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<h4 class="subsection">6.12.5 MPI Plan Creation</h4>
<h5 class="subsubheading">Complex-data MPI DFTs</h5>
<p>Plans for complex-data DFTs (see <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>) are created by:
<p><a name="index-fftw_005fmpi_005fplan_005fdft_005f1d-461"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005f2d-462"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005f3d-463"></a><a name="index-fftw_005fmpi_005fplan_005fdft-464"></a><a name="index-fftw_005fmpi_005fplan_005fmany_005fdft-465"></a>
<pre class="example"> fftw_plan fftw_mpi_plan_dft_1d(ptrdiff_t n0, fftw_complex *in, fftw_complex *out,
MPI_Comm comm, int sign, unsigned flags);
fftw_plan fftw_mpi_plan_dft_2d(ptrdiff_t n0, ptrdiff_t n1,
fftw_complex *in, fftw_complex *out,
MPI_Comm comm, int sign, unsigned flags);
fftw_plan fftw_mpi_plan_dft_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
fftw_complex *in, fftw_complex *out,
MPI_Comm comm, int sign, unsigned flags);
fftw_plan fftw_mpi_plan_dft(int rnk, const ptrdiff_t *n,
fftw_complex *in, fftw_complex *out,
MPI_Comm comm, int sign, unsigned flags);
fftw_plan fftw_mpi_plan_many_dft(int rnk, const ptrdiff_t *n,
ptrdiff_t howmany, ptrdiff_t block, ptrdiff_t tblock,
fftw_complex *in, fftw_complex *out,
MPI_Comm comm, int sign, unsigned flags);
</pre>
<p><a name="index-MPI-communicator-466"></a><a name="index-collective-function-467"></a>These are similar to their serial counterparts (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>)
in specifying the dimensions, sign, and flags of the transform. The
<code>comm</code> argument gives an MPI communicator that specifies the set
of processes to participate in the transform; plan creation is a
collective function that must be called for all processes in the
communicator. The <code>in</code> and <code>out</code> pointers refer only to a
portion of the overall transform data (see <a href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>)
as specified by the ‘<samp><span class="samp">local_size</span></samp>’ functions in the previous
section. Unless <code>flags</code> contains <code>FFTW_ESTIMATE</code>, these
arrays are overwritten during plan creation as for the serial
interface. For multi-dimensional transforms, any dimensions <code>>
1</code> are supported; for one-dimensional transforms, only composite
(non-prime) <code>n0</code> are currently supported (unlike the serial
FFTW). Requesting an unsupported transform size will yield a
<code>NULL</code> plan. (As in the serial interface, highly composite sizes
generally yield the best performance.)
<p><a name="index-advanced-interface-468"></a><a name="index-FFTW_005fMPI_005fDEFAULT_005fBLOCK-469"></a><a name="index-stride-470"></a>The advanced-interface <code>fftw_mpi_plan_many_dft</code> additionally
allows you to specify the block sizes for the first dimension
(<code>block</code>) of the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> input data and the first dimension
(<code>tblock</code>) of the n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> transposed data (at intermediate
steps of the transform, and for the output if
<code>FFTW_TRANSPOSED_OUT</code> is specified in <code>flags</code>). These must
be the same block sizes as were passed to the corresponding
‘<samp><span class="samp">local_size</span></samp>’ function; you can pass <code>FFTW_MPI_DEFAULT_BLOCK</code>
to use FFTW's default block size as in the basic interface. Also, the
<code>howmany</code> parameter specifies that the transform is of contiguous
<code>howmany</code>-tuples rather than individual complex numbers; this
corresponds to the same parameter in the serial advanced interface
(see <a href="Advanced-Complex-DFTs.html#Advanced-Complex-DFTs">Advanced Complex DFTs</a>) with <code>stride = howmany</code> and
<code>dist = 1</code>.
