PaStiX Handbook: Internal functions for low-rank kernels

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Data Structures
struct	pastix_lrblock_s
	The block low-rank structure to hold a matrix in low-rank form. More...

struct	pastix_lr_s
	Structure to define the type of function to use for the low-rank kernels and their parameters. More...

Macros
#define	PASTIX_LRM3_ORTHOU (1 << 0)
	Macro to specify if the U part of a low-rank matrix is orthogonal or not (Used in LRMM functions).

#define	PASTIX_LRM3_ALLOCU (1 << 1)
	Macro to specify if the U part of a low-rank matrix has been allocated and need to be freed or not (Used in LRMM functions).

#define	PASTIX_LRM3_ALLOCV (1 << 2)
	Macro to specify if the V part of a low-rank matrix has been allocated and need to be freed or not (Used in LRMM functions).

#define	PASTIX_LRM3_TRANSB (1 << 3)
	Macro to specify if the the operator on B, still needs to be applied to the V part of the low-rank matrix or not (Used in LRMM functions).

Typedefs
typedef struct pastix_lr_s	pastix_lr_t
	Structure to define the type of function to use for the low-rank kernels and their parameters.

typedef struct pastix_lrblock_s	pastix_lrblock_t
	The block low-rank structure to hold a matrix in low-rank form.

typedef pastix_fixdbl_t(*	fct_ge2lr_t) (int, pastix_fixdbl_t, pastix_int_t, pastix_int_t, pastix_int_t, const void , pastix_int_t, pastix_lrblock_t )
	Type of the functions to compress a dense block into a low-rank form.

typedef pastix_fixdbl_t(*	fct_rradd_t) (const pastix_lr_t , pastix_trans_t, const void , pastix_int_t, pastix_int_t, const pastix_lrblock_t , pastix_int_t, pastix_int_t, pastix_lrblock_t , pastix_int_t, pastix_int_t)
	Type of the functions to add two low-rank blocks together.

typedef enum memory_stats_e	memory_stats_t
	Enum to define the type of block.

Enumerations
enum	memory_stats_e { FR_InDiag = 0 , FR_OffDiag = 1 , LR_InDiag = 2 , LR_InSele = 3 , LR_OffDiag = 4 , LR_DInD = 5 , MEMORY_STATS_SIZE }
	Enum to define the type of block. More...

Functions
static pastix_int_t	core_get_rklimit_max (pastix_int_t M, pastix_int_t N)
	Compute the maximal rank accepted for a given matrix size for testings.

static pastix_int_t	core_get_rklimit_end (pastix_int_t M, pastix_int_t N)
	Compute the maximal rank accepted for a given matrix size for Just-In-Time strategy.

static pastix_int_t	core_get_rklimit_begin (pastix_int_t M, pastix_int_t N)
	Compute the maximal rank accepted for a given matrix size for Minimal-Memory strategy.

static pastix_int_t	core_get_rklimit_test (pastix_int_t M, pastix_int_t N)
	TODO.

Variables
const char *	compmeth_shnames [PastixCompressMethodNbr]
	List of short names for the compression kernels.

const char *	compmeth_lgnames [PastixCompressMethodNbr]
	List of long names for the compression kernels.

double	pastix_lr_minratio
	Define the minimal ratio for which we accept to compress a matrix into a low-rank form or not.

pastix_int_t	pastix_lr_ortho
	Define the orthogonalization method.

pastix_int_t(*	core_get_rklimit )(pastix_int_t, pastix_int_t)
	Compute the maximal rank accepted for a given matrix size. The pointer is set according to the low-rank strategy used.

const fct_ge2lr_t	ge2lrMethods [PastixCompressMethodNbr][4]
	Array of pointers to the multiple arithmetic and algorithmic variants of ge2lr.

const fct_rradd_t	rraddMethods [PastixCompressMethodNbr][4]
	Array of pointers to the multiple arithmetic and algorithmic variants of rradd.

Detailed Description

This module contains all the internal functions for low-rank kernels

Data Type Documentation

◆ pastix_lrblock_s

struct pastix_lrblock_s

The block low-rank structure to hold a matrix in low-rank form.

Definition at line 166 of file pastix_lowrank.h.

Data Fields
int	rk	Rank of the low-rank matrix: -1 is dense, otherwise rank-rk matrix
int	rkmax	Leading dimension of the matrix u
void *	u	Contains the dense matrix if rk=-1, or the u factor from u vT representation
void *	v	Not referenced if rk=-1, otherwise, the v factor

◆ pastix_lr_s

struct pastix_lr_s

Structure to define the type of function to use for the low-rank kernels and their parameters.

Definition at line 201 of file pastix_lowrank.h.

