Previous: scsum1 Up: ../lapack-s.html Next: sgbequ

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