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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
cannam@167 5
cannam@167 6 Copyright (C) 2003 Matteo Frigo.
cannam@167 7
cannam@167 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@167 10 Permission is granted to make and distribute verbatim copies of this
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cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: Real-to-Real Transforms</title>
cannam@167 26
cannam@167 27 <meta name="description" content="FFTW 3.3.8: Real-to-Real Transforms">
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cannam@167 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@167 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
cannam@167 37 <link href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" rel="next" title="Real-to-Real Transform Kinds">
cannam@167 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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cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="Real_002dto_002dReal-Transforms"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 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>
cannam@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="Real_002dto_002dReal-Transforms-1"></a>
cannam@167 78 <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
cannam@167 79 <a name="index-r2r-1"></a>
cannam@167 80
cannam@167 81 <div class="example">
cannam@167 82 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
cannam@167 83 fftw_r2r_kind kind, unsigned flags);
cannam@167 84 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
cannam@167 85 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
cannam@167 86 unsigned flags);
cannam@167 87 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
cannam@167 88 double *in, double *out,
cannam@167 89 fftw_r2r_kind kind0,
cannam@167 90 fftw_r2r_kind kind1,
cannam@167 91 fftw_r2r_kind kind2,
cannam@167 92 unsigned flags);
cannam@167 93 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
cannam@167 94 const fftw_r2r_kind *kind, unsigned flags);
cannam@167 95 </pre></div>
cannam@167 96 <a name="index-fftw_005fplan_005fr2r_005f1d-1"></a>
cannam@167 97 <a name="index-fftw_005fplan_005fr2r_005f2d-1"></a>
cannam@167 98 <a name="index-fftw_005fplan_005fr2r_005f3d-1"></a>
cannam@167 99 <a name="index-fftw_005fplan_005fr2r-1"></a>
cannam@167 100
cannam@167 101 <p>Plan a real input/output (r2r) transform of various kinds in zero or
cannam@167 102 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@167 103 </p>
cannam@167 104 <p>Once you have created a plan for a certain transform type and
cannam@167 105 parameters, then creating another plan of the same type and parameters,
cannam@167 106 but for different arrays, is fast and shares constant data with the
cannam@167 107 first plan (if it still exists).
cannam@167 108 </p>
cannam@167 109 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
cannam@167 110 non-<code>NULL</code> plan is always returned by the basic interface unless
cannam@167 111 you are using a customized FFTW configuration supporting a restricted
cannam@167 112 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
cannam@167 113 not defined).
cannam@167 114 <a name="index-FFTW_005fREDFT00-1"></a>
cannam@167 115 </p>
cannam@167 116 <a name="Arguments-2"></a>
cannam@167 117 <h4 class="subsubheading">Arguments</h4>
cannam@167 118 <ul>
cannam@167 119 <li> <code>rank</code> is the dimensionality of the transform (it should be the
cannam@167 120 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
cannam@167 121 non-negative integer. The &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo;
cannam@167 122 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
cannam@167 123 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
cannam@167 124 of one number from input to output.
cannam@167 125
cannam@167 126 </li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
cannam@167 127 respectively, gives the (physical) size of the transform dimensions.
cannam@167 128 They can be any positive integer.
cannam@167 129
cannam@167 130 <ul class="no-bullet">
cannam@167 131 <li>- <a name="index-row_002dmajor-2"></a>
cannam@167 132 Multi-dimensional arrays are stored in row-major order with dimensions:
cannam@167 133 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
cannam@167 134 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
cannam@167 135 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
cannam@167 136 </li><li>- FFTW is generally best at handling sizes of the form
cannam@167 137 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@167 138 11<sup>e</sup> 13<sup>f</sup>,
cannam@167 139 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
cannam@167 140 are arbitrary. Other sizes are computed by means of a slow,
cannam@167 141 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
cannam@167 142 performance even for prime sizes). (It is possible to customize FFTW
cannam@167 143 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
cannam@167 144 Transforms whose sizes are powers of <em>2</em> are especially fast.
cannam@167 145 </li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
cannam@167 146 size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
cannam@167 147 should be factorizable in the above form.
cannam@167 148 </li></ul>
cannam@167 149
cannam@167 150 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@167 151 transform, which may be the same (yielding an in-place transform).
cannam@167 152 <a name="index-in_002dplace-5"></a>
cannam@167 153 These arrays are overwritten during planning, unless
cannam@167 154 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@167 155 initialized, but they must be allocated.)
cannam@167 156
cannam@167 157 </li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
cannam@167 158 <code>kind[rank]</code>, is the kind of r2r transform used for the
cannam@167 159 corresponding dimension. The valid kind constants are described in
cannam@167 160 <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
cannam@167 161 what is computed is the separable product formed by taking each
cannam@167 162 transform kind along the corresponding dimension, one dimension after
cannam@167 163 another.
cannam@167 164
cannam@167 165 </li><li> <a name="index-flags-4"></a>
cannam@167 166 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
cannam@167 167 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@167 168
cannam@167 169 </li></ul>
cannam@167 170
cannam@167 171 <hr>
cannam@167 172 <div class="header">
cannam@167 173 <p>
cannam@167 174 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>
cannam@167 175 </div>
cannam@167 176
cannam@167 177
cannam@167 178
cannam@167 179 </body>
cannam@167 180 </html>