DLANTB(1) LAPACK auxiliary routine (version 3.2) DLANTB(1)NAME
DLANTB - 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 triangular band matrix A, with ( k + 1 ) diagonals
SYNOPSIS
DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB,
WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER K, LDAB, N
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
PURPOSE
DLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.
DESCRIPTION
DLANTB returns the value
DLANTB = ( 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 DLANTB as described
above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular. =
'U': Upper triangular
= 'L': Lower triangular
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular. =
'N': Non-unit triangular
= 'U': Unit triangular
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANTB is set
to zero.
K (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U', or
the number of sub-diagonals of the matrix A if UPLO = 'L'. K
>= 0.
AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular 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). Note that when DIAG = 'U', the
elements of the array AB corresponding to the diagonal elements
of the matrix A are not referenced, but are assumed to be one.
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'; otherwise, WORK is not refer‐
enced.
LAPACK auxiliary routine (versioNovember 2008 DLANTB(1)
