sitersol1.c File Reference

Example #2 showing how to use ILU to precondition GMRES. More...

#include "slu_sdefs.h"

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Functions
void	spsolve (int n, float x[], float y[])
	Performs sgsisx with original matrix A. More...
void	smatvec_mult (float alpha, float x[], float beta, float y[])
	Performs matrix-vector multipliation sp_sgemv with original matrix A. More...
int	main (int argc, char *argv[])

Variables
char *	GLOBAL_EQUED
superlu_options_t *	GLOBAL_OPTIONS
float *	GLOBAL_R
float *	GLOBAL_C
int *	GLOBAL_PERM_C
int *	GLOBAL_PERM_R
SuperMatrix *	GLOBAL_A
SuperMatrix *	GLOBAL_A_ORIG
SuperMatrix *	GLOBAL_L
SuperMatrix *	GLOBAL_U
SuperLUStat_t *	GLOBAL_STAT
mem_usage_t *	GLOBAL_MEM_USAGE

Detailed Description

This example shows that ILU is computed from the equilibrated matrix, but the preconditioned GMRES is applied to the original system. The driver routine SGSISX is called twice to perform factorization and apply preconditioner separately.

Note that SGSISX performs the following factorization: Pr*Dr*A*Dc*Pc^T ~= LU with Pr being obtained from MC64 statically then partial pivoting dynamically. On return, A is overwritten as A1 = Dr*A*Dc.

We need to save a copy of the original matrix A, then solve the original system, A*x = B, using FGMRES. Each GMRES step requires requires 2 procedures: 1) Apply preconditioner M^{-1} = Dc*Pc^T*U^{-1}*L^{-1}*Pr*Dr 2) Matrix-vector multiplication: w = A*v

Function Documentation

main()

int main	(	int	argc,
		char *	argv[]
	)

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smatvec_mult()

void smatvec_mult	(	float	alpha,
		float	x[],
		float	beta,
		float	y[]
	)

The operations is y := alpha*A*x + beta*y. See documentation of sp_sgemv for further details.

Parameters

[in]	alpha	Scalar factor for A*x
[in]	x	Vector to multiply with A
[in]	beta	Scalar factor for y
[in,out]	y	Vector to add to to matrix-vector multiplication and storage for result.

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spsolve()

void spsolve	(	int	n,
		float	x[],
		float	y[]
	)

See documentation of sgsisx for more details.

Parameters

[in]	n	Dimension of matrices
[out]	x	Solution
[in,out]	y	Right-hand side

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Variable Documentation

GLOBAL_A

SuperMatrix* GLOBAL_A

GLOBAL_A_ORIG

SuperMatrix * GLOBAL_A_ORIG

GLOBAL_C

float * GLOBAL_C

GLOBAL_EQUED

char* GLOBAL_EQUED

GLOBAL_L

SuperMatrix * GLOBAL_L

GLOBAL_MEM_USAGE

mem_usage_t* GLOBAL_MEM_USAGE

GLOBAL_OPTIONS

superlu_options_t* GLOBAL_OPTIONS

GLOBAL_PERM_C

int* GLOBAL_PERM_C

GLOBAL_PERM_R

int * GLOBAL_PERM_R

GLOBAL_R

float* GLOBAL_R

GLOBAL_STAT

SuperLUStat_t* GLOBAL_STAT

GLOBAL_U

SuperMatrix * GLOBAL_U