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Tidy up for ROLI
author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Tue, 17 May 2016 18:50:19 +0100
parents 636c989477e7
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1 <html lang="en">
2 <head>
3 <title>Real-data DFTs - FFTW 3.2.1</title>
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49 <p>
50 <a name="Real-data-DFTs"></a>
51 <a name="Real_002ddata-DFTs"></a>
52 Next:&nbsp;<a rel="next" accesskey="n" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>,
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54 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
55 <hr>
56 </div>
57
58 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
59
60 <pre class="example"> fftw_plan fftw_plan_dft_r2c_1d(int n,
61 double *in, fftw_complex *out,
62 unsigned flags);
63 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
64 double *in, fftw_complex *out,
65 unsigned flags);
66 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
67 double *in, fftw_complex *out,
68 unsigned flags);
69 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
70 double *in, fftw_complex *out,
71 unsigned flags);
72 </pre>
73 <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-176"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-177"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-178"></a><a name="index-fftw_005fplan_005fdft_005fr2c-179"></a><a name="index-r2c-180"></a>
74 Plan a real-input/complex-output discrete Fourier transform (DFT) in
75 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
76
77 <p>Once you have created a plan for a certain transform type and
78 parameters, then creating another plan of the same type and parameters,
79 but for different arrays, is fast and shares constant data with the
80 first plan (if it still exists).
81
82 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
83 non-<code>NULL</code> plan is always returned by the basic interface unless
84 you are using a customized FFTW configuration supporting a restricted
85 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
86 with a multi-dimensional out-of-place c2r transform (see below).
87
88 <h5 class="subsubheading">Arguments</h5>
89
90 <ul>
91 <li><code>rank</code> is the dimensionality of the transform (it should be the
92 size of the array <code>*n</code>), and can be any non-negative integer. The
93 `<samp><span class="samp">_1d</span></samp>', `<samp><span class="samp">_2d</span></samp>', and `<samp><span class="samp">_3d</span></samp>' planners correspond to a
94 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. A
95 <code>rank</code> of zero is equivalent to a transform of size 1, i.e. a copy
96 of one number (with zero imaginary part) from input to output.
97
98 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
99 respectively, gives the size of the <em>logical</em> transform dimensions.
100 They can be any positive integer. This is different in general from the
101 <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>.
102
103 <ul>
104 <li>FFTW is best at handling sizes of the form
105 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
106 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
107 are arbitrary. Other sizes are computed by means of a slow,
108 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
109
110 <p>performance even for prime sizes). (It is possible to customize FFTW
111 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
112 Transforms whose sizes are powers of 2 are especially fast, and
113 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
114 transform to be <em>even</em>.
115 </ul>
116
117 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
118 transform, which may be the same (yielding an in-place transform).
119 <a name="index-in_002dplace-181"></a>These arrays are overwritten during planning, unless
120 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
121 initialized, but they must be allocated.) For an in-place transform, it
122 is important to remember that the real array will require padding,
123 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
124 <a name="index-padding-182"></a>
125 <li><a name="index-flags-183"></a><code>flags</code> is a bitwise OR (`<samp><span class="samp">|</span></samp>') of zero or more planner flags,
126 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
127
128 </ul>
129
130 <p>The inverse transforms, taking complex input (storing the non-redundant
131 half of a logically Hermitian array) to real output, are given by:
132
133 <pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n,
134 fftw_complex *in, double *out,
135 unsigned flags);
136 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
137 fftw_complex *in, double *out,
138 unsigned flags);
139 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
140 fftw_complex *in, double *out,
141 unsigned flags);
142 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
143 fftw_complex *in, double *out,
144 unsigned flags);
145 </pre>
146 <p><a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-184"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f2d-185"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f3d-186"></a><a name="index-fftw_005fplan_005fdft_005fc2r-187"></a><a name="index-c2r-188"></a>
147 The arguments are the same as for the r2c transforms, except that the
148 input and output data formats are reversed.
149
150 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
151 c2r transform (or vice versa) will result in the original data
152 multiplied by the size of the transform (the product of the logical
153 dimensions).
154 <a name="index-normalization-189"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
155 complex DFT of the same input, and a c2r transform is correspondingly
156 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>.
157
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