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<h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>

<p>Multi-dimensional transforms work much the same way as one-dimensional
transforms: you allocate arrays of <code>fftw_complex</code> (preferably
using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
many times as you want with <code>fftw_execute(plan)</code>, and clean up
with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>).  The only
difference is the routine you use to create the plan:

<pre class="example">     fftw_plan fftw_plan_dft_2d(int n0, int n1,
                                fftw_complex *in, fftw_complex *out,
                                int sign, unsigned flags);
     fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
                                fftw_complex *in, fftw_complex *out,
                                int sign, unsigned flags);
     fftw_plan fftw_plan_dft(int rank, const int *n,
                             fftw_complex *in, fftw_complex *out,
                             int sign, unsigned flags);
</pre>
   <p><a name="index-fftw_005fplan_005fdft_005f2d-38"></a><a name="index-fftw_005fplan_005fdft_005f3d-39"></a><a name="index-fftw_005fplan_005fdft-40"></a>
These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
(2d) transforms, <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
and arbitrary <code>rank</code>-dimensional transforms, respectively.  In the
<a name="index-rank-41"></a>third case, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting
an <code>n[0]</code> by <code>n[1]</code> by <small class="dots">...</small> by <code>n[rank-1]</code>
transform.  All of these transforms operate on contiguous arrays in
the C-standard <dfn>row-major</dfn> order, so that the last dimension has
the fastest-varying index in the array.  This layout is described
further in <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.

   <p>You may have noticed that all the planner routines described so far
have overlapping functionality.  For example, you can plan a 1d or 2d
transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency).  This
pattern continues, and FFTW's planning routines in general form a
&ldquo;partial order,&rdquo; sequences of
<a name="index-partial-order-42"></a>interfaces with strictly increasing generality but correspondingly
greater complexity.

   <p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
describe in this tutorial, but there are also the advanced and guru interfaces,
<a name="index-advanced-interface-43"></a><a name="index-guru-interface-44"></a>which allow one to efficiently combine multiple/strided transforms
into a single FFTW plan, transform a subset of a larger
multi-dimensional array, and/or to handle more general complex-number
formats.  For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>.

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author	Geogaddi\David <d.m.ronan@qmul.ac.uk>
date	Wed, 04 May 2016 11:02:59 +0100
parents	25bf17994ef1
children