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SGBCON(3F)							    SGBCON(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SGBCON(	NORM, N, KL, KU, AB, LDAB, IPIV, ANORM,	RCOND, WORK,
			IWORK, INFO )

	 CHARACTER	NORM

	 INTEGER	INFO, KL, KU, LDAB, N

	 REAL		ANORM, RCOND

	 INTEGER	IPIV( *	), IWORK( * )

	 REAL		AB( LDAB, * ), WORK( * )

PURPOSE    [Toc]    [Back]

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

     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    [Toc]    [Back]

     NORM    (input) CHARACTER*1
	     Specifies whether the 1-norm condition number or the infinitynorm
 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) REAL array, dimension (LDAB,N)
	     Details of	the LU factorization of	the band matrix	A, as computed
	     by	SGBTRF.	 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.





									Page 1






SGBCON(3F)							    SGBCON(3F)



     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) REAL array, dimension (3*N)

     IWORK   (workspace) INTEGER array,	dimension (N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0: if INFO = -i,	the i-th argument had an illegal value
SGBCON(3F)							    SGBCON(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SGBCON(	NORM, N, KL, KU, AB, LDAB, IPIV, ANORM,	RCOND, WORK,
			IWORK, INFO )

	 CHARACTER	NORM

	 INTEGER	INFO, KL, KU, LDAB, N

	 REAL		ANORM, RCOND

	 INTEGER	IPIV( *	), IWORK( * )

	 REAL		AB( LDAB, * ), WORK( * )

PURPOSE    [Toc]    [Back]

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

     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    [Toc]    [Back]

     NORM    (input) CHARACTER*1
	     Specifies whether the 1-norm condition number or the infinitynorm
 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) REAL array, dimension (LDAB,N)
	     Details of	the LU factorization of	the band matrix	A, as computed
	     by	SGBTRF.	 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.





									Page 1






SGBCON(3F)							    SGBCON(3F)



     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) REAL array, dimension (3*N)

     IWORK   (workspace) INTEGER array,	dimension (N)

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


									PPPPaaaaggggeeee 2222
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