A class for creating a spline approximation of a function. More...

Public Types
using	exec_space = ExecSpace

using	memory_space = MemorySpace

using	interpolation_mesh_type = InterpolationMesh
	The type of the interpolation mesh used by this class.

using	bsplines_type = BSplines
	The type of the BSplines which are compatible with this class.

using	deriv_type = ddc::Deriv<tag_type>

using	interpolation_domain_type = ddc::DiscreteDomain<interpolation_mesh_type>
	The type of the domain for the interpolation mesh used by this class.

using	batched_interpolation_domain_type = ddc::DiscreteDomain<IDimX...>

using	batch_domain_type

using	batched_spline_domain_type

using	batched_spline_tr_domain_type

using	batched_derivs_domain_type

Public Member Functions
	SplineBuilder (batched_interpolation_domain_type const &batched_interpolation_domain, std::optional< int > cols_per_chunk=std::nullopt, std::optional< unsigned int > preconditionner_max_block_size=std::nullopt)

	SplineBuilder (SplineBuilder const &x)=delete

	SplineBuilder (SplineBuilder &&x)=default
	Create a new SplineBuilder by copy.

	~SplineBuilder ()=default

SplineBuilder &	operator= (SplineBuilder const &x)=delete

SplineBuilder &	operator= (SplineBuilder &&x)=default
	Copy a SplineBuilder.

batched_interpolation_domain_type	batched_interpolation_domain () const noexcept

interpolation_domain_type	interpolation_domain () const noexcept
	Get the domain from which the approximation is defined.

batch_domain_type	batch_domain () const noexcept

ddc::DiscreteDomain< bsplines_type >	spline_domain () const noexcept

batched_spline_domain_type	batched_spline_domain () const noexcept
	Get the domain on which the approximation is defined.

batched_spline_tr_domain_type	batched_spline_tr_domain () const noexcept

batched_derivs_domain_type	batched_derivs_xmin_domain () const noexcept

batched_derivs_domain_type	batched_derivs_xmax_domain () const noexcept

const ddc::detail::Matrix &	get_interpolation_matrix () const noexcept
	Get the interpolation matrix.

template<class Layout >
void	operator() (ddc::ChunkSpan< double, batched_spline_domain_type, Layout, memory_space > spline, ddc::ChunkSpan< double const, batched_interpolation_domain_type, Layout, memory_space > vals, std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type, Layout, memory_space > > const derivs_xmin=std::nullopt, std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type, Layout, memory_space > > const derivs_xmax=std::nullopt) const
	Build a spline approximation of a function.

Static Public Attributes
static constexpr bool	s_odd = BSplines::degree() % 2
	Indicates if the degree of the splines is odd or even.

static constexpr int	s_nbc_xmin = n_boundary_equations(BcXmin, BSplines::degree())
	The number of equations which define the boundary conditions at the lower bound.

static constexpr int	s_nbc_xmax = n_boundary_equations(BcXmax, BSplines::degree())
	The number of equations which define the boundary conditions at the upper bound.

static constexpr ddc::BoundCond	s_bc_xmin = BcXmin
	The boundary condition implemented at the lower bound.

static constexpr ddc::BoundCond	s_bc_xmax = BcXmax
	The boundary condition implemented at the upper bound.

Detailed Description

template<class ExecSpace, class MemorySpace, class BSplines, class InterpolationMesh, ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>
class ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >

A class for creating a spline approximation of a function.

A class which contains an operator () which can be used to build a spline approximation of a function. A spline approximation is represented by coefficients stored in a Chunk of BSplines. The spline is constructed such that it respects the boundary conditions BcXmin and BcXmax, and it interpolates the function at the points on the interpolation_mesh associated with interpolation_mesh_type.

Member Typedef Documentation

◆ exec_space

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::exec_space = ExecSpace

◆ memory_space

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::memory_space = MemorySpace

◆ interpolation_mesh_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::interpolation_mesh_type = InterpolationMesh

The type of the interpolation mesh used by this class.

◆ bsplines_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::bsplines_type = BSplines

The type of the BSplines which are compatible with this class.

◆ deriv_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::deriv_type = ddc::Deriv<tag_type>

◆ interpolation_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::interpolation_domain_type = ddc::DiscreteDomain<interpolation_mesh_type>

The type of the domain for the interpolation mesh used by this class.

