zptcon(l) [redhat man page]

ZPTCON(l)								 )								 ZPTCON(l)

NAME

       ZPTCON  -  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 ZPTTRF

SYNOPSIS

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

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION ANORM, RCOND

	   DOUBLE	  PRECISION D( * ), RWORK( * )

	   COMPLEX*16	  E( * )

PURPOSE

       ZPTCON 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 ZPTTRF.  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) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF.

       E       (input) COMPLEX*16 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 ZPTTRF.

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

       RCOND   (output) DOUBLE PRECISION
	       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) DOUBLE PRECISION 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 							 ZPTCON(l)

zptcon.f(3)							      LAPACK							       zptcon.f(3)

NAME

       zptcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zptcon (N, D, E, ANORM, RCOND, RWORK, INFO)
	   ZPTCON

Function/Subroutine Documentation
   subroutine zptcon (integerN, double precision, dimension( * )D, complex*16, dimension( * )E, double precisionANORM, double precisionRCOND,
       double precision, dimension( * )RWORK, integerINFO)
       ZPTCON

       Purpose:

	    ZPTCON 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
	    ZPTTRF.

	    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))).

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The n diagonal elements of the diagonal matrix D from the
		     factorization of A, as computed by ZPTTRF.

	   E

		     E is COMPLEX*16 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 ZPTTRF.

	   ANORM

		     ANORM is DOUBLE PRECISION
		     The 1-norm of the original matrix A.

	   RCOND

		     RCOND is DOUBLE PRECISION
		     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

		     RWORK is DOUBLE PRECISION array, dimension (N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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.

       Definition at line 120 of file zptcon.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       zptcon.f(3)