CPTCON  -  compute  the reciprocal of the condition number
       (in the 1-norm) of a complex Hermitian  positive  definite
       tridiagonal matrix using the factorization A = L*D*L**H or
       A = U**H*D*U computed by CPTTRF


SYNOPSIS

       SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )

           INTEGER        INFO, N

           REAL           ANORM, RCOND

           REAL           D( * ), RWORK( * )

           COMPLEX        E( * )


PURPOSE

       CPTCON computes the reciprocal of the condition number (in
       the  1-norm)  of  a  complex  Hermitian  positive definite
       tridiagonal matrix using the factorization A = L*D*L**H or
       A = U**H*D*U computed by CPTTRF.  Norm(inv(A)) is computed
       by a direct method, and the reciprocal  of  the  condition
       number is computed as
                        RCOND = 1 / (ANORM * norm(inv(A))).


ARGUMENTS

       N       (input) INTEGER
               The order of the matrix A.  N >= 0.

       D       (input) REAL array, dimension (N)
               The  n  diagonal elements of the diagonal matrix D
               from the factorization of A, as computed  by  CPT­
               TRF.

       E       (input) COMPLEX array, dimension (N-1)
               The  (n-1) off-diagonal elements of the unit bidi­
               agonal factor U or L from the factorization of  A,
               as computed by CPTTRF.

       ANORM   (input) REAL
               The 1-norm of the original matrix A.

       RCOND   (output) REAL
               The  reciprocal  of  the  condition  number of the
               matrix A, computed as RCOND = 1/(ANORM *  AINVNM),
               where  AINVNM  is the 1-norm of inv(A) computed in
               this routine.

       RWORK   (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
               = 0:  successful exit

               gal value


FURTHER DETAILS

       The method used is described in Nicholas J. Higham, "Effi­
       cient Algorithms for Computing the Condition Number  of  a
       Tridiagonal  Matrix",  SIAM J. Sci. Stat. Comput., Vol. 7,
       No. 1, January 1986.


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