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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 d0c2a83c1364
children
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Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@82 4 (version 3.3.8, 24 May 2018).
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Advanced Complex DFTs</title>
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Chris@82 37 <link href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" rel="next" title="Advanced Real-data DFTs">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Advanced-Complex-DFTs"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Advanced-Complex-DFTs-1"></a>
Chris@82 78 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
Chris@82 79
Chris@82 80 <div class="example">
Chris@82 81 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
Chris@82 82 fftw_complex *in, const int *inembed,
Chris@82 83 int istride, int idist,
Chris@82 84 fftw_complex *out, const int *onembed,
Chris@82 85 int ostride, int odist,
Chris@82 86 int sign, unsigned flags);
Chris@82 87 </pre></div>
Chris@82 88 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
Chris@82 89
Chris@82 90 <p>This routine plans multiple multidimensional complex DFTs, and it
Chris@82 91 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
Chris@82 92 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
Chris@82 93 <code>n</code>. In addition, the transform data need not be contiguous, but
Chris@82 94 it may be laid out in memory with an arbitrary stride. To account for
Chris@82 95 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
Chris@82 96 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
Chris@82 97 {<code>i</code>,<code>o</code>}<code>stride</code>, and
Chris@82 98 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
Chris@82 99 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
Chris@82 100 and&nbsp;3, but the advanced interface handles only the general-rank
Chris@82 101 case.
Chris@82 102 </p>
Chris@82 103 <p><code>howmany</code> is the (nonnegative) number of transforms to compute. The resulting
Chris@82 104 plan computes <code>howmany</code> transforms, where the input of the
Chris@82 105 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
Chris@82 106 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
Chris@82 107 obtained in this way can often be faster than calling FFTW multiple
Chris@82 108 times for the individual transforms. The basic <code>fftw_plan_dft</code>
Chris@82 109 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
Chris@82 110 parameters are ignored).
Chris@82 111 <a name="index-howmany-parameter"></a>
Chris@82 112 <a name="index-dist"></a>
Chris@82 113 </p>
Chris@82 114
Chris@82 115 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
Chris@82 116 <code>n</code>, as in the basic interface. In addition, the advanced
Chris@82 117 interface allows the input and output arrays of each transform to be
Chris@82 118 row-major subarrays of larger rank-<code>rank</code> arrays, described by
Chris@82 119 <code>inembed</code> and <code>onembed</code> parameters, respectively.
Chris@82 120 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
Chris@82 121 and <code>n</code> should be elementwise less than or equal to
Chris@82 122 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
Chris@82 123 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
Chris@82 124 physical and logical dimensions, as in the basic interface.)
Chris@82 125 </p>
Chris@82 126 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
Chris@82 127 the input or output arrays is located at <code>j*istride</code> or
Chris@82 128 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
Chris@82 129 <code>j</code> is the ordinary row-major index.) When combined with the
Chris@82 130 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
Chris@82 131 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
Chris@82 132 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
Chris@82 133 <a name="index-stride-1"></a>
Chris@82 134 </p>
Chris@82 135
Chris@82 136 <p>For in-place transforms, the input and output <code>stride</code> and
Chris@82 137 <code>dist</code> parameters should be the same; otherwise, the planner may
Chris@82 138 return <code>NULL</code>.
Chris@82 139 </p>
Chris@82 140 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
Chris@82 141 this function returns. You can safely free or reuse them.
Chris@82 142 </p>
Chris@82 143 <p><strong>Examples</strong>:
Chris@82 144 One transform of one 5 by 6 array contiguous in memory:
Chris@82 145 </p><div class="example">
Chris@82 146 <pre class="example"> int rank = 2;
Chris@82 147 int n[] = {5, 6};
Chris@82 148 int howmany = 1;
Chris@82 149 int idist = odist = 0; /* unused because howmany = 1 */
Chris@82 150 int istride = ostride = 1; /* array is contiguous in memory */
Chris@82 151 int *inembed = n, *onembed = n;
Chris@82 152 </pre></div>
Chris@82 153
Chris@82 154 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
Chris@82 155 stored in memory one after another:
Chris@82 156 </p><div class="example">
Chris@82 157 <pre class="example"> int rank = 2;
Chris@82 158 int n[] = {5, 6};
Chris@82 159 int howmany = 3;
Chris@82 160 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@82 161 between the first element
Chris@82 162 of the first array and the
Chris@82 163 first element of the second array */
Chris@82 164 int istride = ostride = 1; /* array is contiguous in memory */
Chris@82 165 int *inembed = n, *onembed = n;
Chris@82 166 </pre></div>
Chris@82 167
Chris@82 168 <p>Transform each column of a 2d array with 10 rows and 3 columns:
Chris@82 169 </p><div class="example">
Chris@82 170 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
Chris@82 171 int n[] = {10}; /* 1d transforms of length 10 */
Chris@82 172 int howmany = 3;
Chris@82 173 int idist = odist = 1;
Chris@82 174 int istride = ostride = 3; /* distance between two elements in
Chris@82 175 the same column */
Chris@82 176 int *inembed = n, *onembed = n;
Chris@82 177 </pre></div>
Chris@82 178
Chris@82 179 <hr>
Chris@82 180 <div class="header">
Chris@82 181 <p>
Chris@82 182 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 183 </div>
Chris@82 184
Chris@82 185
Chris@82 186
Chris@82 187 </body>
Chris@82 188 </html>