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

#include <spline_builder.hpp>

Collaboration diagram for ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >:

Public Types
using	exec_space = ExecSpace
	The type of the Kokkos execution space used by this class.

using	memory_space = MemorySpace
	The type of the Kokkos memory space used by this class.

using	continuous_dimension_type = InterpolationDDim::continuous_dimension_type
	The type of the interpolation continuous dimension (continuous dimension of interest) used by this class.

using	interpolation_discrete_dimension_type = InterpolationDDim
	The type of the interpolation discrete dimension (discrete dimension of interest) used by this class.

using	bsplines_type = BSplines
	The discrete dimension representing the B-splines.

using	deriv_type = ddc::Deriv< continuous_dimension_type >
	The type of the Deriv dimension at the boundaries.

using	interpolation_domain_type = ddc::DiscreteDomain< interpolation_discrete_dimension_type >
	The type of the domain for the 1D interpolation mesh used by this class.

template<concepts::discrete_domain BatchedInterpolationDDom>
using	batched_interpolation_domain_type = BatchedInterpolationDDom
	The type of the whole domain representing interpolation points.

template<concepts::discrete_domain BatchedInterpolationDDom>
using	batch_domain_type = ddc::remove_dims_of_t< BatchedInterpolationDDom, interpolation_discrete_dimension_type >
	The type of the batch domain (obtained by removing the dimension of interest from the whole domain).

template<concepts::discrete_domain BatchedInterpolationDDom>
using	batched_spline_domain_type = ddc::replace_dim_of_t< BatchedInterpolationDDom, interpolation_discrete_dimension_type, bsplines_type >
	The type of the whole spline domain (cartesian product of 1D spline domain and batch domain) preserving the underlying memory layout (order of dimensions).

template<concepts::discrete_domain BatchedInterpolationDDom>
using	batched_derivs_domain_type = ddc::replace_dim_of_t< BatchedInterpolationDDom, interpolation_discrete_dimension_type, deriv_type >
	The type of the whole Deriv domain (cartesian product of 1D Deriv domain and batch domain) preserving the underlying memory layout (order of dimensions).

Public Member Functions
	SplineBuilder (std::string label, interpolation_domain_type const &interpolation_domain, std::optional< std::size_t > cols_per_chunk=std::nullopt, std::optional< unsigned int > preconditioner_max_block_size=std::nullopt)
	Build a SplineBuilder acting on interpolation_domain.

	SplineBuilder (interpolation_domain_type const &interpolation_domain, std::optional< std::size_t > cols_per_chunk=std::nullopt, std::optional< unsigned int > preconditioner_max_block_size=std::nullopt)
	Build a SplineBuilder acting on interpolation_domain.

template<concepts::discrete_domain BatchedInterpolationDDom>
	SplineBuilder (std::string label, BatchedInterpolationDDom const &batched_interpolation_domain, std::optional< std::size_t > cols_per_chunk=std::nullopt, std::optional< unsigned int > preconditioner_max_block_size=std::nullopt)
	Build a SplineBuilder acting on the interpolation domain contained by batched_interpolation_domain.

template<concepts::discrete_domain BatchedInterpolationDDom>
	SplineBuilder (BatchedInterpolationDDom const &batched_interpolation_domain, std::optional< std::size_t > cols_per_chunk=std::nullopt, std::optional< unsigned int > preconditioner_max_block_size=std::nullopt)
	Build a SplineBuilder acting on the interpolation domain contained by batched_interpolation_domain.

	SplineBuilder (SplineBuilder const &x)=delete
	Copy-constructor is deleted.

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

	~SplineBuilder ()=default
	Destructs.

SplineBuilder &	operator= (SplineBuilder const &x)=delete
	Copy-assignment is deleted.

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

interpolation_domain_type	interpolation_domain () const noexcept
	Get the domain for the 1D interpolation mesh used by this class.

template<concepts::discrete_domain BatchedInterpolationDDom>
BatchedInterpolationDDom	batched_interpolation_domain (BatchedInterpolationDDom const &batched_interpolation_domain) const noexcept
	Get the whole domain representing interpolation points.

template<class BatchedInterpolationDDom >
batch_domain_type< BatchedInterpolationDDom >	batch_domain (BatchedInterpolationDDom const &batched_interpolation_domain) const noexcept
	Get the batch domain.

ddc::DiscreteDomain< bsplines_type >	spline_domain () const noexcept
	Get the 1D domain on which spline coefficients are defined.

