cannam@95: @node Distributed-memory FFTW with MPI, Calling FFTW from Modern Fortran, Multi-threaded FFTW, Top
cannam@95: @chapter Distributed-memory FFTW with MPI
cannam@95: @cindex MPI
cannam@95:
cannam@95: @cindex parallel transform
cannam@95: In this chapter we document the parallel FFTW routines for parallel
cannam@95: systems supporting the MPI message-passing interface. Unlike the
cannam@95: shared-memory threads described in the previous chapter, MPI allows
cannam@95: you to use @emph{distributed-memory} parallelism, where each CPU has
cannam@95: its own separate memory, and which can scale up to clusters of many
cannam@95: thousands of processors. This capability comes at a price, however:
cannam@95: each process only stores a @emph{portion} of the data to be
cannam@95: transformed, which means that the data structures and
cannam@95: programming-interface are quite different from the serial or threads
cannam@95: versions of FFTW.
cannam@95: @cindex data distribution
cannam@95:
cannam@95:
cannam@95: Distributed-memory parallelism is especially useful when you are
cannam@95: transforming arrays so large that they do not fit into the memory of a
cannam@95: single processor. The storage per-process required by FFTW's MPI
cannam@95: routines is proportional to the total array size divided by the number
cannam@95: of processes. Conversely, distributed-memory parallelism can easily
cannam@95: pose an unacceptably high communications overhead for small problems;
cannam@95: the threshold problem size for which parallelism becomes advantageous
cannam@95: will depend on the precise problem you are interested in, your
cannam@95: hardware, and your MPI implementation.
cannam@95:
cannam@95: A note on terminology: in MPI, you divide the data among a set of
cannam@95: ``processes'' which each run in their own memory address space.
cannam@95: Generally, each process runs on a different physical processor, but
cannam@95: this is not required. A set of processes in MPI is described by an
cannam@95: opaque data structure called a ``communicator,'' the most common of
cannam@95: which is the predefined communicator @code{MPI_COMM_WORLD} which
cannam@95: refers to @emph{all} processes. For more information on these and
cannam@95: other concepts common to all MPI programs, we refer the reader to the
cannam@95: documentation at @uref{http://www.mcs.anl.gov/research/projects/mpi/, the MPI home
cannam@95: page}.
cannam@95: @cindex MPI communicator
cannam@95: @ctindex MPI_COMM_WORLD
cannam@95:
cannam@95:
cannam@95: We assume in this chapter that the reader is familiar with the usage
cannam@95: of the serial (uniprocessor) FFTW, and focus only on the concepts new
cannam@95: to the MPI interface.
cannam@95:
cannam@95: @menu
cannam@95: * FFTW MPI Installation::
cannam@95: * Linking and Initializing MPI FFTW::
cannam@95: * 2d MPI example::
cannam@95: * MPI Data Distribution::
cannam@95: * Multi-dimensional MPI DFTs of Real Data::
cannam@95: * Other Multi-dimensional Real-data MPI Transforms::
cannam@95: * FFTW MPI Transposes::
cannam@95: * FFTW MPI Wisdom::
cannam@95: * Avoiding MPI Deadlocks::
cannam@95: * FFTW MPI Performance Tips::
cannam@95: * Combining MPI and Threads::
cannam@95: * FFTW MPI Reference::
cannam@95: * FFTW MPI Fortran Interface::
cannam@95: @end menu
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Installation, Linking and Initializing MPI FFTW, Distributed-memory FFTW with MPI, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Installation
cannam@95:
cannam@95: All of the FFTW MPI code is located in the @code{mpi} subdirectory of
cannam@95: the FFTW package. On Unix systems, the FFTW MPI libraries and header
cannam@95: files are automatically configured, compiled, and installed along with
cannam@95: the uniprocessor FFTW libraries simply by including
cannam@95: @code{--enable-mpi} in the flags to the @code{configure} script
cannam@95: (@pxref{Installation on Unix}).
cannam@95: @fpindex configure
cannam@95:
cannam@95:
cannam@95: Any implementation of the MPI standard, version 1 or later, should
cannam@95: work with FFTW. The @code{configure} script will attempt to
cannam@95: automatically detect how to compile and link code using your MPI
cannam@95: implementation. In some cases, especially if you have multiple
cannam@95: different MPI implementations installed or have an unusual MPI
cannam@95: software package, you may need to provide this information explicitly.
cannam@95:
cannam@95: Most commonly, one compiles MPI code by invoking a special compiler
cannam@95: command, typically @code{mpicc} for C code. The @code{configure}
cannam@95: script knows the most common names for this command, but you can
cannam@95: specify the MPI compilation command explicitly by setting the
cannam@95: @code{MPICC} variable, as in @samp{./configure MPICC=mpicc ...}.
cannam@95: @fpindex mpicc
cannam@95:
cannam@95:
cannam@95: If, instead of a special compiler command, you need to link a certain
cannam@95: library, you can specify the link command via the @code{MPILIBS}
cannam@95: variable, as in @samp{./configure MPILIBS=-lmpi ...}. Note that if
cannam@95: your MPI library is installed in a non-standard location (one the
cannam@95: compiler does not know about by default), you may also have to specify
cannam@95: the location of the library and header files via @code{LDFLAGS} and
cannam@95: @code{CPPFLAGS} variables, respectively, as in @samp{./configure
cannam@95: LDFLAGS=-L/path/to/mpi/libs CPPFLAGS=-I/path/to/mpi/include ...}.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node Linking and Initializing MPI FFTW, 2d MPI example, FFTW MPI Installation, Distributed-memory FFTW with MPI
cannam@95: @section Linking and Initializing MPI FFTW
cannam@95:
cannam@95: Programs using the MPI FFTW routines should be linked with
cannam@95: @code{-lfftw3_mpi -lfftw3 -lm} on Unix in double precision,
cannam@95: @code{-lfftw3f_mpi -lfftw3f -lm} in single precision, and so on
cannam@95: (@pxref{Precision}). You will also need to link with whatever library
cannam@95: is responsible for MPI on your system; in most MPI implementations,
cannam@95: there is a special compiler alias named @code{mpicc} to compile and
cannam@95: link MPI code.
cannam@95: @fpindex mpicc
cannam@95: @cindex linking on Unix
cannam@95: @cindex precision
cannam@95:
cannam@95:
cannam@95: @findex fftw_init_threads
cannam@95: Before calling any FFTW routines except possibly
cannam@95: @code{fftw_init_threads} (@pxref{Combining MPI and Threads}), but after calling
cannam@95: @code{MPI_Init}, you should call the function:
cannam@95:
cannam@95: @example
cannam@95: void fftw_mpi_init(void);
cannam@95: @end example
cannam@95: @findex fftw_mpi_init
cannam@95:
cannam@95: If, at the end of your program, you want to get rid of all memory and
cannam@95: other resources allocated internally by FFTW, for both the serial and
cannam@95: MPI routines, you can call:
cannam@95:
cannam@95: @example
cannam@95: void fftw_mpi_cleanup(void);
cannam@95: @end example
cannam@95: @findex fftw_mpi_cleanup
cannam@95:
cannam@95: which is much like the @code{fftw_cleanup()} function except that it
cannam@95: also gets rid of FFTW's MPI-related data. You must @emph{not} execute
cannam@95: any previously created plans after calling this function.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node 2d MPI example, MPI Data Distribution, Linking and Initializing MPI FFTW, Distributed-memory FFTW with MPI
cannam@95: @section 2d MPI example
cannam@95:
cannam@95: Before we document the FFTW MPI interface in detail, we begin with a
cannam@95: simple example outlining how one would perform a two-dimensional
cannam@95: @code{N0} by @code{N1} complex DFT.
cannam@95:
cannam@95: @example
cannam@95: #include <fftw3-mpi.h>
cannam@95:
cannam@95: int main(int argc, char **argv)
cannam@95: @{
cannam@95: const ptrdiff_t N0 = ..., N1 = ...;
cannam@95: fftw_plan plan;
cannam@95: fftw_complex *data;
cannam@95: ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
cannam@95:
cannam@95: MPI_Init(&argc, &argv);
cannam@95: fftw_mpi_init();
cannam@95:
cannam@95: /* @r{get local data size and allocate} */
cannam@95: alloc_local = fftw_mpi_local_size_2d(N0, N1, MPI_COMM_WORLD,
cannam@95: &local_n0, &local_0_start);
cannam@95: data = fftw_alloc_complex(alloc_local);
cannam@95:
cannam@95: /* @r{create plan for in-place forward DFT} */
cannam@95: plan = fftw_mpi_plan_dft_2d(N0, N1, data, data, MPI_COMM_WORLD,
cannam@95: FFTW_FORWARD, FFTW_ESTIMATE);
cannam@95:
cannam@95: /* @r{initialize data to some function} my_function(x,y) */
cannam@95: for (i = 0; i < local_n0; ++i) for (j = 0; j < N1; ++j)
cannam@95: data[i*N1 + j] = my_function(local_0_start + i, j);
cannam@95:
cannam@95: /* @r{compute transforms, in-place, as many times as desired} */
cannam@95: fftw_execute(plan);
cannam@95:
cannam@95: fftw_destroy_plan(plan);
cannam@95:
cannam@95: MPI_Finalize();
cannam@95: @}
cannam@95: @end example
cannam@95:
cannam@95: As can be seen above, the MPI interface follows the same basic style
cannam@95: of allocate/plan/execute/destroy as the serial FFTW routines. All of
cannam@95: the MPI-specific routines are prefixed with @samp{fftw_mpi_} instead
cannam@95: of @samp{fftw_}. There are a few important differences, however:
cannam@95:
cannam@95: First, we must call @code{fftw_mpi_init()} after calling
cannam@95: @code{MPI_Init} (required in all MPI programs) and before calling any
cannam@95: other @samp{fftw_mpi_} routine.
cannam@95: @findex MPI_Init
cannam@95: @findex fftw_mpi_init
cannam@95:
cannam@95:
cannam@95: Second, when we create the plan with @code{fftw_mpi_plan_dft_2d},
cannam@95: analogous to @code{fftw_plan_dft_2d}, we pass an additional argument:
cannam@95: the communicator, indicating which processes will participate in the
cannam@95: transform (here @code{MPI_COMM_WORLD}, indicating all processes).
cannam@95: Whenever you create, execute, or destroy a plan for an MPI transform,
cannam@95: you must call the corresponding FFTW routine on @emph{all} processes
cannam@95: in the communicator for that transform. (That is, these are
cannam@95: @emph{collective} calls.) Note that the plan for the MPI transform
cannam@95: uses the standard @code{fftw_execute} and @code{fftw_destroy} routines
cannam@95: (on the other hand, there are MPI-specific new-array execute functions
cannam@95: documented below).
cannam@95: @cindex collective function
cannam@95: @findex fftw_mpi_plan_dft_2d
cannam@95: @ctindex MPI_COMM_WORLD
cannam@95:
cannam@95:
cannam@95: Third, all of the FFTW MPI routines take @code{ptrdiff_t} arguments
cannam@95: instead of @code{int} as for the serial FFTW. @code{ptrdiff_t} is a
cannam@95: standard C integer type which is (at least) 32 bits wide on a 32-bit
cannam@95: machine and 64 bits wide on a 64-bit machine. This is to make it easy
cannam@95: to specify very large parallel transforms on a 64-bit machine. (You
cannam@95: can specify 64-bit transform sizes in the serial FFTW, too, but only
cannam@95: by using the @samp{guru64} planner interface. @xref{64-bit Guru
cannam@95: Interface}.)
cannam@95: @tindex ptrdiff_t
cannam@95: @cindex 64-bit architecture
cannam@95:
cannam@95:
cannam@95: Fourth, and most importantly, you don't allocate the entire
cannam@95: two-dimensional array on each process. Instead, you call
cannam@95: @code{fftw_mpi_local_size_2d} to find out what @emph{portion} of the
cannam@95: array resides on each processor, and how much space to allocate.
