108 lines
5 KiB
HTML
108 lines
5 KiB
HTML
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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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into another language, under the above conditions for modified versions,
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<title>Row-major Format (FFTW 3.3.10)</title>
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<meta name="description" content="Row-major Format (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Multi_002ddimensional-Array-Format.html" rel="up" title="Multi-dimensional Array Format">
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<link href="Column_002dmajor-Format.html" rel="next" title="Column-major Format">
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<span id="Row_002dmajor-Format"></span><div class="header">
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<p>
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Next: <a href="Column_002dmajor-Format.html" accesskey="n" rel="next">Column-major Format</a>, Previous: <a href="Multi_002ddimensional-Array-Format.html" accesskey="p" rel="prev">Multi-dimensional Array Format</a>, Up: <a href="Multi_002ddimensional-Array-Format.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Row_002dmajor-Format-1"></span><h4 class="subsection">3.2.1 Row-major Format</h4>
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<span id="index-row_002dmajor"></span>
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<p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
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are expected to be stored as a single contiguous block in
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<em>row-major</em> order (sometimes called “C order”). Basically, this
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means that as you step through adjacent memory locations, the first
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dimension’s index varies most slowly and the last dimension’s index
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varies most quickly.
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</p>
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<p>To be more explicit, let us consider an array of rank <em>d</em> whose
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dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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. Now, we specify a location in the array by a
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sequence of <em>d</em> (zero-based) indices, one for each dimension:
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(i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>).
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If the array is stored in row-major
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order, then this element is located at the position
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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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</p>
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<p>Note that, for the ordinary complex DFT, each element of the array
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must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
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(double-precision) numbers.
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</p>
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<p>In the advanced FFTW interface, the physical dimensions <em>n</em> from
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which the indices are computed can be different from (larger than)
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the logical dimensions of the transform to be computed, in order to
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transform a subset of a larger array.
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<span id="index-advanced-interface-2"></span>
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Note also that, in the advanced interface, the expression above is
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multiplied by a <em>stride</em> to get the actual array index—this is
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useful in situations where each element of the multi-dimensional array
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is actually a data structure (or another array), and you just want to
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transform a single field. In the basic interface, however, the stride
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is 1.
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<span id="index-stride"></span>
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</p>
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