◆ batched_interpolation_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_interpolation_domain_type = ddc::DiscreteDomain<IDimX...>

◆ batch_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batch_domain_type

Initial value:

 
            typename ddc::detail::convert_type_seq_to_discrete_domain<ddc::type_seq_remove_t<
                    ddc::detail::TypeSeq<IDimX...>,
                    ddc::detail::TypeSeq<interpolation_mesh_type>>>

◆ batched_spline_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_spline_domain_type

Initial value:

 
            typename ddc::detail::convert_type_seq_to_discrete_domain<ddc::type_seq_replace_t<
                    ddc::detail::TypeSeq<IDimX...>,
                    ddc::detail::TypeSeq<interpolation_mesh_type>,
                    ddc::detail::TypeSeq<bsplines_type>>>

◆ batched_spline_tr_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_spline_tr_domain_type

Initial value:

 
            typename ddc::detail::convert_type_seq_to_discrete_domain<ddc::type_seq_merge_t<
                    ddc::detail::TypeSeq<bsplines_type>,
                    ddc::type_seq_remove_t<
                            ddc::detail::TypeSeq<IDimX...>,
                            ddc::detail::TypeSeq<interpolation_mesh_type>>>>

◆ batched_derivs_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_derivs_domain_type

Initial value:

 
            typename ddc::detail::convert_type_seq_to_discrete_domain<ddc::type_seq_replace_t<
                    ddc::detail::TypeSeq<IDimX...>,
                    ddc::detail::TypeSeq<interpolation_mesh_type>,
                    ddc::detail::TypeSeq<deriv_type>>>

Constructor & Destructor Documentation

◆ SplineBuilder() [1/3]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::SplineBuilder	(	batched_interpolation_domain_type const &	batched_interpolation_domain,
		std::optional< int >	cols_per_chunk = std::nullopt,
		std::optional< unsigned int >	preconditionner_max_block_size = std::nullopt )

inlineexplicit

◆ SplineBuilder() [2/3]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::SplineBuilder ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX > const & x )

delete

◆ SplineBuilder() [3/3]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::SplineBuilder ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX > && x )

default

Create a new SplineBuilder by copy.

Parameters

x	The SplineBuilder being copied.

◆ ~SplineBuilder()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::~SplineBuilder ( )

default

Member Function Documentation

◆ operator=() [1/2]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

SplineBuilder & ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::operator= ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX > const & x )

delete

◆ operator=() [2/2]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

SplineBuilder & ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::operator= ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX > && x )

default

Copy a SplineBuilder.

Parameters

x	The SplineBuilder being copied.

Returns: A reference to this object.

◆ batched_interpolation_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batched_interpolation_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_interpolation_domain ( ) const

inlinenoexcept

◆ interpolation_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

interpolation_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::interpolation_domain ( ) const

inlinenoexcept

Get the domain from which the approximation is defined.

Get the domain on which values of the function must be provided in order to build a spline approximation of the function.

Returns: The domain for the grid points.

◆ batch_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batch_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batch_domain ( ) const

inlinenoexcept

◆ spline_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

ddc::DiscreteDomain< bsplines_type > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::spline_domain ( ) const

inlinenoexcept

◆ batched_spline_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batched_spline_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_spline_domain ( ) const

inlinenoexcept

Get the domain on which the approximation is defined.

Get the domain of the basis-splines for which the coefficients of the spline approximation must be calculated.

Returns: The domain for the splines.

◆ batched_spline_tr_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batched_spline_tr_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_spline_tr_domain ( ) const

inlinenoexcept

◆ batched_derivs_xmin_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batched_derivs_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_derivs_xmin_domain ( ) const

inlinenoexcept

◆ batched_derivs_xmax_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

batched_derivs_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::batched_derivs_xmax_domain ( ) const

inlinenoexcept

◆ get_interpolation_matrix()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

const ddc::detail::Matrix & ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::get_interpolation_matrix ( ) const

inlinenoexcept

Get the interpolation matrix.

Get the interpolation matrix. This can be useful for debugging (as it allows one to print the matrix) or for more complex quadrature schemes.

Returns: A reference to the interpolation matrix.

◆ operator()()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationMesh , ddc::BoundCond BcXmin, ddc::BoundCond BcXmax, SplineSolver Solver, class... IDimX>

template<class Layout >

void ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationMesh, BcXmin, BcXmax, Solver, IDimX >::operator()	(	ddc::ChunkSpan< double, batched_spline_domain_type, Layout, memory_space >	spline,
		ddc::ChunkSpan< double const, batched_interpolation_domain_type, Layout, memory_space >	vals,
		std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type, Layout, memory_space > > const	derivs_xmin = std::nullopt,
		std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type, Layout, memory_space > > const	derivs_xmax = std::nullopt ) const

Build a spline approximation of a function.

Use the values of a function at known grid points (as specified by SplineBuilder::interpolation_domain) and the derivatives of the function at the boundaries (if necessary for the chosen boundary conditions) to calculate a spline approximation of a function.

The spline approximation is stored as a ChunkSpan of coefficients associated with basis-splines.

Parameters

[out]	spline	The coefficients of the spline calculated by the function.
[in]	vals	The values of the function at the grid points.
[in]	derivs_xmin	The values of the derivatives at the lower boundary.
[in]	derivs_xmax	The values of the derivatives at the upper boundary.