DGTCON  -  estimate the reciprocal of the condition number
       of a real tridiagonal matrix A using the LU  factorization
       as computed by DGTTRF


SYNOPSIS

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

           CHARACTER      NORM

           INTEGER        INFO, N

           DOUBLE         PRECISION ANORM, RCOND

           INTEGER        IPIV( * ), IWORK( * )

           DOUBLE         PRECISION D( * ), DL( *  ),  DU(  *  ),
                          DU2( * ), WORK( * )


PURPOSE

       DGTCON estimates the reciprocal of the condition number of
       a real tridiagonal matrix A using the LU factorization  as
       computed   by   DGTTRF.    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) DOUBLE PRECISION array, dimension (N-1)
               The (n-1) multipliers that  define  the  matrix  L
               from the LU factorization of A as computed by DGT­
               TRF.

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

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

       DU2     (input) DOUBLE PRECISION array, dimension (N-2)
               The (n-2) elements of the second superdiagonal  of
               U.

               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) 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/(ANORM * AINVNM),
               where AINVNM is  an  estimate  of  the  1-norm  of
               inv(A) computed in this routine.

       WORK    (workspace) DOUBLE PRECISION 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 ille­
               gal value


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