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

```
ZLANGB(3F)							    ZLANGB(3F)

```

### NAME[Toc][Back]

```     ZLANGB - return the value of the one norm,	or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of	an n by	n band
matrix A, with kl sub-diagonals and ku super-diagonals
```

### SYNOPSIS[Toc][Back]

```     DOUBLE PRECISION FUNCTION ZLANGB( NORM, N,	KL, KU,	AB, LDAB, WORK )

CHARACTER    NORM

INTEGER      KL, KU, LDAB, N

DOUBLE	      PRECISION	WORK( *	)

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

### PURPOSE[Toc][Back]

```     ZLANGB  returns the value of the one norm,	 or the	Frobenius norm,	or the
infinity norm,  or	the element of	largest	absolute value	of an n	by n
band matrix  A,  with kl sub-diagonals and	ku super-diagonals.

```

### DESCRIPTION[Toc][Back]

```     ZLANGB returns the	value

ZLANGB = ( max(abs(A(i,j))), NORM = 'M'	or 'm'
(
( norm1(A),	     NORM = '1', 'O' or	'o'
(
( normI(A),	     NORM = 'I'	or 'i'
(
( normF(A),	     NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the	one norm of a matrix (maximum column sum),
normI  denotes the	 infinity norm	of a matrix  (maximum row sum) and
normF  denotes the	 Frobenius norm	of a matrix (square root of sum	of
squares).	Note that  max(abs(A(i,j)))  is	not a  matrix norm.

```

### ARGUMENTS[Toc][Back]

```     NORM    (input) CHARACTER*1
Specifies the value to be returned	in ZLANGB as described above.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.  When N = 0, ZLANGB is	set to
zero.

KL	     (input) INTEGER
The number	of sub-diagonals of the	matrix A.  KL >= 0.

Page 1

ZLANGB(3F)							    ZLANGB(3F)

KU	     (input) INTEGER
The number	of super-diagonals of the matrix A.  KU	>= 0.

AB	     (input) COMPLEX*16	array, dimension (LDAB,N)
The band matrix A,	stored in rows 1 to KL+KU+1.  The j-th column
of	A is stored in the j-th	column of the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

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

WORK    (workspace) DOUBLE	PRECISION array, dimension (LWORK),
where LWORK >= N when NORM	= 'I'; otherwise, WORK is not
referenced.
ZLANGB(3F)							    ZLANGB(3F)

```

### NAME[Toc][Back]

```     ZLANGB - return the value of the one norm,	or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of	an n by	n band
matrix A, with kl sub-diagonals and ku super-diagonals
```

### SYNOPSIS[Toc][Back]

```     DOUBLE PRECISION FUNCTION ZLANGB( NORM, N,	KL, KU,	AB, LDAB, WORK )

CHARACTER    NORM

INTEGER      KL, KU, LDAB, N

DOUBLE	      PRECISION	WORK( *	)

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

### PURPOSE[Toc][Back]

```     ZLANGB  returns the value of the one norm,	 or the	Frobenius norm,	or the
infinity norm,  or	the element of	largest	absolute value	of an n	by n
band matrix  A,  with kl sub-diagonals and	ku super-diagonals.

```

### DESCRIPTION[Toc][Back]

```     ZLANGB returns the	value

ZLANGB = ( max(abs(A(i,j))), NORM = 'M'	or 'm'
(
( norm1(A),	     NORM = '1', 'O' or	'o'
(
( normI(A),	     NORM = 'I'	or 'i'
(
( normF(A),	     NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the	one norm of a matrix (maximum column sum),
normI  denotes the	 infinity norm	of a matrix  (maximum row sum) and
normF  denotes the	 Frobenius norm	of a matrix (square root of sum	of
squares).	Note that  max(abs(A(i,j)))  is	not a  matrix norm.

```

### ARGUMENTS[Toc][Back]

```     NORM    (input) CHARACTER*1
Specifies the value to be returned	in ZLANGB as described above.

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.  When N = 0, ZLANGB is	set to
zero.

KL	     (input) INTEGER
The number	of sub-diagonals of the	matrix A.  KL >= 0.

Page 1

ZLANGB(3F)							    ZLANGB(3F)

KU	     (input) INTEGER
The number	of super-diagonals of the matrix A.  KU	>= 0.

AB	     (input) COMPLEX*16	array, dimension (LDAB,N)
The band matrix A,	stored in rows 1 to KL+KU+1.  The j-th column
of	A is stored in the j-th	column of the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

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

WORK    (workspace) DOUBLE	PRECISION array, dimension (LWORK),
where LWORK >= N when NORM	= 'I'; otherwise, WORK is not
referenced.

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