# clansb (l) - Linux Man Pages

## NAME

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

## SYNOPSIS

REAL FUNCTION
CLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

CHARACTER NORM, UPLO

INTEGER K, LDAB, N

REAL WORK( * )

COMPLEX AB( LDAB, * )

## 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.

## DESCRIPTION

CLANSB returns the value

CLANSB max(abs(A(i,j))), NORM aqMaq or aqmaq

(

norm1(A),         NORM aq1aq, aqOaq or aqoaq

(

normI(A),         NORM aqIaq or aqiaq

(

normF(A),         NORM aqFaq, aqfaq, aqEaq or aqeaq 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 CLANSB as described above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the band matrix A is supplied. = aqUaq: Upper triangular part is supplied
= aqLaq: Lower triangular part is supplied
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANSB 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 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 = aqUaq, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = aqLaq, 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) REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = aqIaq or aq1aq or aqOaq; otherwise, WORK is not referenced.