template<class BatchedInterpolationDDom >
batched_spline_domain_type< BatchedInterpolationDDom >	batched_spline_domain (BatchedInterpolationDDom const &batched_interpolation_domain) const noexcept
	Get the whole domain on which spline coefficients are defined.

template<class BatchedInterpolationDDom >
batched_derivs_domain_type< BatchedInterpolationDDom >	batched_derivs_xmin_domain (BatchedInterpolationDDom const &batched_interpolation_domain) const noexcept
	Get the whole domain on which derivatives on lower boundary are defined.

template<class BatchedInterpolationDDom >
batched_derivs_domain_type< BatchedInterpolationDDom >	batched_derivs_xmax_domain (BatchedInterpolationDDom const &batched_interpolation_domain) const noexcept
	Get the whole domain on which derivatives on upper boundary are defined.

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

template<class OutMemorySpace = MemorySpace>
std::tuple< ddc::Chunk< double, ddc::DiscreteDomain< ddc::Deriv< typename InterpolationDDim::continuous_dimension_type > >, ddc::KokkosAllocator< double, OutMemorySpace > >, ddc::Chunk< double, ddc::DiscreteDomain< InterpolationDDim >, ddc::KokkosAllocator< double, OutMemorySpace > >, ddc::Chunk< double, ddc::DiscreteDomain< ddc::Deriv< typename InterpolationDDim::continuous_dimension_type > >, ddc::KokkosAllocator< double, OutMemorySpace > > >	quadrature_coefficients () const
	Compute the quadrature coefficients associated to the b-splines used by this SplineBuilder.

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_nbe_xmin = n_boundary_equations(SBCLower, BSplines::degree())
	The number of equations defining the closure relation at the lower bound.

static constexpr int	s_nbe_xmax = n_boundary_equations(SBCUpper, BSplines::degree())
	The number of equations defining the closure relation at the upper bound.

static constexpr int	s_nbv_xmin
	The number of input values defining the closure relation at the lower bound.

static constexpr int	s_nbv_xmax
	The number of input values defining the closure relation at the upper bound.

static constexpr ddc::SplineBuilderClosure	s_sbc_xmin = SBCLower
	The closure relation implemented at the lower bound.

static constexpr ddc::SplineBuilderClosure	s_sbc_xmax = SBCUpper
	The closure relation implemented at the upper bound.

static constexpr SplineSolver	s_spline_solver = Solver
	The SplineSolver giving the backend used to perform the spline approximation.

Detailed Description

template<class ExecSpace, class MemorySpace, class BSplines, class InterpolationDDim, ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>
class ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >

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 B-splines. The spline is constructed such that it respects the closure relations SBCLower and SBCUpper, and it interpolates the function at the points on the interpolation_discrete_dimension associated with interpolation_discrete_dimension_type.

Template Parameters

ExecSpace	The Kokkos execution space on which the spline approximation is performed.
MemorySpace	The Kokkos memory space on which the data (interpolation function and splines coefficients) is stored.
BSplines	The discrete dimension representing the B-splines.
InterpolationDDim	The discrete dimension on which interpolation points are defined.
SBCLower	The lower closure relation.
SBCUpper	The upper closure relation.
Solver	The SplineSolver giving the backend used to perform the spline approximation.

Definition at line 65 of file spline_builder.hpp.

Member Typedef Documentation

◆ exec_space

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::exec_space = ExecSpace

The type of the Kokkos execution space used by this class.

Definition at line 75 of file spline_builder.hpp.

◆ memory_space

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::memory_space = MemorySpace

The type of the Kokkos memory space used by this class.

Definition at line 78 of file spline_builder.hpp.

◆ continuous_dimension_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::continuous_dimension_type = InterpolationDDim::continuous_dimension_type

The type of the interpolation continuous dimension (continuous dimension of interest) used by this class.

Definition at line 81 of file spline_builder.hpp.

◆ interpolation_discrete_dimension_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::interpolation_discrete_dimension_type = InterpolationDDim

The type of the interpolation discrete dimension (discrete dimension of interest) used by this class.

Definition at line 84 of file spline_builder.hpp.

◆ bsplines_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::bsplines_type = BSplines

The discrete dimension representing the B-splines.

Definition at line 87 of file spline_builder.hpp.

◆ deriv_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::deriv_type = ddc::Deriv<continuous_dimension_type>

The type of the Deriv dimension at the boundaries.

Definition at line 90 of file spline_builder.hpp.

