dg::create Namespace Reference

Contains functions used for matrix creation. More...

Functions
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	derivative (unsigned coord, const aRealTopology< real_type, Nd > &g, dg::bc bc, direction dir=centered)
	Create a derivative along given coordinate.
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	jump (unsigned coord, const aRealTopology< real_type, Nd > &g, dg::bc bc)
	Create a jump matrix along given coordinate.
template<class Topology >
auto	dx (const Topology &g, dg::bc bc, dg::direction dir=centered)
template<class Topology >
auto	dy (const Topology &g, dg::bc bc, dg::direction dir=centered)
	Short for dg::create::derivative( 1, g, bc, dir);
template<class Topology >
auto	dz (const Topology &g, dg::bc bc, dg::direction dir=centered)
	Short for dg::create::derivative( 2, g, bc, dir);
template<class Topology >
auto	jumpX (const Topology &g, bc bc)
	Short for dg::create::jump( 0, g, bc);
template<class Topology >
auto	jumpY (const Topology &g, bc bc)
	Short for dg::create::jump( 1, g, bc);
template<class Topology >
auto	jumpZ (const Topology &g, bc bc)
	Short for dg::create::jump( 2, g, bc);
template<class Topology >
auto	derivative (unsigned coord, const Topology &g, direction dir=centered)
	Short for dg::create::derivative( coord, g, g.bcx(), dir);
template<class Topology >
auto	jump (unsigned coord, const Topology &g)
	Short for dg::create::jump( coord, g, g.bcx());
template<class Topology >
auto	dx (const Topology &g, dg::direction dir=centered)
	Short for dg::create::derivative( 0, g, g.bcx() dir);
template<class Topology >
auto	dy (const Topology &g, dg::direction dir=centered)
	Short for dg::create::derivative( 1, g, g.bcy(), dir);
template<class Topology >
auto	dz (const Topology &g, dg::direction dir=centered)
	Short for dg::create::derivative( 2, g, g.bcz(), dir);
template<class Topology >
auto	jumpX (const Topology &g)
	Short for dg::create::jump( 0, g, g.bcx());
template<class Topology >
auto	jumpY (const Topology &g)
	Short for dg::create::jump( 1, g, g.bcy());
template<class Topology >
auto	jumpZ (const Topology &g)
	Short for dg::create::jump( 2, g, g.bcz());
template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	derivative (unsigned coord, const aRealTopologyX2d< real_type > &g, dg::bc bc, direction dir=centered)
	Create 2d derivative in x-direction.
template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	jump (unsigned coord, const aRealTopologyX2d< real_type > &g, bc bc)
	Matrix that contains 2d jump terms in X direction.
template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	jump (unsigned coord, const aRealTopologyX3d< real_type > &g, bc bc)
	Matrix that contains jump terms in X direction in 3D.
template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	derivative (unsigned coord, const aRealTopologyX3d< real_type > &g, bc bc, direction dir=centered)
	Create 3d derivative in x-direction.
template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dx (const RealGridX1d< real_type > &g, bc bcx, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d.
template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dx (const RealGridX1d< real_type > &g, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d.
template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	jump (const RealGridX1d< real_type > &g, bc bcx)
	Create and assemble a host Matrix for the jump in 1d.
template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	jump (const RealGridX1d< real_type > &g)
	Create and assemble a host Matrix for the jump in 1d.
template<class real_type >
dg::HMatrix_t< real_type >	fast_interpolation1d (const RealGrid1d< real_type > &t, unsigned multiplyn, unsigned multiplyNx)
	Create interpolation matrix for integer multipliers.
template<class real_type >
dg::HMatrix_t< real_type >	fast_projection1d (const RealGrid1d< real_type > &t, unsigned dividen, unsigned divideNx)
	Create projecton matrix for integer dividers.
template<class real_type >
dg::HMatrix_t< real_type >	fast_transform1d (const dg::SquareMatrix< real_type > &opx, const RealGrid1d< real_type > &t)
	Create a block-diagonal matrix.
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	fast_interpolation (unsigned coord, const aRealTopology< real_type, Nd > &t, unsigned multiplyn, unsigned multiplyNx)
	Create interpolation matrix for integer multipliers.
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	fast_projection (unsigned coord, const aRealTopology< real_type, Nd > &t, unsigned dividen, unsigned divideNx)
	Create projecton matrix for integer dividers.
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	fast_transform (unsigned coord, const dg::SquareMatrix< real_type > &opx, const aRealTopology< real_type, Nd > &t)
	Create a block-diagonal matrix.
template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	fast_interpolation (unsigned coord, const aRealMPITopology< real_type, Nd > &t, unsigned multiplyn, unsigned multiplyNx)
