ACA Class Reference

class performing Adaptive Cross Approximation More...

#include <aca.hpp>

Public Member Functions
template<class Matrix , class RowArray , class ColumnArray , class BlockArray , class Input , class Output , class Ranks >
void	multiply (Matrix const &M, Eigen::DenseBase< RowArray > const &rowClusters, Eigen::DenseBase< ColumnArray > const &colClusters, Eigen::DenseBase< BlockArray > const &blocks, Input const &input, Output &output, double eps, int maxRank, Ranks &outRanks)
	Compute matrix-vector product with multilevel low rank approximation. More...
int	get_nEval (void) const
	return number of matrix evaluations
int	get_matrixSize (void) const
	number of matrix elements in processed blocks
double	get_sizeCompression (void) const
	return the size compression ratio

Static Public Member Functions
template<class Matrix , class Result >
static int	low_rank_approx (Matrix const &M, int nRows, int nCols, double eps, int R, Eigen::DenseBase< Result > &U, Eigen::DenseBase< Result > &V)
	compute low rank approximation of a matrix with a prescribed accuracy and maximum rank More...
template<class Matrix , class RowArray , class ColumnArray , class BlockArray >
static std::vector< LowRank< typename Matrix::Scalar > >	decompose (Matrix const &M, Eigen::DenseBase< RowArray > const &rowClusters, Eigen::DenseBase< ColumnArray > const &colClusters, Eigen::DenseBase< BlockArray > const &blocks, double eps, int maxRank)
	decompose a matrix into ACA low rank decomposition More...

Detailed Description

class performing Adaptive Cross Approximation

Definition at line 71 of file aca.hpp.

Member Function Documentation

decompose()

template<class Matrix , class RowArray , class ColumnArray , class BlockArray >

static std::vector<LowRank<typename Matrix::Scalar> > ACA::decompose ( Matrix const &  M, Eigen::DenseBase< RowArray > const &  rowClusters, Eigen::DenseBase< ColumnArray > const &  colClusters, Eigen::DenseBase< BlockArray > const &  blocks, double  eps, int  maxRank  )

inlinestatic

decompose a matrix into ACA low rank decomposition

Template Parameters

Matrix
RowArray
ColumnArray
BlockArray

Parameters

[in]	M	the matrix to decompose
[in]	rowClusters	the matrix of row clusters
[in]	colCluster	the matrix of column clusters
[in]	blocks	the matrix of block indices

Returns

a std::vector of LowRank objects representing the LRA

Definition at line 285 of file aca.hpp.

low_rank_approx()

template<class Matrix , class Result >

static int ACA::low_rank_approx ( Matrix const &  M, int  nRows, int  nCols, double  eps, int  R, Eigen::DenseBase< Result > &  U, Eigen::DenseBase< Result > &  V  )

inlinestatic

compute low rank approximation of a matrix with a prescribed accuracy and maximum rank

The low rank approximation is of the form M = U * V.transpose()

Template Parameters

Matrix	the matrix class
Result	the type of the result (Eigen matrix)

Parameters

[in]	M	the matrix to approximate
[in]	nRows	the number of matrix rows
[in]	nCols	the number of matrix cols
[in]	eps	the prescribed approximation accuracy
[in]	R	the maximum rank (number of iterations)
[out]	U	lhs term of the approximation
[out]	V	rhs term of the approximation

Returns

the actual rank of the approximation ( <= R )

Definition at line 135 of file aca.hpp.

multiply()

template<class Matrix , class RowArray , class ColumnArray , class BlockArray , class Input , class Output , class Ranks >

void ACA::multiply ( Matrix const &  M, Eigen::DenseBase< RowArray > const &  rowClusters, Eigen::DenseBase< ColumnArray > const &  colClusters, Eigen::DenseBase< BlockArray > const &  blocks, Input const &  input, Output &  output, double  eps, int  maxRank, Ranks &  outRanks  )

inline

Compute matrix-vector product with multilevel low rank approximation.

Template Parameters

Matrix	the matrix class
RowArray	type of the array storing the row cluster tree
ColumnArray	type of the array storing the column cluster tree
BlockArray	type of the array storing the block tree
Input	type of the input vector
Output	type of the output vector

Parameters

[in]	rowClusters	the row cluster tree as Eigen matrix
[in]	colClusters	the column cluster tree as Eigen matrix
[in]	blocks	the block tree as Eigen matrix
[in]	input	the input vector
[out]	output	the output vector
[in]	eps	the ACA approximation error
[in]	maxRank	the maximal ACA approximation rank

Definition at line 217 of file aca.hpp.

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

• src/aca/aca.hpp