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| author | Chris Cannam |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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| 9:c0fb53affa76 | 10:37bf6b4a2645 |
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| 1 <html lang="en"> | |
| 2 <head> | |
| 3 <title>Row-major Format - FFTW 3.3.3</title> | |
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| 5 <meta name="description" content="FFTW 3.3.3"> | |
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| 8 <link rel="up" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format"> | |
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| 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. | |
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| 29 Permission is granted to copy and distribute translations of this | |
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| 48 <div class="node"> | |
| 49 <a name="Row-major-Format"></a> | |
| 50 <a name="Row_002dmajor-Format"></a> | |
| 51 <p> | |
| 52 Next: <a rel="next" accesskey="n" href="Column_002dmajor-Format.html#Column_002dmajor-Format">Column-major Format</a>, | |
| 53 Previous: <a rel="previous" accesskey="p" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>, | |
| 54 Up: <a rel="up" accesskey="u" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a> | |
| 55 <hr> | |
| 56 </div> | |
| 57 | |
| 58 <h4 class="subsection">3.2.1 Row-major Format</h4> | |
| 59 | |
| 60 <p><a name="index-row_002dmajor-115"></a> | |
| 61 The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera | |
| 62 are expected to be stored as a single contiguous block in | |
| 63 <dfn>row-major</dfn> order (sometimes called “C order”). Basically, this | |
| 64 means that as you step through adjacent memory locations, the first | |
| 65 dimension's index varies most slowly and the last dimension's index | |
| 66 varies most quickly. | |
| 67 | |
| 68 <p>To be more explicit, let us consider an array of rank d whose | |
| 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 | |
| 70 sequence of d (zero-based) indices, one for each dimension: | |
| 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 | |
| 72 order, then this element is located at the position | |
| 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>)). | |
| 74 | |
| 75 <p>Note that, for the ordinary complex DFT, each element of the array | |
| 76 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of | |
| 77 (double-precision) numbers. | |
| 78 | |
| 79 <p>In the advanced FFTW interface, the physical dimensions n from | |
| 80 which the indices are computed can be different from (larger than) | |
| 81 the logical dimensions of the transform to be computed, in order to | |
| 82 transform a subset of a larger array. | |
| 83 <a name="index-advanced-interface-116"></a>Note also that, in the advanced interface, the expression above is | |
| 84 multiplied by a <dfn>stride</dfn> to get the actual array index—this is | |
| 85 useful in situations where each element of the multi-dimensional array | |
| 86 is actually a data structure (or another array), and you just want to | |
| 87 transform a single field. In the basic interface, however, the stride | |
| 88 is 1. | |
| 89 <a name="index-stride-117"></a> | |
| 90 <!-- =========> --> | |
| 91 | |
| 92 </body></html> | |
| 93 |