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3 <title>Real-data DFTs - FFTW 3.3.3</title>
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14 (version 3.3.3, 25 November 2012).
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16 Copyright (C) 2003 Matteo Frigo.
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48 <div class="node">
49 <a name="Real-data-DFTs"></a>
50 <a name="Real_002ddata-DFTs"></a>
51 <p>
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>,
53 Previous:&nbsp;<a rel="previous" accesskey="p" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
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 n0,
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-185"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-186"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-187"></a><a name="index-fftw_005fplan_005fdft_005fr2c-188"></a><a name="index-r2c-189"></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 rank of the transform (it should be the size of the
92 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
93 &lsquo;<samp><span class="samp">_1d</span></samp>&rsquo;, &lsquo;<samp><span class="samp">_2d</span></samp>&rsquo;, and &lsquo;<samp><span class="samp">_3d</span></samp>&rsquo; planners correspond to a
94 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
95 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
96 copy of one real number (with zero imaginary part) from input to output.
97
98 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
99 for each routine) specify the size of the transform dimensions. They
100 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>) performance even for prime sizes). (It is possible to customize FFTW
109 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
110 Transforms whose sizes are powers of 2 are especially fast, and
111 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
112 transform to be <em>even</em>.
113 </ul>
114
115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
116 transform, which may be the same (yielding an in-place transform).
117 <a name="index-in_002dplace-190"></a>These arrays are overwritten during planning, unless
118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
119 initialized, but they must be allocated.) For an in-place transform, it
120 is important to remember that the real array will require padding,
121 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
122 <a name="index-padding-191"></a>
123 <li><a name="index-flags-192"></a><code>flags</code> is a bitwise OR (&lsquo;<samp><span class="samp">|</span></samp>&rsquo;) of zero or more planner flags,
124 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
125
126 </ul>
127
128 <p>The inverse transforms, taking complex input (storing the non-redundant
129 half of a logically Hermitian array) to real output, are given by:
130
131 <pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n0,
132 fftw_complex *in, double *out,
133 unsigned flags);
134 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
135 fftw_complex *in, double *out,
136 unsigned flags);
137 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
138 fftw_complex *in, double *out,
139 unsigned flags);
140 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
141 fftw_complex *in, double *out,
142 unsigned flags);
143 </pre>
144 <p><a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-193"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f2d-194"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f3d-195"></a><a name="index-fftw_005fplan_005fdft_005fc2r-196"></a><a name="index-c2r-197"></a>
145 The arguments are the same as for the r2c transforms, except that the
146 input and output data formats are reversed.
147
148 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
149 c2r transform (or vice versa) will result in the original data
150 multiplied by the size of the transform (the product of the logical
151 dimensions).
152 <a name="index-normalization-198"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
153 complex DFT of the same input, and a c2r transform is correspondingly
154 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>.
155
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