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NAME
     cptcon - compute the reciprocal of the condition number  (in
     the  1-norm) of a complex Hermitian positive definite tridi-
     agonal 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( * )



     #include <sunperf.h>

     void cptcon(int n, float *d, complex *e, float anorm,  float
               *srcond, int *info) ;

PURPOSE
     CPTCON computes the reciprocal of the condition  number  (in
     the  1-norm) of a complex Hermitian positive definite tridi-
     agonal 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
               CPTTRF.

     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
               < 0:  if INFO = -i, the i-th argument had an ille-
               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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