strumpack::HSS Namespace Reference

Classes
class	HSSFactors
	Contains data related to ULV factorization of an HSS matrix. More...
class	HSSFactorsMPI
	Contains data related to ULV factorization of a distributed HSS matrix. More...
class	HSSMatrix
	Class to represent a sequential/threaded Hierarchically Semi-Separable matrix. More...
class	HSSMatrixBase
	Abstract base class for Hierarchically Semi-Separable (HSS) matrices. More...
class	HSSMatrixMPI
	Distributed memory implementation of the HSS (Hierarchically Semi-Separable) matrix format. More...
class	HSSOptions
	Class containing several options for the HSS code and data-structures. More...
class	TreeLocalRanges

Enumerations
enum class	CompressionAlgorithm { ORIGINAL , STABLE , HARD_RESTART }
enum class	CompressionSketch { GAUSSIAN , SJLT }
enum class	SJLTAlgo { CHUNK , PERM }
enum class	State : char { UNTOUCHED ='U' , PARTIALLY_COMPRESSED ='P' , COMPRESSED ='C' }

Functions
template<typename real_t >
real_t	default_HSS_rel_tol ()
template<typename real_t >
real_t	default_HSS_abs_tol ()
template<>
float	default_HSS_rel_tol ()
template<>
float	default_HSS_abs_tol ()
std::string	get_name (CompressionAlgorithm a)
std::string	get_name (CompressionSketch a)
std::string	get_name (SJLTAlgo a)
template<typename scalar_t >
void	draw (const HSSMatrix< scalar_t > &H, const std::string &name)
template<typename scalar_t >
void	apply_HSS (Trans op, const HSSMatrix< scalar_t > &A, const DenseMatrix< scalar_t > &B, scalar_t beta, DenseMatrix< scalar_t > &C)

Detailed Description

HSS namespace.

Enumeration Type Documentation

CompressionAlgorithm

enum class strumpack::HSS::CompressionAlgorithm

strong

Enumeration of possible versions of the randomized sampling HSS compression algorithms.

Enumerator
ORIGINAL	Start with an initial guess of the rank, double the number of random samples until desired accuracy.
STABLE	Start with an initial guess of the rank, add a fix amount of random vectors, until desired accuracy is reached.
HARD_RESTART	Start with an initial guess of the rank, add a fix amount of random vectors, if not enough, start again from scratch using twice as many random sample vectors.

CompressionSketch

enum class strumpack::HSS::CompressionSketch

strong

Enumeration of possible versions of the randomized sampling HSS sketching matrices.

Enumerator
GAUSSIAN	Sketch using iid gaussian entries mean 0 variance 1.
SJLT	Sketch using the sparse Johnson-Lindenstrauss transform, with nnz entries per row randomly selected each with a value of 1/sqrt(nnz) with pr = 0.5 or -1/sqrt(nnz) with pr = 0.5.

SJLTAlgo

enum class strumpack::HSS::SJLTAlgo

strong

Enumerator
CHUNK	puts nnz nonzeros in each row by spliting the row into col/nnz chunks and putting one nonzero in each
PERM	puts nnz nonzeros on each row by permuting all col indices and taking the first nnz

State

enum class strumpack::HSS::State : char

strong

Enumeration of possible states of an HSS matrix/node. This is used in the adaptive HSS compression algorithms, where a node can be untouched (it is not yet visited by the compression algorithm), partially_compressed (a compression was attempted but failed, so the adaptive algorithm will have to try again), or can be successfully compressed.

Enumerator
UNTOUCHED	Node was not yet visited by the compression algorithm
PARTIALLY_COMPRESSED	Compression was attempted for this node, but failed. The adaptive compression should try again.
COMPRESSED	This HSS node was succesfully compressed.

Function Documentation

apply_HSS()

template<typename scalar_t >

void strumpack::HSS::apply_HSS	(	Trans	op,
		const HSSMatrix< scalar_t > &	A,
		const DenseMatrix< scalar_t > &	B,
		scalar_t	beta,
		DenseMatrix< scalar_t > &	C
	)

Compute C = op(A) * B + beta * C, with HSS matrix A.

Parameters

op	Transpose/complex conjugate or none to be applied to the HSS matrix A.
A	HSS matrix
B	Dense matrix
beta	Scalar
C	Result, should already be allocated to the appropriate size.

default_HSS_abs_tol() [1/2]

template<typename real_t >

real_t strumpack::HSS::default_HSS_abs_tol ( )

inline

Get the default absolute HSS compression tolerance (this is for double precision, might be overloaded for single precision). This can be changed using the HSSOptions object.

default_HSS_abs_tol() [2/2]

template<>

float strumpack::HSS::default_HSS_abs_tol ( )

inline

Get the default absolute HSS compression tolerance for single precision computations. This can be changed using the HSSOptions object.

default_HSS_rel_tol() [1/2]

template<typename real_t >

real_t strumpack::HSS::default_HSS_rel_tol ( )

inline

Get the default relative HSS compression tolerance (this is for double precision, might be overloaded depending on floating point precision). This can be changed using the HSSOptions object. Tuning this parameter (in the HSSOptions object) is crucial for performance of the HSS algorithms.

default_HSS_rel_tol() [2/2]

template<>

float strumpack::HSS::default_HSS_rel_tol ( )

inline

Get the default relative HSS compression tolerance for single precision computations. This can be changed using the HSSOptions object. Tuning this parameter (in the HSSOptions<float> object) is crucial for performance of the HSS algorithms.

draw()

template<typename scalar_t >

void strumpack::HSS::draw	(	const HSSMatrix< scalar_t > &	H,
		const std::string &	name
	)

Write a gnuplot script to draw this an matrix.

Parameters

H	HSS matrix to draw.
name	Name of the HSS matrix. The script will be created in the file plotname.gnuplot.

get_name() [1/3]

std::string strumpack::HSS::get_name

(

CompressionAlgorithm

a

)

Return a string with the name of the compression algorithm.

Parameters

a	type of the randomized compression algorihtm

Returns

name, string with a short description

get_name() [2/3]

std::string strumpack::HSS::get_name

(

CompressionSketch

a

)

Return a string with the name of the compression algorithm.

Parameters

a	type of the randomized compression algorihtm

Returns

name, string with a short description

get_name() [3/3]

std::string strumpack::HSS::get_name

(

SJLTAlgo

a

)

Return a string with the name of the sjlt algorithm.

Parameters

a	type of SJLT sampling algorithm

Returns

name, string with a short description