◆ interpolation_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::interpolation_domain_type = ddc::DiscreteDomain<interpolation_discrete_dimension_type>

The type of the domain for the 1D interpolation mesh used by this class.

Definition at line 93 of file spline_builder.hpp.

◆ batched_interpolation_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_interpolation_domain_type = BatchedInterpolationDDom

The type of the whole domain representing interpolation points.

Template Parameters

The	batched discrete domain on which the interpolation points are defined.

Definition at line 101 of file spline_builder.hpp.

◆ batch_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batch_domain_type = ddc:: remove_dims_of_t<BatchedInterpolationDDom, interpolation_discrete_dimension_type>

The type of the batch domain (obtained by removing the dimension of interest from the whole domain).

Template Parameters

The	batched discrete domain on which the interpolation points are defined.

Example: For batched_interpolation_domain_type = DiscreteDomain<X,Y,Z> and a dimension of interest Y, this is DiscreteDomain<X,Z>

Definition at line 113 of file spline_builder.hpp.

◆ batched_spline_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_spline_domain_type = ddc::replace_dim_of_t< BatchedInterpolationDDom, interpolation_discrete_dimension_type, bsplines_type>

The type of the whole spline domain (cartesian product of 1D spline domain and batch domain) preserving the underlying memory layout (order of dimensions).

Template Parameters

The	batched discrete domain on which the interpolation points are defined.

Example: For batched_interpolation_domain_type = DiscreteDomain<X,Y,Z> and a dimension of interest Y (associated to a B-splines tag BSplinesY), this is DiscreteDomain<X,BSplinesY,Z>.

Definition at line 126 of file spline_builder.hpp.

◆ batched_derivs_domain_type

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

using ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_derivs_domain_type = ddc::replace_dim_of_t< BatchedInterpolationDDom, interpolation_discrete_dimension_type, deriv_type>

The type of the whole Deriv domain (cartesian product of 1D Deriv domain and batch domain) preserving the underlying memory layout (order of dimensions).

Template Parameters

The	batched discrete domain on which the interpolation points are defined.

Example: For batched_interpolation_domain_type = DiscreteDomain<X,Y,Z> and a dimension of interest Y, this is DiscreteDomain<X,Deriv<Y>,Z>

Definition at line 160 of file spline_builder.hpp.

Constructor & Destructor Documentation

◆ SplineBuilder() [1/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder	(	std::string	label,
		interpolation_domain_type const &	interpolation_domain,
		std::optional< std::size_t >	cols_per_chunk = `std::nullopt`,
		std::optional< unsigned int >	preconditioner_max_block_size = `std::nullopt`
	)

inlineexplicit

Build a SplineBuilder acting on interpolation_domain.

Parameters

label	A label used to tag parallel regions and memory allocations for profiling.
interpolation_domain	The domain on which the interpolation points are defined.
cols_per_chunk	A parameter used by the slicer (internal to the solver) to define the size of a chunk of right-hand sides of the linear problem to be computed in parallel (chunks are treated by the linear solver one-after-the-other). This value is optional. If no value is provided then the default value is chosen by the requested solver.
preconditioner_max_block_size	A parameter used by the slicer (internal to the solver) to define the size of a block used by the Block-Jacobi preconditioner. This value is optional. If no value is provided then the default value is chosen by the requested solver.

See also: MatrixSparse

Definition at line 239 of file spline_builder.hpp.

◆ SplineBuilder() [2/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder	(	interpolation_domain_type const &	interpolation_domain,
		std::optional< std::size_t >	cols_per_chunk = `std::nullopt`,
		std::optional< unsigned int >	preconditioner_max_block_size = `std::nullopt`
	)

inlineexplicit

Build a SplineBuilder acting on interpolation_domain.

Parameters

interpolation_domain	The domain on which the interpolation points are defined.
cols_per_chunk	A parameter used by the slicer (internal to the solver) to define the size of a chunk of right-hand sides of the linear problem to be computed in parallel (chunks are treated by the linear solver one-after-the-other). This value is optional. If no value is provided then the default value is chosen by the requested solver.
preconditioner_max_block_size	A parameter used by the slicer (internal to the solver) to define the size of a block used by the Block-Jacobi preconditioner. This value is optional. If no value is provided then the default value is chosen by the requested solver.

See also: MatrixSparse

Definition at line 290 of file spline_builder.hpp.

