# clansb.f - Man Page

## Synopsis

### Functions/Subroutines

real function clansb (NORM, UPLO, N, K, AB, LDAB, WORK)
CLANSB 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.

## Function/Subroutine Documentation

### real function clansb (character NORM, character UPLO, integer N, integer K, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) WORK)

CLANSB 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:

``` CLANSB  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:

CLANSB

```    CLANSB = ( 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 CLANSB 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, CLANSB 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 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 REAL 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

NAG Ltd.

Date:

December 2016

Definition at line 132 of file clansb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clansb(3) is an alias of clansb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK