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

```
CLANHB(3F)							    CLANHB(3F)

```

### NAME[Toc][Back]

```     CLANHB - 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
hermitian band matrix A, with k super-diagonals
```

### SYNOPSIS[Toc][Back]

```     REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB, WORK )

CHARACTER NORM, UPLO

INTEGER   K, LDAB, N

REAL	   WORK( * )

COMPLEX   AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     CLANHB  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
hermitian band matrix A,  with k super-diagonals.

```

### DESCRIPTION[Toc][Back]

```     CLANHB returns the	value

CLANHB = ( 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 CLANHB as described above.

UPLO    (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the band
matrix A is supplied.  = 'U':  Upper triangular
= 'L':  Lower triangular

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

Page 1

CLANHB(3F)							    CLANHB(3F)

K	     (input) INTEGER
The number	of super-diagonals or sub-diagonals of the band	matrix
A.	 K >= 0.

AB	     (input) COMPLEX array, dimension (LDAB,N)
The upper or lower	triangle of the	hermitian band matrix A,
stored in the first K+1 rows of AB.  The j-th column of A is
stored in the j-th	column of the array AB as follows:  if UPLO =
'U', AB(k+1+i-j,j)	= A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L',
AB(1+i-j,j)   = A(i,j) for	j<=i<=min(n,j+k).  Note	that the
imaginary parts of	the diagonal elements need not be set and are
assumed to	be zero.

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

WORK    (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM	= 'I' or '1' or	'O'; otherwise,	WORK
is	not referenced.
CLANHB(3F)							    CLANHB(3F)

```

### NAME[Toc][Back]

```     CLANHB - 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
hermitian band matrix A, with k super-diagonals
```

### SYNOPSIS[Toc][Back]

```     REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB, WORK )

CHARACTER NORM, UPLO

INTEGER   K, LDAB, N

REAL	   WORK( * )

COMPLEX   AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     CLANHB  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
hermitian band matrix A,  with k super-diagonals.

```

### DESCRIPTION[Toc][Back]

```     CLANHB returns the	value

CLANHB = ( 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 CLANHB as described above.

UPLO    (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the band
matrix A is supplied.  = 'U':  Upper triangular
= 'L':  Lower triangular

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

Page 1

CLANHB(3F)							    CLANHB(3F)

K	     (input) INTEGER
The number	of super-diagonals or sub-diagonals of the band	matrix
A.	 K >= 0.

AB	     (input) COMPLEX array, dimension (LDAB,N)
The upper or lower	triangle of the	hermitian band matrix A,
stored in the first K+1 rows of AB.  The j-th column of A is
stored in the j-th	column of the array AB as follows:  if UPLO =
'U', AB(k+1+i-j,j)	= A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L',
AB(1+i-j,j)   = A(i,j) for	j<=i<=min(n,j+k).  Note	that the
imaginary parts of	the diagonal elements need not be set and are
assumed to	be zero.

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

WORK    (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM	= 'I' or '1' or	'O'; 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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