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clantb

```
NAME
CLANTB - return the value of the one norm, or the Frobenius
norm, or the infinity norm, or the element of largest abso-
lute value of an n by n triangular band matrix A, with ( k +
1 ) diagonals

SYNOPSIS
REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK
)

CHARACTER DIAG, NORM, UPLO

INTEGER   K, LDAB, N

REAL      WORK( * )

COMPLEX   AB( LDAB, * )

PURPOSE
CLANTB  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
CLANTB returns the value

CLANTB = ( 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  matrix norm.

ARGUMENTS
NORM    (input) CHARACTER*1
Specifies the value to be returned in CLANTB 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
= 'U':  Unit triangular

N       (input) INTEGER
The order of the matrix A.  N >= 0.  When N = 0,
CLANTB 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) COMPLEX 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 fol-
lows: 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 refer-
enced, but are assumed to be one.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= K+1.

WORK    (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is
not referenced.
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