◆ SplineBuilder() [3/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder	(	std::string	label,
		BatchedInterpolationDDom const &	batched_interpolation_domain,
		std::optional< std::size_t >	cols_per_chunk = `std::nullopt`,
		std::optional< unsigned int >	preconditioner_max_block_size = `std::nullopt`
	)

inlineexplicit

Build a SplineBuilder acting on the interpolation domain contained by batched_interpolation_domain.

Parameters

label	A label used to tag parallel regions and memory allocations for profiling.
batched_interpolation_domain	The whole domain on which the interpolation points are defined.
cols_per_chunk	A parameter used by the slicer (internal to the solver) to define the size of a chunk of right-hand sides of the linear problem to be computed in parallel (chunks are treated by the linear solver one-after-the-other). This value is optional. If no value is provided then the default value is chosen by the requested solver.
preconditioner_max_block_size	A parameter used by the slicer (internal to the solver) to define the size of a block used by the Block-Jacobi preconditioner. This value is optional. If no value is provided then the default value is chosen by the requested solver.

See also: MatrixSparse

Definition at line 321 of file spline_builder.hpp.

◆ SplineBuilder() [4/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder	(	BatchedInterpolationDDom const &	batched_interpolation_domain,
		std::optional< std::size_t >	cols_per_chunk = `std::nullopt`,
		std::optional< unsigned int >	preconditioner_max_block_size = `std::nullopt`
	)

inlineexplicit

Build a SplineBuilder acting on the interpolation domain contained by batched_interpolation_domain.

Parameters

batched_interpolation_domain	The whole domain on which the interpolation points are defined.
cols_per_chunk	A parameter used by the slicer (internal to the solver) to define the size of a chunk of right-hand sides of the linear problem to be computed in parallel (chunks are treated by the linear solver one-after-the-other). This value is optional. If no value is provided then the default value is chosen by the requested solver.
preconditioner_max_block_size	A parameter used by the slicer (internal to the solver) to define the size of a block used by the Block-Jacobi preconditioner. This value is optional. If no value is provided then the default value is chosen by the requested solver.

See also: MatrixSparse

Definition at line 351 of file spline_builder.hpp.

◆ SplineBuilder() [5/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver > const & x )

delete

Copy-constructor is deleted.

◆ SplineBuilder() [6/6]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::SplineBuilder ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver > && x )

default

Move-constructs.

Parameters

x	An rvalue to another SplineBuilder.

◆ ~SplineBuilder()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::~SplineBuilder ( )

default

Destructs.

Member Function Documentation

◆ operator=() [1/2]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

SplineBuilder & ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::operator= ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver > const & x )

delete

Copy-assignment is deleted.

◆ operator=() [2/2]

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

SplineBuilder & ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::operator= ( SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver > && x )

default

Move-assigns.

Parameters

x	An rvalue to another SplineBuilder.

Returns: A reference to this object.

◆ interpolation_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

interpolation_domain_type ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::interpolation_domain ( ) const

inlinenoexcept

Get the domain for the 1D interpolation mesh used by this class.

This is 1D because it is defined along the dimension of interest.

Returns: The 1D domain for the interpolation mesh.

Definition at line 393 of file spline_builder.hpp.

◆ batched_interpolation_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<concepts::discrete_domain BatchedInterpolationDDom>

BatchedInterpolationDDom ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_interpolation_domain ( BatchedInterpolationDDom const & batched_interpolation_domain ) const

inlinenoexcept

Get the whole domain representing interpolation points.

Values of the function must be provided on this domain in order to build a spline representation of the function (cartesian product of 1D interpolation_domain and batch_domain).

Parameters

batched_interpolation_domain The whole domain on which the interpolation points are defined.

Returns: The domain for the interpolation mesh.

Definition at line 409 of file spline_builder.hpp.

◆ batch_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class BatchedInterpolationDDom >

batch_domain_type< BatchedInterpolationDDom > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batch_domain ( BatchedInterpolationDDom const & batched_interpolation_domain ) const

inlinenoexcept

Get the batch domain.

Obtained by removing the dimension of interest from the whole interpolation domain.

Parameters

batched_interpolation_domain The whole domain on which the interpolation points are defined.

Returns: The batch domain.

Definition at line 426 of file spline_builder.hpp.

◆ spline_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

ddc::DiscreteDomain< bsplines_type > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::spline_domain ( ) const

inlinenoexcept

Get the 1D domain on which spline coefficients are defined.

The 1D spline domain corresponding to the dimension of interest.

Returns: The 1D domain for the spline coefficients.

