Documentation

A 2D processor grid.

ProcGrid attempts to create a near optimal 2D grid of P processes for an MxN grid of tiles. The size of the grid is optimized such that the total communication time required for SUMMA and the number of unused processes is minimized. The total communication time of SUMMA is given by:

$T = \frac{MK}{P_{\rm{row}}} \left(\alpha + \frac{mk}{\beta}\right) \left((P/P_{\rm{row}}) - 1\right) + \frac{KN}{P/P_{\rm{row}}} \left(\alpha + \frac{kn}{\beta}\right) \left(P_{\rm{row}} - 1\right)$

where $P_{\rm{row}}$ is the number of process rows; $M$ , $N$ , and $K$ are the number of tile rows and columns in a matrix product with average tiles sizes of $m$ , $n$ , and $k$ , respectively; $P$ is the number or available processes; $\alpha$ is the message latency; and $\beta$ is the message data rate. If we evaluate $dT/dP_{\rm{row}} = 0$ and assume that $\alpha \approx 0$ , the expression simplifies to:

$Nn(2 P_{\rm{row}}^4 - P_{\rm{row}}^3) + Mm(P P_{\rm{row}} - P^2) = 0$

where the positive, real root of $P_{\rm{row}}$ give the optimal optimal communication time.

Definition at line 58 of file proc_grid.h.

Public Types
typedef uint_fast32_t	size_type

Public Member Functions
	ProcGrid ()
	Default constructor. More...

	ProcGrid (World &world, const size_type rows, const size_type cols, const std::size_t row_size, const std::size_t col_size)
	Construct a process grid. More...

	ProcGrid (const ProcGrid &other)
	Copy constructor. More...

ProcGrid &	operator= (const ProcGrid &other)
	Copy assignment operator. More...

size_type	rows () const
	Element row count accessor. More...

size_type	cols () const
	Element column count accessor. More...

size_type	size () const
	Element count accessor. More...

size_type	local_rows () const
	Local element row count accessor. More...

size_type	local_cols () const
	Local element column count accessor. More...

size_type	local_size () const
	Local element count accessor. More...

ProcessID	rank_row () const
	Rank row accessor. More...

ProcessID	rank_col () const
	Rank row accessor. More...

size_type	proc_rows () const
	Process row count accessor. More...

size_type	proc_cols () const
	Process column count accessor. More...

size_type	proc_size () const
	Process grid size accessor. More...

madness::Group	make_row_group (const madness::DistributedID &did) const
	Construct a row group. More...

madness::Group	make_col_group (const madness::DistributedID &did) const
	Construct a column group. More...

ProcessID	map_row (const size_type row) const
	Map a row to the process in this process's column. More...

ProcessID	map_col (const size_type col) const
	Map a column to the process in this process's row. More...

std::shared_ptr< Pmap >	make_pmap () const
	Construct a cyclic process. More...

std::shared_ptr< Pmap >	make_col_phase_pmap (const size_type rows) const
	Construct column phased a cyclic process. More...

std::shared_ptr< Pmap >	make_row_phase_pmap (const size_type cols) const
	Construct row phased a cyclic process. More...

Member Typedef Documentation

◆ size_type

typedef uint_fast32_t TiledArray::detail::ProcGrid::size_type

Definition at line 60 of file proc_grid.h.

Constructor & Destructor Documentation

◆ ProcGrid() [1/3]

TiledArray::detail::ProcGrid::ProcGrid ( )

inline

Default constructor.

All sizes are initialized to zero.

Definition at line 253 of file proc_grid.h.

◆ ProcGrid() [2/3]

TiledArray::detail::ProcGrid::ProcGrid	(	World &	world,
		const size_type	rows,
		const size_type	cols,
		const std::size_t	row_size,
		const std::size_t	col_size
	)

inline

Construct a process grid.

Parameters

world	The world where the process grid will live
rows	The number of tile rows
cols	The number of tile columns
row_size	The number of element rows
col_size	The number of element columns

Definition at line 277 of file proc_grid.h.

◆ ProcGrid() [3/3]

TiledArray::detail::ProcGrid::ProcGrid ( const ProcGrid & other )

inline

Copy constructor.

Parameters

other The other process grid to be copied

Definition at line 349 of file proc_grid.h.

Member Function Documentation

◆ cols()

size_type TiledArray::detail::ProcGrid::cols ( ) const

inline

Element column count accessor.

Returns: The number of element columns

Definition at line 391 of file proc_grid.h.

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◆ local_cols()

size_type TiledArray::detail::ProcGrid::local_cols ( ) const

inline

Local element column count accessor.

Returns: The number of element columns

Definition at line 406 of file proc_grid.h.

◆ local_rows()

size_type TiledArray::detail::ProcGrid::local_rows ( ) const

inline

Local element row count accessor.

Returns: The number of element rows

Definition at line 401 of file proc_grid.h.

◆ local_size()

size_type TiledArray::detail::ProcGrid::local_size ( ) const

inline

Local element count accessor.

