zgtcon(3P) Sun Performance Library zgtcon(3P)NAMEzgtcon - estimate the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by ZGTTRF
SYNOPSIS
SUBROUTINE ZGTCON(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM, RCOND,
WORK, INFO)
CHARACTER * 1 NORM
DOUBLE COMPLEX LOW(*), D(*), UP1(*), UP2(*), WORK(*)
INTEGER N, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
SUBROUTINE ZGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, WORK, INFO)
CHARACTER * 1 NORM
DOUBLE COMPLEX LOW(*), D(*), UP1(*), UP2(*), WORK(*)
INTEGER*8 N, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
F95 INTERFACE
SUBROUTINE GTCON(NORM, [N], LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, [WORK], [INFO])
CHARACTER(LEN=1) :: NORM
COMPLEX(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK
INTEGER :: N, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
SUBROUTINE GTCON_64(NORM, [N], LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, [WORK], [INFO])
CHARACTER(LEN=1) :: NORM
COMPLEX(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK
INTEGER(8) :: N, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
C INTERFACE
#include <sunperf.h>
void zgtcon(char norm, int n, doublecomplex *low, doublecomplex *d,
doublecomplex *up1, doublecomplex *up2, int *ipivot, double
anorm, double *rcond, int *info);
void zgtcon_64(char norm, long n, doublecomplex *low, doublecomplex *d,
doublecomplex *up1, doublecomplex *up2, long *ipivot, double
anorm, double *rcond, long *info);
PURPOSEzgtcon estimates the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by ZGTTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
NORM (input)
Specifies whether the 1-norm condition number or the infin‐
ity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N (input) The order of the matrix A. N >= 0.
LOW (input)
The (n-1) multipliers that define the matrix L from the LU
factorization of A as computed by ZGTTRF.
D (input) The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
UP1 (input)
The (n-1) elements of the first superdiagonal of U.
UP2 (input)
The (n-2) elements of the second superdiagonal of U.
IPIVOT (input)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIVOT(i). IPIVOT(i) will always be
either i or i+1; IPIVOT(i) = i indicates a row interchange
was not required.
ANORM (input)
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND (output)
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
mate of the 1-norm of inv(A) computed in this routine.
WORK (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zgtcon(3P)
