SGTCON(3)                  MathKeisan LAPACK routine                 SGTCON(3)



NAME
       SGTCON  -  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 computed 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 fac-
               torization 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  indicates  a  row  interchange was not
               required.

       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, 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) 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



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