cannam@95: Here, the portion of the array on each process is a @code{local_n0} by
cannam@95: @code{N1} slice of the total array, starting at index
cannam@95: @code{local_0_start}. The total number of @code{fftw_complex} numbers
cannam@95: to allocate is given by the @code{alloc_local} return value, which
cannam@95: @emph{may} be greater than @code{local_n0 * N1} (in case some
cannam@95: intermediate calculations require additional storage). The data
cannam@95: distribution in FFTW's MPI interface is described in more detail by
cannam@95: the next section.
cannam@95: @findex fftw_mpi_local_size_2d
cannam@95: @cindex data distribution
cannam@95:
cannam@95:
cannam@95: Given the portion of the array that resides on the local process, it
cannam@95: is straightforward to initialize the data (here to a function
cannam@95: @code{myfunction}) and otherwise manipulate it. Of course, at the end
cannam@95: of the program you may want to output the data somehow, but
cannam@95: synchronizing this output is up to you and is beyond the scope of this
cannam@95: manual. (One good way to output a large multi-dimensional distributed
cannam@95: array in MPI to a portable binary file is to use the free HDF5
cannam@95: library; see the @uref{http://www.hdfgroup.org/, HDF home page}.)
cannam@95: @cindex HDF5
cannam@95: @cindex MPI I/O
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node MPI Data Distribution, Multi-dimensional MPI DFTs of Real Data, 2d MPI example, Distributed-memory FFTW with MPI
cannam@95: @section MPI Data Distribution
cannam@95: @cindex data distribution
cannam@95:
cannam@95: The most important concept to understand in using FFTW's MPI interface
cannam@95: is the data distribution. With a serial or multithreaded FFT, all of
cannam@95: the inputs and outputs are stored as a single contiguous chunk of
cannam@95: memory. With a distributed-memory FFT, the inputs and outputs are
cannam@95: broken into disjoint blocks, one per process.
cannam@95:
cannam@95: In particular, FFTW uses a @emph{1d block distribution} of the data,
cannam@95: distributed along the @emph{first dimension}. For example, if you
cannam@95: want to perform a @twodims{100,200} complex DFT, distributed over 4
cannam@95: processes, each process will get a @twodims{25,200} slice of the data.
cannam@95: That is, process 0 will get rows 0 through 24, process 1 will get rows
cannam@95: 25 through 49, process 2 will get rows 50 through 74, and process 3
cannam@95: will get rows 75 through 99. If you take the same array but
cannam@95: distribute it over 3 processes, then it is not evenly divisible so the
cannam@95: different processes will have unequal chunks. FFTW's default choice
cannam@95: in this case is to assign 34 rows to processes 0 and 1, and 32 rows to
cannam@95: process 2.
cannam@95: @cindex block distribution
cannam@95:
cannam@95:
cannam@95: FFTW provides several @samp{fftw_mpi_local_size} routines that you can
cannam@95: call to find out what portion of an array is stored on the current
cannam@95: process. In most cases, you should use the default block sizes picked
cannam@95: by FFTW, but it is also possible to specify your own block size. For
cannam@95: example, with a @twodims{100,200} array on three processes, you can
cannam@95: tell FFTW to use a block size of 40, which would assign 40 rows to
cannam@95: processes 0 and 1, and 20 rows to process 2. FFTW's default is to
cannam@95: divide the data equally among the processes if possible, and as best
cannam@95: it can otherwise. The rows are always assigned in ``rank order,''
cannam@95: i.e. process 0 gets the first block of rows, then process 1, and so
cannam@95: on. (You can change this by using @code{MPI_Comm_split} to create a
cannam@95: new communicator with re-ordered processes.) However, you should
cannam@95: always call the @samp{fftw_mpi_local_size} routines, if possible,
cannam@95: rather than trying to predict FFTW's distribution choices.
cannam@95:
cannam@95: In particular, it is critical that you allocate the storage size that
cannam@95: is returned by @samp{fftw_mpi_local_size}, which is @emph{not}
cannam@95: necessarily the size of the local slice of the array. The reason is
cannam@95: that intermediate steps of FFTW's algorithms involve transposing the
cannam@95: array and redistributing the data, so at these intermediate steps FFTW
cannam@95: may require more local storage space (albeit always proportional to
cannam@95: the total size divided by the number of processes). The
cannam@95: @samp{fftw_mpi_local_size} functions know how much storage is required
cannam@95: for these intermediate steps and tell you the correct amount to
cannam@95: allocate.
cannam@95:
cannam@95: @menu
cannam@95: * Basic and advanced distribution interfaces::
cannam@95: * Load balancing::
cannam@95: * Transposed distributions::
cannam@95: * One-dimensional distributions::
cannam@95: @end menu
cannam@95:
cannam@95: @node Basic and advanced distribution interfaces, Load balancing, MPI Data Distribution, MPI Data Distribution
cannam@95: @subsection Basic and advanced distribution interfaces
cannam@95:
cannam@95: As with the planner interface, the @samp{fftw_mpi_local_size}
cannam@95: distribution interface is broken into basic and advanced
cannam@95: (@samp{_many}) interfaces, where the latter allows you to specify the
cannam@95: block size manually and also to request block sizes when computing
cannam@95: multiple transforms simultaneously. These functions are documented
cannam@95: more exhaustively by the FFTW MPI Reference, but we summarize the
cannam@95: basic ideas here using a couple of two-dimensional examples.
cannam@95:
cannam@95: For the @twodims{100,200} complex-DFT example, above, we would find
cannam@95: the distribution by calling the following function in the basic
cannam@95: interface:
cannam@95:
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_2d(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@95: @end example
cannam@95: @findex fftw_mpi_local_size_2d
cannam@95:
cannam@95: Given the total size of the data to be transformed (here, @code{n0 =
cannam@95: 100} and @code{n1 = 200}) and an MPI communicator (@code{comm}), this
cannam@95: function provides three numbers.
cannam@95:
cannam@95: First, it describes the shape of the local data: the current process
cannam@95: should store a @code{local_n0} by @code{n1} slice of the overall
cannam@95: dataset, in row-major order (@code{n1} dimension contiguous), starting
cannam@95: at index @code{local_0_start}. That is, if the total dataset is
cannam@95: viewed as a @code{n0} by @code{n1} matrix, the current process should
cannam@95: store the rows @code{local_0_start} to
cannam@95: @code{local_0_start+local_n0-1}. Obviously, if you are running with
cannam@95: only a single MPI process, that process will store the entire array:
cannam@95: @code{local_0_start} will be zero and @code{local_n0} will be
cannam@95: @code{n0}. @xref{Row-major Format}.
cannam@95: @cindex row-major
cannam@95:
cannam@95:
cannam@95: Second, the return value is the total number of data elements (e.g.,
cannam@95: complex numbers for a complex DFT) that should be allocated for the
cannam@95: input and output arrays on the current process (ideally with
cannam@95: @code{fftw_malloc} or an @samp{fftw_alloc} function, to ensure optimal
cannam@95: alignment). It might seem that this should always be equal to
cannam@95: @code{local_n0 * n1}, but this is @emph{not} the case. FFTW's
cannam@95: distributed FFT algorithms require data redistributions at
cannam@95: intermediate stages of the transform, and in some circumstances this
cannam@95: may require slightly larger local storage. This is discussed in more
cannam@95: detail below, under @ref{Load balancing}.
cannam@95: @findex fftw_malloc
cannam@95: @findex fftw_alloc_complex
cannam@95:
cannam@95:
cannam@95: @cindex advanced interface
cannam@95: The advanced-interface @samp{local_size} function for multidimensional
cannam@95: transforms returns the same three things (@code{local_n0},
cannam@95: @code{local_0_start}, and the total number of elements to allocate),
cannam@95: but takes more inputs:
cannam@95:
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_many(int rnk, const ptrdiff_t *n,
cannam@95: ptrdiff_t howmany,
cannam@95: ptrdiff_t block0,
cannam@95: MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0,
cannam@95: ptrdiff_t *local_0_start);
cannam@95: @end example
cannam@95: @findex fftw_mpi_local_size_many
cannam@95:
cannam@95: The two-dimensional case above corresponds to @code{rnk = 2} and an
cannam@95: array @code{n} of length 2 with @code{n[0] = n0} and @code{n[1] = n1}.
cannam@95: This routine is for any @code{rnk > 1}; one-dimensional transforms
cannam@95: have their own interface because they work slightly differently, as
cannam@95: discussed below.
cannam@95:
cannam@95: First, the advanced interface allows you to perform multiple
cannam@95: transforms at once, of interleaved data, as specified by the
cannam@95: @code{howmany} parameter. (@code{hoamany} is 1 for a single
cannam@95: transform.)
cannam@95:
cannam@95: Second, here you can specify your desired block size in the @code{n0}
cannam@95: dimension, @code{block0}. To use FFTW's default block size, pass
cannam@95: @code{FFTW_MPI_DEFAULT_BLOCK} (0) for @code{block0}. Otherwise, on
cannam@95: @code{P} processes, FFTW will return @code{local_n0} equal to
cannam@95: @code{block0} on the first @code{P / block0} processes (rounded down),
cannam@95: return @code{local_n0} equal to @code{n0 - block0 * (P / block0)} on
cannam@95: the next process, and @code{local_n0} equal to zero on any remaining
cannam@95: processes. In general, we recommend using the default block size
cannam@95: (which corresponds to @code{n0 / P}, rounded up).
cannam@95: @ctindex FFTW_MPI_DEFAULT_BLOCK
cannam@95: @cindex block distribution
cannam@95:
cannam@95:
cannam@95: For example, suppose you have @code{P = 4} processes and @code{n0 =
cannam@95: 21}. The default will be a block size of @code{6}, which will give
cannam@95: @code{local_n0 = 6} on the first three processes and @code{local_n0 =
cannam@95: 3} on the last process. Instead, however, you could specify
cannam@95: @code{block0 = 5} if you wanted, which would give @code{local_n0 = 5}
cannam@95: on processes 0 to 2, @code{local_n0 = 6} on process 3. (This choice,
cannam@95: while it may look superficially more ``balanced,'' has the same
cannam@95: critical path as FFTW's default but requires more communications.)
cannam@95:
cannam@95: @node Load balancing, Transposed distributions, Basic and advanced distribution interfaces, MPI Data Distribution
cannam@95: @subsection Load balancing
cannam@95: @cindex load balancing
cannam@95:
cannam@95: Ideally, when you parallelize a transform over some @math{P}
cannam@95: processes, each process should end up with work that takes equal time.
cannam@95: Otherwise, all of the processes end up waiting on whichever process is
cannam@95: slowest. This goal is known as ``load balancing.'' In this section,
cannam@95: we describe the circumstances under which FFTW is able to load-balance
cannam@95: well, and in particular how you should choose your transform size in
cannam@95: order to load balance.
cannam@95:
cannam@95: Load balancing is especially difficult when you are parallelizing over
cannam@95: heterogeneous machines; for example, if one of your processors is a
cannam@95: old 486 and another is a Pentium IV, obviously you should give the
cannam@95: Pentium more work to do than the 486 since the latter is much slower.
cannam@95: FFTW does not deal with this problem, however---it assumes that your
cannam@95: processes run on hardware of comparable speed, and that the goal is
cannam@95: therefore to divide the problem as equally as possible.
cannam@95:
cannam@95: For a multi-dimensional complex DFT, FFTW can divide the problem
cannam@95: equally among the processes if: (i) the @emph{first} dimension
cannam@95: @code{n0} is divisible by @math{P}; and (ii), the @emph{product} of
cannam@95: the subsequent dimensions is divisible by @math{P}. (For the advanced
cannam@95: interface, where you can specify multiple simultaneous transforms via
cannam@95: some ``vector'' length @code{howmany}, a factor of @code{howmany} is
cannam@95: included in the product of the subsequent dimensions.)
