sgbcon(3F)

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 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 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