cptcon(l) [redhat man page]

CPTCON(l)								 )								 CPTCON(l)

NAME

       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 CPTTRF.

       E       (input) COMPLEX array, dimension (N-1)
	       The (n-1) off-diagonal elements of the unit bidiagonal 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 illegal value

FURTHER DETAILS

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

LAPACK version 3.0						   15 June 2000 							 CPTCON(l)