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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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3 <!-- This manual is for FFTW
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6 Copyright (C) 2003 Matteo Frigo.
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72 <a name="Real_002dto_002dReal-Transforms"></a>
73 <div class="header">
74 <p>
75 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>
76 </div>
77 <hr>
78 <a name="Real_002dto_002dReal-Transforms-1"></a>
79 <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
80 <a name="index-r2r-1"></a>
81
82 <div class="example">
83 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
84 fftw_r2r_kind kind, unsigned flags);
85 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
86 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
87 unsigned flags);
88 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
89 double *in, double *out,
90 fftw_r2r_kind kind0,
91 fftw_r2r_kind kind1,
92 fftw_r2r_kind kind2,
93 unsigned flags);
94 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
95 const fftw_r2r_kind *kind, unsigned flags);
96 </pre></div>
97 <a name="index-fftw_005fplan_005fr2r_005f1d-1"></a>
98 <a name="index-fftw_005fplan_005fr2r_005f2d-1"></a>
99 <a name="index-fftw_005fplan_005fr2r_005f3d-1"></a>
100 <a name="index-fftw_005fplan_005fr2r-1"></a>
101
102 <p>Plan a real input/output (r2r) transform of various kinds in zero or
103 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
104 </p>
105 <p>Once you have created a plan for a certain transform type and
106 parameters, then creating another plan of the same type and parameters,
107 but for different arrays, is fast and shares constant data with the
108 first plan (if it still exists).
109 </p>
110 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
111 non-<code>NULL</code> plan is always returned by the basic interface unless
112 you are using a customized FFTW configuration supporting a restricted
113 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
114 not defined).
115 <a name="index-FFTW_005fREDFT00-1"></a>
116 </p>
117 <a name="Arguments-2"></a>
118 <h4 class="subsubheading">Arguments</h4>
119 <ul>
120 <li> <code>rank</code> is the dimensionality of the transform (it should be the
121 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
122 non-negative integer. The &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo;
123 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
124 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
125 of one number from input to output.
126
127 </li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
128 respectively, gives the (physical) size of the transform dimensions.
129 They can be any positive integer.
130
131 <ul class="no-bullet">
132 <li>- <a name="index-row_002dmajor-2"></a>
133 Multi-dimensional arrays are stored in row-major order with dimensions:
134 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
135 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
136 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
137 </li><li>- FFTW is generally best at handling sizes of the form
138 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
139 11<sup>e</sup> 13<sup>f</sup>,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>) performance even for prime sizes). (It is possible to customize FFTW
142 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
143 Transforms whose sizes are powers of <em>2</em> are especially fast.
144 </li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
145 size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
146 should be factorizable in the above form.
147 </li></ul>
148
149 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
150 transform, which may be the same (yielding an in-place transform).
151 <a name="index-in_002dplace-5"></a>
152 These arrays are overwritten during planning, unless
153 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
154 initialized, but they must be allocated.)
155
156 </li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
157 <code>kind[rank]</code>, is the kind of r2r transform used for the
158 corresponding dimension. The valid kind constants are described in
159 <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
160 what is computed is the separable product formed by taking each
161 transform kind along the corresponding dimension, one dimension after
162 another.
163
164 </li><li> <a name="index-flags-4"></a>
165 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
166 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
167
168 </li></ul>
169
170 <hr>
171 <div class="header">
172 <p>
173 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>
174 </div>
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