The simplest implementation of aRealTopology. More...

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

Public Member Functions
	RealGrid ()=default
	construct an empty grid this leaves the access functions undefined

template<size_t Md = Nd>
	RealGrid (real_type x0, real_type x1, unsigned n, unsigned Nx, dg::bc bcx=dg::PER)
	1D grid

template<size_t Md = Nd>
	RealGrid (real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, dg::bc bcx=PER, dg::bc bcy=PER)
	Construct with equal polynomial coefficients.

template<size_t Md = Nd>
	RealGrid (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=PER, dg::bc bcy=PER, dg::bc bcz=PER)
	Construct with equal polynomial coefficients.

	RealGrid (const std::array< RealGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.

template<class ... Grid1ds>
	RealGrid (const RealGrid< real_type, 1 > &g0, const Grid1ds &...gs)
	Construct from given 1d grids Equivalent to `RealGrid( std::array{g0,gs...})`

	RealGrid (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)
	Construct a topology directly from points and dimensions.

	RealGrid (const aRealTopology< real_type, Nd > &src)
	allow explicit type conversion from any other topology

Public Member Functions inherited from dg::aRealTopology< 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
	Construct 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 \( \vec p\).

std::array< real_type, Nd >	get_q () const
	Get right boundary point \( \vec q\).

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.

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`.

RealGrid< real_type, 1 >	grid (unsigned u) const
	Get axis `u` as a 1d grid.

RealGrid< real_type, 1 >	axis (unsigned u) const
	An alias for "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>
RealGrid< real_type, 1 >	gx () const
	Equivalent to `grid(0)`

template<size_t Md = Nd>
RealGrid< real_type, 1 >	gy () const
	Equivalent to `grid(1)`

template<size_t Md = Nd>
RealGrid< real_type, 1 >	gz () const
	Equivalent to `grid(2)`

std::array< unsigned, Nd >	start () const
	Start coordinate in C-order for `dg::file::NcHyperslab`.

std::array< unsigned, Nd >	count () const
	Count vector in C-order for `dg::file::NcHyperslab`.

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.

void	set (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q, std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N, std::array< dg::bc, Nd > new_bcs)
	Reset the entire grid.

unsigned	size () const
	The total number of points.

void	display (std::ostream &os=std::cout) const
	Display.

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.

Additional Inherited Members
Public Types inherited from dg::aRealTopology< real_type, Nd >
using	value_type = real_type
	value type of abscissas and weights

using	host_vector = thrust::host_vector<real_type>

using	host_grid = RealGrid<real_type, Nd>
	Associated realisation.

Static Public Member Functions inherited from dg::aRealTopology< real_type, Nd >
static constexpr unsigned	ndim ()
	Dimensionality == Nd.

Protected Member Functions inherited from dg::aRealTopology< real_type, Nd >
	~aRealTopology ()=default
	disallow deletion through base class pointer

	aRealTopology ()=default
	default constructor

	aRealTopology (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)
	Construct a topology directly from points and dimensions.

	aRealTopology (const std::array< RealGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.

	aRealTopology (const aRealTopology &src)=default

aRealTopology &	operator= (const aRealTopology &src)=default

Detailed Description

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

The simplest implementation of aRealTopology.

        // 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

◆ RealGrid() [1/8]

template<class real_type , size_t Nd>

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

default

construct an empty grid this leaves the access functions undefined

◆ RealGrid() [2/8]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealGrid< real_type, Nd >::RealGrid	(	real_type	x0,
		real_type	x1,
		unsigned	n,
		unsigned	Nx,
		dg::bc	bcx = dg::PER )

inline

1D grid

Parameters

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

◆ RealGrid() [3/8]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealGrid< real_type, Nd >::RealGrid	(	real_type	x0,
		real_type	x1,
		real_type	y0,
		real_type	y1,
		unsigned	n,
		unsigned	Nx,
		unsigned	Ny,
		dg::bc	bcx = PER,
		dg::bc	bcy = PER )

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

◆ RealGrid() [4/8]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::RealGrid< real_type, Nd >::RealGrid	(	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 = PER,
		dg::bc	bcy = PER,
		dg::bc	bcz = PER )

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

◆ RealGrid() [5/8]

template<class real_type , size_t Nd>

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

inline

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

Parameters

axes	One-dimensional grids for each dimension

◆ RealGrid() [6/8]

template<class real_type , size_t Nd>

template<class ... Grid1ds>

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

inline

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

Parameters

g0	Axis 0 grid
gs	more axes

◆ RealGrid() [7/8]

template<class real_type , size_t Nd>

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

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

◆ RealGrid() [8/8]

template<class real_type , size_t Nd>

dg::RealGrid< real_type, Nd >::RealGrid ( const aRealTopology< real_type, Nd > & src )

inlineexplicit

allow explicit type conversion from any other topology

Parameters

src source

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

topology/grid.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RealGrid() [1/8]

◆ RealGrid() [2/8]

◆ RealGrid() [3/8]

◆ RealGrid() [4/8]

◆ RealGrid() [5/8]

◆ RealGrid() [6/8]

◆ RealGrid() [7/8]

◆ RealGrid() [8/8]