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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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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
cannam@127 7
cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Real-data DFTs</title>
cannam@127 26
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cannam@127 70
cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Real_002ddata-DFTs"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 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@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Real_002ddata-DFTs-1"></a>
cannam@127 79 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
cannam@127 80
cannam@127 81 <div class="example">
cannam@127 82 <pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
cannam@127 83 double *in, fftw_complex *out,
cannam@127 84 unsigned flags);
cannam@127 85 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
cannam@127 86 double *in, fftw_complex *out,
cannam@127 87 unsigned flags);
cannam@127 88 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
cannam@127 89 double *in, fftw_complex *out,
cannam@127 90 unsigned flags);
cannam@127 91 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
cannam@127 92 double *in, fftw_complex *out,
cannam@127 93 unsigned flags);
cannam@127 94 </pre></div>
cannam@127 95 <a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a>
cannam@127 96 <a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a>
cannam@127 97 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a>
cannam@127 98 <a name="index-fftw_005fplan_005fdft_005fr2c-1"></a>
cannam@127 99 <a name="index-r2c-2"></a>
cannam@127 100
cannam@127 101 <p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
cannam@127 102 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@127 103 </p>
cannam@127 104 <p>Once you have created a plan for a certain transform type and
cannam@127 105 parameters, then creating another plan of the same type and parameters,
cannam@127 106 but for different arrays, is fast and shares constant data with the
cannam@127 107 first plan (if it still exists).
cannam@127 108 </p>
cannam@127 109 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
cannam@127 110 non-<code>NULL</code> plan is always returned by the basic interface unless
cannam@127 111 you are using a customized FFTW configuration supporting a restricted
cannam@127 112 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
cannam@127 113 with a multi-dimensional out-of-place c2r transform (see below).
cannam@127 114 </p>
cannam@127 115 <a name="Arguments-1"></a>
cannam@127 116 <h4 class="subsubheading">Arguments</h4>
cannam@127 117 <ul>
cannam@127 118 <li> <code>rank</code> is the rank of the transform (it should be the size of the
cannam@127 119 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@127 120 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
cannam@127 121 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
cannam@127 122 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
cannam@127 123 copy of one real number (with zero imaginary part) from input to output.
cannam@127 124
cannam@127 125 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
cannam@127 126 for each routine) specify the size of the transform dimensions. They
cannam@127 127 can be any positive integer. This is different in general from the
cannam@127 128 <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@127 129
cannam@127 130 <ul class="no-bullet">
cannam@127 131 <li>- FFTW is best at handling sizes of the form
cannam@127 132 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@127 133 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
cannam@127 134 are arbitrary. Other sizes are computed by means of a slow,
cannam@127 135 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
cannam@127 136 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
cannam@127 137 Transforms whose sizes are powers of <em>2</em> are especially fast, and
cannam@127 138 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
cannam@127 139 transform to be <em>even</em>.
cannam@127 140 </li></ul>
cannam@127 141
cannam@127 142 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@127 143 transform, which may be the same (yielding an in-place transform).
cannam@127 144 <a name="index-in_002dplace-3"></a>
cannam@127 145 These arrays are overwritten during planning, unless
cannam@127 146 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@127 147 initialized, but they must be allocated.) For an in-place transform, it
cannam@127 148 is important to remember that the real array will require padding,
cannam@127 149 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
cannam@127 150 <a name="index-padding-2"></a>
cannam@127 151
cannam@127 152 </li><li> <a name="index-flags-3"></a>
cannam@127 153 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
cannam@127 154 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@127 155
cannam@127 156 </li></ul>
cannam@127 157
cannam@127 158 <p>The inverse transforms, taking complex input (storing the non-redundant
cannam@127 159 half of a logically Hermitian array) to real output, are given by:
cannam@127 160 </p>
cannam@127 161 <div class="example">
cannam@127 162 <pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
cannam@127 163 fftw_complex *in, double *out,
cannam@127 164 unsigned flags);
cannam@127 165 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
cannam@127 166 fftw_complex *in, double *out,
cannam@127 167 unsigned flags);
cannam@127 168 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
cannam@127 169 fftw_complex *in, double *out,
cannam@127 170 unsigned flags);
cannam@127 171 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
cannam@127 172 fftw_complex *in, double *out,
cannam@127 173 unsigned flags);
cannam@127 174 </pre></div>
cannam@127 175 <a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a>
cannam@127 176 <a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a>
cannam@127 177 <a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a>
cannam@127 178 <a name="index-fftw_005fplan_005fdft_005fc2r"></a>
cannam@127 179 <a name="index-c2r-2"></a>
cannam@127 180
cannam@127 181 <p>The arguments are the same as for the r2c transforms, except that the
cannam@127 182 input and output data formats are reversed.
cannam@127 183 </p>
cannam@127 184 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
cannam@127 185 c2r transform (or vice versa) will result in the original data
cannam@127 186 multiplied by the size of the transform (the product of the logical
cannam@127 187 dimensions).
cannam@127 188 <a name="index-normalization-6"></a>
cannam@127 189 An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
cannam@127 190 complex DFT of the same input, and a c2r transform is correspondingly
cannam@127 191 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@127 192 </p>
cannam@127 193 <hr>
cannam@127 194 <div class="header">
cannam@127 195 <p>
cannam@127 196 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@127 197 </div>
cannam@127 198
cannam@127 199
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