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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

```NAME
LAPACK-3 - 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

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

CHARACTER    NORM, UPLO

INTEGER      K, LDAB, N

DOUBLE       PRECISION WORK( * )

COMPLEX*16   AB( LDAB, * )

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.

DESCRIPTION
ZLANSB returns the value
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.

ARGUMENTS
NORM    (input) CHARACTER*1
Specifies the value to be returned in ZLANSB 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, ZLANSB is
set to zero.

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

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

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

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```