CLANHB - 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 hermitian band matrix A, with
k super-diagonals
SYNOPSIS
REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB, WORK )
CHARACTER NORM, UPLO
INTEGER K, LDAB, N
REAL WORK( * )
COMPLEX AB( LDAB, * )
PURPOSE
CLANHB 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 hermitian band matrix A, with
k super-diagonals.
DESCRIPTION
CLANHB returns the value
CLANHB = ( 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 CLANHB as
described above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular
part of the band matrix A is supplied. = 'U':
Upper triangular
= 'L': Lower triangular
The order of the matrix A. N >= 0. When N = 0,
CLANHB is set to zero.
K (input) INTEGER
The number of super-diagonals or sub-diagonals of
the band matrix A. K >= 0.
AB (input) COMPLEX array, dimension (LDAB,N)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements
need not be set and are assumed to be zero.
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' or '1' or 'O';
otherwise, WORK is not referenced.
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