	Create interpolation matrix for integer multipliers.
template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	fast_projection (unsigned coord, const aRealMPITopology< real_type, Nd > &t, unsigned dividen, unsigned divideNx)
	Create projecton matrix for integer dividers.
template<class real_type , size_t Nd>
MHMatrix_t< real_type >	fast_transform (unsigned coord, dg::SquareMatrix< real_type > opx, const aRealMPITopology< real_type, Nd > &t)
	Create a block-diagonal matrix.
template<class Topology >
auto	fast_interpolation (const Topology &t, unsigned multiplyn, unsigned multiplyNx, unsigned multiplyNy)
	Create interpolation matrix for integer multipliers in the first 2 grid dimensions.
template<class Topology >
auto	fast_projection (const Topology &t, unsigned dividen, unsigned divideNx, unsigned divideNy)
	Create projection matrix for integer dividers in the first 2 grid dimensions.
template<class Topology >
auto	fast_transform (const dg::SquareMatrix< typename Topology::value_type > &opx, const dg::SquareMatrix< typename Topology::value_type > &opy, const Topology &t)
	Create transform matrix in the first 2 grid dimensions.
template<class real_type >
dg::TriDiagonal< dg::HVec_t< real_type > >	fem_mass (const RealGrid1d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::TriDiagonal< dg::HVec_t< real_type > >	fem_linear2const (const RealGrid1d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	fem_mass (const aRealTopology2d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	inv_fem_mass (const aRealTopology2d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	fem_linear2const (const aRealTopology2d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	inv_fem_linear2const (const aRealTopology2d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	fem_mass2d (const aRealTopology3d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int v_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	inv_fem_mass2d (const aRealTopology3d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
dg::KroneckerTriDiagonal2d< dg::HVec_t< real_type > >	fem_linear2const2d (const aRealTopology3d< real_type > &g)
	\( S_{ij} = \frac{1}{w_i}\int c_i(x) v_j(x) \) finite element projection matrix
template<class real_type >
dg::InverseKroneckerTriDiagonal2d< dg::HVec_t< real_type > >	inv_fem_linear2const2d (const aRealTopology3d< real_type > &g)
	Inverse finite element mass matrix \( S^{-1} \).
template<class real_type >
thrust::host_vector< real_type >	fem_weights (const RealGrid1d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	fem_inv_weights (const RealGrid1d< real_type > &g)
	inverse finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	fem_weights (const aRealTopology2d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	fem_inv_weights (const aRealTopology2d< real_type > &g)
	inverse finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	fem_weights (const aRealTopology3d< real_type > &g)
	finite element weight coefficients
template<class real_type >
thrust::host_vector< real_type >	fem_inv_weights (const aRealTopology3d< real_type > &g)
	inverse finite element weight coefficients
template<class UnaryOp >
dg::SquareMatrix< std::invoke_result_t< UnaryOp, unsigned > >	modal_filter (UnaryOp op, unsigned n)
	Create a modal filter block \( V D V^{-1}\).
template<class RecursiveHostVector , class real_type , size_t Nd>
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const RecursiveHostVector &x, const aRealTopology< real_type, Nd > &g, std::array< dg::bc, Nd > bcx, std::string method="dg")
	Create interpolation matrix of a list of points in given grid.
template<class host_vector , class real_type , typename = std::enable_if_t<dg::is_vector_v<host_vector>>>
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const host_vector &x, const RealGrid1d< real_type > &g, dg::bc bcx=dg::NEU, std::string method="dg")
	Create interpolation matrix.
template<class host_vector , class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const host_vector &x, const host_vector &y, const aRealTopology2d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, std::string method="dg")
	Create interpolation matrix.
template<class host_vector , class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const host_vector &x, const host_vector &y, const host_vector &z, const aRealTopology3d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, dg::bc bcz=dg::PER, std::string method="dg")
	Create interpolation matrix.
template<class real_type , size_t Nd>
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const aRealTopology< real_type, Nd > &g_new, const aRealTopology< real_type, Nd > &g_old, std::string method="dg")
	Create interpolation between two grids.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const thrust::host_vector< real_type > &x, const RealGridX1d< real_type > &g)
	Create interpolation matrix.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const thrust::host_vector< real_type > &x, const thrust::host_vector< real_type > &y, const aRealTopologyX2d< real_type > &g, dg::bc globalbcz=dg::NEU)
