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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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2 <html>
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3 <!-- This manual is for FFTW
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4 (version 3.3.8, 24 May 2018).
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5
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6 Copyright (C) 2003 Matteo Frigo.
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7
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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9
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10 Permission is granted to make and distribute verbatim copies of this
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11 manual provided the copyright notice and this permission notice are
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12 preserved on all copies.
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13
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14 Permission is granted to copy and distribute modified versions of this
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15 manual under the conditions for verbatim copying, provided that the
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16 entire resulting derived work is distributed under the terms of a
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17 permission notice identical to this one.
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18
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19 Permission is granted to copy and distribute translations of this manual
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20 into another language, under the above conditions for modified versions,
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21 except that this permission notice may be stated in a translation
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22 approved by the Free Software Foundation. -->
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23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
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24 <head>
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25 <title>FFTW 3.3.8: Row-major Format</title>
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26
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27 <meta name="description" content="FFTW 3.3.8: Row-major Format">
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28 <meta name="keywords" content="FFTW 3.3.8: Row-major Format">
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33 <link href="index.html#Top" rel="start" title="Top">
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34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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36 <link href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" rel="up" title="Multi-dimensional Array Format">
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37 <link href="Column_002dmajor-Format.html#Column_002dmajor-Format" rel="next" title="Column-major Format">
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38 <link href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" rel="prev" title="Multi-dimensional Array Format">
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39 <style type="text/css">
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40 <!--
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63 ul.no-bullet {list-style: none}
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64 -->
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65 </style>
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66
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67
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68 </head>
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69
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70 <body lang="en">
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71 <a name="Row_002dmajor-Format"></a>
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72 <div class="header">
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73 <p>
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74 Next: <a href="Column_002dmajor-Format.html#Column_002dmajor-Format" accesskey="n" rel="next">Column-major Format</a>, Previous: <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" accesskey="p" rel="prev">Multi-dimensional Array Format</a>, Up: <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" accesskey="u" rel="up">Multi-dimensional Array Format</a> [<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>
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75 </div>
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76 <hr>
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77 <a name="Row_002dmajor-Format-1"></a>
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78 <h4 class="subsection">3.2.1 Row-major Format</h4>
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79 <a name="index-row_002dmajor"></a>
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80
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81 <p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
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82 are expected to be stored as a single contiguous block in
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83 <em>row-major</em> order (sometimes called “C order”). Basically, this
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84 means that as you step through adjacent memory locations, the first
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85 dimension’s index varies most slowly and the last dimension’s index
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86 varies most quickly.
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87 </p>
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88 <p>To be more explicit, let us consider an array of rank <em>d</em> whose
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89 dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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90 . Now, we specify a location in the array by a
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91 sequence of <em>d</em> (zero-based) indices, one for each dimension:
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92 (i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>).
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93 If the array is stored in row-major
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94 order, then this element is located at the position
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95 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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96 </p>
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97 <p>Note that, for the ordinary complex DFT, each element of the array
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98 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
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99 (double-precision) numbers.
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100 </p>
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101 <p>In the advanced FFTW interface, the physical dimensions <em>n</em> from
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102 which the indices are computed can be different from (larger than)
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103 the logical dimensions of the transform to be computed, in order to
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104 transform a subset of a larger array.
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105 <a name="index-advanced-interface-2"></a>
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106 Note also that, in the advanced interface, the expression above is
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107 multiplied by a <em>stride</em> to get the actual array index—this is
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108 useful in situations where each element of the multi-dimensional array
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109 is actually a data structure (or another array), and you just want to
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110 transform a single field. In the basic interface, however, the stride
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111 is 1.
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112 <a name="index-stride"></a>
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113 </p>
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114
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115
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116
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117 </body>
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118 </html>
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