dg::RealMPIGrid< real_type, Nd > Struct Template Reference

The simplest implementation of aRealMPITopology3d. More...

Inheritance diagram for dg::RealMPIGrid< real_type, Nd >:

Public Member Functions
	RealMPIGrid ()=default
	construct an empty grid this leaves the access functions undefined
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, unsigned n, unsigned N, MPI_Comm comm)
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, unsigned n, unsigned Nx, dg::bc bcx, MPI_Comm comm)
	1D grid
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, MPI_Comm comm)
	Construct with equal polynomial coefficients.
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, dg::bc bcx, dg::bc bcy, MPI_Comm comm)
	Construct with equal polynomial coefficients.
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, real_type y0, real_type y1, real_type z0, real_type z1, unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, MPI_Comm comm)
	Construct with equal polynomial coefficients.
template<size_t Md = Nd>
	RealMPIGrid (real_type x0, real_type x1, real_type y0, real_type y1, real_type z0, real_type z1, unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, dg::bc bcx, dg::bc bcy, dg::bc bcz, MPI_Comm comm)
	Construct with equal polynomial coefficients.
	RealMPIGrid (const std::array< RealMPIGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.
template<class ... Grid1ds>
	RealMPIGrid (const RealMPIGrid< real_type, 1 > &g0, const Grid1ds &...gs)
	Construct from given 1d grids Equivalent to RealMPIGrid( std::array{g0,gs...})
	RealMPIGrid (std::array< real_type, Nd > p, std::array< real_type, Nd > q, std::array< unsigned, Nd > n, std::array< unsigned, Nd > N, std::array< dg::bc, Nd > bcs, std::array< MPI_Comm, Nd > comms)
	Construct a topology directly from points and dimensions.
	RealMPIGrid (const aRealMPITopology< real_type, Nd > &src)
Public Member Functions inherited from dg::aRealMPITopology< real_type, Nd >
unsigned	shape (unsigned u=0) const
	$n_u{N}_u$ the total number of points of an axis
host_vector	abscissas (unsigned u=0) const
	Get the grid abscissas of the u axis.
host_vector	weights (unsigned u=0) const
	Get the weights of the u axis.
std::array< unsigned, Nd >	get_shape () const
	$n_u{N}_u$ the total number of points of an axis
std::array< host_vector, Nd >	get_abscissas () const
	Construct abscissas for all axes.
std::array< host_vector, Nd >	get_weights () const
	Construct weights for all axes.
std::array< real_type, Nd >	get_p () const
	Get left boundary point $\overrightarrow{p}$.
std::array< real_type, Nd >	get_q () const
	Get right boundary point $\overrightarrow{q}$.
std::array< real_type, Nd >	get_l () const
	Get grid length $l_u=q_u-p_u$ for all axes.
std::array< real_type, Nd >	get_h () const
	Get grid constant $h_u=\frac{q_u-p_u}{N_u}$ for all axes.
std::array< unsigned, Nd >	get_N () const
	Get number of cells $N_u$ for all axes.
std::array< unsigned, Nd >	get_n () const
	Get number of polynomial coefficients $n_u$ for all axes.
std::array< dg::bc, Nd >	get_bc () const
	Get boundary condition $b_u$ for all axes.
std::array< MPI_Comm, Nd >	get_comms () const
	Get 1d Cartesian communicator $c_u$ for all axes.
real_type	p (unsigned u=0) const
	Get left boundary point $p_u$ for axis u.
real_type	q (unsigned u=0) const
	Get right boundary point $q_u$ for axis u.
real_type	h (unsigned u=0) const
	Get grid constant $h_u=\frac{q_u-p_u}{N_u}$ for axis u.
real_type	l (unsigned u=0) const
	Get grid length $l_u=q_u-p_u$ for axis u.
unsigned	n (unsigned u=0) const
	Get number of polynomial coefficients $n_u$ for axis u.
unsigned	N (unsigned u=0) const
	Get number of cells $N_u$ for axis u.
dg::bc	bc (unsigned u=0) const
	Get boundary condition $b_u$ for axis u.
MPI_Comm	comm (unsigned u) const
	Get 1d Cartesian communicator $c_u$ for axis u.
template<size_t Md = Nd>
std::enable_if_t< Md==1, MPI_Comm >	comm () const
	Equivalent to comm(0)
MPI_Comm	communicator () const
	Return Nd dimensional MPI cartesian communicator that is used in this grid.
template<size_t Md = Nd>
std::enable_if_t<(Md >=2), MPI_Comm >	get_perp_comm () const
	MPI Cartesian communicator in the first two dimensions (x and y)
