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man pages->IRIX man pages -> complib/cgbcon (3)
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### Contents

CGBCON(3F)							    CGBCON(3F)

### NAME[Toc][Back]

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[Toc][Back]

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[Toc][Back]

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[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) 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.

Page 1

CGBCON(3F)							    CGBCON(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) 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
CGBCON(3F)							    CGBCON(3F)

### NAME[Toc][Back]

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[Toc][Back]

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[Toc][Back]

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[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) 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.

Page 1

CGBCON(3F)							    CGBCON(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) 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

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