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# dlangb

```
NAME
DLANGB - 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 band matrix A, with kl sub-diagonals
and ku super-diagonals

SYNOPSIS
DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
WORK )

CHARACTER    NORM

INTEGER      KL, KU, LDAB, N

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

PURPOSE
DLANGB  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
DLANGB returns the value

DLANGB = ( 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 DLANGB as
described above.

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

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

0.

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

AB      (input) DOUBLE PRECISION 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.
```