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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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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
5
6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
24 <head>
25 <title>FFTW 3.3.8: Real-data DFTs</title>
26
27 <meta name="description" content="FFTW 3.3.8: Real-data DFTs">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
37 <link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="next" title="Real-data DFT Array Format">
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68 </head>
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70 <body lang="en">
71 <a name="Real_002ddata-DFTs"></a>
72 <div class="header">
73 <p>
74 Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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_002ddata-DFTs-1"></a>
78 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
79
80 <div class="example">
81 <pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
82 double *in, fftw_complex *out,
83 unsigned flags);
84 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
85 double *in, fftw_complex *out,
86 unsigned flags);
87 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
88 double *in, fftw_complex *out,
89 unsigned flags);
90 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
91 double *in, fftw_complex *out,
92 unsigned flags);
93 </pre></div>
94 <a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a>
95 <a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a>
96 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a>
97 <a name="index-fftw_005fplan_005fdft_005fr2c-1"></a>
98 <a name="index-r2c-2"></a>
99
100 <p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
101 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
102 </p>
103 <p>Once you have created a plan for a certain transform type and
104 parameters, then creating another plan of the same type and parameters,
105 but for different arrays, is fast and shares constant data with the
106 first plan (if it still exists).
107 </p>
108 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
109 non-<code>NULL</code> plan is always returned by the basic interface unless
110 you are using a customized FFTW configuration supporting a restricted
111 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
112 with a multi-dimensional out-of-place c2r transform (see below).
113 </p>
114 <a name="Arguments-1"></a>
115 <h4 class="subsubheading">Arguments</h4>
116 <ul>
117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
118 array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html#Complex-Multi_002dDimensional-DFTs">Complex Multi-Dimensional DFTs</a>, for the definition of &ldquo;rank&rdquo;.) The
119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
122 copy of one real number (with zero imaginary part) from input to output.
123
124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
125 for each routine) specify the size of the transform dimensions. They
126 can be any positive integer. This is different in general from the
127 <em>physical</em> array dimensions, which are described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
128
129 <ul class="no-bullet">
130 <li>- FFTW is best at handling sizes of the form
131 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
132 11<sup>e</sup> 13<sup>f</sup>,
133 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
134 are arbitrary. Other sizes are computed by means of a slow,
135 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
136 performance even for prime sizes). (It is possible to customize FFTW
137 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
138 Transforms whose sizes are powers of <em>2</em> are especially fast, and
139 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
140 transform to be <em>even</em>.
141 </li></ul>
142
143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
144 transform, which may be the same (yielding an in-place transform).
145 <a name="index-in_002dplace-3"></a>
146 These arrays are overwritten during planning, unless
147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
148 initialized, but they must be allocated.) For an in-place transform, it
149 is important to remember that the real array will require padding,
150 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
151 <a name="index-padding-2"></a>
152
153 </li><li> <a name="index-flags-3"></a>
154 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
155 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
156
157 </li></ul>
158
159 <p>The inverse transforms, taking complex input (storing the non-redundant
160 half of a logically Hermitian array) to real output, are given by:
161 </p>
162 <div class="example">
163 <pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
164 fftw_complex *in, double *out,
165 unsigned flags);
166 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
167 fftw_complex *in, double *out,
168 unsigned flags);
169 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
170 fftw_complex *in, double *out,
171 unsigned flags);
172 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
173 fftw_complex *in, double *out,
174 unsigned flags);
175 </pre></div>
176 <a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a>
177 <a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a>
178 <a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a>
179 <a name="index-fftw_005fplan_005fdft_005fc2r"></a>
180 <a name="index-c2r-2"></a>
181
182 <p>The arguments are the same as for the r2c transforms, except that the
183 input and output data formats are reversed.
184 </p>
185 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
186 c2r transform (or vice versa) will result in the original data
187 multiplied by the size of the transform (the product of the logical
188 dimensions).
189 <a name="index-normalization-6"></a>
190 An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
191 complex DFT of the same input, and a c2r transform is correspondingly
192 equivalent to <code>FFTW_BACKWARD</code>. For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
193 </p>
194 <hr>
195 <div class="header">
196 <p>
197 Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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>
198 </div>
199
200
201
202 </body>
203 </html>