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# dlansb

```
NAME
DLANSB - return the value of the one norm, or the Frobenius
norm, or the infinity norm, or the element of largest abso-
lute value of an n by n symmetric band matrix A, with k
super-diagonals

SYNOPSIS
DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB,
LDAB, WORK )

CHARACTER    NORM, UPLO

INTEGER      K, LDAB, N

DOUBLE       PRECISION AB( LDAB, * ), WORK( * )

PURPOSE
DLANSB  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.

DESCRIPTION
DLANSB returns the value

DLANSB = ( 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
NORM    (input) CHARACTER*1
Specifies the value to be returned in DLANSB 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 part is supplied
= 'L':  Lower triangular part is supplied

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

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

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

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