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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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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>