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<h4 class="subsection">3.2.1 Row-major Format</h4>

<p><a name="index-row_002dmajor-115"></a>
The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
are expected to be stored as a single contiguous block in
<dfn>row-major</dfn> order (sometimes called &ldquo;C order&rdquo;).  Basically, this
means that as you step through adjacent memory locations, the first
dimension's index varies most slowly and the last dimension's index
varies most quickly.

   <p>To be more explicit, let us consider an array of rank d 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 d (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>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>In the advanced FFTW interface, the physical dimensions n 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-116"></a>Note also that, in the advanced interface, the expression above is
multiplied by a <dfn>stride</dfn> 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-117"></a>
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author	Chris Cannam
date	Wed, 20 Mar 2013 15:35:50 +0000
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