zgbcon(3P) Sun Performance Library zgbcon(3P)NAMEzgbcon - estimate the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-norm,
SYNOPSIS
SUBROUTINE ZGBCON(NORM, N, KL, KU, A, LDA, IPIVOT, ANORM,
RCOND, WORK, WORK2, INFO)
CHARACTER * 1 NORM
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER N, KL, KU, LDA, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION WORK2(*)
SUBROUTINE ZGBCON_64(NORM, N, KL, KU, A, LDA, IPIVOT, ANORM,
RCOND, WORK, WORK2, INFO)
CHARACTER * 1 NORM
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, KL, KU, LDA, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION WORK2(*)
F95 INTERFACE
SUBROUTINE GBCON(NORM, [N], KL, KU, A, [LDA], IPIVOT, ANORM,
RCOND, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: NORM
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, KL, KU, LDA, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: WORK2
SUBROUTINE GBCON_64(NORM, [N], KL, KU, A, [LDA], IPIVOT, ANORM,
RCOND, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: NORM
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, KL, KU, LDA, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void zgbcon(char norm, int n, int kl, int ku, doublecomplex *a, int
lda, int *ipivot, double anorm, double *rcond, int *info);
void zgbcon_64(char norm, long n, long kl, long ku, doublecomplex *a,
long lda, long *ipivot, double anorm, double *rcond, long
*info);
PURPOSEzgbcon estimates the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by ZGBTRF.
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
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.
KL (input)
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
The number of superdiagonals within the band of A. KU >= 0.
A (input) Details of the LU factorization of the band matrix A, as com‐
puted by ZGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDA (input)
The leading dimension of the array A. LDA >= 2*KL+KU+1.
IPIVOT (input)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIVOT(i).
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/(norm(A) * norm(inv(A))).
WORK (workspace)
dimension(2*N)
WORK2 (workspace)
dimension (N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zgbcon(3P)
