Averaging, prolongation and partial reductions

\( I \) and \( P = I^\dagger\) More...

Collaboration diagram for Averaging, prolongation and partial reductions:

Classes
struct	dg::Average< IMatrix, ContainerType >
	Topological average computations in a Cartesian topology. More...

Functions
template<class real_type , size_t Nd, size_t Md>
dg::SparseMatrix< int, real_type, thrust::host_vector >	dg::create::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 >	dg::create::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 >	dg::create::projection (std::array< unsigned, Md > axes, const aRealTopology< real_type, Nd > &g_old)
	Projection matrix along given axes.

Detailed Description

\( I \) and \( P = I^\dagger\)

Function Documentation

projection()

template<class real_type , size_t Nd, size_t Md>

dg::SparseMatrix< int, real_type, thrust::host_vector > dg::create::projection	(	std::array< unsigned, Md >	axes,
		const aRealTopology< real_type, Nd > &	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

prolongation()

template<class real_type , size_t Nd, size_t Md>

dg::SparseMatrix< int, real_type, thrust::host_vector > dg::create::prolongation	(	const aRealTopology< real_type, Nd > &	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

reduction()

template<class real_type , size_t Nd, size_t Md>

dg::SparseMatrix< int, real_type, thrust::host_vector > dg::create::reduction	(	std::array< unsigned, Md >	axes,
		const aRealTopology< real_type, Nd > &	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