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

```
ZTBCON(3F)							    ZTBCON(3F)

```

### NAME[Toc][Back]

```     ZTBCON - estimate the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the	infinity-norm
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZTBCON(	NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,	RWORK,
INFO )

CHARACTER	DIAG, NORM, UPLO

INTEGER	INFO, KD, LDAB,	N

DOUBLE		PRECISION RCOND

DOUBLE		PRECISION RWORK( * )

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

### PURPOSE[Toc][Back]

```     ZTBCON estimates the reciprocal of	the condition number of	a triangular
band matrix A, in either the 1-norm or the	infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)),
then 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.

UPLO    (input) CHARACTER*1
= 'U':  A is upper	triangular;
= 'L':  A is lower	triangular.

DIAG    (input) CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

KD	     (input) INTEGER
The number	of superdiagonals or subdiagonals of the triangular
band matrix A.  KD	>= 0.

AB	     (input) COMPLEX*16	array, dimension (LDAB,N)
The upper or lower	triangular band	matrix A, stored in the	first
kd+1 rows of the array. The j-th column of	A is stored in the j

Page 1

ZTBCON(3F)							    ZTBCON(3F)

th	column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
= A(i,j) for j<=i<=min(n,j+kd).  If DIAG =	'U', the diagonal
elements of A are not referenced and are assumed to be 1.

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

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
ZTBCON(3F)							    ZTBCON(3F)

```

### NAME[Toc][Back]

```     ZTBCON - estimate the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the	infinity-norm
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZTBCON(	NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,	RWORK,
INFO )

CHARACTER	DIAG, NORM, UPLO

INTEGER	INFO, KD, LDAB,	N

DOUBLE		PRECISION RCOND

DOUBLE		PRECISION RWORK( * )

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

### PURPOSE[Toc][Back]

```     ZTBCON estimates the reciprocal of	the condition number of	a triangular
band matrix A, in either the 1-norm or the	infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)),
then 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.

UPLO    (input) CHARACTER*1
= 'U':  A is upper	triangular;
= 'L':  A is lower	triangular.

DIAG    (input) CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

KD	     (input) INTEGER
The number	of superdiagonals or subdiagonals of the triangular
band matrix A.  KD	>= 0.

AB	     (input) COMPLEX*16	array, dimension (LDAB,N)
The upper or lower	triangular band	matrix A, stored in the	first
kd+1 rows of the array. The j-th column of	A is stored in the j

Page 1

ZTBCON(3F)							    ZTBCON(3F)

th	column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
= A(i,j) for j<=i<=min(n,j+kd).  If DIAG =	'U', the diagonal
elements of A are not referenced and are assumed to be 1.

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

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

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