cgbcon(l) [redhat man page]

CGBCON(l)								 )								 CGBCON(l)

NAME

       CGBCON - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

       SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO )

	   CHARACTER	  NORM

	   INTEGER	  INFO, KL, KU, LDAB, N

	   REAL 	  ANORM, RCOND

	   INTEGER	  IPIV( * )

	   REAL 	  RWORK( * )

	   COMPLEX	  AB( LDAB, * ), WORK( * )

PURPOSE

       CGBCON  estimates  the  reciprocal  of  the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
       using the LU factorization computed by CGBTRF.

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

       KL      (input) INTEGER
	       The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
	       The number of superdiagonals within the band of A.  KU >= 0.

       AB      (input) COMPLEX array, dimension (LDAB,N)
	       Details of the LU factorization of the band matrix A, as computed by CGBTRF.  U is stored as an upper triangular band  matrix  with
	       KL+KU  superdiagonals  in  rows	1  to  KL+KU+1,  and  the  multipliers used during the factorization are stored in rows KL+KU+2 to
	       2*KL+KU+1.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

       IPIV    (input) INTEGER array, dimension (N)
	       The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).

       ANORM   (input) REAL
	       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) REAL
	       The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

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

       RWORK   (workspace) REAL array, dimension (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 							 CGBCON(l)

cgbcon.f(3)							      LAPACK							       cgbcon.f(3)

NAME

       cgbcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cgbcon (NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO)
	   CGBCON

Function/Subroutine Documentation
   subroutine cgbcon (characterNORM, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV,
       realANORM, realRCOND, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
       CGBCON

       Purpose:

	    CGBCON estimates the reciprocal of the condition number of a complex
	    general band matrix A, in either the 1-norm or the infinity-norm,
	    using the LU factorization computed by CGBTRF.

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

	   KL

		     KL is INTEGER
		     The number of subdiagonals within the band of A.  KL >= 0.

	   KU

		     KU is INTEGER
		     The number of superdiagonals within the band of A.  KU >= 0.

	   AB

		     AB is COMPLEX array, dimension (LDAB,N)
		     Details of the LU factorization of the band matrix A, as
		     computed by CGBTRF.  U is stored as an upper triangular band
		     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
		     the multipliers used during the factorization are stored in
		     rows KL+KU+2 to 2*KL+KU+1.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

	   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).

	   ANORM

		     ANORM is REAL
		     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 REAL
		     The reciprocal of the condition number of the matrix A,
		     computed as RCOND = 1/(norm(A) * norm(inv(A))).

	   WORK

		     WORK is COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL 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

       Definition at line 147 of file cgbcon.f.

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

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