zgtcon(3F)

NAME
     ZGTCON - estimate the reciprocal of the condition number of a complex
     tridiagonal matrix A using the LU factorization as computed by ZGTTRF

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

         CHARACTER      NORM

         INTEGER        INFO, N

         DOUBLE         PRECISION ANORM, RCOND

         INTEGER        IPIV( * )

         COMPLEX*16     D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )

PURPOSE
     ZGTCON estimates the reciprocal of the condition number of a complex
     tridiagonal matrix A using the LU factorization as computed by ZGTTRF.

     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) COMPLEX*16 array, dimension (N-1)
             The (n-1) multipliers that define the matrix L from the LU
             factorization of A as computed by ZGTTRF.

     D       (input) COMPLEX*16 array, dimension (N)
             The n diagonal elements of the upper triangular matrix U from the
             LU factorization of A.

     DU      (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) elements of the first superdiagonal of U.

     DU2     (input) COMPLEX*16 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, computed
             as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the
             1-norm of inv(A) computed in this routine.

     WORK    (workspace) COMPLEX*16 array, dimension (2*N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value