RealMPIGrid< real_type, 1 >	grid (unsigned u) const
	Get axis u as a 1d grid.
RealMPIGrid< real_type, 1 >	axis (unsigned u) const
	An alias for "grid".
const RealGrid< real_type, Nd > &	local () const
	The local grid as a shared memory grid.
const RealGrid< real_type, Nd > &	global () const
	The global grid as a shared memory grid.
template<size_t Md = Nd>
real_type	x0 () const
	Equivalent to p(0)
template<size_t Md = Nd>
real_type	x1 () const
	Equivalent to p(1)
template<size_t Md = Nd>
real_type	y0 () const
	Equivalent to p(2)
template<size_t Md = Nd>
real_type	y1 () const
	Equivalent to q(0)
template<size_t Md = Nd>
real_type	z0 () const
	Equivalent to q(1)
template<size_t Md = Nd>
real_type	z1 () const
	Equivalent to q(2)
template<size_t Md = Nd>
real_type	lx () const
	Equivalent to l(0)
template<size_t Md = Nd>
real_type	ly () const
	Equivalent to l(1)
template<size_t Md = Nd>
real_type	lz () const
	Equivalent to l(2)
template<size_t Md = Nd>
real_type	hx () const
	Equivalent to h(0)
template<size_t Md = Nd>
real_type	hy () const
	Equivalent to h(1)
template<size_t Md = Nd>
real_type	hz () const
	Equivalent to h(2)
template<size_t Md = Nd>
unsigned	nx () const
	Equivalent to n(0)
template<size_t Md = Nd>
unsigned	ny () const
	Equivalent to n(1)
template<size_t Md = Nd>
unsigned	nz () const
	Equivalent to n(2)
template<size_t Md = Nd>
unsigned	Nx () const
	Equivalent to N(0)
template<size_t Md = Nd>
unsigned	Ny () const
	Equivalent to N(1)
template<size_t Md = Nd>
unsigned	Nz () const
	Equivalent to N(2)
template<size_t Md = Nd>
dg::bc	bcx () const
	Equivalent to bc(0)
template<size_t Md = Nd>
dg::bc	bcy () const
	Equivalent to bc(1)
template<size_t Md = Nd>
dg::bc	bcz () const
	Equivalent to bc(2)
template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gx () const
	Equivalent to grid(0)
template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gy () const
	Equivalent to grid(1)
template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gz () const
	Equivalent to grid(2)
template<size_t Md = Nd>
std::enable_if_t<(Md >=2), void >	multiplyCellNumbers (real_type fx, real_type fy)
	Multiply the number of cells in the first two dimensions with a given factor.
template<size_t Md = Nd>
std::enable_if_t<(Md==1), void >	set (unsigned new_n, unsigned new_Nx)
	Set n and N in a 1-dimensional grid.
template<size_t Md = Nd>
std::enable_if_t<(Md==2), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny)
	Set n and N in a 2-dimensional grid.
template<size_t Md = Nd>
std::enable_if_t<(Md==3), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny, unsigned new_Nz)
	Set n and N in a 3-dimensional grid.
void	set (unsigned new_n, std::array< unsigned, Nd > new_N)
	Same as set( {new_n, new_n,...}, new_N);
void	set_axis (unsigned coord, unsigned new_n, unsigned new_N)
	Set n and N for axis coord.
void	set (std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N)
	Set the number of polynomials and cells.
void	set_pq (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q)
	Reset the boundaries of the grid.
void	set_bcs (std::array< dg::bc, Nd > new_bcs)
	Reset the boundary conditions of the grid.
unsigned	size () const
	The total global number of points.
unsigned	local_size () const
	The total local number of points.
void	display (std::ostream &os=std::cout) const
	Display global and local grid paramters.
template<size_t Md = Nd>
std::enable_if_t<(Md==1), bool >	contains (real_type x) const
	Check if the grid contains a point.
template<class Vector >
bool	contains (const Vector &x) const
	Check if the grid contains a point.
bool	local2globalIdx (int localIdx, int rank, int &globalIdx) const
	Convert the index of a local vector and the rank of the containing process to a global index.
bool	global2localIdx (int globalIdx, int &localIdx, int &rank) const
	Convert the global index of a vector to a local index and the rank of the containing process.
std::array< unsigned, Nd >	start () const
	The global start coordinate in C-order of dg::file::MPINcHyperslab that the local grid represents.
std::array< unsigned, Nd >	count () const
	Count vector in C-order for dg::file::MPINcHyperslab.