Data Fields
pastix_compress_when_t	compress_when	When to compress in the full solver
pastix_compress_method_t	compress_method	Compression method
pastix_int_t	compress_min_width	Minimum width to compress a supernode
pastix_int_t	compress_min_height	Minimum height to compress an off-diagonal block
int	compress_preselect	Enable/disable the compression of preselected blocks
int	use_reltol	Enable/disable relative tolerance vs absolute one
int	ilu_lvl	The ILU levels above which the blocks are originally compressed
double	tolerance	Absolute compression tolerance
fct_rradd_t	core_rradd	Recompression function
fct_ge2lr_t	core_ge2lr	Compression function

Macro Definition Documentation

◆ PASTIX_LRM3_ORTHOU

#define PASTIX_LRM3_ORTHOU (1 << 0)

Macro to specify if the U part of a low-rank matrix is orthogonal or not (Used in LRMM functions).

Definition at line 41 of file pastix_lowrank.h.

◆ PASTIX_LRM3_ALLOCU

#define PASTIX_LRM3_ALLOCU (1 << 1)

Macro to specify if the U part of a low-rank matrix has been allocated and need to be freed or not (Used in LRMM functions).

Definition at line 45 of file pastix_lowrank.h.

◆ PASTIX_LRM3_ALLOCV

#define PASTIX_LRM3_ALLOCV (1 << 2)

Macro to specify if the V part of a low-rank matrix has been allocated and need to be freed or not (Used in LRMM functions).

Definition at line 49 of file pastix_lowrank.h.

◆ PASTIX_LRM3_TRANSB

#define PASTIX_LRM3_TRANSB (1 << 3)

Macro to specify if the the operator on B, still needs to be applied to the V part of the low-rank matrix or not (Used in LRMM functions).

Definition at line 53 of file pastix_lowrank.h.

Typedef Documentation

◆ pastix_lr_t

typedef struct pastix_lr_s pastix_lr_t

Structure to define the type of function to use for the low-rank kernels and their parameters.

Definition at line 161 of file pastix_lowrank.h.

◆ fct_ge2lr_t

typedef pastix_fixdbl_t(* fct_ge2lr_t) (int, pastix_fixdbl_t, pastix_int_t, pastix_int_t, pastix_int_t, const void *, pastix_int_t, pastix_lrblock_t *)

Type of the functions to compress a dense block into a low-rank form.

Definition at line 176 of file pastix_lowrank.h.

◆ fct_rradd_t

typedef pastix_fixdbl_t(* fct_rradd_t) (const pastix_lr_t *, pastix_trans_t, const void *, pastix_int_t, pastix_int_t, const pastix_lrblock_t *, pastix_int_t, pastix_int_t, pastix_lrblock_t *, pastix_int_t, pastix_int_t)

Type of the functions to add two low-rank blocks together.

Definition at line 187 of file pastix_lowrank.h.

Enumeration Type Documentation

◆ memory_stats_e

enum memory_stats_e

Enum to define the type of block.

Enumerator
FR_InDiag	Full-rank block inside a diagonal block from the non-split partition
FR_OffDiag	Full-rank block outside a diagonal block from the non-split partition
LR_InDiag	Non selected Low-rank block inside a diagonal block from the non-split partition
LR_InSele	Selected low-rank block inside a diagonal block from the non-split partition
LR_OffDiag	Low-rank block outside a diagonal block from the non-split partition
LR_DInD	Non-compressible diagonal block inside a diagonal block from the non-split partition

Definition at line 217 of file pastix_lowrank.h.

Function Documentation

◆ core_get_rklimit_max()

static pastix_int_t core_get_rklimit_max	(	pastix_int_t	M,
		pastix_int_t	N
	)

inlinestatic

Compute the maximal rank accepted for a given matrix size for testings.

Parameters

[in]	M	The number of rows of the matrix
[in]	N	The number of columns of the matrix

Returns: The maximal rank accepted for this matrix size.

Definition at line 85 of file pastix_lowrank.h.

◆ core_get_rklimit_end()

static pastix_int_t core_get_rklimit_end	(	pastix_int_t	M,
		pastix_int_t	N
	)

inlinestatic

Compute the maximal rank accepted for a given matrix size for Just-In-Time strategy.

Parameters

[in]	M	The number of rows of the matrix
[in]	N	The number of columns of the matrix

Returns: The maximal rank accepted for this matrix size.

Definition at line 108 of file pastix_lowrank.h.

References pastix_lr_minratio.

Referenced by pastix_subtask_bcsc2ctab().

◆ core_get_rklimit_begin()

static pastix_int_t core_get_rklimit_begin	(	pastix_int_t	M,
		pastix_int_t	N
	)

inlinestatic

Compute the maximal rank accepted for a given matrix size for Minimal-Memory strategy.

Parameters

[in]	M	The number of rows of the matrix
[in]	N	The number of columns of the matrix

Returns: The maximal rank accepted for this matrix size.

Definition at line 131 of file pastix_lowrank.h.

References pastix_lr_minratio.

