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comparison src/fftw-3.3.8/doc/html/Row_002dmajor-Format.html @ 167:bd3cc4d1df30
Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Tue, 19 Nov 2019 14:52:55 +0000 |
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| 166:cbd6d7e562c7 | 167:bd3cc4d1df30 |
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| 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> | |
| 2 <html> | |
| 3 <!-- This manual is for FFTW | |
| 4 (version 3.3.8, 24 May 2018). | |
| 5 | |
| 6 Copyright (C) 2003 Matteo Frigo. | |
| 7 | |
| 8 Copyright (C) 2003 Massachusetts Institute of Technology. | |
| 9 | |
| 10 Permission is granted to make and distribute verbatim copies of this | |
| 11 manual provided the copyright notice and this permission notice are | |
| 12 preserved on all copies. | |
| 13 | |
| 14 Permission is granted to copy and distribute modified versions of this | |
| 15 manual under the conditions for verbatim copying, provided that the | |
| 16 entire resulting derived work is distributed under the terms of a | |
| 17 permission notice identical to this one. | |
| 18 | |
| 19 Permission is granted to copy and distribute translations of this manual | |
| 20 into another language, under the above conditions for modified versions, | |
| 21 except that this permission notice may be stated in a translation | |
| 22 approved by the Free Software Foundation. --> | |
| 23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> | |
| 24 <head> | |
| 25 <title>FFTW 3.3.8: Row-major Format</title> | |
| 26 | |
| 27 <meta name="description" content="FFTW 3.3.8: Row-major Format"> | |
| 28 <meta name="keywords" content="FFTW 3.3.8: Row-major Format"> | |
| 29 <meta name="resource-type" content="document"> | |
| 30 <meta name="distribution" content="global"> | |
| 31 <meta name="Generator" content="makeinfo"> | |
| 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> | |
| 33 <link href="index.html#Top" rel="start" title="Top"> | |
| 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> | |
| 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> | |
| 36 <link href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" rel="up" title="Multi-dimensional Array Format"> | |
| 37 <link href="Column_002dmajor-Format.html#Column_002dmajor-Format" rel="next" title="Column-major Format"> | |
| 38 <link href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" rel="prev" title="Multi-dimensional Array Format"> | |
| 39 <style type="text/css"> | |
| 40 <!-- | |
| 41 a.summary-letter {text-decoration: none} | |
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| 64 --> | |
| 65 </style> | |
| 66 | |
| 67 | |
| 68 </head> | |
| 69 | |
| 70 <body lang="en"> | |
| 71 <a name="Row_002dmajor-Format"></a> | |
| 72 <div class="header"> | |
| 73 <p> | |
| 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> | |
| 75 </div> | |
| 76 <hr> | |
| 77 <a name="Row_002dmajor-Format-1"></a> | |
| 78 <h4 class="subsection">3.2.1 Row-major Format</h4> | |
| 79 <a name="index-row_002dmajor"></a> | |
| 80 | |
| 81 <p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera | |
| 82 are expected to be stored as a single contiguous block in | |
| 83 <em>row-major</em> order (sometimes called “C order”). Basically, this | |
| 84 means that as you step through adjacent memory locations, the first | |
| 85 dimension’s index varies most slowly and the last dimension’s index | |
| 86 varies most quickly. | |
| 87 </p> | |
| 88 <p>To be more explicit, let us consider an array of rank <em>d</em> whose | |
| 89 dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> | |
| 90 . Now, we specify a location in the array by a | |
| 91 sequence of <em>d</em> (zero-based) indices, one for each dimension: | |
| 92 (i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>). | |
| 93 If the array is stored in row-major | |
| 94 order, then this element is located at the position | |
| 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>)). | |
| 96 </p> | |
| 97 <p>Note that, for the ordinary complex DFT, each element of the array | |
| 98 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of | |
| 99 (double-precision) numbers. | |
| 100 </p> | |
| 101 <p>In the advanced FFTW interface, the physical dimensions <em>n</em> from | |
| 102 which the indices are computed can be different from (larger than) | |
| 103 the logical dimensions of the transform to be computed, in order to | |
| 104 transform a subset of a larger array. | |
| 105 <a name="index-advanced-interface-2"></a> | |
| 106 Note also that, in the advanced interface, the expression above is | |
| 107 multiplied by a <em>stride</em> to get the actual array index—this is | |
| 108 useful in situations where each element of the multi-dimensional array | |
| 109 is actually a data structure (or another array), and you just want to | |
| 110 transform a single field. In the basic interface, however, the stride | |
| 111 is 1. | |
| 112 <a name="index-stride"></a> | |
| 113 </p> | |
| 114 | |
| 115 | |
| 116 | |
| 117 </body> | |
| 118 </html> |