	Create interpolation matrix.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const thrust::host_vector< real_type > &x, const thrust::host_vector< real_type > &y, const thrust::host_vector< real_type > &z, const aRealTopologyX3d< real_type > &g, dg::bc globalbcz=dg::NEU)
	Create interpolation matrix.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const RealGridX1d< real_type > &g_new, const RealGridX1d< real_type > &g_old)
	Create interpolation between two grids.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const aRealTopologyX2d< real_type > &g_new, const aRealTopologyX2d< real_type > &g_old)
	Create interpolation between two grids.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	interpolation (const aRealTopologyX3d< real_type > &g_new, const aRealTopologyX3d< real_type > &g_old)
	Create interpolation between two grids.
template<class real_type >
thrust::host_vector< real_type >	forward_transform (const thrust::host_vector< real_type > &in, const aRealTopologyX2d< real_type > &g)
	Transform a vector from XSPACE to LSPACE.
template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	derivative (unsigned coord, const aRealMPITopology< real_type, Nd > &g, dg::bc bc, direction dir=centered)
	Create a derivative along the given coordinate for mpi.
template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	jump (unsigned coord, const aRealMPITopology< real_type, Nd > &g, dg::bc bc)
	Create a jump matrix along given coordinate for mpi.
template<class MPITopology , typename = std::enable_if_t<dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>
dg::MIHMatrix_t< typename MPITopology::value_type >	interpolation (const MPITopology &g_new, const MPITopology &g_old, std::string method="dg")
	Create interpolation between two grids.
template<class MPITopology , typename = std::enable_if_t<dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>
dg::MIHMatrix_t< typename MPITopology::value_type >	projection (const MPITopology &g_new, const MPITopology &g_old, std::string method="dg")
	Create a projection between two grids.
template<class RecursiveHostVector , class real_type , size_t Nd>
dg::MIHMatrix_t< real_type >	interpolation (const RecursiveHostVector &x, const aRealMPITopology< real_type, Nd > &g, std::array< dg::bc, Nd > bcx, std::string method="dg")
	Create interpolation matrix of a list of points in given grid.
template<class host_vector , class real_type >
dg::MIHMatrix_t< real_type >	interpolation (const host_vector &x, const RealMPIGrid1d< real_type > &g, dg::bc bcx=dg::NEU, std::string method="dg")
	Create an MPI row distributed interpolation 1d matrix.
template<class host_vector , class real_type >
dg::MIHMatrix_t< real_type >	interpolation (const host_vector &x, const host_vector &y, const aRealMPITopology2d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, std::string method="dg")
	Create an MPI row distributed interpolation 2d matrix.
template<class host_vector , class real_type >
dg::MIHMatrix_t< real_type >	interpolation (const host_vector &x, const host_vector &y, const host_vector &z, const aRealMPITopology3d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, dg::bc bcz=dg::PER, std::string method="dg")
	Create an MPI row distributed interpolation 3d matrix.
template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>
dg::MIHMatrix_t< typename MPITopology::value_type >	prolongation (const MPITopology &g_new, std::array< unsigned, Md > axes)
	Prolongation matrix along given axes / Transpose of reduction.
template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>
dg::MIHMatrix_t< typename MPITopology::value_type >	reduction (std::array< unsigned, Md > axes, const MPITopology &g_old)
	Reduction matrix along given axes.
template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>
dg::MIHMatrix_t< typename MPITopology::value_type >	projection (std::array< unsigned, Md > axes, const MPITopology &g_old)
	Projection matrix along given axes.
template<class T >
T	lu_pivot (dg::SquareMatrix< T > &m, std::vector< unsigned > &p)
	LU Decomposition with partial pivoting.
template<class T >
dg::SquareMatrix< T >	inverse (const dg::SquareMatrix< T > &in)
	Invert a square matrix.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	diagonal (const thrust::host_vector< real_type > &diagonal)
	Create a diagonal matrix.
template<class real_type , size_t Nd>
dg::SparseMatrix< int, real_type, thrust::host_vector >	projection (const aRealTopology< real_type, Nd > &g_new, const aRealTopology< real_type, Nd > &g_old, std::string method="dg")
	Create a projection between two grids.
template<class real_type , size_t Nd>
dg::SparseMatrix< int, real_type, thrust::host_vector >	transformation (const aRealTopology< real_type, Nd > &g_new, const aRealTopology< real_type, Nd > &g_old)
	Create a transformation matrix between two grids.
template<class real_type , size_t Nd>
dg::IHMatrix_t< real_type >	backproject (const aRealTopology< real_type, Nd > &g)