cannam@95:
cannam@95: For a one-dimensional complex DFT, the length @code{N} of the data
cannam@95: should be divisible by @math{P} @emph{squared} to be able to divide
cannam@95: the problem equally among the processes.
cannam@95:
cannam@95: @node Transposed distributions, One-dimensional distributions, Load balancing, MPI Data Distribution
cannam@95: @subsection Transposed distributions
cannam@95:
cannam@95: Internally, FFTW's MPI transform algorithms work by first computing
cannam@95: transforms of the data local to each process, then by globally
cannam@95: @emph{transposing} the data in some fashion to redistribute the data
cannam@95: among the processes, transforming the new data local to each process,
cannam@95: and transposing back. For example, a two-dimensional @code{n0} by
cannam@95: @code{n1} array, distributed across the @code{n0} dimension, is
cannam@95: transformd by: (i) transforming the @code{n1} dimension, which are
cannam@95: local to each process; (ii) transposing to an @code{n1} by @code{n0}
cannam@95: array, distributed across the @code{n1} dimension; (iii) transforming
cannam@95: the @code{n0} dimension, which is now local to each process; (iv)
cannam@95: transposing back.
cannam@95: @cindex transpose
cannam@95:
cannam@95:
cannam@95: However, in many applications it is acceptable to compute a
cannam@95: multidimensional DFT whose results are produced in transposed order
cannam@95: (e.g., @code{n1} by @code{n0} in two dimensions). This provides a
cannam@95: significant performance advantage, because it means that the final
cannam@95: transposition step can be omitted. FFTW supports this optimization,
cannam@95: which you specify by passing the flag @code{FFTW_MPI_TRANSPOSED_OUT}
cannam@95: to the planner routines. To compute the inverse transform of
cannam@95: transposed output, you specify @code{FFTW_MPI_TRANSPOSED_IN} to tell
cannam@95: it that the input is transposed. In this section, we explain how to
cannam@95: interpret the output format of such a transform.
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_OUT
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_IN
cannam@95:
cannam@95:
cannam@95: Suppose you have are transforming multi-dimensional data with (at
cannam@95: least two) dimensions @ndims{}. As always, it is distributed along
cannam@95: the first dimension @dimk{0}. Now, if we compute its DFT with the
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT} flag, the resulting output data are stored
cannam@95: with the first @emph{two} dimensions transposed: @ndimstrans{},
cannam@95: distributed along the @dimk{1} dimension. Conversely, if we take the
cannam@95: @ndimstrans{} data and transform it with the
cannam@95: @code{FFTW_MPI_TRANSPOSED_IN} flag, then the format goes back to the
cannam@95: original @ndims{} array.
cannam@95:
cannam@95: There are two ways to find the portion of the transposed array that
cannam@95: resides on the current process. First, you can simply call the
cannam@95: appropriate @samp{local_size} function, passing @ndimstrans{} (the
cannam@95: transposed dimensions). This would mean calling the @samp{local_size}
cannam@95: function twice, once for the transposed and once for the
cannam@95: non-transposed dimensions. Alternatively, you can call one of the
cannam@95: @samp{local_size_transposed} functions, which returns both the
cannam@95: non-transposed and transposed data distribution from a single call.
cannam@95: For example, for a 3d transform with transposed output (or input), you
cannam@95: might call:
cannam@95:
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_3d_transposed(
cannam@95: ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: @end example
cannam@95: @findex fftw_mpi_local_size_3d_transposed
cannam@95:
cannam@95: Here, @code{local_n0} and @code{local_0_start} give the size and
cannam@95: starting index of the @code{n0} dimension for the
cannam@95: @emph{non}-transposed data, as in the previous sections. For
cannam@95: @emph{transposed} data (e.g. the output for
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT}), @code{local_n1} and
cannam@95: @code{local_1_start} give the size and starting index of the @code{n1}
cannam@95: dimension, which is the first dimension of the transposed data
cannam@95: (@code{n1} by @code{n0} by @code{n2}).
cannam@95:
cannam@95: (Note that @code{FFTW_MPI_TRANSPOSED_IN} is completely equivalent to
cannam@95: performing @code{FFTW_MPI_TRANSPOSED_OUT} and passing the first two
cannam@95: dimensions to the planner in reverse order, or vice versa. If you
cannam@95: pass @emph{both} the @code{FFTW_MPI_TRANSPOSED_IN} and
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT} flags, it is equivalent to swapping the
cannam@95: first two dimensions passed to the planner and passing @emph{neither}
cannam@95: flag.)
cannam@95:
cannam@95: @node One-dimensional distributions, , Transposed distributions, MPI Data Distribution
cannam@95: @subsection One-dimensional distributions
cannam@95:
cannam@95: For one-dimensional distributed DFTs using FFTW, matters are slightly
cannam@95: more complicated because the data distribution is more closely tied to
cannam@95: how the algorithm works. In particular, you can no longer pass an
cannam@95: arbitrary block size and must accept FFTW's default; also, the block
cannam@95: sizes may be different for input and output. Also, the data
cannam@95: distribution depends on the flags and transform direction, in order
cannam@95: for forward and backward transforms to work correctly.
cannam@95:
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_1d(ptrdiff_t n0, MPI_Comm comm,
cannam@95: int sign, unsigned flags,
cannam@95: ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
cannam@95: ptrdiff_t *local_no, ptrdiff_t *local_o_start);
cannam@95: @end example
cannam@95: @findex fftw_mpi_local_size_1d
cannam@95:
cannam@95: This function computes the data distribution for a 1d transform of
cannam@95: size @code{n0} with the given transform @code{sign} and @code{flags}.
cannam@95: Both input and output data use block distributions. The input on the
cannam@95: current process will consist of @code{local_ni} numbers starting at
cannam@95: index @code{local_i_start}; e.g. if only a single process is used,
cannam@95: then @code{local_ni} will be @code{n0} and @code{local_i_start} will
cannam@95: be @code{0}. Similarly for the output, with @code{local_no} numbers
cannam@95: starting at index @code{local_o_start}. The return value of
cannam@95: @code{fftw_mpi_local_size_1d} will be the total number of elements to
cannam@95: allocate on the current process (which might be slightly larger than
cannam@95: the local size due to intermediate steps in the algorithm).
cannam@95:
cannam@95: As mentioned above (@pxref{Load balancing}), the data will be divided
cannam@95: equally among the processes if @code{n0} is divisible by the
cannam@95: @emph{square} of the number of processes. In this case,
cannam@95: @code{local_ni} will equal @code{local_no}. Otherwise, they may be
cannam@95: different.
cannam@95:
cannam@95: For some applications, such as convolutions, the order of the output
cannam@95: data is irrelevant. In this case, performance can be improved by
cannam@95: specifying that the output data be stored in an FFTW-defined
cannam@95: ``scrambled'' format. (In particular, this is the analogue of
cannam@95: transposed output in the multidimensional case: scrambled output saves
cannam@95: a communications step.) If you pass @code{FFTW_MPI_SCRAMBLED_OUT} in
cannam@95: the flags, then the output is stored in this (undocumented) scrambled
cannam@95: order. Conversely, to perform the inverse transform of data in
cannam@95: scrambled order, pass the @code{FFTW_MPI_SCRAMBLED_IN} flag.
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_OUT
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_IN
cannam@95:
cannam@95:
cannam@95: In MPI FFTW, only composite sizes @code{n0} can be parallelized; we
cannam@95: have not yet implemented a parallel algorithm for large prime sizes.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node Multi-dimensional MPI DFTs of Real Data, Other Multi-dimensional Real-data MPI Transforms, MPI Data Distribution, Distributed-memory FFTW with MPI
cannam@95: @section Multi-dimensional MPI DFTs of Real Data
cannam@95:
cannam@95: FFTW's MPI interface also supports multi-dimensional DFTs of real
cannam@95: data, similar to the serial r2c and c2r interfaces. (Parallel
cannam@95: one-dimensional real-data DFTs are not currently supported; you must
cannam@95: use a complex transform and set the imaginary parts of the inputs to
cannam@95: zero.)
cannam@95:
cannam@95: The key points to understand for r2c and c2r MPI transforms (compared
cannam@95: to the MPI complex DFTs or the serial r2c/c2r transforms), are:
cannam@95:
cannam@95: @itemize @bullet
cannam@95:
cannam@95: @item
cannam@95: Just as for serial transforms, r2c/c2r DFTs transform @ndims{} real
cannam@95: data to/from @ndimshalf{} complex data: the last dimension of the
cannam@95: complex data is cut in half (rounded down), plus one. As for the
cannam@95: serial transforms, the sizes you pass to the @samp{plan_dft_r2c} and
cannam@95: @samp{plan_dft_c2r} are the @ndims{} dimensions of the real data.
cannam@95:
cannam@95: @item
cannam@95: @cindex padding
cannam@95: Although the real data is @emph{conceptually} @ndims{}, it is
cannam@95: @emph{physically} stored as an @ndimspad{} array, where the last
cannam@95: dimension has been @emph{padded} to make it the same size as the
cannam@95: complex output. This is much like the in-place serial r2c/c2r
cannam@95: interface (@pxref{Multi-Dimensional DFTs of Real Data}), except that
cannam@95: in MPI the padding is required even for out-of-place data. The extra
cannam@95: padding numbers are ignored by FFTW (they are @emph{not} like
cannam@95: zero-padding the transform to a larger size); they are only used to
cannam@95: determine the data layout.
cannam@95:
cannam@95: @item
cannam@95: @cindex data distribution
cannam@95: The data distribution in MPI for @emph{both} the real and complex data
cannam@95: is determined by the shape of the @emph{complex} data. That is, you
cannam@95: call the appropriate @samp{local size} function for the @ndimshalf{}
cannam@95: complex data, and then use the @emph{same} distribution for the real
cannam@95: data except that the last complex dimension is replaced by a (padded)
cannam@95: real dimension of twice the length.
cannam@95:
cannam@95: @end itemize
cannam@95:
cannam@95: For example suppose we are performing an out-of-place r2c transform of
cannam@95: @threedims{L,M,N} real data [padded to @threedims{L,M,2(N/2+1)}],
cannam@95: resulting in @threedims{L,M,N/2+1} complex data. Similar to the
cannam@95: example in @ref{2d MPI example}, we might do something like:
cannam@95:
cannam@95: @example
cannam@95: #include <fftw3-mpi.h>
cannam@95:
cannam@95: int main(int argc, char **argv)
cannam@95: @{
cannam@95: const ptrdiff_t L = ..., M = ..., N = ...;
cannam@95: fftw_plan plan;
cannam@95: double *rin;
cannam@95: fftw_complex *cout;
cannam@95: ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
cannam@95:
cannam@95: MPI_Init(&argc, &argv);
cannam@95: fftw_mpi_init();
cannam@95:
cannam@95: /* @r{get local data size and allocate} */
cannam@95: alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
cannam@95: &local_n0, &local_0_start);
cannam@95: rin = fftw_alloc_real(2 * alloc_local);
cannam@95: cout = fftw_alloc_complex(alloc_local);
cannam@95:
cannam@95: /* @r{create plan for out-of-place r2c DFT} */
cannam@95: plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
cannam@95: FFTW_MEASURE);
cannam@95:
cannam@95: /* @r{initialize rin to some function} my_func(x,y,z) */
cannam@95: for (i = 0; i < local_n0; ++i)
cannam@95: for (j = 0; j < M; ++j)
cannam@95: for (k = 0; k < N; ++k)
cannam@95: rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
cannam@95:
cannam@95: /* @r{compute transforms as many times as desired} */
cannam@95: fftw_execute(plan);
cannam@95:
cannam@95: fftw_destroy_plan(plan);
cannam@95:
cannam@95: MPI_Finalize();
cannam@95: @}
cannam@95: @end example
cannam@95:
cannam@95: @findex fftw_alloc_real
cannam@95: @cindex row-major
cannam@95: Note that we allocated @code{rin} using @code{fftw_alloc_real} with an
cannam@95: argument of @code{2 * alloc_local}: since @code{alloc_local} is the
cannam@95: number of @emph{complex} values to allocate, the number of @emph{real}
cannam@95: values is twice as many. The @code{rin} array is then
cannam@95: @threedims{local_n0,M,2(N/2+1)} in row-major order, so its
cannam@95: @code{(i,j,k)} element is at the index @code{(i*M + j) * (2*(N/2+1)) +
cannam@95: k} (@pxref{Multi-dimensional Array Format }).
