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1 <html lang="en">
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2 <head>
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3 <title>Row-major Format - FFTW 3.3.4</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.3.4">
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7 <link title="Top" rel="start" href="index.html#Top">
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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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9 <link rel="prev" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format">
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10 <link rel="next" href="Column_002dmajor-Format.html#Column_002dmajor-Format" title="Column-major Format">
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11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.3.4, 20 September 2013).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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19
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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33 -->
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <a name="Row-major-Format"></a>
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50 <a name="Row_002dmajor-Format"></a>
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51 <p>
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52 Next: <a rel="next" accesskey="n" href="Column_002dmajor-Format.html#Column_002dmajor-Format">Column-major Format</a>,
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53 Previous: <a rel="previous" accesskey="p" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>,
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54 Up: <a rel="up" accesskey="u" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>
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55 <hr>
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56 </div>
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57
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58 <h4 class="subsection">3.2.1 Row-major Format</h4>
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59
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60 <p><a name="index-row_002dmajor-115"></a>
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61 The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
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62 are expected to be stored as a single contiguous block in
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63 <dfn>row-major</dfn> order (sometimes called “C order”). Basically, this
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64 means that as you step through adjacent memory locations, the first
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65 dimension's index varies most slowly and the last dimension's index
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66 varies most quickly.
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67
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68 <p>To be more explicit, let us consider an array of rank d whose
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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
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70 sequence of d (zero-based) indices, one for each dimension:
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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
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72 order, then this element is located at the position
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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>)).
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74
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75 <p>Note that, for the ordinary complex DFT, each element of the array
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76 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
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77 (double-precision) numbers.
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78
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79 <p>In the advanced FFTW interface, the physical dimensions n from
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80 which the indices are computed can be different from (larger than)
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81 the logical dimensions of the transform to be computed, in order to
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82 transform a subset of a larger array.
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83 <a name="index-advanced-interface-116"></a>Note also that, in the advanced interface, the expression above is
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84 multiplied by a <dfn>stride</dfn> to get the actual array index—this is
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85 useful in situations where each element of the multi-dimensional array
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86 is actually a data structure (or another array), and you just want to
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87 transform a single field. In the basic interface, however, the stride
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88 is 1.
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89 <a name="index-stride-117"></a>
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90 <!-- =========> -->
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91
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92 </body></html>
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93
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