<h5 class="subsubheading">MPI flags</h5>
<p>The <code>flags</code> can be any of those for the serial FFTW
(see <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>), and in addition may include one or more of
the following MPI-specific flags, which improve performance at the
cost of changing the output or input data formats.
<ul>
<li><a name="index-FFTW_005fMPI_005fSCRAMBLED_005fOUT-471"></a><a name="index-FFTW_005fMPI_005fSCRAMBLED_005fIN-472"></a><code>FFTW_MPI_SCRAMBLED_OUT</code>, <code>FFTW_MPI_SCRAMBLED_IN</code>: valid for
1d transforms only, these flags indicate that the output/input of the
transform are in an undocumented “scrambled” order. A forward
<code>FFTW_MPI_SCRAMBLED_OUT</code> transform can be inverted by a backward
<code>FFTW_MPI_SCRAMBLED_IN</code> (times the usual 1/<i>N</i> normalization).
See <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions">One-dimensional distributions</a>.
<li><a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT-473"></a><a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN-474"></a><code>FFTW_MPI_TRANSPOSED_OUT</code>, <code>FFTW_MPI_TRANSPOSED_IN</code>: valid
for multidimensional (<code>rnk > 1</code>) transforms only, these flags
specify that the output or input of an n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> transform is
transposed to n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>. See <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>.
</ul>
<h5 class="subsubheading">Real-data MPI DFTs</h5>
<p><a name="index-r2c-475"></a>Plans for real-input/output (r2c/c2r) DFTs (see <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data">Multi-dimensional MPI DFTs of Real Data</a>) are created by:
<p><a name="index-fftw_005fmpi_005fplan_005fdft_005fr2c_005f2d-476"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fr2c_005f2d-477"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fr2c_005f3d-478"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fr2c-479"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fc2r_005f2d-480"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fc2r_005f2d-481"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fc2r_005f3d-482"></a><a name="index-fftw_005fmpi_005fplan_005fdft_005fc2r-483"></a>
<pre class="example"> fftw_plan fftw_mpi_plan_dft_r2c_2d(ptrdiff_t n0, ptrdiff_t n1,
double *in, fftw_complex *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_r2c_2d(ptrdiff_t n0, ptrdiff_t n1,
double *in, fftw_complex *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_r2c_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
double *in, fftw_complex *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_r2c(int rnk, const ptrdiff_t *n,
double *in, fftw_complex *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_c2r_2d(ptrdiff_t n0, ptrdiff_t n1,
fftw_complex *in, double *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_c2r_2d(ptrdiff_t n0, ptrdiff_t n1,
fftw_complex *in, double *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_c2r_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
fftw_complex *in, double *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_dft_c2r(int rnk, const ptrdiff_t *n,
fftw_complex *in, double *out,
MPI_Comm comm, unsigned flags);
</pre>
<p>Similar to the serial interface (see <a href="Real_002ddata-DFTs.html#Real_002ddata-DFTs">Real-data DFTs</a>), these
transform logically n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> real data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) complex
data, representing the non-redundant half of the conjugate-symmetry
output of a real-input DFT (see <a href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>).
However, the real array must be stored within a padded n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × [2 (n<sub>d-1</sub>/2 + 1)]
<p>array (much like the in-place serial r2c transforms, but here for
out-of-place transforms as well). Currently, only multi-dimensional
(<code>rnk > 1</code>) r2c/c2r transforms are supported (requesting a plan
for <code>rnk = 1</code> will yield <code>NULL</code>). As explained above
(see <a href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data">Multi-dimensional MPI DFTs of Real Data</a>), the data
distribution of both the real and complex arrays is given by the
‘<samp><span class="samp">local_size</span></samp>’ function called for the dimensions of the
<em>complex</em> array. Similar to the other planning functions, the
input and output arrays are overwritten when the plan is created
except in <code>FFTW_ESTIMATE</code> mode.
