DLANTB - return the value of the one norm, or the Frobe
nius 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 Frobe
nius norm of a matrix (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 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 tri
angular. = 'N': Non-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 col
umn 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
(LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK
is not referenced.
Man(1) output converted with
man2html