SGBCON (3lapack)

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