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RedHat 9 (Linux i386) - man page for zgbcon (redhat section l)

ZGBCON(l)					)					ZGBCON(l)

NAME
       ZGBCON  - 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 ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO )

	   CHARACTER	  NORM

	   INTEGER	  INFO, KL, KU, LDAB, N

	   DOUBLE	  PRECISION ANORM, RCOND

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION RWORK( * )

	   COMPLEX*16	  AB( LDAB, * ), WORK( * )

PURPOSE
       ZGBCON 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 ZGB-
       TRF.

       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 num-
	       ber 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*16 array, dimension (LDAB,N)
	       Details of the LU factorization of the band matrix A, as computed by ZGBTRF.  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) 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/(norm(A) * norm(inv(A))).

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

       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

LAPACK version 3.0			   15 June 2000 				ZGBCON(l)


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