Mercurial > hg > sv-dependency-builds

comparison src/fftw-3.3.3/doc/html/Advanced-Complex-DFTs.html @ 10:37bf6b4a2645

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
parents
children
comparison
equal deleted inserted replaced
9:c0fb53affa76 10:37bf6b4a2645
1 <html lang="en">
2 <head>
3 <title>Advanced Complex DFTs - FFTW 3.3.3</title>
4 <meta http-equiv="Content-Type" content="text/html">
5 <meta name="description" content="FFTW 3.3.3">
6 <meta name="generator" content="makeinfo 4.13">
7 <link title="Top" rel="start" href="index.html#Top">
8 <link rel="up" href="Advanced-Interface.html#Advanced-Interface" title="Advanced Interface">
9 <link rel="prev" href="Advanced-Interface.html#Advanced-Interface" title="Advanced Interface">
10 <link rel="next" href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" title="Advanced Real-data DFTs">
11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
12 <!--
13 This manual is for FFTW
14 (version 3.3.3, 25 November 2012).
15
16 Copyright (C) 2003 Matteo Frigo.
17
18 Copyright (C) 2003 Massachusetts Institute of Technology.
19
20 Permission is granted to make and distribute verbatim copies of
21 this manual provided the copyright notice and this permission
22 notice are preserved on all copies.
23
24 Permission is granted to copy and distribute modified versions of
25 this manual under the conditions for verbatim copying, provided
26 that the entire resulting derived work is distributed under the
27 terms of a permission notice identical to this one.
28
29 Permission is granted to copy and distribute translations of this
30 manual into another language, under the above conditions for
31 modified versions, except that this permission notice may be
32 stated in a translation approved by the Free Software Foundation.
33 -->
34 <meta http-equiv="Content-Style-Type" content="text/css">
35 <style type="text/css"><!--
36 pre.display { font-family:inherit }
37 pre.format { font-family:inherit }
38 pre.smalldisplay { font-family:inherit; font-size:smaller }
39 pre.smallformat { font-family:inherit; font-size:smaller }
40 pre.smallexample { font-size:smaller }
41 pre.smalllisp { font-size:smaller }
42 span.sc { font-variant:small-caps }
43 span.roman { font-family:serif; font-weight:normal; }
44 span.sansserif { font-family:sans-serif; font-weight:normal; }
45 --></style>
46 </head>
47 <body>
48 <div class="node">
49 <a name="Advanced-Complex-DFTs"></a>
50 <p>
51 Next:&nbsp;<a rel="next" accesskey="n" href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs">Advanced Real-data DFTs</a>,
52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>,
53 Up:&nbsp;<a rel="up" accesskey="u" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>
54 <hr>
55 </div>
56
57 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
58
59 <pre class="example"> fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
60 fftw_complex *in, const int *inembed,
61 int istride, int idist,
62 fftw_complex *out, const int *onembed,
63 int ostride, int odist,
64 int sign, unsigned flags);
65 </pre>
66 <p><a name="index-fftw_005fplan_005fmany_005fdft-232"></a>
67 This routine plans multiple multidimensional complex DFTs, and it
68 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
69 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
70 <code>n</code>. In addition, the transform data need not be contiguous, but
71 it may be laid out in memory with an arbitrary stride. To account for
72 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
73 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
74 {<code>i</code>,<code>o</code>}<code>stride</code>, and
75 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
76 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
77 and&nbsp;3, but the advanced interface handles only the general-rank
78 case.
79
80 <p><code>howmany</code> is the number of transforms to compute. The resulting
81 plan computes <code>howmany</code> transforms, where the input of the
82 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
83 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
84 obtained in this way can often be faster than calling FFTW multiple
85 times for the individual transforms. The basic <code>fftw_plan_dft</code>
86 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
87 parameters are ignored).
88 <a name="index-howmany-parameter-233"></a><a name="index-dist-234"></a>
89
90 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
91 <code>n</code>, as in the basic interface. In addition, the advanced
92 interface allows the input and output arrays of each transform to be
93 row-major subarrays of larger rank-<code>rank</code> arrays, described by
94 <code>inembed</code> and <code>onembed</code> parameters, respectively.
95 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
96 and <code>n</code> should be elementwise less than or equal to
97 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
98 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
99 physical and logical dimensions, as in the basic interface.)
100
101 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
102 the input or output arrays is located at <code>j*istride</code> or
103 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
104 <code>j</code> is the ordinary row-major index.) When combined with the
105 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
106 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
107 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
108 <a name="index-stride-235"></a>
109
110 <p>For in-place transforms, the input and output <code>stride</code> and
111 <code>dist</code> parameters should be the same; otherwise, the planner may
112 return <code>NULL</code>.
113
114 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
115 this function returns. You can safely free or reuse them.
116
117 <p><strong>Examples</strong>:
118 One transform of one 5 by 6 array contiguous in memory:
119 <pre class="example"> int rank = 2;
120 int n[] = {5, 6};
121 int howmany = 1;
122 int idist = odist = 0; /* unused because howmany = 1 */
123 int istride = ostride = 1; /* array is contiguous in memory */
124 int *inembed = n, *onembed = n;
125 </pre>
126 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
127 stored in memory one after another:
128 <pre class="example"> int rank = 2;
129 int n[] = {5, 6};
130 int howmany = 3;
131 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
132 between the first element
133 of the first array and the
134 first element of the second array */
135 int istride = ostride = 1; /* array is contiguous in memory */
136 int *inembed = n, *onembed = n;
137 </pre>
138 <p>Transform each column of a 2d array with 10 rows and 3 columns:
139 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
140 int n[] = {10}; /* 1d transforms of length 10 */
141 int howmany = 3;
142 int idist = odist = 1;
143 int istride = ostride = 3; /* distance between two elements in
144 the same column */
145 int *inembed = n, *onembed = n;
146 </pre>
147 <!-- =========> -->
148 </body></html>
149