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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
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cannam@127 6 Copyright (C) 2003 Matteo Frigo.
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cannam@127 25 <title>FFTW 3.3.5: Advanced Complex DFTs</title>
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cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Advanced-Complex-DFTs"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 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>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Advanced-Complex-DFTs-1"></a>
cannam@127 79 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
cannam@127 80
cannam@127 81 <div class="example">
cannam@127 82 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
cannam@127 83 fftw_complex *in, const int *inembed,
cannam@127 84 int istride, int idist,
cannam@127 85 fftw_complex *out, const int *onembed,
cannam@127 86 int ostride, int odist,
cannam@127 87 int sign, unsigned flags);
cannam@127 88 </pre></div>
cannam@127 89 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
cannam@127 90
cannam@127 91 <p>This routine plans multiple multidimensional complex DFTs, and it
cannam@127 92 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
cannam@127 93 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
cannam@127 94 <code>n</code>. In addition, the transform data need not be contiguous, but
cannam@127 95 it may be laid out in memory with an arbitrary stride. To account for
cannam@127 96 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
cannam@127 97 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
cannam@127 98 {<code>i</code>,<code>o</code>}<code>stride</code>, and
cannam@127 99 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
cannam@127 100 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
cannam@127 101 and&nbsp;3, but the advanced interface handles only the general-rank
cannam@127 102 case.
cannam@127 103 </p>
cannam@127 104 <p><code>howmany</code> is the number of transforms to compute. The resulting
cannam@127 105 plan computes <code>howmany</code> transforms, where the input of the
cannam@127 106 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
cannam@127 107 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
cannam@127 108 obtained in this way can often be faster than calling FFTW multiple
cannam@127 109 times for the individual transforms. The basic <code>fftw_plan_dft</code>
cannam@127 110 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
cannam@127 111 parameters are ignored).
cannam@127 112 <a name="index-howmany-parameter"></a>
cannam@127 113 <a name="index-dist"></a>
cannam@127 114 </p>
cannam@127 115
cannam@127 116 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
cannam@127 117 <code>n</code>, as in the basic interface. In addition, the advanced
cannam@127 118 interface allows the input and output arrays of each transform to be
cannam@127 119 row-major subarrays of larger rank-<code>rank</code> arrays, described by
cannam@127 120 <code>inembed</code> and <code>onembed</code> parameters, respectively.
cannam@127 121 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
cannam@127 122 and <code>n</code> should be elementwise less than or equal to
cannam@127 123 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
cannam@127 124 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
cannam@127 125 physical and logical dimensions, as in the basic interface.)
cannam@127 126 </p>
cannam@127 127 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
cannam@127 128 the input or output arrays is located at <code>j*istride</code> or
cannam@127 129 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
cannam@127 130 <code>j</code> is the ordinary row-major index.) When combined with the
cannam@127 131 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
cannam@127 132 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
cannam@127 133 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
cannam@127 134 <a name="index-stride-1"></a>
cannam@127 135 </p>
cannam@127 136
cannam@127 137 <p>For in-place transforms, the input and output <code>stride</code> and
cannam@127 138 <code>dist</code> parameters should be the same; otherwise, the planner may
cannam@127 139 return <code>NULL</code>.
cannam@127 140 </p>
cannam@127 141 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
cannam@127 142 this function returns. You can safely free or reuse them.
cannam@127 143 </p>
cannam@127 144 <p><strong>Examples</strong>:
cannam@127 145 One transform of one 5 by 6 array contiguous in memory:
cannam@127 146 </p><div class="example">
cannam@127 147 <pre class="example"> int rank = 2;
cannam@127 148 int n[] = {5, 6};
cannam@127 149 int howmany = 1;
cannam@127 150 int idist = odist = 0; /* unused because howmany = 1 */
cannam@127 151 int istride = ostride = 1; /* array is contiguous in memory */
cannam@127 152 int *inembed = n, *onembed = n;
cannam@127 153 </pre></div>
cannam@127 154
cannam@127 155 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
cannam@127 156 stored in memory one after another:
cannam@127 157 </p><div class="example">
cannam@127 158 <pre class="example"> int rank = 2;
cannam@127 159 int n[] = {5, 6};
cannam@127 160 int howmany = 3;
cannam@127 161 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
cannam@127 162 between the first element
cannam@127 163 of the first array and the
cannam@127 164 first element of the second array */
cannam@127 165 int istride = ostride = 1; /* array is contiguous in memory */
cannam@127 166 int *inembed = n, *onembed = n;
cannam@127 167 </pre></div>
cannam@127 168
cannam@127 169 <p>Transform each column of a 2d array with 10 rows and 3 columns:
cannam@127 170 </p><div class="example">
cannam@127 171 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
cannam@127 172 int n[] = {10}; /* 1d transforms of length 10 */
cannam@127 173 int howmany = 3;
cannam@127 174 int idist = odist = 1;
cannam@127 175 int istride = ostride = 3; /* distance between two elements in
cannam@127 176 the same column */
cannam@127 177 int *inembed = n, *onembed = n;
cannam@127 178 </pre></div>
cannam@127 179
cannam@127 180 <hr>
cannam@127 181 <div class="header">
cannam@127 182 <p>
cannam@127 183 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>
cannam@127 184 </div>
cannam@127 185
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