DLANGB(1) LAPACK auxiliary routine (version 3.2) DLANGB(1)NAME
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
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 consistent 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 col‐
umn of A is stored in the j-th column of the array AB as fol‐
lows: 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 (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
enced.
LAPACK auxiliary routine (versioNovember 2008 DLANGB(1)
