
SGBCON(l) ) SGBCON(l)
NAME
SGBCON  estimate the reciprocal of the condition number of a real general band matrix A,
in either the 1norm or the infinitynorm,
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 general band matrix A,
in either the 1norm or the infinitynorm, 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 1norm condition number or the infinitynorm condition num
ber is required:
= '1' or 'O': 1norm;
= 'I': Infinitynorm.
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 computed 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 1norm of the original matrix A. If NORM = 'I', the
infinitynorm of the original matrix A.
RCOND (output) REAL
The reciprocal of the condition number of the matrix A, computed 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 ith argument had an illegal value
LAPACK version 3.0 15 June 2000 SGBCON(l) 