Definition at line 440 of file spline_builder.hpp.

◆ batched_spline_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class BatchedInterpolationDDom >

batched_spline_domain_type< BatchedInterpolationDDom > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_spline_domain ( BatchedInterpolationDDom const & batched_interpolation_domain ) const

inlinenoexcept

Get the whole domain on which spline coefficients are defined.

Spline approximations (spline-transformed functions) are computed on this domain.

Parameters

batched_interpolation_domain The whole domain on which the interpolation points are defined.

Returns: The domain for the spline coefficients.

Definition at line 455 of file spline_builder.hpp.

◆ batched_derivs_xmin_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class BatchedInterpolationDDom >

batched_derivs_domain_type< BatchedInterpolationDDom > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_derivs_xmin_domain ( BatchedInterpolationDDom const & batched_interpolation_domain ) const

inlinenoexcept

Get the whole domain on which derivatives on lower boundary are defined.

This is only used with SplineBuilderClosure::HERMITE closure relations.

Parameters

batched_interpolation_domain The whole domain on which the interpolation points are defined.

Returns: The domain for the Derivs values.

Definition at line 499 of file spline_builder.hpp.

◆ batched_derivs_xmax_domain()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class BatchedInterpolationDDom >

batched_derivs_domain_type< BatchedInterpolationDDom > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::batched_derivs_xmax_domain ( BatchedInterpolationDDom const & batched_interpolation_domain ) const

inlinenoexcept

Get the whole domain on which derivatives on upper boundary are defined.

This is only used with SplineBuilderClosure::HERMITE closure relations.

Parameters

batched_interpolation_domain The whole domain on which the interpolation points are defined.

Returns: The domain for the Derivs values.

Definition at line 520 of file spline_builder.hpp.

◆ operator()()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class Layout , class BatchedInterpolationDDom >

void ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::operator()	(	ddc::ChunkSpan< double, batched_spline_domain_type< BatchedInterpolationDDom >, Layout, memory_space >	spline,
		ddc::ChunkSpan< double const, BatchedInterpolationDDom, Layout, memory_space >	vals,
		std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type< BatchedInterpolationDDom >, Layout, memory_space > >	derivs_xmin = `std::nullopt`,
		std::optional< ddc::ChunkSpan< double const, batched_derivs_domain_type< BatchedInterpolationDDom >, Layout, memory_space > >	derivs_xmax = `std::nullopt`
	)		const

Compute a spline approximation of a function.

Use the values of a function (defined on SplineBuilder::batched_interpolation_domain) and the derivatives of the function at the boundaries (in the case of SplineBuilderClosure::HERMITE only, defined on SplineBuilder::batched_derivs_xmin_domain and SplineBuilder::batched_derivs_xmax_domain) to calculate a spline approximation of this function.

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

Parameters

[out]	spline	The coefficients of the spline computed by this SplineBuilder.
[in]	vals	The values of the function on the interpolation mesh.
[in]	derivs_xmin	The values of the derivatives at the lower boundary (used only with SplineBuilderClosure::HERMITE lower closure relation).
[in]	derivs_xmax	The values of the derivatives at the upper boundary (used only with SplineBuilderClosure::HERMITE upper closure relation).

Definition at line 916 of file spline_builder.hpp.

◆ quadrature_coefficients()

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

template<class OutMemorySpace >

std::tuple< ddc::Chunk< double, ddc::DiscreteDomain< ddc::Deriv< typename InterpolationDDim::continuous_dimension_type > >, ddc::KokkosAllocator< double, OutMemorySpace > >, ddc::Chunk< double, ddc::DiscreteDomain< InterpolationDDim >, ddc::KokkosAllocator< double, OutMemorySpace > >, ddc::Chunk< double, ddc::DiscreteDomain< ddc::Deriv< typename InterpolationDDim::continuous_dimension_type > >, ddc::KokkosAllocator< double, OutMemorySpace > > > ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::quadrature_coefficients ( ) const

Compute the quadrature coefficients associated to the b-splines used by this SplineBuilder.

Those coefficients can be used to perform integration way faster than SplineEvaluator::integrate().

This function solves matrix equation A^t*Q=integral_bsplines. In case of HERMITE closure relations, integral_bsplines contains the integral coefficients at the boundaries, and Q thus has to be split in three parts (quadrature coefficients for the derivatives at lower boundary, for the values inside the domain and for the derivatives at upper boundary).