Referenced by pastix_subtask_bcsc2ctab().

◆ core_get_rklimit_test()

static pastix_int_t core_get_rklimit_test	(	pastix_int_t	M,
		pastix_int_t	N
	)

inlinestatic

TODO.

Parameters

[in]	M	The number of rows of the matrix
[in]	N	The number of columns of the matrix

Returns: TODO

Definition at line 154 of file pastix_lowrank.h.

Variable Documentation

◆ compmeth_shnames

const char* compmeth_shnames[PastixCompressMethodNbr]

extern

List of short names for the compression kernels.

Definition at line 27 of file lowrank.c.

Referenced by pastixWelcome().

◆ compmeth_lgnames

const char* compmeth_lgnames[PastixCompressMethodNbr]

extern

List of long names for the compression kernels.

Definition at line 35 of file lowrank.c.

◆ pastix_lr_minratio

double pastix_lr_minratio

extern

Define the minimal ratio for which we accept to compress a matrix into a low-rank form or not.

See also: core_get_rklimit()

Definition at line 24 of file lowrank.c.

Referenced by core_get_rklimit_begin(), core_get_rklimit_end(), and pastix_subtask_bcsc2ctab().

◆ pastix_lr_ortho

pastix_int_t pastix_lr_ortho

extern

Define the orthogonalization method.

Definition at line 25 of file lowrank.c.

Referenced by core_crradd_qr(), core_drradd_qr(), core_srradd_qr(), core_zrradd_qr(), and pastix_subtask_bcsc2ctab().

◆ core_get_rklimit

pastix_int_t(* core_get_rklimit) (pastix_int_t, pastix_int_t)	(	pastix_int_t	M,
		pastix_int_t	N
	)

extern

Compute the maximal rank accepted for a given matrix size. The pointer is set according to the low-rank strategy used.

Parameters

[in]	M	The number of rows of the matrix
[in]	N	The number of columns of the matrix

Returns: The maximal rank accepted for this matrix size.

Definition at line 46 of file kernels_trace.c.

Referenced by coeftab_cmemory_lr(), coeftab_dmemory_lr(), coeftab_smemory_lr(), coeftab_zmemory_lr(), core_cge2lr_qrcp(), core_cge2lr_qrrt(), core_cge2lr_svd(), core_clr2lr(), core_clr2null(), core_clrmm_Cnull(), core_clrsze(), core_crradd_qr(), core_crradd_svd(), core_dge2lr_qrcp(), core_dge2lr_qrrt(), core_dge2lr_svd(), core_dlr2lr(), core_dlr2null(), core_dlrmm_Cnull(), core_dlrsze(), core_drradd_qr(), core_drradd_svd(), core_sge2lr_qrcp(), core_sge2lr_qrrt(), core_sge2lr_svd(), core_slr2lr(), core_slr2null(), core_slrmm_Cnull(), core_slrsze(), core_srradd_qr(), core_srradd_svd(), core_zge2lr_qrcp(), core_zge2lr_qrrt(), core_zge2lr_svd(), core_zlr2lr(), core_zlr2null(), core_zlrmm_Cnull(), core_zlrsze(), core_zrradd_qr(), core_zrradd_svd(), and pastix_subtask_bcsc2ctab().

◆ ge2lrMethods

const fct_ge2lr_t ge2lrMethods[PastixCompressMethodNbr][4]

extern

Array of pointers to the multiple arithmetic and algorithmic variants of ge2lr.

Definition at line 43 of file lowrank.c.

Referenced by pastix_subtask_bcsc2ctab().

◆ rraddMethods

const fct_rradd_t rraddMethods[PastixCompressMethodNbr][4]

extern

Array of pointers to the multiple arithmetic and algorithmic variants of rradd.

Definition at line 52 of file lowrank.c.

Referenced by pastix_subtask_bcsc2ctab().

Data Structures

Macros

Typedefs

Enumerations

Functions

Variables

Detailed Description

Data Type Documentation

◆ pastix_lrblock_s

◆ pastix_lr_s

Macro Definition Documentation

◆ PASTIX_LRM3_ORTHOU

◆ PASTIX_LRM3_ALLOCU

◆ PASTIX_LRM3_ALLOCV

◆ PASTIX_LRM3_TRANSB

Typedef Documentation

◆ pastix_lr_t

◆ fct_ge2lr_t

◆ fct_rradd_t

Enumeration Type Documentation

◆ memory_stats_e

Function Documentation

◆ core_get_rklimit_max()

◆ core_get_rklimit_end()

◆ core_get_rklimit_begin()

◆ core_get_rklimit_test()

Variable Documentation

◆ compmeth_shnames

◆ compmeth_lgnames

◆ pastix_lr_minratio

◆ pastix_lr_ortho

◆ core_get_rklimit

◆ ge2lrMethods

◆ rraddMethods