cannam@95:
cannam@95: @cindex transpose
cannam@95: @ctindex FFTW_TRANSPOSED_OUT
cannam@95: @ctindex FFTW_TRANSPOSED_IN
cannam@95: As for the complex transforms, improved performance can be obtained by
cannam@95: specifying that the output is the transpose of the input or vice versa
cannam@95: (@pxref{Transposed distributions}). In our @threedims{L,M,N} r2c
cannam@95: example, including @code{FFTW_TRANSPOSED_OUT} in the flags means that
cannam@95: the input would be a padded @threedims{L,M,2(N/2+1)} real array
cannam@95: distributed over the @code{L} dimension, while the output would be a
cannam@95: @threedims{M,L,N/2+1} complex array distributed over the @code{M}
cannam@95: dimension. To perform the inverse c2r transform with the same data
cannam@95: distributions, you would use the @code{FFTW_TRANSPOSED_IN} flag.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node Other Multi-dimensional Real-data MPI Transforms, FFTW MPI Transposes, Multi-dimensional MPI DFTs of Real Data, Distributed-memory FFTW with MPI
cannam@95: @section Other multi-dimensional Real-Data MPI Transforms
cannam@95:
cannam@95: @cindex r2r
cannam@95: FFTW's MPI interface also supports multi-dimensional @samp{r2r}
cannam@95: transforms of all kinds supported by the serial interface
cannam@95: (e.g. discrete cosine and sine transforms, discrete Hartley
cannam@95: transforms, etc.). Only multi-dimensional @samp{r2r} transforms, not
cannam@95: one-dimensional transforms, are currently parallelized.
cannam@95:
cannam@95: @tindex fftw_r2r_kind
cannam@95: These are used much like the multidimensional complex DFTs discussed
cannam@95: above, except that the data is real rather than complex, and one needs
cannam@95: to pass an r2r transform kind (@code{fftw_r2r_kind}) for each
cannam@95: dimension as in the serial FFTW (@pxref{More DFTs of Real Data}).
cannam@95:
cannam@95: For example, one might perform a two-dimensional @twodims{L,M} that is
cannam@95: an REDFT10 (DCT-II) in the first dimension and an RODFT10 (DST-II) in
cannam@95: the second dimension with code like:
cannam@95:
cannam@95: @example
cannam@95: const ptrdiff_t L = ..., M = ...;
cannam@95: fftw_plan plan;
cannam@95: double *data;
cannam@95: ptrdiff_t alloc_local, local_n0, local_0_start, i, j;
cannam@95:
cannam@95: /* @r{get local data size and allocate} */
cannam@95: alloc_local = fftw_mpi_local_size_2d(L, M, MPI_COMM_WORLD,
cannam@95: &local_n0, &local_0_start);
cannam@95: data = fftw_alloc_real(alloc_local);
cannam@95:
cannam@95: /* @r{create plan for in-place REDFT10 x RODFT10} */
cannam@95: plan = fftw_mpi_plan_r2r_2d(L, M, data, data, MPI_COMM_WORLD,
cannam@95: FFTW_REDFT10, FFTW_RODFT10, FFTW_MEASURE);
cannam@95:
cannam@95: /* @r{initialize data to some function} my_function(x,y) */
cannam@95: for (i = 0; i < local_n0; ++i) for (j = 0; j < M; ++j)
cannam@95: data[i*M + j] = my_function(local_0_start + i, j);
cannam@95:
cannam@95: /* @r{compute transforms, in-place, as many times as desired} */
cannam@95: fftw_execute(plan);
cannam@95:
cannam@95: fftw_destroy_plan(plan);
cannam@95: @end example
cannam@95:
cannam@95: @findex fftw_alloc_real
cannam@95: Notice that we use the same @samp{local_size} functions as we did for
cannam@95: complex data, only now we interpret the sizes in terms of real rather
cannam@95: than complex values, and correspondingly use @code{fftw_alloc_real}.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Transposes, FFTW MPI Wisdom, Other Multi-dimensional Real-data MPI Transforms, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Transposes
cannam@95: @cindex transpose
cannam@95:
cannam@95: The FFTW's MPI Fourier transforms rely on one or more @emph{global
cannam@95: transposition} step for their communications. For example, the
cannam@95: multidimensional transforms work by transforming along some
cannam@95: dimensions, then transposing to make the first dimension local and
cannam@95: transforming that, then transposing back. Because global
cannam@95: transposition of a block-distributed matrix has many other potential
cannam@95: uses besides FFTs, FFTW's transpose routines can be called directly,
cannam@95: as documented in this section.
cannam@95:
cannam@95: @menu
cannam@95: * Basic distributed-transpose interface::
cannam@95: * Advanced distributed-transpose interface::
cannam@95: * An improved replacement for MPI_Alltoall::
cannam@95: @end menu
cannam@95:
cannam@95: @node Basic distributed-transpose interface, Advanced distributed-transpose interface, FFTW MPI Transposes, FFTW MPI Transposes
cannam@95: @subsection Basic distributed-transpose interface
cannam@95:
cannam@95: In particular, suppose that we have an @code{n0} by @code{n1} array in
cannam@95: row-major order, block-distributed across the @code{n0} dimension. To
cannam@95: transpose this into an @code{n1} by @code{n0} array block-distributed
cannam@95: across the @code{n1} dimension, we would create a plan by calling the
cannam@95: following function:
cannam@95:
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_transpose(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: @end example
cannam@95: @findex fftw_mpi_plan_transpose
cannam@95:
cannam@95: The input and output arrays (@code{in} and @code{out}) can be the
cannam@95: same. The transpose is actually executed by calling
cannam@95: @code{fftw_execute} on the plan, as usual.
cannam@95: @findex fftw_execute
cannam@95:
cannam@95:
cannam@95: The @code{flags} are the usual FFTW planner flags, but support
cannam@95: two additional flags: @code{FFTW_MPI_TRANSPOSED_OUT} and/or
cannam@95: @code{FFTW_MPI_TRANSPOSED_IN}. What these flags indicate, for
cannam@95: transpose plans, is that the output and/or input, respectively, are
cannam@95: @emph{locally} transposed. That is, on each process input data is
cannam@95: normally stored as a @code{local_n0} by @code{n1} array in row-major
cannam@95: order, but for an @code{FFTW_MPI_TRANSPOSED_IN} plan the input data is
cannam@95: stored as @code{n1} by @code{local_n0} in row-major order. Similarly,
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT} means that the output is @code{n0} by
cannam@95: @code{local_n1} instead of @code{local_n1} by @code{n0}.
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_OUT
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_IN
cannam@95:
cannam@95:
cannam@95: To determine the local size of the array on each process before and
cannam@95: after the transpose, as well as the amount of storage that must be
cannam@95: allocated, one should call @code{fftw_mpi_local_size_2d_transposed},
cannam@95: just as for a 2d DFT as described in the previous section:
cannam@95: @cindex data distribution
cannam@95:
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_2d_transposed
cannam@95: (ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: @end example
cannam@95: @findex fftw_mpi_local_size_2d_transposed
cannam@95:
cannam@95: Again, the return value is the local storage to allocate, which in
cannam@95: this case is the number of @emph{real} (@code{double}) values rather
cannam@95: than complex numbers as in the previous examples.
cannam@95:
cannam@95: @node Advanced distributed-transpose interface, An improved replacement for MPI_Alltoall, Basic distributed-transpose interface, FFTW MPI Transposes
cannam@95: @subsection Advanced distributed-transpose interface
cannam@95:
cannam@95: The above routines are for a transpose of a matrix of numbers (of type
cannam@95: @code{double}), using FFTW's default block sizes. More generally, one
cannam@95: can perform transposes of @emph{tuples} of numbers, with
cannam@95: user-specified block sizes for the input and output:
cannam@95:
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_many_transpose
cannam@95: (ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t howmany,
cannam@95: ptrdiff_t block0, ptrdiff_t block1,
cannam@95: double *in, double *out, MPI_Comm comm, unsigned flags);
cannam@95: @end example
cannam@95: @findex fftw_mpi_plan_many_transpose
cannam@95:
cannam@95: In this case, one is transposing an @code{n0} by @code{n1} matrix of
cannam@95: @code{howmany}-tuples (e.g. @code{howmany = 2} for complex numbers).
cannam@95: The input is distributed along the @code{n0} dimension with block size
cannam@95: @code{block0}, and the @code{n1} by @code{n0} output is distributed
cannam@95: along the @code{n1} dimension with block size @code{block1}. If
cannam@95: @code{FFTW_MPI_DEFAULT_BLOCK} (0) is passed for a block size then FFTW
cannam@95: uses its default block size. To get the local size of the data on
cannam@95: each process, you should then call @code{fftw_mpi_local_size_many_transposed}.
cannam@95: @ctindex FFTW_MPI_DEFAULT_BLOCK
cannam@95: @findex fftw_mpi_local_size_many_transposed
cannam@95:
cannam@95: @node An improved replacement for MPI_Alltoall, , Advanced distributed-transpose interface, FFTW MPI Transposes
cannam@95: @subsection An improved replacement for MPI_Alltoall
cannam@95:
cannam@95: We close this section by noting that FFTW's MPI transpose routines can
cannam@95: be thought of as a generalization for the @code{MPI_Alltoall} function
cannam@95: (albeit only for floating-point types), and in some circumstances can
cannam@95: function as an improved replacement.
cannam@95: @findex MPI_Alltoall
cannam@95:
cannam@95:
cannam@95: @code{MPI_Alltoall} is defined by the MPI standard as:
cannam@95:
cannam@95: @example
cannam@95: int MPI_Alltoall(void *sendbuf, int sendcount, MPI_Datatype sendtype,
cannam@95: void *recvbuf, int recvcnt, MPI_Datatype recvtype,
cannam@95: MPI_Comm comm);
cannam@95: @end example
cannam@95:
cannam@95: In particular, for @code{double*} arrays @code{in} and @code{out},
cannam@95: consider the call:
cannam@95:
cannam@95: @example
cannam@95: MPI_Alltoall(in, howmany, MPI_DOUBLE, out, howmany MPI_DOUBLE, comm);
cannam@95: @end example
cannam@95:
cannam@95: This is completely equivalent to:
cannam@95:
cannam@95: @example
cannam@95: MPI_Comm_size(comm, &P);
cannam@95: plan = fftw_mpi_plan_many_transpose(P, P, howmany, 1, 1, in, out, comm, FFTW_ESTIMATE);
cannam@95: fftw_execute(plan);
cannam@95: fftw_destroy_plan(plan);
cannam@95: @end example
cannam@95:
cannam@95: That is, computing a @twodims{P,P} transpose on @code{P} processes,
cannam@95: with a block size of 1, is just a standard all-to-all communication.
cannam@95:
cannam@95: However, using the FFTW routine instead of @code{MPI_Alltoall} may
cannam@95: have certain advantages. First of all, FFTW's routine can operate
cannam@95: in-place (@code{in == out}) whereas @code{MPI_Alltoall} can only
cannam@95: operate out-of-place.
cannam@95: @cindex in-place
cannam@95:
cannam@95:
cannam@95: Second, even for out-of-place plans, FFTW's routine may be faster,
cannam@95: especially if you need to perform the all-to-all communication many
cannam@95: times and can afford to use @code{FFTW_MEASURE} or
cannam@95: @code{FFTW_PATIENT}. It should certainly be no slower, not including
cannam@95: the time to create the plan, since one of the possible algorithms that
cannam@95: FFTW uses for an out-of-place transpose @emph{is} simply to call
cannam@95: @code{MPI_Alltoall}. However, FFTW also considers several other
cannam@95: possible algorithms that, depending on your MPI implementation and
cannam@95: your hardware, may be faster.
