SGBCON(1) LAPACK routine (version 3.2) SGBCON(1)NAME
SGBCON - estimates the reciprocal of the condition number of a real
general band matrix A, in either the 1-norm or the infinity-norm,
SYNOPSIS
SUBROUTINE SGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK,
IWORK, INFO )
CHARACTER NORM
INTEGER INFO, KL, KU, LDAB, N
REAL ANORM, RCOND
INTEGER IPIV( * ), IWORK( * )
REAL AB( LDAB, * ), WORK( * )
PURPOSE
SGBCON estimates the reciprocal of the condition number of a real gen‐
eral band matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by SGBTRF.
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) CHARACTER*1
Specifies whether the 1-norm condition number or the infinity-
norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N (input) INTEGER
The order of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB (input) REAL array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as com‐
puted by SGBTRF. 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.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).
ANORM (input) REAL
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) REAL
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 SGBCON(1)