A discrete function f can then be integrated using sum_j Q_j*f_j for j in interpolation_domain. If closure relation is HERMITE, sum_j Qderiv_j*(d^j f/dx^j) for j in derivs_domain must be added at the boundary.

Please refer to section 2.8.1 of Emily's Bourne phd (https://theses.fr/2022AIXM0412) for more information and to the (Non)PeriodicSplineBuilderTest for example usage to compute integrals.

Template Parameters

OutMemorySpace The Kokkos::MemorySpace on which the quadrature coefficients are be returned (but they are computed on ExecSpace then copied).

Returns: A tuple containing the three Chunks containing the quadrature coefficients (if HERMITE is not used, first and third are empty).

Definition at line 1139 of file spline_builder.hpp.

Member Data Documentation

◆ s_odd

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr bool ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_odd = BSplines::degree() % 2

staticconstexpr

Indicates if the degree of the splines is odd or even.

Definition at line 166 of file spline_builder.hpp.

◆ s_nbe_xmin

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr int ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_nbe_xmin = n_boundary_equations(SBCLower, BSplines::degree())

staticconstexpr

The number of equations defining the closure relation at the lower bound.

Definition at line 169 of file spline_builder.hpp.

◆ s_nbe_xmax

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr int ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_nbe_xmax = n_boundary_equations(SBCUpper, BSplines::degree())

staticconstexpr

The number of equations defining the closure relation at the upper bound.

Definition at line 172 of file spline_builder.hpp.

◆ s_nbv_xmin

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr int ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_nbv_xmin

staticconstexpr

Initial value:

= SBCLower == SplineBuilderClosure::HOMOGENEOUS_HERMITE
                                              ? 0
                                              : n_boundary_equations(SBCLower, BSplines::degree())

The number of input values defining the closure relation at the lower bound.

Definition at line 175 of file spline_builder.hpp.

◆ s_nbv_xmax

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr int ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_nbv_xmax

staticconstexpr

Initial value:

= SBCUpper == SplineBuilderClosure::HOMOGENEOUS_HERMITE
                                              ? 0
                                              : n_boundary_equations(SBCUpper, BSplines::degree())

The number of input values defining the closure relation at the upper bound.

Definition at line 180 of file spline_builder.hpp.

◆ s_sbc_xmin

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr ddc::SplineBuilderClosure ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_sbc_xmin = SBCLower

staticconstexpr

The closure relation implemented at the lower bound.

Definition at line 197 of file spline_builder.hpp.

◆ s_sbc_xmax

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr ddc::SplineBuilderClosure ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_sbc_xmax = SBCUpper

staticconstexpr

The closure relation implemented at the upper bound.

Definition at line 200 of file spline_builder.hpp.

◆ s_spline_solver

template<class ExecSpace , class MemorySpace , class BSplines , class InterpolationDDim , ddc::SplineBuilderClosure SBCLower, ddc::SplineBuilderClosure SBCUpper, SplineSolver Solver>

constexpr SplineSolver ddc::SplineBuilder< ExecSpace, MemorySpace, BSplines, InterpolationDDim, SBCLower, SBCUpper, Solver >::s_spline_solver = Solver

staticconstexpr

The SplineSolver giving the backend used to perform the spline approximation.

Definition at line 203 of file spline_builder.hpp.

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

spline_builder.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ exec_space

◆ memory_space

◆ continuous_dimension_type

◆ interpolation_discrete_dimension_type

◆ bsplines_type

◆ deriv_type

◆ interpolation_domain_type

◆ batched_interpolation_domain_type

◆ batch_domain_type

◆ batched_spline_domain_type

◆ batched_derivs_domain_type

Constructor & Destructor Documentation

◆ SplineBuilder() [1/6]

◆ SplineBuilder() [2/6]

◆ SplineBuilder() [3/6]

◆ SplineBuilder() [4/6]

◆ SplineBuilder() [5/6]

◆ SplineBuilder() [6/6]

◆ ~SplineBuilder()

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ interpolation_domain()

◆ batched_interpolation_domain()

◆ batch_domain()

◆ spline_domain()

◆ batched_spline_domain()

◆ batched_derivs_xmin_domain()

◆ batched_derivs_xmax_domain()

◆ operator()()

◆ quadrature_coefficients()

Member Data Documentation

◆ s_odd

◆ s_nbe_xmin

◆ s_nbe_xmax

◆ s_nbv_xmin

◆ s_nbv_xmax

◆ s_sbc_xmin

◆ s_sbc_xmax

◆ s_spline_solver