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<h3 class="section">6.6 Other multi-dimensional Real-Data MPI Transforms</h3>
<p><a name="index-r2r-393"></a>FFTW's MPI interface also supports multi-dimensional ‘<samp><span class="samp">r2r</span></samp>’
transforms of all kinds supported by the serial interface
(e.g. discrete cosine and sine transforms, discrete Hartley
transforms, etc.). Only multi-dimensional ‘<samp><span class="samp">r2r</span></samp>’ transforms, not
one-dimensional transforms, are currently parallelized.
<p><a name="index-fftw_005fr2r_005fkind-394"></a>These are used much like the multidimensional complex DFTs discussed
above, except that the data is real rather than complex, and one needs
to pass an r2r transform kind (<code>fftw_r2r_kind</code>) for each
dimension as in the serial FFTW (see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>).
<p>For example, one might perform a two-dimensional L × M that is
an REDFT10 (DCT-II) in the first dimension and an RODFT10 (DST-II) in
the second dimension with code like:
<pre class="example"> const ptrdiff_t L = ..., M = ...;
fftw_plan plan;
double *data;
ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
/* <span class="roman">get local data size and allocate</span> */
alloc_local = fftw_mpi_local_size_2d(L, M, MPI_COMM_WORLD,
&local_n0, &local_0_start);
data = fftw_alloc_real(alloc_local);
/* <span class="roman">create plan for in-place REDFT10 x RODFT10</span> */
plan = fftw_mpi_plan_r2r_2d(L, M, data, data, MPI_COMM_WORLD,
FFTW_REDFT10, FFTW_RODFT10, FFTW_MEASURE);
/* <span class="roman">initialize data to some function</span> my_function(x,y) */
for (i = 0; i < local_n0; ++i) for (j = 0; j < M; ++j)
data[i*M + j] = my_function(local_0_start + i, j);
/* <span class="roman">compute transforms, in-place, as many times as desired</span> */
fftw_execute(plan);
fftw_destroy_plan(plan);
</pre>
<p><a name="index-fftw_005falloc_005freal-395"></a>Notice that we use the same ‘<samp><span class="samp">local_size</span></samp>’ functions as we did for
complex data, only now we interpret the sizes in terms of real rather
than complex values, and correspondingly use <code>fftw_alloc_real</code>.
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