1D grid More...

Public Types
using	value_type = real_type

using	host_vector = thrust::host_vector< real_type >
	The host vector type used by host functions like evaluate. More...

using	host_grid = RealGrid1d< real_type >

Public Member Functions
	RealGrid1d ()=default
	construct an empty grid this leaves the access functions undefined More...

	RealGrid1d (real_type x0, real_type x1, unsigned n, unsigned N, bc bcx=PER)
	1D grid More...

real_type	x0 () const
	left boundary More...

real_type	x1 () const
	right boundary More...

real_type	lx () const
	total length of interval More...

real_type	h () const
	cell size More...

unsigned	N () const
	number of cells More...

unsigned	n () const
	number of polynomial coefficients More...

bc	bcx () const
	boundary conditions More...

void	set (real_type x0, real_type x1, bc bcx)
	reset the boundaries of the grid More...

void	set (unsigned n, unsigned N)
	reset the cell numbers in the grid More...

void	set (real_type x0, real_type x1, unsigned n, unsigned N, bc bcx)
	Reset all values of the grid. More...

unsigned	size () const
	`n()*N()` (Total number of grid points) More...

const DLT< real_type > &	dlt () const
	the discrete legendre transformation More...

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

void	shift (bool &negative, real_type &x) const
	Shift any point coordinate to a corresponding grid coordinate according to the boundary condition. More...

void	shift (bool &negative, real_type &x, bc bcx) const
	Shift any point coordinate to a corresponding grid coordinate according to the boundary condition. More...

bool	contains (real_type x) const
	Check if the grid contains a point. More...

Detailed Description

template<class real_type>
struct dg::RealGrid1d< real_type >

1D grid

This code snippet demonstrates how to discretize and integrate a function

// create a one-dimensional grid on the domain [0,2] with 3 polynomial coefficients and 20 cells
dg::Grid1d g1d( 0, 2, 3, 20);
 
// create the Gaussian weights (volume form) for the integration
const dg::HVec w1d = dg::create::weights( g1d);
 
// discretize the exponential function on the grid
const dg::HVec vec = dg::evaluate( exp, g1d);
 
// now compute the scalar product (the integral)
double integral = dg::blas1::dot( w1d, vec);
 
// integral is now: e^2-1

Member Typedef Documentation

◆ host_grid

template<class real_type >

using dg::RealGrid1d< real_type >::host_grid = RealGrid1d<real_type>

◆ host_vector

template<class real_type >

using dg::RealGrid1d< real_type >::host_vector = thrust::host_vector<real_type>

The host vector type used by host functions like evaluate.

◆ value_type

template<class real_type >

using dg::RealGrid1d< real_type >::value_type = real_type

Constructor & Destructor Documentation

◆ RealGrid1d() [1/2]

template<class real_type >

dg::RealGrid1d< real_type >::RealGrid1d ( )

default

construct an empty grid this leaves the access functions undefined

◆ RealGrid1d() [2/2]

template<class real_type >

dg::RealGrid1d< real_type >::RealGrid1d	(	real_type	x0,
		real_type	x1,
		unsigned	n,
		unsigned	N,
		bc	bcx = `PER`
	)

inline

1D grid

Parameters

x0	left boundary
x1	right boundary
n	# of polynomial coefficients (1<=n<=20, note that the library is optimized for n=3 )
N	# of cells
bcx	boundary conditions

Member Function Documentation

◆ bcx()

template<class real_type >

bc dg::RealGrid1d< real_type >::bcx ( ) const

inline

boundary conditions

Returns

◆ contains()

template<class real_type >

bool dg::RealGrid1d< real_type >::contains ( real_type x ) const

inline

Check if the grid contains a point.

Note: Does not consider periodicity!!

Parameters

x	point to check

Returns: true if x0()<=x<=x1(), false else

Attention: returns false if x is NaN or INF

◆ display()

template<class real_type >

void dg::RealGrid1d< real_type >::display ( std::ostream & os = std::cout ) const

inline

◆ dlt()

template<class real_type >

const DLT< real_type > & dg::RealGrid1d< real_type >::dlt ( ) const

inline

the discrete legendre transformation

Returns

◆ h()

template<class real_type >

real_type dg::RealGrid1d< real_type >::h ( ) const

inline

cell size

Returns

◆ lx()

template<class real_type >

real_type dg::RealGrid1d< real_type >::lx ( ) const

inline

total length of interval

Returns

◆ N()