cannam@95: @ctindex FFTW_MEASURE
cannam@95: @ctindex FFTW_PATIENT
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Wisdom, Avoiding MPI Deadlocks, FFTW MPI Transposes, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Wisdom
cannam@95: @cindex wisdom
cannam@95: @cindex saving plans to disk
cannam@95:
cannam@95: FFTW's ``wisdom'' facility (@pxref{Words of Wisdom-Saving Plans}) can
cannam@95: be used to save MPI plans as well as to save uniprocessor plans.
cannam@95: However, for MPI there are several unavoidable complications.
cannam@95:
cannam@95: @cindex MPI I/O
cannam@95: First, the MPI standard does not guarantee that every process can
cannam@95: perform file I/O (at least, not using C stdio routines)---in general,
cannam@95: we may only assume that process 0 is capable of I/O.@footnote{In fact,
cannam@95: even this assumption is not technically guaranteed by the standard,
cannam@95: although it seems to be universal in actual MPI implementations and is
cannam@95: widely assumed by MPI-using software. Technically, you need to query
cannam@95: the @code{MPI_IO} attribute of @code{MPI_COMM_WORLD} with
cannam@95: @code{MPI_Attr_get}. If this attribute is @code{MPI_PROC_NULL}, no
cannam@95: I/O is possible. If it is @code{MPI_ANY_SOURCE}, any process can
cannam@95: perform I/O. Otherwise, it is the rank of a process that can perform
cannam@95: I/O ... but since it is not guaranteed to yield the @emph{same} rank
cannam@95: on all processes, you have to do an @code{MPI_Allreduce} of some kind
cannam@95: if you want all processes to agree about which is going to do I/O.
cannam@95: And even then, the standard only guarantees that this process can
cannam@95: perform output, but not input. See e.g. @cite{Parallel Programming
cannam@95: with MPI} by P. S. Pacheco, section 8.1.3. Needless to say, in our
cannam@95: experience virtually no MPI programmers worry about this.} So, if we
cannam@95: want to export the wisdom from a single process to a file, we must
cannam@95: first export the wisdom to a string, then send it to process 0, then
cannam@95: write it to a file.
cannam@95:
cannam@95: Second, in principle we may want to have separate wisdom for every
cannam@95: process, since in general the processes may run on different hardware
cannam@95: even for a single MPI program. However, in practice FFTW's MPI code
cannam@95: is designed for the case of homogeneous hardware (@pxref{Load
cannam@95: balancing}), and in this case it is convenient to use the same wisdom
cannam@95: for every process. Thus, we need a mechanism to synchronize the wisdom.
cannam@95:
cannam@95: To address both of these problems, FFTW provides the following two
cannam@95: functions:
cannam@95:
cannam@95: @example
cannam@95: void fftw_mpi_broadcast_wisdom(MPI_Comm comm);
cannam@95: void fftw_mpi_gather_wisdom(MPI_Comm comm);
cannam@95: @end example
cannam@95: @findex fftw_mpi_gather_wisdom
cannam@95: @findex fftw_mpi_broadcast_wisdom
cannam@95:
cannam@95: Given a communicator @code{comm}, @code{fftw_mpi_broadcast_wisdom}
cannam@95: will broadcast the wisdom from process 0 to all other processes.
cannam@95: Conversely, @code{fftw_mpi_gather_wisdom} will collect wisdom from all
cannam@95: processes onto process 0. (If the plans created for the same problem
cannam@95: by different processes are not the same, @code{fftw_mpi_gather_wisdom}
cannam@95: will arbitrarily choose one of the plans.) Both of these functions
cannam@95: may result in suboptimal plans for different processes if the
cannam@95: processes are running on non-identical hardware. Both of these
cannam@95: functions are @emph{collective} calls, which means that they must be
cannam@95: executed by all processes in the communicator.
cannam@95: @cindex collective function
cannam@95:
cannam@95:
cannam@95: So, for example, a typical code snippet to import wisdom from a file
cannam@95: and use it on all processes would be:
cannam@95:
cannam@95: @example
cannam@95: @{
cannam@95: int rank;
cannam@95:
cannam@95: fftw_mpi_init();
cannam@95: MPI_Comm_rank(MPI_COMM_WORLD, &rank);
cannam@95: if (rank == 0) fftw_import_wisdom_from_filename("mywisdom");
cannam@95: fftw_mpi_broadcast_wisdom(MPI_COMM_WORLD);
cannam@95: @}
cannam@95: @end example
cannam@95:
cannam@95: (Note that we must call @code{fftw_mpi_init} before importing any
cannam@95: wisdom that might contain MPI plans.) Similarly, a typical code
cannam@95: snippet to export wisdom from all processes to a file is:
cannam@95: @findex fftw_mpi_init
cannam@95:
cannam@95: @example
cannam@95: @{
cannam@95: int rank;
cannam@95:
cannam@95: fftw_mpi_gather_wisdom(MPI_COMM_WORLD);
cannam@95: MPI_Comm_rank(MPI_COMM_WORLD, &rank);
cannam@95: if (rank == 0) fftw_export_wisdom_to_filename("mywisdom");
cannam@95: @}
cannam@95: @end example
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node Avoiding MPI Deadlocks, FFTW MPI Performance Tips, FFTW MPI Wisdom, Distributed-memory FFTW with MPI
cannam@95: @section Avoiding MPI Deadlocks
cannam@95: @cindex deadlock
cannam@95:
cannam@95: An MPI program can @emph{deadlock} if one process is waiting for a
cannam@95: message from another process that never gets sent. To avoid deadlocks
cannam@95: when using FFTW's MPI routines, it is important to know which
cannam@95: functions are @emph{collective}: that is, which functions must
cannam@95: @emph{always} be called in the @emph{same order} from @emph{every}
cannam@95: process in a given communicator. (For example, @code{MPI_Barrier} is
cannam@95: the canonical example of a collective function in the MPI standard.)
cannam@95: @cindex collective function
cannam@95: @findex MPI_Barrier
cannam@95:
cannam@95:
cannam@95: The functions in FFTW that are @emph{always} collective are: every
cannam@95: function beginning with @samp{fftw_mpi_plan}, as well as
cannam@95: @code{fftw_mpi_broadcast_wisdom} and @code{fftw_mpi_gather_wisdom}.
cannam@95: Also, the following functions from the ordinary FFTW interface are
cannam@95: collective when they are applied to a plan created by an
cannam@95: @samp{fftw_mpi_plan} function: @code{fftw_execute},
cannam@95: @code{fftw_destroy_plan}, and @code{fftw_flops}.
cannam@95: @findex fftw_execute
cannam@95: @findex fftw_destroy_plan
cannam@95: @findex fftw_flops
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Performance Tips, Combining MPI and Threads, Avoiding MPI Deadlocks, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Performance Tips
cannam@95:
cannam@95: In this section, we collect a few tips on getting the best performance
cannam@95: out of FFTW's MPI transforms.
cannam@95:
cannam@95: First, because of the 1d block distribution, FFTW's parallelization is
cannam@95: currently limited by the size of the first dimension.
cannam@95: (Multidimensional block distributions may be supported by a future
cannam@95: version.) More generally, you should ideally arrange the dimensions so
cannam@95: that FFTW can divide them equally among the processes. @xref{Load
cannam@95: balancing}.
cannam@95: @cindex block distribution
cannam@95: @cindex load balancing
cannam@95:
cannam@95:
cannam@95: Second, if it is not too inconvenient, you should consider working
cannam@95: with transposed output for multidimensional plans, as this saves a
cannam@95: considerable amount of communications. @xref{Transposed distributions}.
cannam@95: @cindex transpose
cannam@95:
cannam@95:
cannam@95: Third, the fastest choices are generally either an in-place transform
cannam@95: or an out-of-place transform with the @code{FFTW_DESTROY_INPUT} flag
cannam@95: (which allows the input array to be used as scratch space). In-place
cannam@95: is especially beneficial if the amount of data per process is large.
cannam@95: @ctindex FFTW_DESTROY_INPUT
cannam@95:
cannam@95:
cannam@95: Fourth, if you have multiple arrays to transform at once, rather than
cannam@95: calling FFTW's MPI transforms several times it usually seems to be
cannam@95: faster to interleave the data and use the advanced interface. (This
cannam@95: groups the communications together instead of requiring separate
cannam@95: messages for each transform.)
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node Combining MPI and Threads, FFTW MPI Reference, FFTW MPI Performance Tips, Distributed-memory FFTW with MPI
cannam@95: @section Combining MPI and Threads
cannam@95: @cindex threads
cannam@95:
cannam@95: In certain cases, it may be advantageous to combine MPI
cannam@95: (distributed-memory) and threads (shared-memory) parallelization.
cannam@95: FFTW supports this, with certain caveats. For example, if you have a
cannam@95: cluster of 4-processor shared-memory nodes, you may want to use
cannam@95: threads within the nodes and MPI between the nodes, instead of MPI for
cannam@95: all parallelization.
cannam@95:
cannam@95: In particular, it is possible to seamlessly combine the MPI FFTW
cannam@95: routines with the multi-threaded FFTW routines (@pxref{Multi-threaded
cannam@95: FFTW}). However, some care must be taken in the initialization code,
cannam@95: which should look something like this:
cannam@95:
cannam@95: @example
cannam@95: int threads_ok;
cannam@95:
cannam@95: int main(int argc, char **argv)
cannam@95: @{
cannam@95: int provided;
cannam@95: MPI_Init_thread(&argc, &argv, MPI_THREAD_FUNNELED, &provided);
cannam@95: threads_ok = provided >= MPI_THREAD_FUNNELED;
cannam@95:
cannam@95: if (threads_ok) threads_ok = fftw_init_threads();
cannam@95: fftw_mpi_init();
cannam@95:
cannam@95: ...
cannam@95: if (threads_ok) fftw_plan_with_nthreads(...);
cannam@95: ...
cannam@95:
cannam@95: MPI_Finalize();
cannam@95: @}
cannam@95: @end example
cannam@95: @findex fftw_mpi_init
cannam@95: @findex fftw_init_threads
cannam@95: @findex fftw_plan_with_nthreads
cannam@95:
cannam@95: First, note that instead of calling @code{MPI_Init}, you should call
cannam@95: @code{MPI_Init_threads}, which is the initialization routine defined
cannam@95: by the MPI-2 standard to indicate to MPI that your program will be
cannam@95: multithreaded. We pass @code{MPI_THREAD_FUNNELED}, which indicates
cannam@95: that we will only call MPI routines from the main thread. (FFTW will
cannam@95: launch additional threads internally, but the extra threads will not
cannam@95: call MPI code.) (You may also pass @code{MPI_THREAD_SERIALIZED} or
cannam@95: @code{MPI_THREAD_MULTIPLE}, which requests additional multithreading
cannam@95: support from the MPI implementation, but this is not required by
cannam@95: FFTW.) The @code{provided} parameter returns what level of threads
cannam@95: support is actually supported by your MPI implementation; this
cannam@95: @emph{must} be at least @code{MPI_THREAD_FUNNELED} if you want to call
cannam@95: the FFTW threads routines, so we define a global variable
cannam@95: @code{threads_ok} to record this. You should only call
cannam@95: @code{fftw_init_threads} or @code{fftw_plan_with_nthreads} if
cannam@95: @code{threads_ok} is true. For more information on thread safety in
cannam@95: MPI, see the
cannam@95: @uref{http://www.mpi-forum.org/docs/mpi-20-html/node162.htm, MPI and
cannam@95: Threads} section of the MPI-2 standard.
