gsrfs(3P) Sun Performance Library gsrfs(3P)NAME
gsrfs: cgsrfs, dgsrfs, sgsrfs, zgsrfs - improves the computed solution
to a system of linear equations and provides error bounds and backward
error estimates for the solution. It is a SuperLU routine.
SYNOPSIS
#include <sunperf.h>
void sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix
*U, int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr, Super‐
LUStat_t *stat, int *info)
void dgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix
*U, int *perm_c, int *perm_r, char *equed, double *R, double *C,
SuperMatrix *B, SuperMatrix *X, double *ferr, double *berr,
SuperLUStat_t *stat, int *info)
void cgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix
*U, int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr, Super‐
LUStat_t *stat, int *info)
void zgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix
*U, int *perm_c, int *perm_r, char *equed, double *R, double *C,
SuperMatrix *B, SuperMatrix *X, double *ferr, double *berr,
SuperLUStat_t *stat, int *info)
void sgsrfs_64(trans_t trans, SuperMatrix_64 *A, SuperMatrix_64 *L,
SuperMatrix_64 *U, long *perm_c, long *perm_r, char *equed,
float *R, float *C, SuperMatrix_64 *B, SuperMatrix_64 *X, float
*ferr, float *berr, SuperLUStat_t_64 *stat, long *info)
void dgsrfs_64(trans_t trans, SuperMatrix_64 *A, SuperMatrix_64 *L,
SuperMatrix_64 *U, long *perm_c, long *perm_r, char *equed, dou‐
ble *R, double *C, SuperMatrix_64 *B, SuperMatrix_64 *X, double
*ferr, double *berr, SuperLUStat_t_64 *stat, long *info)
void cgsrfs_64(trans_t trans, SuperMatrix_64 *A, SuperMatrix_64 *L,
SuperMatrix_64 *U, long *perm_c, long *perm_r, char *equed,
float *R, float *C, SuperMatrix_64 *B, SuperMatrix_64 *X, float
*ferr, float *berr, SuperLUStat_t_64 *stat, long *info)
void zgsrfs_64(trans_t trans, SuperMatrix_64 *A, SuperMatrix_64 *L,
SuperMatrix_64 *U, long *perm_c, long *perm_r, char *equed, dou‐
ble *R, double *C, SuperMatrix_64 *B, SuperMatrix_64 *X, double
*ferr, double *berr, SuperLUStat_t_64 *stat, long *info)
PURPOSEgsrfs improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solu‐
tion. If equilibration was performed, the system becomes:
(diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
ARGUMENTS
trans_t trans (input)
Specifies the form of the system of equations:
= NOTRANS: A * X = B (No transpose)
= TRANS: A'* X = B (Transpose)
= CONJ: A**H * X = B (Conjugate transpose)
SuperMatrix *A (input)
Original matrix A in the system, or the scaled A if equilibra‐
tion was done. The type of A can be:
Stype = SLU_NC; Dtype = SLU_S; Mtype = SLU_GE.
SuperMatrix *L (input)
The factor L from the factorization Pr*A=L*U. It uses com‐
pressed row subscripts storage for supernodes, i.e., L has
types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU
SuperMatrix *U (input)
The factor U from the factorization Pr*A*Pc=L*U. It uses col‐
umn-wise storage scheme, i.e., U has types: Stype = SLU_NC,
Dtype = SLU_S, Mtype = SLU_TRU.
int *perm_c (input)
Column permutation vector of size (A->ncol) which defines the
permutation matrix Pc. perm_c[i] = j means column i of A is in
position j in A*Pc.
int *perm_r (input)
Row permutation vector of size (A->nrow) which defines the per‐
mutation matrix Pr. perm_r[i] = j means row i of A is in posi‐
tion j in Pr*A.
char *equed (input)
Specifies the form of equilibration that was done.
= 'N':
No equilibration
= 'R': Row equilibration, i.e., A has been premultiplied by
diag(R).
= 'C': Column equilibration, i.e., A has been postmultiplied by
diag(C).
= 'B': Both row and column equilibration, i.e., A has been
replaced by diag(R) * A * diag(C).
float *R (input)
The row scale factors for A; dimension (A->nrow).
If equed = 'R' or 'B', A is premultiplied by diag(R).
If equed = 'N' or 'C', R is not accessed.
float *C (input)
The column scale factors for A; dimension (A->ncol).
If equed = 'C' or 'B', A is postmultiplied by diag(C).
If equed = 'N' or 'R', C is not accessed.
SuperMatrix *B (input)
The right hand side matrix B.
B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
If equed = 'R' or 'B', B is premultiplied by diag(R).
SuperMatrix *X (input/output)
X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
On entry, the solution matrix X, as computed by sgstrs(). On
exit, the improved solution matrix X.
if *equed = 'C' or 'B', X should be premultiplied by diag(C) in
order to obtain the solution to the original system.
float *ferr (output)
The estimated forward error bound for each solution vector X(j)
(the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), ferr(j) is
an estimated upper bound for the magnitude of the largest ele‐
ment in (X(j) - XTRUE) divided by the magnitude of the largest
element in X(j). The estimate is as reliable as the estimate
for condition number RCOND, and is almost always a slight over‐
estimate of the true error.
ferr is of dimension B->ncol.
float *berr (output)
The component-wise relative backward error of each solution vec‐
tor X(j) (i.e., the smallest relative change in any element of A
or B that makes X(j) an exact solution).
berr is of dimension B->ncol.
SuperLUStat_t *stat (output)
Records the statistics on runtime and floating-point operation
count.
int *info (output)
= 0:
successful exit
< 0: if info = -i, the i-th argument had an illegal value
COPYRIGHT
Copyright (c) 2003, The Regents of the University of California,
through Lawrence Berkeley National Laboratory (subject to receipt of
any required approvals from U.S. Dept. of Energy)
SEE ALSO
SuperMatrix
set_default_options
StatInit
StatFree
gstrs
http://crd.lbl.gov/~xiaoye/SuperLU/
James W. Demmel, Stanley C. Eisenstat, John R. Gilbert, Xiaoye S. Li
and Joseph W. H. Liu, "A supernodal approach to sparse partial pivot‐
ing", SIAM J. Matrix Analysis and Applications, Vol. 20, Num. 3, 1999,
pp. 720-755.
6 Mar 2009 gsrfs(3P)
