Storage class of the static attributes of the discrete dimension. More...

Public Types
using	discrete_dimension_type = UniformBSplines
	The type of the discrete dimension representing the B-splines.

using	discrete_domain_type = DiscreteDomain<DDim>
	The type of a DiscreteDomain whose elements identify the B-splines.

using	discrete_element_type = DiscreteElement<DDim>
	The type of a DiscreteElement identifying a B-spline.

using	discrete_vector_type = DiscreteVector<DDim>
	The type of a DiscreteVector representing an "index displacement" between two B-splines.

Public Member Functions
	Impl ()=default

	Impl (ddc::Coordinate< Tag > rmin, ddc::Coordinate< Tag > rmax, std::size_t ncells)
	Constructs a spline basis (B-splines) with n equidistant knots over .

template<class OriginMemorySpace >
	Impl (Impl< DDim, OriginMemorySpace > const &impl)
	Copy-constructs from another Impl with a different Kokkos memory space.

	Impl (Impl const &x)=default
	Copy-constructs.

	Impl (Impl &&x)=default
	Move-constructs.

	~Impl ()=default
	Destructs.

Impl &	operator= (Impl const &x)=default
	Copy-assigns.

Impl &	operator= (Impl &&x)=default
	Move-assigns.

KOKKOS_INLINE_FUNCTION discrete_element_type	eval_basis (DSpan1D values, ddc::Coordinate< Tag > const &x) const
	Evaluates non-zero B-splines at a given coordinate.

KOKKOS_INLINE_FUNCTION discrete_element_type	eval_deriv (DSpan1D derivs, ddc::Coordinate< Tag > const &x) const
	Evaluates non-zero B-spline derivatives at a given coordinate.

KOKKOS_INLINE_FUNCTION discrete_element_type	eval_basis_and_n_derivs (ddc::DSpan2D derivs, ddc::Coordinate< Tag > const &x, std::size_t n) const
	Evaluates non-zero B-spline values and derivatives at a given coordinate.

template<class Layout , class MemorySpace2 >
KOKKOS_INLINE_FUNCTION ddc::ChunkSpan< double, ddc::DiscreteDomain< DDim >, Layout, MemorySpace2 >	integrals (ddc::ChunkSpan< double, discrete_domain_type, Layout, MemorySpace2 > int_vals) const
	Compute the integrals of the B-splines.

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag >	get_knot (int knot_idx) const noexcept
	Returns the coordinate of the knot corresponding to the given index.

KOKKOS_INLINE_FUNCTION double	get_first_support_knot (discrete_element_type const &ix) const
	Returns the coordinate of the first support knot associated to a DiscreteElement identifying a B-spline.

KOKKOS_INLINE_FUNCTION double	get_last_support_knot (discrete_element_type const &ix) const
	Returns the coordinate of the last support knot associated to a DiscreteElement identifying a B-spline.

KOKKOS_INLINE_FUNCTION double	get_support_knot_n (discrete_element_type const &ix, int n) const
	Returns the coordinate of the (n+1)-th knot in the support of the identified B-spline.

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag >	rmin () const noexcept
	Returns the coordinate of the lower bound of the domain on which the B-splines are defined.

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag >	rmax () const noexcept
	Returns the coordinate of the upper bound of the domain on which the B-splines are defined.

KOKKOS_INLINE_FUNCTION double	length () const noexcept
	Returns the length of the domain.

KOKKOS_INLINE_FUNCTION std::size_t	size () const noexcept
	Returns the number of elements necessary to construct a spline representation of a function.

KOKKOS_INLINE_FUNCTION discrete_domain_type	full_domain () const
	Returns the discrete domain including eventual additional B-splines in the periodic case.

KOKKOS_INLINE_FUNCTION std::size_t	nbasis () const noexcept
	Returns the number of basis functions.

KOKKOS_INLINE_FUNCTION std::size_t	ncells () const noexcept
	Returns the number of cells over which the B-splines are defined.

Friends
template<class ODDim , class OMemorySpace >
class	Impl

Detailed Description

template<class Tag, std::size_t D>
template<class DDim, class MemorySpace>
class ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >

Storage class of the static attributes of the discrete dimension.

Template Parameters

DDim	The name of the discrete dimension.
MemorySpace	The Kokkos memory space where the attributes are being stored.

Member Typedef Documentation

◆ discrete_dimension_type

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

using ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::discrete_dimension_type = UniformBSplines

The type of the discrete dimension representing the B-splines.

◆ discrete_domain_type

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

using ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::discrete_domain_type = DiscreteDomain<DDim>

The type of a DiscreteDomain whose elements identify the B-splines.

◆ discrete_element_type

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

using ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::discrete_element_type = DiscreteElement<DDim>

The type of a DiscreteElement identifying a B-spline.

◆ discrete_vector_type

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

using ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::discrete_vector_type = DiscreteVector<DDim>

The type of a DiscreteVector representing an "index displacement" between two B-splines.

