uses hybrid cross approximation (HCA) for computing low rank approximation More...

#include <TLowRankApx.hh>

Inheritance diagram for THCA< T >:

Classes
struct	stat_t

class	TGeneratorFn
	class defining kernel generator function used by HCA More...

Public Member Functions
	THCA (const coeff_fn_t coeff, const TGeneratorFn generator, const real_t aca_eps, const uint ipol_order, const bool recompress=true)

virtual TMatrix *	build (const TBlockCluster *bc, const TTruncAcc &acc) const

Protected Member Functions
void	setup_interpolation ()
	build interpolation points for unit cube in

void	transform_ipol_points (const TGeomCluster *cl, tensor_grid_t &grid, const uint ipol_order) const
	transform interpolation points to local cluster

void	compute_row (const idx_t row_idx, const tensor_grid_t &rowcl_grid, const tensor_grid_t &colcl_grid, const BLAS::Matrix< value_t > &A, const BLAS::Matrix< value_t > &B, const size_t rank, BLAS::Vector< value_t > &row, const uint ipol_order) const
	compute single corrected row of kernel generator matrix

void	compute_col (const idx_t col_idx, const tensor_grid_t &rowcl_grid, const tensor_grid_t &colcl_grid, const BLAS::Matrix< value_t > &A, const BLAS::Matrix< value_t > &B, const size_t rank, BLAS::Vector< value_t > &col, const uint ipol_order) const
	compute single corrected row of kernel generator matrix

void	compute_U (const TIndexSet &rowis, const size_t rank, BLAS::Matrix< value_t > &U, const std::vector< idx_t > &col_pivot, const tensor_grid_t &colcl_grid, const uint ipol_order) const
	compute matrix U

void	compute_V (const TIndexSet &colis, const size_t rank, BLAS::Matrix< value_t > &V, const std::vector< idx_t > &row_pivot, const tensor_grid_t &rowcl_grid, const uint ipol_order) const
	compute matrix V

Detailed Description

template<typename T>
class HLIB::THCA< T >

THCA provides a low rank approximation algorithm with a guaranteed approximation quality. It is based on the generator function $\gamma(x,y)$ of a BEM kernel function $k(x,y)$ and it's derivatives $D_x \gamma(x, y_{l})$ and $D_y \gamma(x, y_{l})$ .

The class THCA needs a user implemented generator function of type TGeneratorFn, in which the function itself and the integrals of the corresponding derivates are defined.

Furthermore, HCA is based on interpolation, of which the order defines the accuracy of the final result. This interpolation order together with an accuracy for the approximation of the generator function is specific to the given problem, and hence, user defined.

Constructor & Destructor Documentation

◆ THCA()

THCA	(	const coeff_fn_t *	coeff,
		const TGeneratorFn *	generator,
		const real_t	aca_eps,
		const uint	ipol_order,
		const bool	recompress = `true`
	)

construct HCA based on matrix coefficient function coeff and kernel generator function generator.

The accuracy of the HCA algorithm is defined by aca_eps, the relative accuracy of the internal ACA algorithm and the interpolation order ipol_order. If recompress is true, the resulting low-rank matrix will be recompressed by using SVD for optimal rank.

Member Function Documentation

◆ build()

virtual TMatrix* build	(	const TBlockCluster *	bc,
		const TTruncAcc &	acc
	)		const

virtual

build low rank matrix for block cluster bct with rank defined by accuracy acc

Implements TLowRankApx.

Classes

Public Member Functions