clangb(3)

NAME

CLANGB - return the value of the one norm, or the Frobe

nius 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

REAL FUNCTION CLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
    CHARACTER NORM
    INTEGER   KL, KU, LDAB, N
    REAL      WORK( * )
    COMPLEX   AB( LDAB, * )

PURPOSE

CLANGB 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

CLANGB returns the value

CLANGB = ( 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 ma

trix (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 CLANGB as

described above.

N (input) INTEGER

The order of the matrix A. N >= 0. When N = 0,

CLANGB 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) COMPLEX 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) REAL array, dimension (LWORK),

where LWORK >= N when NORM = 'I'; otherwise, WORK

is not referenced.

LAPACK version 3.0 15 June 2000

CLANGB(3)