DGTCON(3)                  MathKeisan LAPACK routine                 DGTCON(3)



NAME
       DGTCON  -  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 fac-
               torization of A as computed by DGTTRF.

       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.

       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  indicates  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,  com-
               puted  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 illegal value



 LAPACK routine (version 3.1)    November 2006                       DGTCON(3)