SuperLU 6.0.1
Functions | Variables
zitersol.c File Reference

Example #1 showing how to use ILU to precondition GMRES. More...

#include "slu_zdefs.h"
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Functions

void zpsolve (int n, doublecomplex x[], doublecomplex y[])
 Performs zgsisx with original matrix A. More...
 
void zmatvec_mult (doublecomplex alpha, doublecomplex x[], doublecomplex beta, doublecomplex y[])
 Performs matrix-vector multipliation sp_zgem with original matrix A. More...
 
int main (int argc, char *argv[])
 

Variables

superlu_options_tGLOBAL_OPTIONS
 
double * GLOBAL_R
 
double * GLOBAL_C
 
int * GLOBAL_PERM_C
 
int * GLOBAL_PERM_R
 
SuperMatrixGLOBAL_A
 
SuperMatrixGLOBAL_L
 
SuperMatrixGLOBAL_U
 
SuperLUStat_tGLOBAL_STAT
 
mem_usage_tGLOBAL_MEM_USAGE
 

Detailed Description

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

Note that ZGSISX 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 can solve the transformed system, A1*y = Dr*B, using FGMRES. B is first overwritten as Dr*B. Then GMRES step requires requires 2 procedures: 1) Apply preconditioner M^{-1} = Pc^T*U^{-1}*L^{-1}*Pr 2) Matrix-vector multiplication: w = A1*v

Function Documentation

◆ main()

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

void zmatvec_mult ( doublecomplex  alpha,
doublecomplex  x[],
doublecomplex  beta,
doublecomplex  y[] 
)

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

Parameters
[in]alphaScalar factor for A*x
[in]xVector to multiply with A
[in]betaScalar factor for y
[in,out]yVector to add to to matrix-vector multiplication and storage for result.
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◆ zpsolve()

void zpsolve ( int  n,
doublecomplex  x[],
doublecomplex  y[] 
)

See documentation of zgsisx for more details.

Parameters
[in]nDimension of matrices
[out]xSolution
[in,out]yRight-hand side
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Variable Documentation

◆ GLOBAL_A

SuperMatrix* GLOBAL_A

◆ GLOBAL_C

double * GLOBAL_C

◆ 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

double* GLOBAL_R

◆ GLOBAL_STAT

SuperLUStat_t* GLOBAL_STAT

◆ GLOBAL_U

SuperMatrix * GLOBAL_U