# zlansb.f man page

zlansb.f —

## Synopsis

### Functions/Subroutines

DOUBLE PRECISION functionzlansb(NORM, UPLO, N, K, AB, LDAB, WORK)ZLANSBreturns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

## Function/Subroutine Documentation

### DOUBLE PRECISION function zlansb (characterNORM, characterUPLO, integerN, integerK, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

**ZLANSB** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

**Purpose:**

```
ZLANSB 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 symmetric band matrix A, with k super-diagonals.
```

**Returns:**

ZLANSB

```
ZLANSB = ( 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 consistent matrix norm.
```

**Parameters:**

*NORM*

```
NORM is CHARACTER*1
Specifies the value to be returned in ZLANSB as described
above.
```

*UPLO*

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

*N*

```
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANSB is
set to zero.
```

*K*

```
K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A. K >= 0.
```

*AB*

```
AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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).
```

*LDAB*

```
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= K+1.
```

*WORK*

```
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 130 of file zlansb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlansb(3) is an alias of zlansb.f(3).