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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 2cd0e3b3e1fd
children
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Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
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Chris@42 6 Copyright (C) 2003 Matteo Frigo.
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Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: Advanced Complex DFTs</title>
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Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Advanced-Complex-DFTs"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 75 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@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Advanced-Complex-DFTs-1"></a>
Chris@42 79 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
Chris@42 80
Chris@42 81 <div class="example">
Chris@42 82 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
Chris@42 83 fftw_complex *in, const int *inembed,
Chris@42 84 int istride, int idist,
Chris@42 85 fftw_complex *out, const int *onembed,
Chris@42 86 int ostride, int odist,
Chris@42 87 int sign, unsigned flags);
Chris@42 88 </pre></div>
Chris@42 89 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
Chris@42 90
Chris@42 91 <p>This routine plans multiple multidimensional complex DFTs, and it
Chris@42 92 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
Chris@42 93 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
Chris@42 94 <code>n</code>. In addition, the transform data need not be contiguous, but
Chris@42 95 it may be laid out in memory with an arbitrary stride. To account for
Chris@42 96 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
Chris@42 97 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
Chris@42 98 {<code>i</code>,<code>o</code>}<code>stride</code>, and
Chris@42 99 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
Chris@42 100 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
Chris@42 101 and&nbsp;3, but the advanced interface handles only the general-rank
Chris@42 102 case.
Chris@42 103 </p>
Chris@42 104 <p><code>howmany</code> is the number of transforms to compute. The resulting
Chris@42 105 plan computes <code>howmany</code> transforms, where the input of the
Chris@42 106 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
Chris@42 107 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
Chris@42 108 obtained in this way can often be faster than calling FFTW multiple
Chris@42 109 times for the individual transforms. The basic <code>fftw_plan_dft</code>
Chris@42 110 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
Chris@42 111 parameters are ignored).
Chris@42 112 <a name="index-howmany-parameter"></a>
Chris@42 113 <a name="index-dist"></a>
Chris@42 114 </p>
Chris@42 115
Chris@42 116 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
Chris@42 117 <code>n</code>, as in the basic interface. In addition, the advanced
Chris@42 118 interface allows the input and output arrays of each transform to be
Chris@42 119 row-major subarrays of larger rank-<code>rank</code> arrays, described by
Chris@42 120 <code>inembed</code> and <code>onembed</code> parameters, respectively.
Chris@42 121 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
Chris@42 122 and <code>n</code> should be elementwise less than or equal to
Chris@42 123 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
Chris@42 124 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
Chris@42 125 physical and logical dimensions, as in the basic interface.)
Chris@42 126 </p>
Chris@42 127 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
Chris@42 128 the input or output arrays is located at <code>j*istride</code> or
Chris@42 129 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
Chris@42 130 <code>j</code> is the ordinary row-major index.) When combined with the
Chris@42 131 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
Chris@42 132 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
Chris@42 133 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
Chris@42 134 <a name="index-stride-1"></a>
Chris@42 135 </p>
Chris@42 136
Chris@42 137 <p>For in-place transforms, the input and output <code>stride</code> and
Chris@42 138 <code>dist</code> parameters should be the same; otherwise, the planner may
Chris@42 139 return <code>NULL</code>.
Chris@42 140 </p>
Chris@42 141 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
Chris@42 142 this function returns. You can safely free or reuse them.
Chris@42 143 </p>
Chris@42 144 <p><strong>Examples</strong>:
Chris@42 145 One transform of one 5 by 6 array contiguous in memory:
Chris@42 146 </p><div class="example">
Chris@42 147 <pre class="example"> int rank = 2;
Chris@42 148 int n[] = {5, 6};
Chris@42 149 int howmany = 1;
Chris@42 150 int idist = odist = 0; /* unused because howmany = 1 */
Chris@42 151 int istride = ostride = 1; /* array is contiguous in memory */
Chris@42 152 int *inembed = n, *onembed = n;
Chris@42 153 </pre></div>
Chris@42 154
Chris@42 155 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
Chris@42 156 stored in memory one after another:
Chris@42 157 </p><div class="example">
Chris@42 158 <pre class="example"> int rank = 2;
Chris@42 159 int n[] = {5, 6};
Chris@42 160 int howmany = 3;
Chris@42 161 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@42 162 between the first element
Chris@42 163 of the first array and the
Chris@42 164 first element of the second array */
Chris@42 165 int istride = ostride = 1; /* array is contiguous in memory */
Chris@42 166 int *inembed = n, *onembed = n;
Chris@42 167 </pre></div>
Chris@42 168
Chris@42 169 <p>Transform each column of a 2d array with 10 rows and 3 columns:
Chris@42 170 </p><div class="example">
Chris@42 171 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
Chris@42 172 int n[] = {10}; /* 1d transforms of length 10 */
Chris@42 173 int howmany = 3;
Chris@42 174 int idist = odist = 1;
Chris@42 175 int istride = ostride = 3; /* distance between two elements in
Chris@42 176 the same column */
Chris@42 177 int *inembed = n, *onembed = n;
Chris@42 178 </pre></div>
Chris@42 179
Chris@42 180 <hr>
Chris@42 181 <div class="header">
Chris@42 182 <p>
Chris@42 183 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@42 184 </div>
Chris@42 185
Chris@42 186
Chris@42 187
Chris@42 188 </body>
Chris@42 189 </html>