cannam@95: @cindex thread safety
cannam@95:
cannam@95:
cannam@95: Second, we must call @code{fftw_init_threads} @emph{before}
cannam@95: @code{fftw_mpi_init}. This is critical for technical reasons having
cannam@95: to do with how FFTW initializes its list of algorithms.
cannam@95:
cannam@95: Then, if you call @code{fftw_plan_with_nthreads(N)}, @emph{every} MPI
cannam@95: process will launch (up to) @code{N} threads to parallelize its transforms.
cannam@95:
cannam@95: For example, in the hypothetical cluster of 4-processor nodes, you
cannam@95: might wish to launch only a single MPI process per node, and then call
cannam@95: @code{fftw_plan_with_nthreads(4)} on each process to use all
cannam@95: processors in the nodes.
cannam@95:
cannam@95: This may or may not be faster than simply using as many MPI processes
cannam@95: as you have processors, however. On the one hand, using threads
cannam@95: within a node eliminates the need for explicit message passing within
cannam@95: the node. On the other hand, FFTW's transpose routines are not
cannam@95: multi-threaded, and this means that the communications that do take
cannam@95: place will not benefit from parallelization within the node.
cannam@95: Moreover, many MPI implementations already have optimizations to
cannam@95: exploit shared memory when it is available, so adding the
cannam@95: multithreaded FFTW on top of this may be superfluous.
cannam@95: @cindex transpose
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Reference, FFTW MPI Fortran Interface, Combining MPI and Threads, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Reference
cannam@95:
cannam@95: This chapter provides a complete reference to all FFTW MPI functions,
cannam@95: datatypes, and constants. See also @ref{FFTW Reference} for information
cannam@95: on functions and types in common with the serial interface.
cannam@95:
cannam@95: @menu
cannam@95: * MPI Files and Data Types::
cannam@95: * MPI Initialization::
cannam@95: * Using MPI Plans::
cannam@95: * MPI Data Distribution Functions::
cannam@95: * MPI Plan Creation::
cannam@95: * MPI Wisdom Communication::
cannam@95: @end menu
cannam@95:
cannam@95: @node MPI Files and Data Types, MPI Initialization, FFTW MPI Reference, FFTW MPI Reference
cannam@95: @subsection MPI Files and Data Types
cannam@95:
cannam@95: All programs using FFTW's MPI support should include its header file:
cannam@95:
cannam@95: @example
cannam@95: #include <fftw3-mpi.h>
cannam@95: @end example
cannam@95:
cannam@95: Note that this header file includes the serial-FFTW @code{fftw3.h}
cannam@95: header file, and also the @code{mpi.h} header file for MPI, so you
cannam@95: need not include those files separately.
cannam@95:
cannam@95: You must also link to @emph{both} the FFTW MPI library and to the
cannam@95: serial FFTW library. On Unix, this means adding @code{-lfftw3_mpi
cannam@95: -lfftw3 -lm} at the end of the link command.
cannam@95:
cannam@95: @cindex precision
cannam@95: Different precisions are handled as in the serial interface:
cannam@95: @xref{Precision}. That is, @samp{fftw_} functions become
cannam@95: @code{fftwf_} (in single precision) etcetera, and the libraries become
cannam@95: @code{-lfftw3f_mpi -lfftw3f -lm} etcetera on Unix. Long-double
cannam@95: precision is supported in MPI, but quad precision (@samp{fftwq_}) is
cannam@95: not due to the lack of MPI support for this type.
cannam@95:
cannam@95: @node MPI Initialization, Using MPI Plans, MPI Files and Data Types, FFTW MPI Reference
cannam@95: @subsection MPI Initialization
cannam@95:
cannam@95: Before calling any other FFTW MPI (@samp{fftw_mpi_}) function, and
cannam@95: before importing any wisdom for MPI problems, you must call:
cannam@95:
cannam@95: @findex fftw_mpi_init
cannam@95: @example
cannam@95: void fftw_mpi_init(void);
cannam@95: @end example
cannam@95:
cannam@95: @findex fftw_init_threads
cannam@95: If FFTW threads support is used, however, @code{fftw_mpi_init} should
cannam@95: be called @emph{after} @code{fftw_init_threads} (@pxref{Combining MPI
cannam@95: and Threads}). Calling @code{fftw_mpi_init} additional times (before
cannam@95: @code{fftw_mpi_cleanup}) has no effect.
cannam@95:
cannam@95:
cannam@95: If you want to deallocate all persistent data and reset FFTW to the
cannam@95: pristine state it was in when you started your program, you can call:
cannam@95:
cannam@95: @findex fftw_mpi_cleanup
cannam@95: @example
cannam@95: void fftw_mpi_cleanup(void);
cannam@95: @end example
cannam@95:
cannam@95: @findex fftw_cleanup
cannam@95: (This calls @code{fftw_cleanup}, so you need not call the serial
cannam@95: cleanup routine too, although it is safe to do so.) After calling
cannam@95: @code{fftw_mpi_cleanup}, all existing plans become undefined, and you
cannam@95: should not attempt to execute or destroy them. You must call
cannam@95: @code{fftw_mpi_init} again after @code{fftw_mpi_cleanup} if you want
cannam@95: to resume using the MPI FFTW routines.
cannam@95:
cannam@95: @node Using MPI Plans, MPI Data Distribution Functions, MPI Initialization, FFTW MPI Reference
cannam@95: @subsection Using MPI Plans
cannam@95:
cannam@95: Once an MPI plan is created, you can execute and destroy it using
cannam@95: @code{fftw_execute}, @code{fftw_destroy_plan}, and the other functions
cannam@95: in the serial interface that operate on generic plans (@pxref{Using
cannam@95: Plans}).
cannam@95:
cannam@95: @cindex collective function
cannam@95: @cindex MPI communicator
cannam@95: The @code{fftw_execute} and @code{fftw_destroy_plan} functions, applied to
cannam@95: MPI plans, are @emph{collective} calls: they must be called for all processes
cannam@95: in the communicator that was used to create the plan.
cannam@95:
cannam@95: @cindex new-array execution
cannam@95: You must @emph{not} use the serial new-array plan-execution functions
cannam@95: @code{fftw_execute_dft} and so on (@pxref{New-array Execute
cannam@95: Functions}) with MPI plans. Such functions are specialized to the
cannam@95: problem type, and there are specific new-array execute functions for MPI plans:
cannam@95:
cannam@95: @findex fftw_mpi_execute_dft
cannam@95: @findex fftw_mpi_execute_dft_r2c
cannam@95: @findex fftw_mpi_execute_dft_c2r
cannam@95: @findex fftw_mpi_execute_r2r
cannam@95: @example
cannam@95: void fftw_mpi_execute_dft(fftw_plan p, fftw_complex *in, fftw_complex *out);
cannam@95: void fftw_mpi_execute_dft_r2c(fftw_plan p, double *in, fftw_complex *out);
cannam@95: void fftw_mpi_execute_dft_c2r(fftw_plan p, fftw_complex *in, double *out);
cannam@95: void fftw_mpi_execute_r2r(fftw_plan p, double *in, double *out);
cannam@95: @end example
cannam@95:
cannam@95: @cindex alignment
cannam@95: @findex fftw_malloc
cannam@95: These functions have the same restrictions as those of the serial
cannam@95: new-array execute functions. They are @emph{always} safe to apply to
cannam@95: the @emph{same} @code{in} and @code{out} arrays that were used to
cannam@95: create the plan. They can only be applied to new arrarys if those
cannam@95: arrays have the same types, dimensions, in-placeness, and alignment as
cannam@95: the original arrays, where the best way to ensure the same alignment
cannam@95: is to use FFTW's @code{fftw_malloc} and related allocation functions
cannam@95: for all arrays (@pxref{Memory Allocation}). Note that distributed
cannam@95: transposes (@pxref{FFTW MPI Transposes}) use
cannam@95: @code{fftw_mpi_execute_r2r}, since they count as rank-zero r2r plans
cannam@95: from FFTW's perspective.
cannam@95:
cannam@95: @node MPI Data Distribution Functions, MPI Plan Creation, Using MPI Plans, FFTW MPI Reference
cannam@95: @subsection MPI Data Distribution Functions
cannam@95:
cannam@95: @cindex data distribution
cannam@95: As described above (@pxref{MPI Data Distribution}), in order to
cannam@95: allocate your arrays, @emph{before} creating a plan, you must first
cannam@95: call one of the following routines to determine the required
cannam@95: allocation size and the portion of the array locally stored on a given
cannam@95: process. The @code{MPI_Comm} communicator passed here must be
cannam@95: equivalent to the communicator used below for plan creation.
cannam@95:
cannam@95: The basic interface for multidimensional transforms consists of the
cannam@95: functions:
cannam@95:
cannam@95: @findex fftw_mpi_local_size_2d
cannam@95: @findex fftw_mpi_local_size_3d
cannam@95: @findex fftw_mpi_local_size
cannam@95: @findex fftw_mpi_local_size_2d_transposed
cannam@95: @findex fftw_mpi_local_size_3d_transposed
cannam@95: @findex fftw_mpi_local_size_transposed
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_2d(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@95: ptrdiff_t fftw_mpi_local_size_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@95: ptrdiff_t fftw_mpi_local_size(int rnk, const ptrdiff_t *n, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@95:
cannam@95: ptrdiff_t fftw_mpi_local_size_2d_transposed(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: ptrdiff_t fftw_mpi_local_size_3d_transposed(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: ptrdiff_t fftw_mpi_local_size_transposed(int rnk, const ptrdiff_t *n, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: @end example
cannam@95:
cannam@95: These functions return the number of elements to allocate (complex
cannam@95: numbers for DFT/r2c/c2r plans, real numbers for r2r plans), whereas
cannam@95: the @code{local_n0} and @code{local_0_start} return the portion
cannam@95: (@code{local_0_start} to @code{local_0_start + local_n0 - 1}) of the
cannam@95: first dimension of an @ndims{} array that is stored on the local
cannam@95: process. @xref{Basic and advanced distribution interfaces}. For
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT} plans, the @samp{_transposed} variants
cannam@95: are useful in order to also return the local portion of the first
cannam@95: dimension in the @ndimstrans{} transposed output. @xref{Transposed
cannam@95: distributions}. The advanced interface for multidimensional
cannam@95: transforms is:
cannam@95:
cannam@95: @cindex advanced interface
cannam@95: @findex fftw_mpi_local_size_many
cannam@95: @findex fftw_mpi_local_size_many_transposed
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_many(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
cannam@95: ptrdiff_t block0, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@95: ptrdiff_t fftw_mpi_local_size_many_transposed(int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
cannam@95: ptrdiff_t block0, ptrdiff_t block1, MPI_Comm comm,
cannam@95: ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
cannam@95: ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
cannam@95: @end example
cannam@95:
cannam@95: These differ from the basic interface in only two ways. First, they
cannam@95: allow you to specify block sizes @code{block0} and @code{block1} (the
cannam@95: latter for the transposed output); you can pass
cannam@95: @code{FFTW_MPI_DEFAULT_BLOCK} to use FFTW's default block size as in
cannam@95: the basic interface. Second, you can pass a @code{howmany} parameter,
cannam@95: corresponding to the advanced planning interface below: this is for
cannam@95: transforms of contiguous @code{howmany}-tuples of numbers
cannam@95: (@code{howmany = 1} in the basic interface).