<p>As for the complex DFTs above, there is an advance interface that
allows you to manually specify block sizes and to transform contiguous
<code>howmany</code>-tuples of real/complex numbers:
<p><a name="index-fftw_005fmpi_005fplan_005fmany_005fdft_005fr2c-484"></a><a name="index-fftw_005fmpi_005fplan_005fmany_005fdft_005fc2r-485"></a>
<pre class="example"> fftw_plan fftw_mpi_plan_many_dft_r2c
(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
ptrdiff_t iblock, ptrdiff_t oblock,
double *in, fftw_complex *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_many_dft_c2r
(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
ptrdiff_t iblock, ptrdiff_t oblock,
fftw_complex *in, double *out,
MPI_Comm comm, unsigned flags);
</pre>
<h5 class="subsubheading">MPI r2r transforms</h5>
<p><a name="index-r2r-486"></a>There are corresponding plan-creation routines for r2r
transforms (see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>), currently supporting
multidimensional (<code>rnk > 1</code>) transforms only (<code>rnk = 1</code> will
yield a <code>NULL</code> plan):
<pre class="example"> fftw_plan fftw_mpi_plan_r2r_2d(ptrdiff_t n0, ptrdiff_t n1,
double *in, double *out,
MPI_Comm comm,
fftw_r2r_kind kind0, fftw_r2r_kind kind1,
unsigned flags);
fftw_plan fftw_mpi_plan_r2r_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
double *in, double *out,
MPI_Comm comm,
fftw_r2r_kind kind0, fftw_r2r_kind kind1, fftw_r2r_kind kind2,
unsigned flags);
fftw_plan fftw_mpi_plan_r2r(int rnk, const ptrdiff_t *n,
double *in, double *out,
MPI_Comm comm, const fftw_r2r_kind *kind,
unsigned flags);
fftw_plan fftw_mpi_plan_many_r2r(int rnk, const ptrdiff_t *n,
ptrdiff_t iblock, ptrdiff_t oblock,
double *in, double *out,
MPI_Comm comm, const fftw_r2r_kind *kind,
unsigned flags);
</pre>
<p>The parameters are much the same as for the complex DFTs above, except
that the arrays are of real numbers (and hence the outputs of the
‘<samp><span class="samp">local_size</span></samp>’ data-distribution functions should be interpreted as
counts of real rather than complex numbers). Also, the <code>kind</code>
parameters specify the r2r kinds along each dimension as for the
serial interface (see <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>). See <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms">Other Multi-dimensional Real-data MPI Transforms</a>.
<h5 class="subsubheading">MPI transposition</h5>
<p><a name="index-transpose-487"></a>
FFTW also provides routines to plan a transpose of a distributed
<code>n0</code> by <code>n1</code> array of real numbers, or an array of
<code>howmany</code>-tuples of real numbers with specified block sizes
(see <a href="FFTW-MPI-Transposes.html#FFTW-MPI-Transposes">FFTW MPI Transposes</a>):
<p><a name="index-fftw_005fmpi_005fplan_005ftranspose-488"></a><a name="index-fftw_005fmpi_005fplan_005fmany_005ftranspose-489"></a>
<pre class="example"> fftw_plan fftw_mpi_plan_transpose(ptrdiff_t n0, ptrdiff_t n1,
double *in, double *out,
MPI_Comm comm, unsigned flags);
fftw_plan fftw_mpi_plan_many_transpose
(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t howmany,
ptrdiff_t block0, ptrdiff_t block1,
double *in, double *out, MPI_Comm comm, unsigned flags);
</pre>
<p><a name="index-new_002darray-execution-490"></a><a name="index-fftw_005fmpi_005fexecute_005fr2r-491"></a>These plans are used with the <code>fftw_mpi_execute_r2r</code> new-array
execute function (see <a href="Using-MPI-Plans.html#Using-MPI-Plans">Using MPI Plans</a>), since they count as (rank
zero) r2r plans from FFTW's perspective.
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