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author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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cannam@95 3 <title>Guru Complex DFTs - FFTW 3.3.3</title>
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cannam@95 48 <div class="node">
cannam@95 49 <a name="Guru-Complex-DFTs"></a>
cannam@95 50 <p>
cannam@95 51 Next:&nbsp;<a rel="next" accesskey="n" href="Guru-Real_002ddata-DFTs.html#Guru-Real_002ddata-DFTs">Guru Real-data DFTs</a>,
cannam@95 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Guru-vector-and-transform-sizes.html#Guru-vector-and-transform-sizes">Guru vector and transform sizes</a>,
cannam@95 53 Up:&nbsp;<a rel="up" accesskey="u" href="Guru-Interface.html#Guru-Interface">Guru Interface</a>
cannam@95 54 <hr>
cannam@95 55 </div>
cannam@95 56
cannam@95 57 <h4 class="subsection">4.5.3 Guru Complex DFTs</h4>
cannam@95 58
cannam@95 59 <pre class="example"> fftw_plan fftw_plan_guru_dft(
cannam@95 60 int rank, const fftw_iodim *dims,
cannam@95 61 int howmany_rank, const fftw_iodim *howmany_dims,
cannam@95 62 fftw_complex *in, fftw_complex *out,
cannam@95 63 int sign, unsigned flags);
cannam@95 64
cannam@95 65 fftw_plan fftw_plan_guru_split_dft(
cannam@95 66 int rank, const fftw_iodim *dims,
cannam@95 67 int howmany_rank, const fftw_iodim *howmany_dims,
cannam@95 68 double *ri, double *ii, double *ro, double *io,
cannam@95 69 unsigned flags);
cannam@95 70 </pre>
cannam@95 71 <p><a name="index-fftw_005fplan_005fguru_005fdft-248"></a><a name="index-fftw_005fplan_005fguru_005fsplit_005fdft-249"></a>
cannam@95 72 These two functions plan a complex-data, multi-dimensional DFT
cannam@95 73 for the interleaved and split format, respectively.
cannam@95 74 Transform dimensions are given by (<code>rank</code>, <code>dims</code>) over a
cannam@95 75 multi-dimensional vector (loop) of dimensions (<code>howmany_rank</code>,
cannam@95 76 <code>howmany_dims</code>). <code>dims</code> and <code>howmany_dims</code> should point
cannam@95 77 to <code>fftw_iodim</code> arrays of length <code>rank</code> and
cannam@95 78 <code>howmany_rank</code>, respectively.
cannam@95 79
cannam@95 80 <p><a name="index-flags-250"></a><code>flags</code> is a bitwise OR (&lsquo;<samp><span class="samp">|</span></samp>&rsquo;) of zero or more planner flags,
cannam@95 81 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@95 82
cannam@95 83 <p>In the <code>fftw_plan_guru_dft</code> function, the pointers <code>in</code> and
cannam@95 84 <code>out</code> point to the interleaved input and output arrays,
cannam@95 85 respectively. The sign can be either -1 (=
cannam@95 86 <code>FFTW_FORWARD</code>) or +1 (= <code>FFTW_BACKWARD</code>). If the
cannam@95 87 pointers are equal, the transform is in-place.
cannam@95 88
cannam@95 89 <p>In the <code>fftw_plan_guru_split_dft</code> function,
cannam@95 90 <code>ri</code> and <code>ii</code> point to the real and imaginary input arrays,
cannam@95 91 and <code>ro</code> and <code>io</code> point to the real and imaginary output
cannam@95 92 arrays. The input and output pointers may be the same, indicating an
cannam@95 93 in-place transform. For example, for <code>fftw_complex</code> pointers
cannam@95 94 <code>in</code> and <code>out</code>, the corresponding parameters are:
cannam@95 95
cannam@95 96 <pre class="example"> ri = (double *) in;
cannam@95 97 ii = (double *) in + 1;
cannam@95 98 ro = (double *) out;
cannam@95 99 io = (double *) out + 1;
cannam@95 100 </pre>
cannam@95 101 <p>Because <code>fftw_plan_guru_split_dft</code> accepts split arrays, strides
cannam@95 102 are expressed in units of <code>double</code>. For a contiguous
cannam@95 103 <code>fftw_complex</code> array, the overall stride of the transform should
cannam@95 104 be 2, the distance between consecutive real parts or between
cannam@95 105 consecutive imaginary parts; see <a href="Guru-vector-and-transform-sizes.html#Guru-vector-and-transform-sizes">Guru vector and transform sizes</a>. Note that the dimension strides are applied equally to the
cannam@95 106 real and imaginary parts; real and imaginary arrays with different
cannam@95 107 strides are not supported.
cannam@95 108
cannam@95 109 <p>There is no <code>sign</code> parameter in <code>fftw_plan_guru_split_dft</code>.
cannam@95 110 This function always plans for an <code>FFTW_FORWARD</code> transform. To
cannam@95 111 plan for an <code>FFTW_BACKWARD</code> transform, you can exploit the
cannam@95 112 identity that the backwards DFT is equal to the forwards DFT with the
cannam@95 113 real and imaginary parts swapped. For example, in the case of the
cannam@95 114 <code>fftw_complex</code> arrays above, the <code>FFTW_BACKWARD</code> transform
cannam@95 115 is computed by the parameters:
cannam@95 116
cannam@95 117 <pre class="example"> ri = (double *) in + 1;
cannam@95 118 ii = (double *) in;
cannam@95 119 ro = (double *) out + 1;
cannam@95 120 io = (double *) out;
cannam@95 121 </pre>
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