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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents 37bf6b4a2645
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Chris@10 3 <title>Advanced Complex DFTs - FFTW 3.3.3</title>
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Chris@10 48 <div class="node">
Chris@10 49 <a name="Advanced-Complex-DFTs"></a>
Chris@10 50 <p>
Chris@10 51 Next:&nbsp;<a rel="next" accesskey="n" href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs">Advanced Real-data DFTs</a>,
Chris@10 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>,
Chris@10 53 Up:&nbsp;<a rel="up" accesskey="u" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>
Chris@10 54 <hr>
Chris@10 55 </div>
Chris@10 56
Chris@10 57 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
Chris@10 58
Chris@10 59 <pre class="example"> fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
Chris@10 60 fftw_complex *in, const int *inembed,
Chris@10 61 int istride, int idist,
Chris@10 62 fftw_complex *out, const int *onembed,
Chris@10 63 int ostride, int odist,
Chris@10 64 int sign, unsigned flags);
Chris@10 65 </pre>
Chris@10 66 <p><a name="index-fftw_005fplan_005fmany_005fdft-232"></a>
Chris@10 67 This routine plans multiple multidimensional complex DFTs, and it
Chris@10 68 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
Chris@10 69 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
Chris@10 70 <code>n</code>. In addition, the transform data need not be contiguous, but
Chris@10 71 it may be laid out in memory with an arbitrary stride. To account for
Chris@10 72 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
Chris@10 73 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
Chris@10 74 {<code>i</code>,<code>o</code>}<code>stride</code>, and
Chris@10 75 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
Chris@10 76 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
Chris@10 77 and&nbsp;3, but the advanced interface handles only the general-rank
Chris@10 78 case.
Chris@10 79
Chris@10 80 <p><code>howmany</code> is the number of transforms to compute. The resulting
Chris@10 81 plan computes <code>howmany</code> transforms, where the input of the
Chris@10 82 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
Chris@10 83 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
Chris@10 84 obtained in this way can often be faster than calling FFTW multiple
Chris@10 85 times for the individual transforms. The basic <code>fftw_plan_dft</code>
Chris@10 86 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
Chris@10 87 parameters are ignored).
Chris@10 88 <a name="index-howmany-parameter-233"></a><a name="index-dist-234"></a>
Chris@10 89
Chris@10 90 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
Chris@10 91 <code>n</code>, as in the basic interface. In addition, the advanced
Chris@10 92 interface allows the input and output arrays of each transform to be
Chris@10 93 row-major subarrays of larger rank-<code>rank</code> arrays, described by
Chris@10 94 <code>inembed</code> and <code>onembed</code> parameters, respectively.
Chris@10 95 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
Chris@10 96 and <code>n</code> should be elementwise less than or equal to
Chris@10 97 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
Chris@10 98 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
Chris@10 99 physical and logical dimensions, as in the basic interface.)
Chris@10 100
Chris@10 101 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
Chris@10 102 the input or output arrays is located at <code>j*istride</code> or
Chris@10 103 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
Chris@10 104 <code>j</code> is the ordinary row-major index.) When combined with the
Chris@10 105 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
Chris@10 106 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
Chris@10 107 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
Chris@10 108 <a name="index-stride-235"></a>
Chris@10 109
Chris@10 110 <p>For in-place transforms, the input and output <code>stride</code> and
Chris@10 111 <code>dist</code> parameters should be the same; otherwise, the planner may
Chris@10 112 return <code>NULL</code>.
Chris@10 113
Chris@10 114 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
Chris@10 115 this function returns. You can safely free or reuse them.
Chris@10 116
Chris@10 117 <p><strong>Examples</strong>:
Chris@10 118 One transform of one 5 by 6 array contiguous in memory:
Chris@10 119 <pre class="example"> int rank = 2;
Chris@10 120 int n[] = {5, 6};
Chris@10 121 int howmany = 1;
Chris@10 122 int idist = odist = 0; /* unused because howmany = 1 */
Chris@10 123 int istride = ostride = 1; /* array is contiguous in memory */
Chris@10 124 int *inembed = n, *onembed = n;
Chris@10 125 </pre>
Chris@10 126 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
Chris@10 127 stored in memory one after another:
Chris@10 128 <pre class="example"> int rank = 2;
Chris@10 129 int n[] = {5, 6};
Chris@10 130 int howmany = 3;
Chris@10 131 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@10 132 between the first element
Chris@10 133 of the first array and the
Chris@10 134 first element of the second array */
Chris@10 135 int istride = ostride = 1; /* array is contiguous in memory */
Chris@10 136 int *inembed = n, *onembed = n;
Chris@10 137 </pre>
Chris@10 138 <p>Transform each column of a 2d array with 10 rows and 3 columns:
Chris@10 139 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
Chris@10 140 int n[] = {10}; /* 1d transforms of length 10 */
Chris@10 141 int howmany = 3;
Chris@10 142 int idist = odist = 1;
Chris@10 143 int istride = ostride = 3; /* distance between two elements in
Chris@10 144 the same column */
Chris@10 145 int *inembed = n, *onembed = n;
Chris@10 146 </pre>
Chris@10 147 <!-- =========> -->
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Chris@10 149