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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">
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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.
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Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Real-data DFTs</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Real-data DFTs">
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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_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="next" title="Real-data DFT Array Format">
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Chris@82 67
Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Real_002ddata-DFTs"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 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>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Real_002ddata-DFTs-1"></a>
Chris@82 78 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
Chris@82 79
Chris@82 80 <div class="example">
Chris@82 81 <pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
Chris@82 82 double *in, fftw_complex *out,
Chris@82 83 unsigned flags);
Chris@82 84 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
Chris@82 85 double *in, fftw_complex *out,
Chris@82 86 unsigned flags);
Chris@82 87 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
Chris@82 88 double *in, fftw_complex *out,
Chris@82 89 unsigned flags);
Chris@82 90 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
Chris@82 91 double *in, fftw_complex *out,
Chris@82 92 unsigned flags);
Chris@82 93 </pre></div>
Chris@82 94 <a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a>
Chris@82 95 <a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a>
Chris@82 96 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a>
Chris@82 97 <a name="index-fftw_005fplan_005fdft_005fr2c-1"></a>
Chris@82 98 <a name="index-r2c-2"></a>
Chris@82 99
Chris@82 100 <p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
Chris@82 101 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@82 102 </p>
Chris@82 103 <p>Once you have created a plan for a certain transform type and
Chris@82 104 parameters, then creating another plan of the same type and parameters,
Chris@82 105 but for different arrays, is fast and shares constant data with the
Chris@82 106 first plan (if it still exists).
Chris@82 107 </p>
Chris@82 108 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@82 109 non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@82 110 you are using a customized FFTW configuration supporting a restricted
Chris@82 111 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
Chris@82 112 with a multi-dimensional out-of-place c2r transform (see below).
Chris@82 113 </p>
Chris@82 114 <a name="Arguments-1"></a>
Chris@82 115 <h4 class="subsubheading">Arguments</h4>
Chris@82 116 <ul>
Chris@82 117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
Chris@82 118 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
Chris@82 119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
Chris@82 120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@82 121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@82 122 copy of one real number (with zero imaginary part) from input to output.
Chris@82 123
Chris@82 124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
Chris@82 125 for each routine) specify the size of the transform dimensions. They
Chris@82 126 can be any positive integer. This is different in general from the
Chris@82 127 <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>.
Chris@82 128
Chris@82 129 <ul class="no-bullet">
Chris@82 130 <li>- FFTW is best at handling sizes of the form
Chris@82 131 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@82 132 11<sup>e</sup> 13<sup>f</sup>,
Chris@82 133 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@82 134 are arbitrary. Other sizes are computed by means of a slow,
Chris@82 135 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
Chris@82 136 performance even for prime sizes). (It is possible to customize FFTW
Chris@82 137 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@82 138 Transforms whose sizes are powers of <em>2</em> are especially fast, and
Chris@82 139 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
Chris@82 140 transform to be <em>even</em>.
Chris@82 141 </li></ul>
Chris@82 142
Chris@82 143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@82 144 transform, which may be the same (yielding an in-place transform).
Chris@82 145 <a name="index-in_002dplace-3"></a>
Chris@82 146 These arrays are overwritten during planning, unless
Chris@82 147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@82 148 initialized, but they must be allocated.) For an in-place transform, it
Chris@82 149 is important to remember that the real array will require padding,
Chris@82 150 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
Chris@82 151 <a name="index-padding-2"></a>
Chris@82 152
Chris@82 153 </li><li> <a name="index-flags-3"></a>
Chris@82 154 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@82 155 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@82 156
Chris@82 157 </li></ul>
Chris@82 158
Chris@82 159 <p>The inverse transforms, taking complex input (storing the non-redundant
Chris@82 160 half of a logically Hermitian array) to real output, are given by:
Chris@82 161 </p>
Chris@82 162 <div class="example">
Chris@82 163 <pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
Chris@82 164 fftw_complex *in, double *out,
Chris@82 165 unsigned flags);
Chris@82 166 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
Chris@82 167 fftw_complex *in, double *out,
Chris@82 168 unsigned flags);
Chris@82 169 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
Chris@82 170 fftw_complex *in, double *out,
Chris@82 171 unsigned flags);
Chris@82 172 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
Chris@82 173 fftw_complex *in, double *out,
Chris@82 174 unsigned flags);
Chris@82 175 </pre></div>
Chris@82 176 <a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a>
Chris@82 177 <a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a>
Chris@82 178 <a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a>
Chris@82 179 <a name="index-fftw_005fplan_005fdft_005fc2r"></a>
Chris@82 180 <a name="index-c2r-2"></a>
Chris@82 181
Chris@82 182 <p>The arguments are the same as for the r2c transforms, except that the
Chris@82 183 input and output data formats are reversed.
Chris@82 184 </p>
Chris@82 185 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
Chris@82 186 c2r transform (or vice versa) will result in the original data
Chris@82 187 multiplied by the size of the transform (the product of the logical
Chris@82 188 dimensions).
Chris@82 189 <a name="index-normalization-6"></a>
Chris@82 190 An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
Chris@82 191 complex DFT of the same input, and a c2r transform is correspondingly
Chris@82 192 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>.
Chris@82 193 </p>
Chris@82 194 <hr>
Chris@82 195 <div class="header">
Chris@82 196 <p>
Chris@82 197 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>
Chris@82 198 </div>
Chris@82 199
Chris@82 200
Chris@82 201
Chris@82 202 </body>
Chris@82 203 </html>