Additional Inherited Members
Public Types inherited from dg::aRealMPITopology< real_type, Nd >
using	value_type = real_type
	value type of abscissas and weights
using	host_vector = MPI_Vector<thrust::host_vector<real_type>>
using	host_grid = RealMPIGrid<real_type, Nd>
Static Public Member Functions inherited from dg::aRealMPITopology< real_type, Nd >
static constexpr unsigned	ndim ()
	Dimensionality == Nd.
Protected Member Functions inherited from dg::aRealMPITopology< real_type, Nd >
	~aRealMPITopology ()=default
	disallow deletion through base class pointer
	aRealMPITopology ()=default
	default constructor
	aRealMPITopology (std::array< real_type, Nd > p, std::array< real_type, Nd > q, std::array< unsigned, Nd > n, std::array< unsigned, Nd > N, std::array< dg::bc, Nd > bcs, std::array< MPI_Comm, Nd > comms)
	Construct a topology directly from points and dimensions.
	aRealMPITopology (const std::array< RealMPIGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.
	aRealMPITopology (const aRealMPITopology &src)=default
aRealMPITopology &	operator= (const aRealMPITopology &src)=default

Detailed Description

template<class real_type, size_t Nd>
struct dg::RealMPIGrid< real_type, Nd >

The simplest implementation of aRealMPITopology3d.

        // This code snippet demonstrates how to discretize and compute the norm of a
        // function on both shared and distributed memory systems
#ifdef WITH_MPI
        // In an MPI environment define a 2d Cartesian communicator
        MPI_Comm comm2d = dg::mpi_cart_create( MPI_COMM_WORLD, {0,0}, {1,1});
#endif
        // create a grid of the domain [0,2]x[0,2] with 20 cells in x and y and
        // 3 polynomial coefficients
        dg::x::Grid2d g2d( 0, 2, 0, 2, 3, 20, 20
#ifdef WITH_MPI
        , comm2d // in MPI distribute among processes
#endif
        );
 
        // define the function to integrate
        const double amp = 2.;
        auto function = [=] (double x, double y){
            return amp*exp(x)*exp(y);
        };
 
        // create the Gaussian weights (volume form) for the integration
        const dg::x::DVec w2d = dg::create::weights( g2d);
 
        // discretize the function on the grid
        const dg::x::DVec vec = dg::evaluate( function, g2d);
 
        // now compute the scalar product (the L2 norm)
        double square_norm = dg::blas2::dot( vec, w2d, vec);
 
        // norm is now (or at least converges to): (e^4-1)^2
        CHECK( fabs( square_norm - (exp(4)-1)*(exp(4)-1)) < 1e-6);

Constructor & Destructor Documentation

RealMPIGrid() [1/11]

template<class real_type , size_t Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( )

default

construct an empty grid this leaves the access functions undefined

RealMPIGrid() [2/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, unsigned n, unsigned N, MPI_Comm comm )

inline

RealMPIGrid() [3/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, unsigned n, unsigned Nx, dg::bc bcx, MPI_Comm comm )

inline

1D grid

Parameters

x0	left boundary
x1	right boundary
n	# of polynomial coefficients (1<=n<=20)
Nx	# of cells
bcx	boundary conditions

Parameters

comm	a one-dimensional Cartesian communicator

Note

the parameters given in the constructor are global parameters

RealMPIGrid() [4/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, MPI_Comm comm )

inline

Construct with equal polynomial coefficients.