cannam@95:
cannam@95: The corresponding basic and advanced routines for one-dimensional
cannam@95: transforms (currently only complex DFTs) are:
cannam@95:
cannam@95: @findex fftw_mpi_local_size_1d
cannam@95: @findex fftw_mpi_local_size_many_1d
cannam@95: @example
cannam@95: ptrdiff_t fftw_mpi_local_size_1d(
cannam@95: ptrdiff_t n0, MPI_Comm comm, int sign, unsigned flags,
cannam@95: ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
cannam@95: ptrdiff_t *local_no, ptrdiff_t *local_o_start);
cannam@95: ptrdiff_t fftw_mpi_local_size_many_1d(
cannam@95: ptrdiff_t n0, ptrdiff_t howmany,
cannam@95: MPI_Comm comm, int sign, unsigned flags,
cannam@95: ptrdiff_t *local_ni, ptrdiff_t *local_i_start,
cannam@95: ptrdiff_t *local_no, ptrdiff_t *local_o_start);
cannam@95: @end example
cannam@95:
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_OUT
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_IN
cannam@95: As above, the return value is the number of elements to allocate
cannam@95: (complex numbers, for complex DFTs). The @code{local_ni} and
cannam@95: @code{local_i_start} arguments return the portion
cannam@95: (@code{local_i_start} to @code{local_i_start + local_ni - 1}) of the
cannam@95: 1d array that is stored on this process for the transform
cannam@95: @emph{input}, and @code{local_no} and @code{local_o_start} are the
cannam@95: corresponding quantities for the input. The @code{sign}
cannam@95: (@code{FFTW_FORWARD} or @code{FFTW_BACKWARD}) and @code{flags} must
cannam@95: match the arguments passed when creating a plan. Although the inputs
cannam@95: and outputs have different data distributions in general, it is
cannam@95: guaranteed that the @emph{output} data distribution of an
cannam@95: @code{FFTW_FORWARD} plan will match the @emph{input} data distribution
cannam@95: of an @code{FFTW_BACKWARD} plan and vice versa; similarly for the
cannam@95: @code{FFTW_MPI_SCRAMBLED_OUT} and @code{FFTW_MPI_SCRAMBLED_IN} flags.
cannam@95: @xref{One-dimensional distributions}.
cannam@95:
cannam@95: @node MPI Plan Creation, MPI Wisdom Communication, MPI Data Distribution Functions, FFTW MPI Reference
cannam@95: @subsection MPI Plan Creation
cannam@95:
cannam@95: @subsubheading Complex-data MPI DFTs
cannam@95:
cannam@95: Plans for complex-data DFTs (@pxref{2d MPI example}) are created by:
cannam@95:
cannam@95: @findex fftw_mpi_plan_dft_1d
cannam@95: @findex fftw_mpi_plan_dft_2d
cannam@95: @findex fftw_mpi_plan_dft_3d
cannam@95: @findex fftw_mpi_plan_dft
cannam@95: @findex fftw_mpi_plan_many_dft
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_dft_1d(ptrdiff_t n0, fftw_complex *in, fftw_complex *out,
cannam@95: MPI_Comm comm, int sign, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: fftw_complex *in, fftw_complex *out,
cannam@95: MPI_Comm comm, int sign, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: fftw_complex *in, fftw_complex *out,
cannam@95: MPI_Comm comm, int sign, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft(int rnk, const ptrdiff_t *n,
cannam@95: fftw_complex *in, fftw_complex *out,
cannam@95: MPI_Comm comm, int sign, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_many_dft(int rnk, const ptrdiff_t *n,
cannam@95: ptrdiff_t howmany, ptrdiff_t block, ptrdiff_t tblock,
cannam@95: fftw_complex *in, fftw_complex *out,
cannam@95: MPI_Comm comm, int sign, unsigned flags);
cannam@95: @end example
cannam@95:
cannam@95: @cindex MPI communicator
cannam@95: @cindex collective function
cannam@95: These are similar to their serial counterparts (@pxref{Complex DFTs})
cannam@95: in specifying the dimensions, sign, and flags of the transform. The
cannam@95: @code{comm} argument gives an MPI communicator that specifies the set
cannam@95: of processes to participate in the transform; plan creation is a
cannam@95: collective function that must be called for all processes in the
cannam@95: communicator. The @code{in} and @code{out} pointers refer only to a
cannam@95: portion of the overall transform data (@pxref{MPI Data Distribution})
cannam@95: as specified by the @samp{local_size} functions in the previous
cannam@95: section. Unless @code{flags} contains @code{FFTW_ESTIMATE}, these
cannam@95: arrays are overwritten during plan creation as for the serial
cannam@95: interface. For multi-dimensional transforms, any dimensions @code{>
cannam@95: 1} are supported; for one-dimensional transforms, only composite
cannam@95: (non-prime) @code{n0} are currently supported (unlike the serial
cannam@95: FFTW). Requesting an unsupported transform size will yield a
cannam@95: @code{NULL} plan. (As in the serial interface, highly composite sizes
cannam@95: generally yield the best performance.)
cannam@95:
cannam@95: @cindex advanced interface
cannam@95: @ctindex FFTW_MPI_DEFAULT_BLOCK
cannam@95: @cindex stride
cannam@95: The advanced-interface @code{fftw_mpi_plan_many_dft} additionally
cannam@95: allows you to specify the block sizes for the first dimension
cannam@95: (@code{block}) of the @ndims{} input data and the first dimension
cannam@95: (@code{tblock}) of the @ndimstrans{} transposed data (at intermediate
cannam@95: steps of the transform, and for the output if
cannam@95: @code{FFTW_TRANSPOSED_OUT} is specified in @code{flags}). These must
cannam@95: be the same block sizes as were passed to the corresponding
cannam@95: @samp{local_size} function; you can pass @code{FFTW_MPI_DEFAULT_BLOCK}
cannam@95: to use FFTW's default block size as in the basic interface. Also, the
cannam@95: @code{howmany} parameter specifies that the transform is of contiguous
cannam@95: @code{howmany}-tuples rather than individual complex numbers; this
cannam@95: corresponds to the same parameter in the serial advanced interface
cannam@95: (@pxref{Advanced Complex DFTs}) with @code{stride = howmany} and
cannam@95: @code{dist = 1}.
cannam@95:
cannam@95: @subsubheading MPI flags
cannam@95:
cannam@95: The @code{flags} can be any of those for the serial FFTW
cannam@95: (@pxref{Planner Flags}), and in addition may include one or more of
cannam@95: the following MPI-specific flags, which improve performance at the
cannam@95: cost of changing the output or input data formats.
cannam@95:
cannam@95: @itemize @bullet
cannam@95:
cannam@95: @item
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_OUT
cannam@95: @ctindex FFTW_MPI_SCRAMBLED_IN
cannam@95: @code{FFTW_MPI_SCRAMBLED_OUT}, @code{FFTW_MPI_SCRAMBLED_IN}: valid for
cannam@95: 1d transforms only, these flags indicate that the output/input of the
cannam@95: transform are in an undocumented ``scrambled'' order. A forward
cannam@95: @code{FFTW_MPI_SCRAMBLED_OUT} transform can be inverted by a backward
cannam@95: @code{FFTW_MPI_SCRAMBLED_IN} (times the usual 1/@i{N} normalization).
cannam@95: @xref{One-dimensional distributions}.
cannam@95:
cannam@95: @item
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_OUT
cannam@95: @ctindex FFTW_MPI_TRANSPOSED_IN
cannam@95: @code{FFTW_MPI_TRANSPOSED_OUT}, @code{FFTW_MPI_TRANSPOSED_IN}: valid
cannam@95: for multidimensional (@code{rnk > 1}) transforms only, these flags
cannam@95: specify that the output or input of an @ndims{} transform is
cannam@95: transposed to @ndimstrans{}. @xref{Transposed distributions}.
cannam@95:
cannam@95: @end itemize
cannam@95:
cannam@95: @subsubheading Real-data MPI DFTs
cannam@95:
cannam@95: @cindex r2c
cannam@95: Plans for real-input/output (r2c/c2r) DFTs (@pxref{Multi-dimensional
cannam@95: MPI DFTs of Real Data}) are created by:
cannam@95:
cannam@95: @findex fftw_mpi_plan_dft_r2c_2d
cannam@95: @findex fftw_mpi_plan_dft_r2c_2d
cannam@95: @findex fftw_mpi_plan_dft_r2c_3d
cannam@95: @findex fftw_mpi_plan_dft_r2c
cannam@95: @findex fftw_mpi_plan_dft_c2r_2d
cannam@95: @findex fftw_mpi_plan_dft_c2r_2d
cannam@95: @findex fftw_mpi_plan_dft_c2r_3d
cannam@95: @findex fftw_mpi_plan_dft_c2r
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_dft_r2c_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: double *in, fftw_complex *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_r2c_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: double *in, fftw_complex *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_r2c_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: double *in, fftw_complex *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_r2c(int rnk, const ptrdiff_t *n,
cannam@95: double *in, fftw_complex *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_c2r_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: fftw_complex *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_c2r_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: fftw_complex *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_c2r_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: fftw_complex *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_dft_c2r(int rnk, const ptrdiff_t *n,
cannam@95: fftw_complex *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: @end example
cannam@95:
cannam@95: Similar to the serial interface (@pxref{Real-data DFTs}), these
cannam@95: transform logically @ndims{} real data to/from @ndimshalf{} complex
cannam@95: data, representing the non-redundant half of the conjugate-symmetry
cannam@95: output of a real-input DFT (@pxref{Multi-dimensional Transforms}).
cannam@95: However, the real array must be stored within a padded @ndimspad{}
cannam@95: array (much like the in-place serial r2c transforms, but here for
cannam@95: out-of-place transforms as well). Currently, only multi-dimensional
cannam@95: (@code{rnk > 1}) r2c/c2r transforms are supported (requesting a plan
cannam@95: for @code{rnk = 1} will yield @code{NULL}). As explained above
cannam@95: (@pxref{Multi-dimensional MPI DFTs of Real Data}), the data
cannam@95: distribution of both the real and complex arrays is given by the
cannam@95: @samp{local_size} function called for the dimensions of the
cannam@95: @emph{complex} array. Similar to the other planning functions, the
cannam@95: input and output arrays are overwritten when the plan is created
cannam@95: except in @code{FFTW_ESTIMATE} mode.
cannam@95:
cannam@95: As for the complex DFTs above, there is an advance interface that
cannam@95: allows you to manually specify block sizes and to transform contiguous
cannam@95: @code{howmany}-tuples of real/complex numbers:
cannam@95:
cannam@95: @findex fftw_mpi_plan_many_dft_r2c
cannam@95: @findex fftw_mpi_plan_many_dft_c2r
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_many_dft_r2c
cannam@95: (int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
cannam@95: ptrdiff_t iblock, ptrdiff_t oblock,
cannam@95: double *in, fftw_complex *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_many_dft_c2r
cannam@95: (int rnk, const ptrdiff_t *n, ptrdiff_t howmany,
cannam@95: ptrdiff_t iblock, ptrdiff_t oblock,
cannam@95: fftw_complex *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: @end example
cannam@95:
cannam@95: @subsubheading MPI r2r transforms
cannam@95:
cannam@95: @cindex r2r
cannam@95: There are corresponding plan-creation routines for r2r
cannam@95: transforms (@pxref{More DFTs of Real Data}), currently supporting
cannam@95: multidimensional (@code{rnk > 1}) transforms only (@code{rnk = 1} will
cannam@95: yield a @code{NULL} plan):
cannam@95:
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_r2r_2d(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm,
cannam@95: fftw_r2r_kind kind0, fftw_r2r_kind kind1,
cannam@95: unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_r2r_3d(ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm,
cannam@95: fftw_r2r_kind kind0, fftw_r2r_kind kind1, fftw_r2r_kind kind2,
cannam@95: unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_r2r(int rnk, const ptrdiff_t *n,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm, const fftw_r2r_kind *kind,
cannam@95: unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_many_r2r(int rnk, const ptrdiff_t *n,
cannam@95: ptrdiff_t iblock, ptrdiff_t oblock,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm, const fftw_r2r_kind *kind,
cannam@95: unsigned flags);
cannam@95: @end example
cannam@95:
cannam@95: The parameters are much the same as for the complex DFTs above, except
cannam@95: that the arrays are of real numbers (and hence the outputs of the
cannam@95: @samp{local_size} data-distribution functions should be interpreted as
cannam@95: counts of real rather than complex numbers). Also, the @code{kind}
cannam@95: parameters specify the r2r kinds along each dimension as for the
cannam@95: serial interface (@pxref{Real-to-Real Transform Kinds}). @xref{Other
cannam@95: Multi-dimensional Real-data MPI Transforms}.