	Create a matrix \( PI\) that projects values to an equidistant grid.
template<class real_type , size_t Nd>
dg::IHMatrix_t< real_type >	inv_backproject (const aRealTopology< real_type, Nd > &g)
	Create a matrix \( (PI)^{-1}\) that transforms values from an equidistant grid back to a dg grid.
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	projection (const RealGridX1d< real_type > &g_new, const RealGridX1d< real_type > &g_old, std::string method="dg")
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	projection (const aRealTopologyX2d< real_type > &g_new, const aRealTopologyX2d< real_type > &g_old, std::string method="dg")
template<class real_type >
dg::SparseMatrix< int, real_type, thrust::host_vector >	projection (const aRealTopologyX3d< real_type > &g_new, const aRealTopologyX3d< real_type > &g_old, std::string method="dg")
template<class real_type , size_t Nd, size_t Md>
dg::SparseMatrix< int, real_type, thrust::host_vector >	prolongation (const aRealTopology< real_type, Nd > &g_new, std::array< unsigned, Md > axes)
	Prolongation matrix along given axes / Transpose of reduction.
template<class real_type , size_t Nd, size_t Md>
dg::SparseMatrix< int, real_type, thrust::host_vector >	reduction (std::array< unsigned, Md > axes, const aRealTopology< real_type, Nd > &g_old)
	Reduction matrix along given axes.
template<class real_type , size_t Nd, size_t Md>
dg::SparseMatrix< int, real_type, thrust::host_vector >	projection (std::array< unsigned, Md > axes, const aRealTopology< real_type, Nd > &g_old)
	Projection matrix along given axes.
template<class real_type >
dg::IHMatrix_t< real_type >	window_stencil (unsigned window_size, const RealGrid1d< real_type > &g, dg::bc bcx)
	A 1d centered window stencil.
template<class real_type >
dg::IHMatrix_t< real_type >	limiter_stencil (const RealGrid1d< real_type > &g, dg::bc bound)
	A stencil for the dg Slope limiter.
template<class real_type >
dg::IHMatrix_t< real_type >	window_stencil (std::array< int, 2 > window_size, const aRealTopology2d< real_type > &g, dg::bc bcx, dg::bc bcy)
	A 2d centered window stencil.
template<class real_type >
dg::IHMatrix_t< real_type >	limiter_stencil (enum coo3d direction, const aRealTopology2d< real_type > &g, dg::bc bound)
	A stencil for the dg Slope limiter.
template<class real_type >
dg::IHMatrix_t< real_type >	limiter_stencil (enum coo3d direction, const aRealTopology3d< real_type > &g, dg::bc bound)
	A stencil for the dg Slope limiter.
template<class real_type >
dg::IHMatrix_t< real_type >	window_stencil (std::array< int, 2 > window_size, const aRealTopology3d< real_type > &g, dg::bc bcx, dg::bc bcy)
	A 2d centered window stencil.
template<class real_type >
dg::MIHMatrix_t< real_type >	window_stencil (std::array< int, 2 > window_size, const aRealMPITopology2d< real_type > &g, dg::bc bcx, dg::bc bcy)
	A 2d centered window stencil.
template<class real_type >
dg::MIHMatrix_t< real_type >	window_stencil (std::array< int, 2 > window_size, const aRealMPITopology3d< real_type > &g, dg::bc bcx, dg::bc bcy)
	A 2d centered window stencil.
template<class Geometry >
Geometry::host_vector	volume (const Geometry &g)
	Create the volume element on the grid (including weights!!)
template<class Geometry >
Geometry::host_vector	inv_volume (const Geometry &g)
	Create the inverse volume element on the grid (including weights!!)
template<class Topology >
auto	weights (const Topology &g)
	Nodal weight coefficients.
template<class Topology >
auto	weights (const Topology &g, std::array< bool, Topology::ndim()> remains)
	Nodal weight coefficients on a subset of dimensions.
template<class Topology >
auto	inv_weights (const Topology &g)
	Inverse nodal weight coefficients.
template<class real_type >
dg::IHMatrix_t< real_type >	backscatter (const RealGrid1d< real_type > &g)
	Create a matrix \( B_{eq} F\) that interpolates values to an equidistant grid ready for visualisation.
template<class real_type >
dg::IHMatrix_t< real_type >	backscatter (const aRealTopology2d< real_type > &g)
	Create a matrix \( B_{eq} F\) that interpolates values to an equidistant grid ready for visualisation.
template<class real_type >
dg::IHMatrix_t< real_type >	backscatter (const aRealTopology3d< real_type > &g)
	Create a matrix \( B_{eq} F\) that interpolates values to an equidistant grid ready for visualisation.
template<class real_type >
dg::IHMatrix_t< real_type >	inv_backscatter (const RealGrid1d< real_type > &g)
	Create a matrix \( (B_{eq} F)^{-1}\) that transforms values from an equidistant grid back to a dg grid.
template<class real_type >
dg::IHMatrix_t< real_type >	inv_backscatter (const aRealTopology2d< real_type > &g)
	Create a matrix \( (B_{eq} F)^{-1}\) that transforms values from an equidistant grid back to a dg grid.
template<class real_type >
dg::IHMatrix_t< real_type >	inv_backscatter (const aRealTopology3d< real_type > &g)
	Create a matrix \( (B_{eq} F)^{-1}\) that transforms values from an equidistant grid back to a dg grid.

