CPTCON(3F)							    CPTCON(3F)

NAME    [Toc]    [Back]

     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    [Toc]    [Back]

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

	 INTEGER	INFO, N

	 REAL		ANORM, RCOND

	 REAL		D( * ),	RWORK( * )

	 COMPLEX	E( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     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




									Page 1






CPTCON(3F)							    CPTCON(3F)



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.
CPTCON(3F)							    CPTCON(3F)

NAME    [Toc]    [Back]

     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    [Toc]    [Back]

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

	 INTEGER	INFO, N

	 REAL		ANORM, RCOND

	 REAL		D( * ),	RWORK( * )

	 COMPLEX	E( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     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




									Page 1






CPTCON(3F)							    CPTCON(3F)



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.


									PPPPaaaaggggeeee 2222