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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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cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
cannam@167 2 <html>
cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
cannam@167 5
cannam@167 6 Copyright (C) 2003 Matteo Frigo.
cannam@167 7
cannam@167 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@167 10 Permission is granted to make and distribute verbatim copies of this
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cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: Real-data DFTs</title>
cannam@167 26
cannam@167 27 <meta name="description" content="FFTW 3.3.8: Real-data DFTs">
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cannam@167 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@167 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
cannam@167 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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cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="Real_002ddata-DFTs"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 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>
cannam@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="Real_002ddata-DFTs-1"></a>
cannam@167 78 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
cannam@167 79
cannam@167 80 <div class="example">
cannam@167 81 <pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
cannam@167 82 double *in, fftw_complex *out,
cannam@167 83 unsigned flags);
cannam@167 84 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
cannam@167 85 double *in, fftw_complex *out,
cannam@167 86 unsigned flags);
cannam@167 87 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
cannam@167 88 double *in, fftw_complex *out,
cannam@167 89 unsigned flags);
cannam@167 90 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
cannam@167 91 double *in, fftw_complex *out,
cannam@167 92 unsigned flags);
cannam@167 93 </pre></div>
cannam@167 94 <a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a>
cannam@167 95 <a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a>
cannam@167 96 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a>
cannam@167 97 <a name="index-fftw_005fplan_005fdft_005fr2c-1"></a>
cannam@167 98 <a name="index-r2c-2"></a>
cannam@167 99
cannam@167 100 <p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
cannam@167 101 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@167 102 </p>
cannam@167 103 <p>Once you have created a plan for a certain transform type and
cannam@167 104 parameters, then creating another plan of the same type and parameters,
cannam@167 105 but for different arrays, is fast and shares constant data with the
cannam@167 106 first plan (if it still exists).
cannam@167 107 </p>
cannam@167 108 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
cannam@167 109 non-<code>NULL</code> plan is always returned by the basic interface unless
cannam@167 110 you are using a customized FFTW configuration supporting a restricted
cannam@167 111 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
cannam@167 112 with a multi-dimensional out-of-place c2r transform (see below).
cannam@167 113 </p>
cannam@167 114 <a name="Arguments-1"></a>
cannam@167 115 <h4 class="subsubheading">Arguments</h4>
cannam@167 116 <ul>
cannam@167 117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
cannam@167 118 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
cannam@167 119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
cannam@167 120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
cannam@167 121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
cannam@167 122 copy of one real number (with zero imaginary part) from input to output.
cannam@167 123
cannam@167 124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
cannam@167 125 for each routine) specify the size of the transform dimensions. They
cannam@167 126 can be any positive integer. This is different in general from the
cannam@167 127 <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>.
cannam@167 128
cannam@167 129 <ul class="no-bullet">
cannam@167 130 <li>- FFTW is best at handling sizes of the form
cannam@167 131 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@167 132 11<sup>e</sup> 13<sup>f</sup>,
cannam@167 133 where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
cannam@167 134 are arbitrary. Other sizes are computed by means of a slow,
cannam@167 135 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
cannam@167 136 performance even for prime sizes). (It is possible to customize FFTW
cannam@167 137 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
cannam@167 138 Transforms whose sizes are powers of <em>2</em> are especially fast, and
cannam@167 139 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
cannam@167 140 transform to be <em>even</em>.
cannam@167 141 </li></ul>
cannam@167 142
cannam@167 143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@167 144 transform, which may be the same (yielding an in-place transform).
cannam@167 145 <a name="index-in_002dplace-3"></a>
cannam@167 146 These arrays are overwritten during planning, unless
cannam@167 147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@167 148 initialized, but they must be allocated.) For an in-place transform, it
cannam@167 149 is important to remember that the real array will require padding,
cannam@167 150 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
cannam@167 151 <a name="index-padding-2"></a>
cannam@167 152
cannam@167 153 </li><li> <a name="index-flags-3"></a>
cannam@167 154 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
cannam@167 155 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@167 156
cannam@167 157 </li></ul>
cannam@167 158
cannam@167 159 <p>The inverse transforms, taking complex input (storing the non-redundant
cannam@167 160 half of a logically Hermitian array) to real output, are given by:
cannam@167 161 </p>
cannam@167 162 <div class="example">
cannam@167 163 <pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
cannam@167 164 fftw_complex *in, double *out,
cannam@167 165 unsigned flags);
cannam@167 166 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
cannam@167 167 fftw_complex *in, double *out,
cannam@167 168 unsigned flags);
cannam@167 169 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
cannam@167 170 fftw_complex *in, double *out,
cannam@167 171 unsigned flags);
cannam@167 172 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
cannam@167 173 fftw_complex *in, double *out,
cannam@167 174 unsigned flags);
cannam@167 175 </pre></div>
cannam@167 176 <a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a>
cannam@167 177 <a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a>
cannam@167 178 <a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a>
cannam@167 179 <a name="index-fftw_005fplan_005fdft_005fc2r"></a>
cannam@167 180 <a name="index-c2r-2"></a>
cannam@167 181
cannam@167 182 <p>The arguments are the same as for the r2c transforms, except that the
cannam@167 183 input and output data formats are reversed.
cannam@167 184 </p>
cannam@167 185 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
cannam@167 186 c2r transform (or vice versa) will result in the original data
cannam@167 187 multiplied by the size of the transform (the product of the logical
cannam@167 188 dimensions).
cannam@167 189 <a name="index-normalization-6"></a>
cannam@167 190 An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
cannam@167 191 complex DFT of the same input, and a c2r transform is correspondingly
cannam@167 192 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>.
cannam@167 193 </p>
cannam@167 194 <hr>
cannam@167 195 <div class="header">
cannam@167 196 <p>
cannam@167 197 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>
cannam@167 198 </div>
cannam@167 199
cannam@167 200
cannam@167 201
cannam@167 202 </body>
cannam@167 203 </html>