|
Chris@10
|
1 <html lang="en">
|
|
Chris@10
|
2 <head>
|
|
Chris@10
|
3 <title>Row-major Format - FFTW 3.3.3</title>
|
|
Chris@10
|
4 <meta http-equiv="Content-Type" content="text/html">
|
|
Chris@10
|
5 <meta name="description" content="FFTW 3.3.3">
|
|
Chris@10
|
6 <meta name="generator" content="makeinfo 4.13">
|
|
Chris@10
|
7 <link title="Top" rel="start" href="index.html#Top">
|
|
Chris@10
|
8 <link rel="up" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format">
|
|
Chris@10
|
9 <link rel="prev" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format">
|
|
Chris@10
|
10 <link rel="next" href="Column_002dmajor-Format.html#Column_002dmajor-Format" title="Column-major Format">
|
|
Chris@10
|
11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
|
|
Chris@10
|
12 <!--
|
|
Chris@10
|
13 This manual is for FFTW
|
|
Chris@10
|
14 (version 3.3.3, 25 November 2012).
|
|
Chris@10
|
15
|
|
Chris@10
|
16 Copyright (C) 2003 Matteo Frigo.
|
|
Chris@10
|
17
|
|
Chris@10
|
18 Copyright (C) 2003 Massachusetts Institute of Technology.
|
|
Chris@10
|
19
|
|
Chris@10
|
20 Permission is granted to make and distribute verbatim copies of
|
|
Chris@10
|
21 this manual provided the copyright notice and this permission
|
|
Chris@10
|
22 notice are preserved on all copies.
|
|
Chris@10
|
23
|
|
Chris@10
|
24 Permission is granted to copy and distribute modified versions of
|
|
Chris@10
|
25 this manual under the conditions for verbatim copying, provided
|
|
Chris@10
|
26 that the entire resulting derived work is distributed under the
|
|
Chris@10
|
27 terms of a permission notice identical to this one.
|
|
Chris@10
|
28
|
|
Chris@10
|
29 Permission is granted to copy and distribute translations of this
|
|
Chris@10
|
30 manual into another language, under the above conditions for
|
|
Chris@10
|
31 modified versions, except that this permission notice may be
|
|
Chris@10
|
32 stated in a translation approved by the Free Software Foundation.
|
|
Chris@10
|
33 -->
|
|
Chris@10
|
34 <meta http-equiv="Content-Style-Type" content="text/css">
|
|
Chris@10
|
35 <style type="text/css"><!--
|
|
Chris@10
|
36 pre.display { font-family:inherit }
|
|
Chris@10
|
37 pre.format { font-family:inherit }
|
|
Chris@10
|
38 pre.smalldisplay { font-family:inherit; font-size:smaller }
|
|
Chris@10
|
39 pre.smallformat { font-family:inherit; font-size:smaller }
|
|
Chris@10
|
40 pre.smallexample { font-size:smaller }
|
|
Chris@10
|
41 pre.smalllisp { font-size:smaller }
|
|
Chris@10
|
42 span.sc { font-variant:small-caps }
|
|
Chris@10
|
43 span.roman { font-family:serif; font-weight:normal; }
|
|
Chris@10
|
44 span.sansserif { font-family:sans-serif; font-weight:normal; }
|
|
Chris@10
|
45 --></style>
|
|
Chris@10
|
46 </head>
|
|
Chris@10
|
47 <body>
|
|
Chris@10
|
48 <div class="node">
|
|
Chris@10
|
49 <a name="Row-major-Format"></a>
|
|
Chris@10
|
50 <a name="Row_002dmajor-Format"></a>
|
|
Chris@10
|
51 <p>
|
|
Chris@10
|
52 Next: <a rel="next" accesskey="n" href="Column_002dmajor-Format.html#Column_002dmajor-Format">Column-major Format</a>,
|
|
Chris@10
|
53 Previous: <a rel="previous" accesskey="p" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>,
|
|
Chris@10
|
54 Up: <a rel="up" accesskey="u" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>
|
|
Chris@10
|
55 <hr>
|
|
Chris@10
|
56 </div>
|
|
Chris@10
|
57
|
|
Chris@10
|
58 <h4 class="subsection">3.2.1 Row-major Format</h4>
|
|
Chris@10
|
59
|
|
Chris@10
|
60 <p><a name="index-row_002dmajor-115"></a>
|
|
Chris@10
|
61 The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
|
|
Chris@10
|
62 are expected to be stored as a single contiguous block in
|
|
Chris@10
|
63 <dfn>row-major</dfn> order (sometimes called “C order”). Basically, this
|
|
Chris@10
|
64 means that as you step through adjacent memory locations, the first
|
|
Chris@10
|
65 dimension's index varies most slowly and the last dimension's index
|
|
Chris@10
|
66 varies most quickly.
|
|
Chris@10
|
67
|
|
Chris@10
|
68 <p>To be more explicit, let us consider an array of rank d whose
|
|
Chris@10
|
69 dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>. Now, we specify a location in the array by a
|
|
Chris@10
|
70 sequence of d (zero-based) indices, one for each dimension:
|
|
Chris@10
|
71 (i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>). If the array is stored in row-major
|
|
Chris@10
|
72 order, then this element is located at the position
|
|
Chris@10
|
73 i<sub>d-1</sub> + n<sub>d-1</sub> * (i<sub>d-2</sub> + n<sub>d-2</sub> * (... + n<sub>1</sub> * i<sub>0</sub>)).
|
|
Chris@10
|
74
|
|
Chris@10
|
75 <p>Note that, for the ordinary complex DFT, each element of the array
|
|
Chris@10
|
76 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
|
|
Chris@10
|
77 (double-precision) numbers.
|
|
Chris@10
|
78
|
|
Chris@10
|
79 <p>In the advanced FFTW interface, the physical dimensions n from
|
|
Chris@10
|
80 which the indices are computed can be different from (larger than)
|
|
Chris@10
|
81 the logical dimensions of the transform to be computed, in order to
|
|
Chris@10
|
82 transform a subset of a larger array.
|
|
Chris@10
|
83 <a name="index-advanced-interface-116"></a>Note also that, in the advanced interface, the expression above is
|
|
Chris@10
|
84 multiplied by a <dfn>stride</dfn> to get the actual array index—this is
|
|
Chris@10
|
85 useful in situations where each element of the multi-dimensional array
|
|
Chris@10
|
86 is actually a data structure (or another array), and you just want to
|
|
Chris@10
|
87 transform a single field. In the basic interface, however, the stride
|
|
Chris@10
|
88 is 1.
|
|
Chris@10
|
89 <a name="index-stride-117"></a>
|
|
Chris@10
|
90 <!-- =========> -->
|
|
Chris@10
|
91
|
|
Chris@10
|
92 </body></html>
|
|
Chris@10
|
93
|