Parameters

x0	left boundary in x
x1	right boundary in x
y0	lower boundary in y
y1	upper boundary in y
n	# of polynomial coefficients for both x and y dimension (1<=n<=20)
Nx	# of points in x
Ny	# of points in y

Parameters

comm	a two-dimensional Cartesian communicator

Note

the parameters given in the constructor are global parameters

RealMPIGrid() [5/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, dg::bc bcx, dg::bc bcy, MPI_Comm comm )

inline

Construct with equal polynomial coefficients.

Parameters

x0	left boundary in x
x1	right boundary in x
y0	lower boundary in y
y1	upper boundary in y
n	# of polynomial coefficients for both x and y dimension (1<=n<=20)
Nx	# of points in x
Ny	# of points in y

Parameters

bcx	boundary condition in x
bcy	boundary condition in y

Parameters

comm	a two-dimensional Cartesian communicator

Note

the parameters given in the constructor are global parameters

RealMPIGrid() [6/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, real_type y0, real_type y1, real_type z0, real_type z1, unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, MPI_Comm comm )

inline

Construct with equal polynomial coefficients.

Parameters

x0	left boundary in x
x1	right boundary in x
y0	lower boundary in y
y1	upper boundary in y
z0	lower boundary in z
z1	upper boundary in z
n	# of polynomial coefficients for x and y dimension ( z-direction is set to 1) (1<=n<=20)
Nx	# of points in x
Ny	# of points in y
Nz	# of points in z

Parameters

comm	a three-dimensional Cartesian communicator

Note

the parameters given in the constructor are global parameters

RealMPIGrid() [7/11]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( real_type x0, real_type x1, real_type y0, real_type y1, real_type z0, real_type z1, unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, dg::bc bcx, dg::bc bcy, dg::bc bcz, MPI_Comm comm )

inline

Construct with equal polynomial coefficients.

Parameters

x0	left boundary in x
x1	right boundary in x
y0	lower boundary in y
y1	upper boundary in y
z0	lower boundary in z
z1	upper boundary in z
n	# of polynomial coefficients for x and y dimension ( z-direction is set to 1) (1<=n<=20)
Nx	# of points in x
Ny	# of points in y
Nz	# of points in z

Parameters

bcx	boundary condition in x
bcy	boundary condition in y
bcz	boundary condition in z

Parameters

comm	a three-dimensional Cartesian communicator

Note

the parameters given in the constructor are global parameters

RealMPIGrid() [8/11]

template<class real_type , size_t Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( const std::array< RealMPIGrid< real_type, 1 >, Nd > & axes )

inline

Construct a topology as the product of 1d axes grids.

Parameters

axes	One-dimensional grids for each dimension

RealMPIGrid() [9/11]

template<class real_type , size_t Nd>

template<class ... Grid1ds>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( const RealMPIGrid< real_type, 1 > & g0, const Grid1ds &... gs )

inline

Construct from given 1d grids Equivalent to RealMPIGrid( std::array{g0,gs...})

Parameters

g0	Axis 0 grid
gs	more axes

RealMPIGrid() [10/11]

template<class real_type , size_t Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( std::array< real_type, Nd > p, std::array< real_type, Nd > q, std::array< unsigned, Nd > n, std::array< unsigned, Nd > N, std::array< dg::bc, Nd > bcs, std::array< MPI_Comm, Nd > comms )

inline

Construct a topology directly from points and dimensions.

Parameters

p	left boundary point
q	right boundary point
n	number of polynomial coefficients for each axis
N	number of cells for each axis
bcs	boundary condition for each axis
comms	The 1d MPI Cartesian communicators for each axis that make up an Nd dimensional Cartesian communicator (see dg::mpi_cart_split, dg::mpi_cart_kron)

RealMPIGrid() [11/11]

template<class real_type , size_t Nd>

dg::RealMPIGrid< real_type, Nd >::RealMPIGrid ( const aRealMPITopology< real_type, Nd > & src )

inlineexplicit

allow explicit type conversion from any other topology

Parameters

src

source

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

• topology/mpi_grid.h