Detailed Description

Contains functions used for matrix creation.

Function Documentation

forward_transform()

template<class real_type >

thrust::host_vector< real_type > dg::create::forward_transform	(	const thrust::host_vector< real_type > &	in,
		const aRealTopologyX2d< real_type > &	g )

Transform a vector from XSPACE to LSPACE.

Parameters

in	input
g	grid

Returns

the vector in LSPACE

projection()

template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>

dg::MIHMatrix_t< typename MPITopology::value_type > dg::create::projection	(	std::array< unsigned, Md >	axes,
		const MPITopology &	g_old )

Projection matrix along given axes.

For example if you have 2d vectors in the x-y plane that you want to reduce along the y-direction:

dg::Grid2d g2d( ...);
auto project = dg::create::projection ( std::array{1u}, g2d);

Template Parameters

Nd	Full grid number of dimenensions
Md	Number of dimensions to reduce Md<Nd

Parameters

axes	Axis numbers in g_old along which to reduce axes[i]<g_old.ndim()
g_old	Grid of the old, un-reduced vectors

Returns

matrix that acts on vectors on the un-reduced grid g_old and produces vectors on g_old w/o axes

See also

prolongation Average

Projection is the adjoint of a prolongation

Note

In MPI this represents an "Allreduce" i.e. all ranks along the reduction direction get the result

prolongation()

template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>

dg::MIHMatrix_t< typename MPITopology::value_type > dg::create::prolongation	(	const MPITopology &	g_new,
		std::array< unsigned, Md >	axes )

Prolongation matrix along given axes / Transpose of reduction.

For example if you have 2d vectors in the x-y plane that you want to prolong along the z-direction:

dg::Grid3d g3d( ...);
// Create prolongation along the 2 axis of g3d to g3d
auto prolong = dg::create::prolongation ( g3d, std::array{2u});
// Means you have vectors in the 0 and 1 axis

Template Parameters

Nd	Prolongated grid number of dimenensions
Md	Number of dimensions to prolongate Md<Nd

Parameters

g_new	the grid of the new, prolongated vectors
axes	Axis numbers in g_new along which to prolong. Does not need to be sorted but axes[i] < Nd

Returns

matrix that acts on vectors on the reduced grid g_new w/o axes and produces vectors on g_new

See also

Prolongation is the transpose of a reduction and adjoint of projection

Note

In MPI there is no communication involved

reduction()

template<class MPITopology , size_t Md, typename = std::enable_if_t< dg::is_vector_v< typename MPITopology::host_vector, MPIVectorTag>>>

dg::MIHMatrix_t< typename MPITopology::value_type > dg::create::reduction	(	std::array< unsigned, Md >	axes,
		const MPITopology &	g_old )

Reduction matrix along given axes.

For example if you have 2d vectors in the x-y plane that you want to reduce along the y-direction:

dg::Grid2d g2d( ...);
auto reduce = dg::create::reduction ( std::array{1u}, g2d);

Template Parameters

Nd	Full grid number of dimenensions
Md	Number of dimensions to reduce Md<Nd

Parameters

axes	Axis numbers in g_old along which to reduce
g_old	Grid of the old, un-reduced vectors

Returns

matrix that acts on vectors on the un-reduced grid g_old and produces vectors on g_old w/o axes

Note

Weights multiply through in 1/W R W

See also

projection Average

Reduction is the transpose of a prolongation

Note

In MPI this represents an "Allreduce" i.e. all ranks along the reduction direction get the result