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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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3 <!-- This manual is for FFTW
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25 <title>FFTW 3.3.5: Row-major Format</title>
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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">
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72 <a name="Row_002dmajor-Format"></a>
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74 <p>
75 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> &nbsp; [<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>
76 </div>
77 <hr>
78 <a name="Row_002dmajor-Format-1"></a>
79 <h4 class="subsection">3.2.1 Row-major Format</h4>
80 <a name="index-row_002dmajor"></a>
81
82 <p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
83 are expected to be stored as a single contiguous block in
84 <em>row-major</em> order (sometimes called &ldquo;C order&rdquo;). Basically, this
85 means that as you step through adjacent memory locations, the first
86 dimension&rsquo;s index varies most slowly and the last dimension&rsquo;s index
87 varies most quickly.
88 </p>
89 <p>To be more explicit, let us consider an array of rank <em>d</em> whose
90 dimensions are n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>. 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>).If the array is stored in row-major
93 order, then this element is located at the position
94 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>)).</p>
95 <p>Note that, for the ordinary complex DFT, each element of the array
96 must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
97 (double-precision) numbers.
98 </p>
99 <p>In the advanced FFTW interface, the physical dimensions <em>n</em> from
100 which the indices are computed can be different from (larger than)
101 the logical dimensions of the transform to be computed, in order to
102 transform a subset of a larger array.
103 <a name="index-advanced-interface-2"></a>
104 Note also that, in the advanced interface, the expression above is
105 multiplied by a <em>stride</em> to get the actual array index&mdash;this is
106 useful in situations where each element of the multi-dimensional array
107 is actually a data structure (or another array), and you just want to
108 transform a single field. In the basic interface, however, the stride
109 is 1.
110 <a name="index-stride"></a>
111 </p>
112
113
114
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