template<class real_type >

unsigned dg::RealGrid1d< real_type >::N ( ) const

inline

number of cells

Returns

◆ n()

template<class real_type >

unsigned dg::RealGrid1d< real_type >::n ( ) const

inline

number of polynomial coefficients

Returns

◆ set() [1/3]

template<class real_type >

void dg::RealGrid1d< real_type >::set	(	real_type	x0,
		real_type	x1,
		bc	bcx
	)

inline

reset the boundaries of the grid

Parameters

x0	new left boundary
x1	new right boundary ( > x0)
bcx	new boundary condition

◆ set() [2/3]

template<class real_type >

void dg::RealGrid1d< real_type >::set	(	real_type	x0,
		real_type	x1,
		unsigned	n,
		unsigned	N,
		bc	bcx
	)

inline

Reset all values of the grid.

Parameters

x0	new left boundary
x1	new right boundary
n	new # of polynomial coefficients
N	new # of cells
bcx	new boundary condition

◆ set() [3/3]

template<class real_type >

void dg::RealGrid1d< real_type >::set	(	unsigned	n,
		unsigned	N
	)

inline

reset the cell numbers in the grid

Parameters

n	new # of polynomial coefficients (0<n<21)
N	new # of cells (>0)

◆ shift() [1/2]

template<class real_type >

void dg::RealGrid1d< real_type >::shift	(	bool &	negative,
		real_type &	x
	)		const

inline

Shift any point coordinate to a corresponding grid coordinate according to the boundary condition.

If the given point is already inside the grid, the function does nothing, else along each dimension the following happens: check the boundary condition. If dg::PER, the point will be shifted topologically back onto the domain (modulo operation). Else the point will be mirrored at the closest boundary. If the boundary is a Dirichlet boundary (happens for dg::DIR, dg::DIR_NEU and dg::NEU_DIR; the latter two apply dg::DIR to the respective left or right boundary ) an additional sign flag is swapped. This process is repeated until the result lies inside the grid. This function forms the basis for extending/periodifying a function discretized on the grid beyond the grid boundaries.

See also: interpolate

Note: For periodic boundaries the right boundary point is considered outside the grid and is shifted to the left boundary point.

Parameters

negative	swap value if there was a sign swap (happens when a point is mirrored along a Dirichlet boundary)
x	point to shift (inout) the result is guaranteed to lie inside the grid

◆ shift() [2/2]

template<class real_type >

void dg::RealGrid1d< real_type >::shift	(	bool &	negative,
		real_type &	x,
		bc	bcx
	)		const

inline

Shift any point coordinate to a corresponding grid coordinate according to the boundary condition.

If the given point is already inside the grid, the function does nothing, else along each dimension the following happens: check the boundary condition. If dg::PER, the point will be shifted topologically back onto the domain (modulo operation). Else the point will be mirrored at the closest boundary. If the boundary is a Dirichlet boundary (happens for dg::DIR, dg::DIR_NEU and dg::NEU_DIR; the latter two apply dg::DIR to the respective left or right boundary ) an additional sign flag is swapped. This process is repeated until the result lies inside the grid. This function forms the basis for extending/periodifying a function discretized on the grid beyond the grid boundaries.

See also: interpolate

Note: For periodic boundaries the right boundary point is considered outside the grid and is shifted to the left boundary point.

Parameters

negative	swap value if there was a sign swap (happens when a point is mirrored along a Dirichlet boundary)
x	point to shift (inout) the result is guaranteed to lie inside the grid
bcx	overrule grid internal boundary condition with this value

◆ size()

template<class real_type >

unsigned dg::RealGrid1d< real_type >::size ( ) const

inline

n()*N() (Total number of grid points)

◆ x0()

template<class real_type >

real_type dg::RealGrid1d< real_type >::x0 ( ) const

inline

left boundary

Returns

◆ x1()

template<class real_type >

real_type dg::RealGrid1d< real_type >::x1 ( ) const

inline

right boundary

Returns

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

topology/grid.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ host_grid

◆ host_vector

◆ value_type

Constructor & Destructor Documentation

◆ RealGrid1d() [1/2]

◆ RealGrid1d() [2/2]

Member Function Documentation

◆ bcx()

◆ contains()

◆ display()

◆ dlt()

◆ h()

◆ lx()

◆ N()

◆ n()

◆ set() [1/3]

◆ set() [2/3]

◆ set() [3/3]

◆ shift() [1/2]

◆ shift() [2/2]

◆ size()

◆ x0()

◆ x1()