DGBCON(3)      LAPACK routine of NEC Numeric Library Collection      DGBCON(3)



NAME
       DGBCON

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



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)
                     NORM is 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)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KL        (input)
                     KL is INTEGER
                     The number of subdiagonals within the band of A.  KL >= 0.

           KU        (input)
                     KU is INTEGER
                     The number of superdiagonals within the band of A.  KU >= 0.

           AB        (input)
                     AB is 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)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

           IPIV      (input)
                     IPIV is INTEGER array, dimension (N)
                     The pivot indices; for 1 <= i <= N, row i of the matrix was
                     interchanged with row IPIV(i).

           ANORM     (input)
                     ANORM is 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)
                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(norm(A) * norm(inv(A))).

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (3*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value



LAPACK routine                  31 October 2017                      DGBCON(3)