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sgtcon

 NAME
      SGTCON - estimate the reciprocal of the condition number of
      a real tridiagonal matrix A using the LU factorization as
      computed by SGTTRF

 SYNOPSIS
      SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM,
                         RCOND, WORK, IWORK, INFO )

          CHARACTER      NORM

          INTEGER        INFO, N

          REAL           ANORM, RCOND

          INTEGER        IPIV( * ), IWORK( * )

          REAL           D( * ), DL( * ), DU( * ), DU2( * ), WORK(
                         * )

 PURPOSE
      SGTCON estimates the reciprocal of the condition number of a
      real tridiagonal matrix A using the LU factorization as com-
      puted by SGTTRF.

      An estimate is obtained for norm(inv(A)), and the reciprocal
      of the condition number is computed as RCOND = 1 / (ANORM *
      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.

      DL      (input) REAL array, dimension (N-1)
              The (n-1) multipliers that define the matrix L from
              the LU factorization of A as computed by SGTTRF.

      D       (input) REAL array, dimension (N)
              The n diagonal elements of the upper triangular
              matrix U from the LU factorization of A.

      DU      (input) REAL array, dimension (N-1)
              The (n-1) elements of the first superdiagonal of U.

      DU2     (input) REAL array, dimension (N-2)

              The (n-2) elements of the second superdiagonal of U.

      IPIV    (input) INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, row i of the
              matrix was interchanged with row IPIV(i).  IPIV(i)
              will always be either i or i+1; IPIV(i) = i indi-
              cates a row interchange was not required.

      ANORM   (input) REAL
              The 1-norm of the original matrix A.

      RCOND   (output) REAL
              The reciprocal of the condition number of the matrix
              A, computed as RCOND = 1/(ANORM * AINVNM), where
              AINVNM is an estimate of the 1-norm of inv(A) com-
              puted in this routine.

      WORK    (workspace) REAL array, dimension (2*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