zgtcon(l) [redhat man page]

ZGTCON(l)								 )								 ZGTCON(l)

NAME

       ZGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF

SYNOPSIS

       SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO )

	   CHARACTER	  NORM

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION ANORM, RCOND

	   INTEGER	  IPIV( * )

	   COMPLEX*16	  D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )

PURPOSE

       ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF.
       An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

       NORM    (input) CHARACTER*1
	       Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
	       = '1' or 'O':  1-norm;
	       = 'I':	      Infinity-norm.

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

       DL      (input) COMPLEX*16 array, dimension (N-1)
	       The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.

       D       (input) COMPLEX*16 array, dimension (N)
	       The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

       DU      (input) COMPLEX*16 array, dimension (N-1)
	       The (n-1) elements of the first superdiagonal of U.

       DU2     (input) COMPLEX*16 array, dimension (N-2)
	       The (n-2) elements of the second superdiagonal of U.

       IPIV    (input) INTEGER array, dimension (N)
	       The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i).  IPIV(i) will always be either i or i+1;
	       IPIV(i) = i indicates a row interchange was not required.

       ANORM   (input) DOUBLE PRECISION
	       If NORM = '1' or 'O', the 1-norm of the original matrix A.  If NORM = 'I', the infinity-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 an estimate of the
	       1-norm of inv(A) computed in this routine.

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

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

LAPACK version 3.0						   15 June 2000 							 ZGTCON(l)

zgtcon.f(3)							      LAPACK							       zgtcon.f(3)

NAME

       zgtcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
	   ZGTCON

Function/Subroutine Documentation
   subroutine zgtcon (characterNORM, integerN, complex*16, dimension( * )DL, complex*16, dimension( * )D, complex*16, dimension( * )DU,
       complex*16, dimension( * )DU2, integer, dimension( * )IPIV, double precisionANORM, double precisionRCOND, complex*16, dimension( * )WORK,
       integerINFO)
       ZGTCON

       Purpose:

	    ZGTCON estimates the reciprocal of the condition number of a complex
	    tridiagonal matrix A using the LU factorization as computed by
	    ZGTTRF.

	    An estimate is obtained for norm(inv(A)), and the reciprocal of the
	    condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
	   NORM

		     NORM is CHARACTER*1
		     Specifies whether the 1-norm condition number or the
		     infinity-norm condition number is required:
		     = '1' or 'O':  1-norm;
		     = 'I':	    Infinity-norm.

	   N

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

	   DL

		     DL is COMPLEX*16 array, dimension (N-1)
		     The (n-1) multipliers that define the matrix L from the
		     LU factorization of A as computed by ZGTTRF.

	   D

		     D is COMPLEX*16 array, dimension (N)
		     The n diagonal elements of the upper triangular matrix U from
		     the LU factorization of A.

	   DU

		     DU is COMPLEX*16 array, dimension (N-1)
		     The (n-1) elements of the first superdiagonal of U.

	   DU2

		     DU2 is COMPLEX*16 array, dimension (N-2)
		     The (n-2) elements of the second superdiagonal of U.

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     The pivot indices; for 1 <= i <= n, row i of the matrix was
		     interchanged with row IPIV(i).  IPIV(i) will always be either
		     i or i+1; IPIV(i) = i indicates a row interchange was not
		     required.

	   ANORM

		     ANORM is DOUBLE PRECISION
		     If NORM = '1' or 'O', the 1-norm of the original matrix A.
		     If NORM = 'I', the infinity-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 an
		     estimate of the 1-norm of inv(A) computed in this routine.

	   WORK

		     WORK is COMPLEX*16 array, dimension (2*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:
	   September 2012

       Definition at line 141 of file zgtcon.f.

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

Version 3.4.2							  Tue Sep 25 2012						       zgtcon.f(3)