Constructor & Destructor Documentation

◆ Impl() [1/5]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::Impl ( )

default

◆ Impl() [2/5]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::Impl	(	ddc::Coordinate< Tag >	rmin,
		ddc::Coordinate< Tag >	rmax,
		std::size_t	ncells )

inlineexplicit

Constructs a spline basis (B-splines) with n equidistant knots over .

Parameters

rmin	the real ddc::coordinate of the first knot
rmax	the real ddc::coordinate of the last knot
ncells	the number of cells in the range [rmin, rmax]

◆ Impl() [3/5]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

template<class OriginMemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::Impl ( Impl< DDim, OriginMemorySpace > const & impl )

inlineexplicit

Copy-constructs from another Impl with a different Kokkos memory space.

Parameters

impl	A reference to the other Impl

◆ Impl() [4/5]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::Impl ( Impl< DDim, MemorySpace > const & x )

default

Copy-constructs.

Parameters

x	A reference to another Impl

◆ Impl() [5/5]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::Impl ( Impl< DDim, MemorySpace > && x )

default

Move-constructs.

Parameters

x	An rvalue to another Impl

◆ ~Impl()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::~Impl ( )

default

Destructs.

Member Function Documentation

◆ operator=() [1/2]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

Impl & ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::operator= ( Impl< DDim, MemorySpace > const & x )

default

Copy-assigns.

Parameters

x	A reference to another Impl

Returns: A reference to the copied Impl

◆ operator=() [2/2]

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

Impl & ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::operator= ( Impl< DDim, MemorySpace > && x )

default

Move-assigns.

Parameters

x	An rvalue to another Impl

Returns: A reference to the moved Impl

◆ eval_basis()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION discrete_element_type ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::eval_basis	(	DSpan1D	values,
		ddc::Coordinate< Tag > const &	x ) const

inline

Evaluates non-zero B-splines at a given coordinate.

The values are computed for every B-spline with support at the given coordinate x. There are only (degree+1) B-splines which are non-zero at any given point. It is these B-splines which are evaluated. This can be useful to calculate a spline approximation of a function. A spline approximation at coordinate x is a linear combination of these B-spline evaluations weighted with the spline coefficients of the spline-transformed initial discrete function.

Parameters

[out]	values	The values of the B-splines evaluated at coordinate x. It has to be a 1D mdspan with (degree+1) elements.
[in]	x	The coordinate where B-splines are evaluated. It has to be in the range of break points coordinates.

Returns: The index of the first B-spline which is evaluated.

◆ eval_deriv()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION ddc::DiscreteElement< DDim > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::eval_deriv	(	DSpan1D	derivs,
		ddc::Coordinate< Tag > const &	x ) const

Evaluates non-zero B-spline derivatives at a given coordinate.

The derivatives are computed for every B-spline with support at the given coordinate x. There are only (degree+1) B-splines which are non-zero at any given point. It is these B-splines which are derivated. A spline approximation of a derivative at coordinate x is a linear combination of those B-spline derivatives weighted with the spline coefficients of the spline-transformed initial discrete function.

Parameters

[out]	derivs	The derivatives of the B-splines evaluated at coordinate x. It has to be a 1D mdspan with (degree+1) elements.
[in]	x	The coordinate where B-spline derivatives are evaluated. It has to be in the range of break points coordinates.

Returns: The index of the first B-spline which is evaluated.

◆ eval_basis_and_n_derivs()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION ddc::DiscreteElement< DDim > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::eval_basis_and_n_derivs	(	ddc::DSpan2D	derivs,
		ddc::Coordinate< Tag > const &	x,
		std::size_t	n ) const

Evaluates non-zero B-spline values and derivatives at a given coordinate.

The values and derivatives are computed for every B-spline with support at the given coordinate x. There are only (degree+1) B-splines which are non-zero at any given point. It is these B-splines which are evaluated and derivated. A spline approximation of a derivative at coordinate x is a linear combination of those B-spline derivatives weighted with spline coefficients of the spline-transformed initial discrete function.

Parameters

[out]	derivs	The values and derivatives of the B-splines evaluated at coordinate x. It has to be a 2D mdspan of sizes (degree+1, n+1).
[in]	x	The coordinate where B-spline derivatives are evaluated. It has to be in the range of break points coordinates.
[in]	n	The number of derivatives to evaluate (in addition to the B-spline values themselves).

Returns: The index of the first B-spline which is evaluated.

◆ integrals()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

template<class Layout , class MemorySpace2 >

KOKKOS_INLINE_FUNCTION ddc::ChunkSpan< double, ddc::DiscreteDomain< DDim >, Layout, MemorySpace2 > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::integrals ( ddc::ChunkSpan< double, discrete_domain_type, Layout, MemorySpace2 > int_vals ) const

Compute the integrals of the B-splines.

The integral of each of the B-splines over their support within the domain on which this basis was defined.

Parameters

[out] int_vals The values of the integrals. It has to be a 1D Chunkspan of size (nbasis).

Returns: The values of the integrals.

