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# sgbcon

```
NAME
SGBCON - estimate 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 general 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 RCOND is com-
puted 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 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 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, 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 i-th argument had an illegal
value
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