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 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 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 (MAX(1,LWORK)),

where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.