Returns: The number of elements assigned to this process

Definition at line 411 of file proc_grid.h.

◆ make_col_group()

madness::Group TiledArray::detail::ProcGrid::make_col_group ( const madness::DistributedID & did ) const

inline

Construct a column group.

Parameters

did	The distributed id for the result group

Returns: A Group object that includes all processes in rank_col

Definition at line 469 of file proc_grid.h.

◆ make_col_phase_pmap()

std::shared_ptr<Pmap> TiledArray::detail::ProcGrid::make_col_phase_pmap ( const size_type rows ) const

inline

Construct column phased a cyclic process.

Construct a cyclic process map where the column phase of the process matches that of this process grid.

Parameters

rows	The number of rows in the process map

Returns: Cyclic process map with matching column phase

Definition at line 528 of file proc_grid.h.

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◆ make_pmap()

std::shared_ptr<Pmap> TiledArray::detail::ProcGrid::make_pmap ( ) const

inline

Construct a cyclic process.

Construct a cyclic process map with the same phase as the process grid.

Returns: Cyclic process map

Definition at line 515 of file proc_grid.h.

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◆ make_row_group()

madness::Group TiledArray::detail::ProcGrid::make_row_group ( const madness::DistributedID & did ) const

inline

Construct a row group.

Parameters

did	The distributed id for the result group

Returns: A Group object that includes all processes in rank_row

Definition at line 443 of file proc_grid.h.

◆ make_row_phase_pmap()

std::shared_ptr<Pmap> TiledArray::detail::ProcGrid::make_row_phase_pmap ( const size_type cols ) const

inline

Construct row phased a cyclic process.

Construct a cyclic process map where the column phase of the process matches that of this process grid.

Parameters

cols	The number of columns in the process map

Returns: Cyclic process map with matching column phase

Definition at line 541 of file proc_grid.h.

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◆ map_col()

ProcessID TiledArray::detail::ProcGrid::map_col ( const size_type col ) const

inline

Map a column to the process in this process's row.

Parameters

col	The column to be mapped

Returns: The process the corresponds to the process coordinate (rank_row,col)

Definition at line 506 of file proc_grid.h.

◆ map_row()

ProcessID TiledArray::detail::ProcGrid::map_row ( const size_type row ) const

inline

Map a row to the process in this process's column.

Parameters

row	The row to be mapped

Returns: The process the corresponds to the process coordinate (row,rank_col)

Definition at line 496 of file proc_grid.h.

◆ operator=()

ProcGrid& TiledArray::detail::ProcGrid::operator= ( const ProcGrid & other )

inline

Copy assignment operator.

Parameters

other The other process grid to be copied

Definition at line 366 of file proc_grid.h.

◆ proc_cols()

size_type TiledArray::detail::ProcGrid::proc_cols ( ) const

inline

Process column count accessor.

Returns: The number of columns in the process grid

Definition at line 431 of file proc_grid.h.

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◆ proc_rows()

size_type TiledArray::detail::ProcGrid::proc_rows ( ) const

inline

Process row count accessor.

Returns: The number of rows in the process grid

Definition at line 426 of file proc_grid.h.

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◆ proc_size()

size_type TiledArray::detail::ProcGrid::proc_size ( ) const

inline

Process grid size accessor.

Returns: The number of processes included in the process grid (may be less than the number of process in world).

Definition at line 437 of file proc_grid.h.

◆ rank_col()

ProcessID TiledArray::detail::ProcGrid::rank_col ( ) const

inline

Rank row accessor.

Returns: The column of this process in the process grid

Definition at line 421 of file proc_grid.h.

◆ rank_row()

ProcessID TiledArray::detail::ProcGrid::rank_row ( ) const

inline

Rank row accessor.

Returns: The row of this process in the process grid

Definition at line 416 of file proc_grid.h.

◆ rows()

size_type TiledArray::detail::ProcGrid::rows ( ) const

inline

Element row count accessor.

Returns: The number of element rows

Definition at line 386 of file proc_grid.h.

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◆ size()

size_type TiledArray::detail::ProcGrid::size ( ) const

inline

Element count accessor.

Returns: The total number of elements

Definition at line 396 of file proc_grid.h.

The documentation for this class was generated from the following file:

TiledArray/proc_grid.h

Documentation

Public Types

Public Member Functions

Member Typedef Documentation

◆ size_type

Constructor & Destructor Documentation

◆ ProcGrid() [1/3]

◆ ProcGrid() [2/3]

◆ ProcGrid() [3/3]

Member Function Documentation

◆ cols()

◆ local_cols()

◆ local_rows()

◆ local_size()

◆ make_col_group()

◆ make_col_phase_pmap()

◆ make_pmap()

◆ make_row_group()

◆ make_row_phase_pmap()

◆ map_col()

◆ map_row()

◆ operator=()

◆ proc_cols()

◆ proc_rows()

◆ proc_size()

◆ rank_col()

◆ rank_row()

◆ rows()

◆ size()