ZGTCON(3)      LAPACK routine of NEC Numeric Library Collection      ZGTCON(3)



NAME
       ZGTCON

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



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)
                     NORM is 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)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

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

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

           DU2       (input)
                     DU2 is COMPLEX*16 array, dimension (N-2)
                     The (n-2) elements of the second superdiagonal of U.

           IPIV      (input)
                     IPIV is 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)
                     ANORM is 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)
                     RCOND is 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      (output)
                     WORK is COMPLEX*16 array, dimension (2*N)

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



LAPACK routine                  31 October 2017                      ZGTCON(3)