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

```
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

PPPPaaaaggggeeee 2222```
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