CPTTRF  -  compute  the  L*D*L' factorization of a complex
       Hermitian positive definite tridiagonal matrix A


SYNOPSIS

       SUBROUTINE CPTTRF( N, D, E, INFO )

           INTEGER        INFO, N

           REAL           D( * )

           COMPLEX        E( * )


PURPOSE

       CPTTRF computes the L*D*L' factorization of a complex Her­
       mitian positive definite tridiagonal matrix A. The factor­
       ization may also be  regarded  as  having  the  form  A  =
       U'*D*U.


ARGUMENTS

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

       D       (input/output) REAL array, dimension (N)
               On entry, the n diagonal elements of the tridiago­
               nal matrix A.  On exit, the n diagonal elements of
               the  diagonal  matrix D from the L*D*L' factoriza­
               tion of A.

       E       (input/output) COMPLEX array, dimension (N-1)
               On entry, the (n-1) subdiagonal  elements  of  the
               tridiagonal matrix A.  On exit, the (n-1) subdiag­
               onal elements of the unit bidiagonal factor L from
               the  L*D*L'  factorization  of  A.   E can also be
               regarded as the superdiagonal of the unit bidiago­
               nal factor U from the U'*D*U factorization of A.

       INFO    (output) INTEGER
               = 0: successful exit
               <  0: if INFO = -k, the k-th argument had an ille­
               gal value
               > 0: if INFO = k, the leading minor of order k  is
               not positive definite; if k < N, the factorization
               could not be completed, while if k = N,  the  fac­
               torization was completed, but D(N) = 0.


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