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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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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>