◆ get_knot()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::get_knot ( int knot_idx ) const

inlinenoexcept

Returns the coordinate of the knot corresponding to the given index.

Returns the coordinate of the knot corresponding to the given index. The domain over which the B-splines are defined is comprised of ncells+1 break points however there are a total of ncells+1+2*degree knots. The additional knots which control the shape of the B-splines near the boundary are added equidistantly before and after the break points. The knot index is therefore in the interval [-degree, ncells+degree]

Parameters

[in] knot_idx Integer identifying index of the knot.

Returns: Coordinate of the knot.

◆ get_first_support_knot()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION double ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::get_first_support_knot ( discrete_element_type const & ix ) const

inline

Returns the coordinate of the first support knot associated to a DiscreteElement identifying a B-spline.

Each B-spline has a support defined over (degree+2) knots. For a B-spline identified by the provided DiscreteElement, this function returns the first knot in the support of the B-spline. In other words it returns the lower bound of the support.

Parameters

[in] ix DiscreteElement identifying the B-spline.

Returns: Coordinate of the knot.

◆ get_last_support_knot()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION double ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::get_last_support_knot ( discrete_element_type const & ix ) const

inline

Returns the coordinate of the last support knot associated to a DiscreteElement identifying a B-spline.

Each B-spline has a support defined over (degree+2) knots. For a B-spline identified by the provided DiscreteElement, this function returns the last knot in the support of the B-spline. In other words it returns the upper bound of the support.

Parameters

[in] ix DiscreteElement identifying the B-spline.

Returns: Coordinate of the knot.

◆ get_support_knot_n()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION double ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::get_support_knot_n	(	discrete_element_type const &	ix,
		int	n ) const

inline

Returns the coordinate of the (n+1)-th knot in the support of the identified B-spline.

Each B-spline has a support defined over (degree+2) knots. For a B-spline identified by the provided DiscreteElement, this function returns the (n+1)-th knot in the support of the B-spline.

Parameters

[in]	ix	DiscreteElement identifying the B-spline.
[in]	n	Integer indexing a knot in the support of the B-spline.

Returns: Coordinate of the knot.

◆ rmin()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::rmin ( ) const

inlinenoexcept

Returns the coordinate of the lower bound of the domain on which the B-splines are defined.

Returns: Coordinate of the lower bound of the domain.

◆ rmax()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION ddc::Coordinate< Tag > ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::rmax ( ) const

inlinenoexcept

Returns the coordinate of the upper bound of the domain on which the B-splines are defined.

Returns: Coordinate of the upper bound of the domain.

◆ length()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION double ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::length ( ) const

inlinenoexcept

Returns the length of the domain.

Returns: The length of the domain.

◆ size()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION std::size_t ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::size ( ) const

inlinenoexcept

Returns the number of elements necessary to construct a spline representation of a function.

For a non-periodic domain the number of elements necessary to construct a spline representation of a function is equal to the number of basis functions. However in the periodic case it additionally includes degree additional elements which allow the first B-splines to be evaluated close to rmax (where they also appear due to the periodicity).

Returns: The number of elements necessary to construct a spline representation of a function.

◆ full_domain()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION discrete_domain_type ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::full_domain ( ) const

inline

Returns the discrete domain including eventual additional B-splines in the periodic case.

See size().

Returns: The discrete domain including eventual additional B-splines.

◆ nbasis()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION std::size_t ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::nbasis ( ) const

inlinenoexcept

Returns the number of basis functions.

The number of functions in the spline basis.

Returns: The number of basis functions.

◆ ncells()

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

KOKKOS_INLINE_FUNCTION std::size_t ddc::UniformBSplines< Tag, D >::Impl< DDim, MemorySpace >::ncells ( ) const

inlinenoexcept

Returns the number of cells over which the B-splines are defined.

The number of cells over which the B-splines and any spline representation are defined. In other words the number of polynomials that comprise a spline representation on the domain where the basis is defined.

Returns: The number of cells over which the B-splines are defined.

Friends And Related Symbol Documentation

◆ Impl

template<class Tag , std::size_t D>

template<class DDim , class MemorySpace >

template<class ODDim , class OMemorySpace >

friend class Impl

friend

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

bsplines_uniform.hpp

DDC 0.0.0

a discrete domain computation library

Public Types

Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ discrete_dimension_type

◆ discrete_domain_type

◆ discrete_element_type

◆ discrete_vector_type

Constructor & Destructor Documentation

◆ Impl() [1/5]

◆ Impl() [2/5]

◆ Impl() [3/5]

◆ Impl() [4/5]

◆ Impl() [5/5]

◆ ~Impl()

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ eval_basis()

◆ eval_deriv()

◆ eval_basis_and_n_derivs()

◆ integrals()

◆ get_knot()

◆ get_first_support_knot()

◆ get_last_support_knot()

◆ get_support_knot_n()

◆ rmin()

◆ rmax()

◆ length()

◆ size()

◆ full_domain()

◆ nbasis()

◆ ncells()

Friends And Related Symbol Documentation

◆ Impl