cannam@95:
cannam@95: @subsubheading MPI transposition
cannam@95: @cindex transpose
cannam@95:
cannam@95: FFTW also provides routines to plan a transpose of a distributed
cannam@95: @code{n0} by @code{n1} array of real numbers, or an array of
cannam@95: @code{howmany}-tuples of real numbers with specified block sizes
cannam@95: (@pxref{FFTW MPI Transposes}):
cannam@95:
cannam@95: @findex fftw_mpi_plan_transpose
cannam@95: @findex fftw_mpi_plan_many_transpose
cannam@95: @example
cannam@95: fftw_plan fftw_mpi_plan_transpose(ptrdiff_t n0, ptrdiff_t n1,
cannam@95: double *in, double *out,
cannam@95: MPI_Comm comm, unsigned flags);
cannam@95: fftw_plan fftw_mpi_plan_many_transpose
cannam@95: (ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t howmany,
cannam@95: ptrdiff_t block0, ptrdiff_t block1,
cannam@95: double *in, double *out, MPI_Comm comm, unsigned flags);
cannam@95: @end example
cannam@95:
cannam@95: @cindex new-array execution
cannam@95: @findex fftw_mpi_execute_r2r
cannam@95: These plans are used with the @code{fftw_mpi_execute_r2r} new-array
cannam@95: execute function (@pxref{Using MPI Plans }), since they count as (rank
cannam@95: zero) r2r plans from FFTW's perspective.
cannam@95:
cannam@95: @node MPI Wisdom Communication, , MPI Plan Creation, FFTW MPI Reference
cannam@95: @subsection MPI Wisdom Communication
cannam@95:
cannam@95: To facilitate synchronizing wisdom among the different MPI processes,
cannam@95: we provide two functions:
cannam@95:
cannam@95: @findex fftw_mpi_gather_wisdom
cannam@95: @findex fftw_mpi_broadcast_wisdom
cannam@95: @example
cannam@95: void fftw_mpi_gather_wisdom(MPI_Comm comm);
cannam@95: void fftw_mpi_broadcast_wisdom(MPI_Comm comm);
cannam@95: @end example
cannam@95:
cannam@95: The @code{fftw_mpi_gather_wisdom} function gathers all wisdom in the
cannam@95: given communicator @code{comm} to the process of rank 0 in the
cannam@95: communicator: that process obtains the union of all wisdom on all the
cannam@95: processes. As a side effect, some other processes will gain
cannam@95: additional wisdom from other processes, but only process 0 will gain
cannam@95: the complete union.
cannam@95:
cannam@95: The @code{fftw_mpi_broadcast_wisdom} does the reverse: it exports
cannam@95: wisdom from process 0 in @code{comm} to all other processes in the
cannam@95: communicator, replacing any wisdom they currently have.
cannam@95:
cannam@95: @xref{FFTW MPI Wisdom}.
cannam@95:
cannam@95: @c ------------------------------------------------------------
cannam@95: @node FFTW MPI Fortran Interface, , FFTW MPI Reference, Distributed-memory FFTW with MPI
cannam@95: @section FFTW MPI Fortran Interface
cannam@95: @cindex Fortran interface
cannam@95:
cannam@95: @cindex iso_c_binding
cannam@95: The FFTW MPI interface is callable from modern Fortran compilers
cannam@95: supporting the Fortran 2003 @code{iso_c_binding} standard for calling
cannam@95: C functions. As described in @ref{Calling FFTW from Modern Fortran},
cannam@95: this means that you can directly call FFTW's C interface from Fortran
cannam@95: with only minor changes in syntax. There are, however, a few things
cannam@95: specific to the MPI interface to keep in mind:
cannam@95:
cannam@95: @itemize @bullet
cannam@95:
cannam@95: @item
cannam@95: Instead of including @code{fftw3.f03} as in @ref{Overview of Fortran
cannam@95: interface }, you should @code{include 'fftw3-mpi.f03'} (after
cannam@95: @code{use, intrinsic :: iso_c_binding} as before). The
cannam@95: @code{fftw3-mpi.f03} file includes @code{fftw3.f03}, so you should
cannam@95: @emph{not} @code{include} them both yourself. (You will also want to
cannam@95: include the MPI header file, usually via @code{include 'mpif.h'} or
cannam@95: similar, although though this is not needed by @code{fftw3-mpi.f03}
cannam@95: @i{per se}.) (To use the @samp{fftwl_} @code{long double} extended-precision routines in supporting compilers, you should include @code{fftw3f-mpi.f03} in @emph{addition} to @code{fftw3-mpi.f03}. @xref{Extended and quadruple precision in Fortran}.)
cannam@95:
cannam@95: @item
cannam@95: Because of the different storage conventions between C and Fortran,
cannam@95: you reverse the order of your array dimensions when passing them to
cannam@95: FFTW (@pxref{Reversing array dimensions}). This is merely a
cannam@95: difference in notation and incurs no performance overhead. However,
cannam@95: it means that, whereas in C the @emph{first} dimension is distributed,
cannam@95: in Fortran the @emph{last} dimension of your array is distributed.
cannam@95:
cannam@95: @item
cannam@95: @cindex MPI communicator
cannam@95: In Fortran, communicators are stored as @code{integer} types; there is
cannam@95: no @code{MPI_Comm} type, nor is there any way to access a C
cannam@95: @code{MPI_Comm}. Fortunately, this is taken care of for you by the
cannam@95: FFTW Fortran interface: whenever the C interface expects an
cannam@95: @code{MPI_Comm} type, you should pass the Fortran communicator as an
cannam@95: @code{integer}.@footnote{Technically, this is because you aren't
cannam@95: actually calling the C functions directly. You are calling wrapper
cannam@95: functions that translate the communicator with @code{MPI_Comm_f2c}
cannam@95: before calling the ordinary C interface. This is all done
cannam@95: transparently, however, since the @code{fftw3-mpi.f03} interface file
cannam@95: renames the wrappers so that they are called in Fortran with the same
cannam@95: names as the C interface functions.}
cannam@95:
cannam@95: @item
cannam@95: Because you need to call the @samp{local_size} function to find out
cannam@95: how much space to allocate, and this may be @emph{larger} than the
cannam@95: local portion of the array (@pxref{MPI Data Distribution}), you should
cannam@95: @emph{always} allocate your arrays dynamically using FFTW's allocation
cannam@95: routines as described in @ref{Allocating aligned memory in Fortran}.
cannam@95: (Coincidentally, this also provides the best performance by
cannam@95: guaranteeding proper data alignment.)
cannam@95:
cannam@95: @item
cannam@95: Because all sizes in the MPI FFTW interface are declared as
cannam@95: @code{ptrdiff_t} in C, you should use @code{integer(C_INTPTR_T)} in
cannam@95: Fortran (@pxref{FFTW Fortran type reference}).
cannam@95:
cannam@95: @item
cannam@95: @findex fftw_execute_dft
cannam@95: @findex fftw_mpi_execute_dft
cannam@95: @cindex new-array execution
cannam@95: In Fortran, because of the language semantics, we generally recommend
cannam@95: using the new-array execute functions for all plans, even in the
cannam@95: common case where you are executing the plan on the same arrays for
cannam@95: which the plan was created (@pxref{Plan execution in Fortran}).
cannam@95: However, note that in the MPI interface these functions are changed:
cannam@95: @code{fftw_execute_dft} becomes @code{fftw_mpi_execute_dft},
cannam@95: etcetera. @xref{Using MPI Plans}.
cannam@95:
cannam@95: @end itemize
cannam@95:
cannam@95: For example, here is a Fortran code snippet to perform a distributed
cannam@95: @twodims{L,M} complex DFT in-place. (This assumes you have already
cannam@95: initialized MPI with @code{MPI_init} and have also performed
cannam@95: @code{call fftw_mpi_init}.)
cannam@95:
cannam@95: @example
cannam@95: use, intrinsic :: iso_c_binding
cannam@95: include 'fftw3-mpi.f03'
cannam@95: integer(C_INTPTR_T), parameter :: L = ...
cannam@95: integer(C_INTPTR_T), parameter :: M = ...
cannam@95: type(C_PTR) :: plan, cdata
cannam@95: complex(C_DOUBLE_COMPLEX), pointer :: data(:,:)
cannam@95: integer(C_INTPTR_T) :: i, j, alloc_local, local_M, local_j_offset
cannam@95:
cannam@95: ! @r{get local data size and allocate (note dimension reversal)}
cannam@95: alloc_local = fftw_mpi_local_size_2d(M, L, MPI_COMM_WORLD, &
cannam@95: local_M, local_j_offset)
cannam@95: cdata = fftw_alloc_complex(alloc_local)
cannam@95: call c_f_pointer(cdata, data, [L,local_M])
cannam@95:
cannam@95: ! @r{create MPI plan for in-place forward DFT (note dimension reversal)}
cannam@95: plan = fftw_mpi_plan_dft_2d(M, L, data, data, MPI_COMM_WORLD, &
cannam@95: FFTW_FORWARD, FFTW_MEASURE)
cannam@95:
cannam@95: ! @r{initialize data to some function} my_function(i,j)
cannam@95: do j = 1, local_M
cannam@95: do i = 1, L
cannam@95: data(i, j) = my_function(i, j + local_j_offset)
cannam@95: end do
cannam@95: end do
cannam@95:
cannam@95: ! @r{compute transform (as many times as desired)}
cannam@95: call fftw_mpi_execute_dft(plan, data, data)
cannam@95:
cannam@95: call fftw_destroy_plan(plan)
cannam@95: call fftw_free(cdata)
cannam@95: @end example
cannam@95:
cannam@95: Note that when we called @code{fftw_mpi_local_size_2d} and
cannam@95: @code{fftw_mpi_plan_dft_2d} with the dimensions in reversed order,
cannam@95: since a @twodims{L,M} Fortran array is viewed by FFTW in C as a
cannam@95: @twodims{M, L} array. This means that the array was distributed over
cannam@95: the @code{M} dimension, the local portion of which is a
cannam@95: @twodims{L,local_M} array in Fortran. (You must @emph{not} use an
cannam@95: @code{allocate} statement to allocate an @twodims{L,local_M} array,
cannam@95: however; you must allocate @code{alloc_local} complex numbers, which
cannam@95: may be greater than @code{L * local_M}, in order to reserve space for
cannam@95: intermediate steps of the transform.) Finally, we mention that
cannam@95: because C's array indices are zero-based, the @code{local_j_offset}
cannam@95: argument can conveniently be interpreted as an offset in the 1-based
cannam@95: @code{j} index (rather than as a starting index as in C).
cannam@95:
cannam@95: If instead you had used the @code{ior(FFTW_MEASURE,
cannam@95: FFTW_MPI_TRANSPOSED_OUT)} flag, the output of the transform would be a
cannam@95: transposed @twodims{M,local_L} array, associated with the @emph{same}
cannam@95: @code{cdata} allocation (since the transform is in-place), and which
cannam@95: you could declare with:
cannam@95:
cannam@95: @example
cannam@95: complex(C_DOUBLE_COMPLEX), pointer :: tdata(:,:)
cannam@95: ...
cannam@95: call c_f_pointer(cdata, tdata, [M,local_L])
cannam@95: @end example
cannam@95:
cannam@95: where @code{local_L} would have been obtained by changing the
cannam@95: @code{fftw_mpi_local_size_2d} call to:
cannam@95:
cannam@95: @example
cannam@95: alloc_local = fftw_mpi_local_size_2d_transposed(M, L, MPI_COMM_WORLD, &
cannam@95: local_M, local_j_offset, local_L, local_i_offset)
cannam@95: @end example