris@82 6 Copyright (C) 2003 Matteo Frigo.
Chris@82 7
Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@82 9
Chris@82 10 Permission is granted to make and distribute verbatim copies of this
Chris@82 11 manual provided the copyright notice and this permission notice are
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Real-to-Real Transforms</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Real-to-Real Transforms">
Chris@82 28 <meta name="keywords" content="FFTW 3.3.8: Real-to-Real Transforms">
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Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
Chris@82 37 <link href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" rel="next" title="Real-to-Real Transform Kinds">
Chris@82 38 <link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="prev" title="Real-data DFT Array Format">
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Chris@82 66
Chris@82 67
Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Real_002dto_002dReal-Transforms"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Real_002dto_002dReal-Transforms-1"></a>
Chris@82 78 <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
Chris@82 79 <a name="index-r2r-1"></a>
Chris@82 80
Chris@82 81 <div class="example">
Chris@82 82 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
Chris@82 83 fftw_r2r_kind kind, unsigned flags);
Chris@82 84 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
Chris@82 85 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
Chris@82 86 unsigned flags);
Chris@82 87 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
Chris@82 88 double *in, double *out,
Chris@82 89 fftw_r2r_kind kind0,
Chris@82 90 fftw_r2r_kind kind1,
Chris@82 91 fftw_r2r_kind kind2,
Chris@82 92 unsigned flags);
Chris@82 93 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
Chris@82 94 const fftw_r2r_kind *kind, unsigned flags);
Chris@82 95 </pre></div>
Chris@82 96 <a name="index-fftw_005fplan_005fr2r_005f1d-1"></a>
Chris@82 97 <a name="index-fftw_005fplan_005fr2r_005f2d-1"></a>
Chris@82 98 <a name="index-fftw_005fplan_005fr2r_005f3d-1"></a>
Chris@82 99 <a name="index-fftw_005fplan_005fr2r-1"></a>
Chris@82 100
Chris@82 101 <p>Plan a real input/output (r2r) transform of various kinds in zero or
Chris@82 102 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@82 103 </p>
Chris@82 104 <p>Once you have created a plan for a certain transform type and
Chris@82 105 parameters, then creating another plan of the same type and parameters,
Chris@82 106 but for different arrays, is fast and shares constant data with the
Chris@82 107 first plan (if it still exists).
Chris@82 108 </p>
Chris@82 109 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@82 110 non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@82 111 you are using a customized FFTW configuration supporting a restricted
Chris@82 112 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
Chris@82 113 not defined).
Chris@82 114 <a name="index-FFTW_005fREDFT00-1"></a>
Chris@82 115 </p>
Chris@82 116 <a name="Arguments-2"></a>
Chris@82 117 <h4 class="subsubheading">Arguments</h4>
Chris@82 118 <ul>
Chris@82 119 <li> <code>rank</code> is the dimensionality of the transform (it should be the
Chris@82 120 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
Chris@82 121 non-negative integer. The &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo;
Chris@82 122 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
Chris@82 123 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
Chris@82 124 of one number from input to output.
Chris@82 125
Chris@82 126 </li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
Chris@82 127 respectively, gives the (physical) size of the transform dimensions.
Chris@82 128 They can be any positive integer.
Chris@82 129
Chris@82 130 <ul class="no-bullet">
Chris@82 131 <li>- <a name="index-row_002dmajor-2"></a>
Chris@82 132 Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@82 133 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@82 134 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@82 135 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@82 136 </li><li>- FFTW is generally best at handling sizes of the form
Chris@82 137 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@82 138 11<sup>e</sup> 13<sup>f</sup>,
Chris@82 139 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@82 140 are arbitrary. Other sizes are computed by means of a slow,
Chris@82 141 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
Chris@82 142 performance even for prime sizes). (It is possible to customize FFTW
Chris@82 143 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@82 144 Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@82 145 </li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
Chris@82 146 size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
Chris@82 147 should be factorizable in the above form.
Chris@82 148 </li></ul>
Chris@82 149
Chris@82 150 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@82 151 transform, which may be the same (yielding an in-place transform).
Chris@82 152 <a name="index-in_002dplace-5"></a>
Chris@82 153 These arrays are overwritten during planning, unless
Chris@82 154 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@82 155 initialized, but they must be allocated.)
Chris@82 156
Chris@82 157 </li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
Chris@82 158 <code>kind[rank]</code>, is the kind of r2r transform used for the
Chris@82 159 corresponding dimension. The valid kind constants are described in
Chris@82 160 <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
Chris@82 161 what is computed is the separable product formed by taking each
Chris@82 162 transform kind along the corresponding dimension, one dimension after
Chris@82 163 another.
Chris@82 164
Chris@82 165 </li><li> <a name="index-flags-4"></a>
Chris@82 166 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@82 167 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@82 168
Chris@82 169 </li></ul>
Chris@82 170
Chris@82 171 <hr>
Chris@82 172 <div class="header">
Chris@82 173 <p>
Chris@82 174 Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 175 </div>
Chris@82 176
Chris@82 177
Chris@82 178
Chris@82 179 </body>
Chris@82 180 </html>