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<a name="Row_002dmajor-Format-1"></a>
<h4 class="subsection">3.2.1 Row-major Format</h4>
<a name="index-row_002dmajor"></a>

<p>The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
are expected to be stored as a single contiguous block in
<em>row-major</em> order (sometimes called &ldquo;C order&rdquo;).  Basically, this
means that as you step through adjacent memory locations, the first
dimension&rsquo;s index varies most slowly and the last dimension&rsquo;s index
varies most quickly.
</p>
<p>To be more explicit, let us consider an array of rank <em>d</em> whose
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
sequence of <em>d</em> (zero-based) indices, one for each dimension:
(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
order, then this element is located at the position
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>
<p>Note that, for the ordinary complex DFT, each element of the array
must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
(double-precision) numbers.
</p>
<p>In the advanced FFTW interface, the physical dimensions <em>n</em> from
which the indices are computed can be different from (larger than)
the logical dimensions of the transform to be computed, in order to
transform a subset of a larger array.
<a name="index-advanced-interface-2"></a>
Note also that, in the advanced interface, the expression above is
multiplied by a <em>stride</em> to get the actual array index&mdash;this is
useful in situations where each element of the multi-dimensional array
is actually a data structure (or another array), and you just want to
transform a single field. In the basic interface, however, the stride
is 1.
<a name="index-stride"></a>
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author	Chris Cannam <cannam@all-day-breakfast.com>
date	Mon, 02 Mar 2020 14:03:47 +0000
parents	7867fa7e1b6b
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