gscon(3P) Sun Performance Library gscon(3P)NAME
gscon: cgscon, dgscon, sgscon, zgscon - estimates the reciprocal of the
condition number of a general real matrix A, in either the 1-norm or
the infinity-norm, using the LU factorization computed by SuperLU rou‐
tine sgstrf.
SYNOPSIS
#include <sunperf.h>
void sgscon(char *norm, SuperMatrix *L, SuperMatrix *U, float anorm,
float *rcond, SuperLUStat_t *stat, int *info)
void dgscon(char *norm, SuperMatrix *L, SuperMatrix *U, double anorm,
double *rcond, SuperLUStat_t *stat, int *info)
void cgscon(char *norm, SuperMatrix *L, SuperMatrix *U, float anorm,
float *rcond, SuperLUStat_t *stat, int *info)
void zgscon(char *norm, SuperMatrix *L, SuperMatrix *U, double anorm,
double *rcond, SuperLUStat_t *stat, int *info)
void sgscon_64(char *norm, SuperMatrix_64 *L, SuperMatrix_64 *U, float
anorm, float *rcond, SuperLUStat_t_64 *stat, long *info)
void dgscon_64(char *norm, SuperMatrix_64 *L, SuperMatrix_64 *U, double
anorm, double *rcond, SuperLUStat_t_64 *stat, long *info)
void cgscon_64(char *norm, SuperMatrix_64 *L, SuperMatrix_64 *U, float
anorm, float *rcond, SuperLUStat_t_64 *stat, long *info)
void zgscon_64(char *norm, SuperMatrix_64 *L, SuperMatrix_64 *U, double
anorm, double *rcond, SuperLUStat_t_64 *stat, long *info)
PURPOSEgscon estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm, using the LU
factorization computed by SuperLU routine sgetrf.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
rcond = 1 / (norm(A) * norm(inv(A))).
ARGUMENTS
char *norm (input)
Specifies whether the 1-norm condition number or the infinity-
norm condition number is required:
= '1' or 'O':
1-norm;
= 'I': Infinity-norm.
SuperMatrix *L (input)The factor L from the factorization Pr*A*Pc=L*U as computed by sgstrf(). L
uses compressed row subscripts storage for supernodes, i.e., L has types:
Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.
SuperMatrix *U (input)The factor U from the factorization Pr*A*Pc=L*U as computed by sgstrf(). U
usescolumn-wise storage scheme, i.e., U has types: Stype = SLU_NC, Dtype =
SLU_C, Mtype = TRU.
float anorm (input)If norm = '1' or 'O', anorm contains the 1-norm of the original matrix A.
If norm = 'I', anorm contains the infinity-norm of the original matrix A.
float *rcond (output)The reciprocal of the condition number of the matrix A, computed as
RCOND = 1/(norm(A) * norm(inv(A))).
SuperLUStat_t *stat (output)Data structure that stores statistics of the computation. On exit,
stat->ops[SOLVE] is updated.
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
StatInit
StatFree
gstrf
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 gscon(3P)
