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date Fri, 07 Feb 2020 11:51:13 +0000
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Chris@10 3 <title>Real-data DFTs - FFTW 3.3.3</title>
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Chris@10 48 <div class="node">
Chris@10 49 <a name="Real-data-DFTs"></a>
Chris@10 50 <a name="Real_002ddata-DFTs"></a>
Chris@10 51 <p>
Chris@10 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>,
Chris@10 53 Previous:&nbsp;<a rel="previous" accesskey="p" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
Chris@10 54 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
Chris@10 55 <hr>
Chris@10 56 </div>
Chris@10 57
Chris@10 58 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
Chris@10 59
Chris@10 60 <pre class="example"> fftw_plan fftw_plan_dft_r2c_1d(int n0,
Chris@10 61 double *in, fftw_complex *out,
Chris@10 62 unsigned flags);
Chris@10 63 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
Chris@10 64 double *in, fftw_complex *out,
Chris@10 65 unsigned flags);
Chris@10 66 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
Chris@10 67 double *in, fftw_complex *out,
Chris@10 68 unsigned flags);
Chris@10 69 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
Chris@10 70 double *in, fftw_complex *out,
Chris@10 71 unsigned flags);
Chris@10 72 </pre>
Chris@10 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>
Chris@10 74 Plan a real-input/complex-output discrete Fourier transform (DFT) in
Chris@10 75 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@10 76
Chris@10 77 <p>Once you have created a plan for a certain transform type and
Chris@10 78 parameters, then creating another plan of the same type and parameters,
Chris@10 79 but for different arrays, is fast and shares constant data with the
Chris@10 80 first plan (if it still exists).
Chris@10 81
Chris@10 82 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@10 83 non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@10 84 you are using a customized FFTW configuration supporting a restricted
Chris@10 85 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
Chris@10 86 with a multi-dimensional out-of-place c2r transform (see below).
Chris@10 87
Chris@10 88 <h5 class="subsubheading">Arguments</h5>
Chris@10 89
Chris@10 90 <ul>
Chris@10 91 <li><code>rank</code> is the rank of the transform (it should be the size of the
Chris@10 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
Chris@10 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
Chris@10 94 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@10 95 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@10 96 copy of one real number (with zero imaginary part) from input to output.
Chris@10 97
Chris@10 98 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
Chris@10 99 for each routine) specify the size of the transform dimensions. They
Chris@10 100 can be any positive integer. This is different in general from the
Chris@10 101 <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>.
Chris@10 102
Chris@10 103 <ul>
Chris@10 104 <li>FFTW is best at handling sizes of the form
Chris@10 105 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@10 106 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
Chris@10 107 are arbitrary. Other sizes are computed by means of a slow,
Chris@10 108 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
Chris@10 109 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@10 110 Transforms whose sizes are powers of 2 are especially fast, and
Chris@10 111 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
Chris@10 112 transform to be <em>even</em>.
Chris@10 113 </ul>
Chris@10 114
Chris@10 115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@10 116 transform, which may be the same (yielding an in-place transform).
Chris@10 117 <a name="index-in_002dplace-190"></a>These arrays are overwritten during planning, unless
Chris@10 118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@10 119 initialized, but they must be allocated.) For an in-place transform, it
Chris@10 120 is important to remember that the real array will require padding,
Chris@10 121 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
Chris@10 122 <a name="index-padding-191"></a>
Chris@10 123 <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,
Chris@10 124 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@10 125
Chris@10 126 </ul>
Chris@10 127
Chris@10 128 <p>The inverse transforms, taking complex input (storing the non-redundant
Chris@10 129 half of a logically Hermitian array) to real output, are given by:
Chris@10 130
Chris@10 131 <pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n0,
Chris@10 132 fftw_complex *in, double *out,
Chris@10 133 unsigned flags);
Chris@10 134 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
Chris@10 135 fftw_complex *in, double *out,
Chris@10 136 unsigned flags);
Chris@10 137 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
Chris@10 138 fftw_complex *in, double *out,
Chris@10 139 unsigned flags);
Chris@10 140 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
Chris@10 141 fftw_complex *in, double *out,
Chris@10 142 unsigned flags);
Chris@10 143 </pre>
Chris@10 144 <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>
Chris@10 145 The arguments are the same as for the r2c transforms, except that the
Chris@10 146 input and output data formats are reversed.
Chris@10 147
Chris@10 148 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
Chris@10 149 c2r transform (or vice versa) will result in the original data
Chris@10 150 multiplied by the size of the transform (the product of the logical
Chris@10 151 dimensions).
Chris@10 152 <a name="index-normalization-198"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
Chris@10 153 complex DFT of the same input, and a c2r transform is correspondingly
Chris@10 154 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>.
Chris@10 155
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