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