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<h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>

<pre class="example">     fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
                                  fftw_complex *in, const int *inembed,
                                  int istride, int idist,
                                  fftw_complex *out, const int *onembed,
                                  int ostride, int odist,
                                  int sign, unsigned flags);
</pre>
   <p><a name="index-fftw_005fplan_005fmany_005fdft-223"></a>
This plans multidimensional complex DFTs, and is exactly the same as
<code>fftw_plan_dft</code> except for the new parameters <code>howmany</code>,
{<code>i</code>,<code>o</code>}<code>nembed</code>, {<code>i</code>,<code>o</code>}<code>stride</code>,
and {<code>i</code>,<code>o</code>}<code>dist</code>.

   <p><code>howmany</code> is the number of transforms to compute, where the
<code>k</code>-th transform is of the arrays starting at <code>in+k*idist</code> and
<code>out+k*odist</code>.  The resulting plans can often be faster than
calling FFTW multiple times for the individual transforms.  The basic
<code>fftw_plan_dft</code> interface corresponds to <code>howmany=1</code> (in which
case the <code>dist</code> parameters are ignored).
<a name="index-howmany-parameter-224"></a><a name="index-dist-225"></a>
The two <code>nembed</code> parameters (which should be arrays of length
<code>rank</code>) indicate the sizes of the input and output array
dimensions, respectively, where the transform is of a subarray of size
<code>n</code>.  (Each dimension of <code>n</code> should be <code>&lt;=</code> the
corresponding dimension of the <code>nembed</code> arrays.)  That is, the
input and output arrays are stored in row-major order with size given by
<code>nembed</code> (not counting the strides and howmany multiplicities).
Passing <code>NULL</code> for an <code>nembed</code> parameter is equivalent to
passing <code>n</code> (i.e. same physical and logical dimensions, as in the
basic interface.)

   <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
the input or output arrays is located at <code>j*istride</code> or
<code>j*ostride</code>, respectively.  (For a multi-dimensional array,
<code>j</code> is the ordinary row-major index.)  When combined with the
<code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
(The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
<a name="index-stride-226"></a>
For in-place transforms, the input and output <code>stride</code> and
<code>dist</code> parameters should be the same; otherwise, the planner may
return <code>NULL</code>.

   <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
this function returns.  You can safely free or reuse them.

   <p>So, for example, to transform a sequence of contiguous arrays, stored
one after another, one would use a <code>stride</code> of 1 and a <code>dist</code>
of N, where N is the product of the dimensions.  In
another example, to transform an array of contiguous &ldquo;vectors&rdquo; of
length M, one would use a <code>howmany</code> of M, a
<code>stride</code> of M, and a <code>dist</code> of 1.
<a name="index-vector-227"></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