SLANGB - 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 band matrix A, with kl sub-
diagonals and ku super-diagonals
SYNOPSIS
REAL FUNCTION SLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
CHARACTER NORM
INTEGER KL, KU, LDAB, N
REAL AB( LDAB, * ), WORK( * )
PURPOSE
SLANGB 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
SLANGB returns the value
SLANGB = ( 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 SLANGB as
described above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0,
SLANGB is set to zero.
KL (input) INTEGER
The number of sub-diagonals of the matrix A. KL
>= 0.
The number of super-diagonals of the matrix A. KU
>= 0.
AB (input) REAL 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.
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