DGBCON(3)

NAME
DGBCON - the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

SUBROUTINE DGBCON(
    NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER
    NORM

INTEGER
    INFO, KL, KU, LDAB, N

DOUBLE
    PRECISION ANORM, RCOND

INTEGER
    IPIV( * ), IWORK( * )

DOUBLE
    PRECISION AB( LDAB, * ), WORK( * )

PURPOSE
DGBCON 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 DGBTRF.
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) DOUBLE PRECISION array, dimension (LDAB,N)
    Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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) DOUBLE PRECISION
    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) DOUBLE PRECISION
    The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK    (workspace) DOUBLE PRECISION 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