CLANHE
November 2006
Purpose
CLANHE returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex hermitian matrix A.
the infinity norm, or the element of largest absolute value of a
complex hermitian matrix A.
Description
CLANHE returns the value
CLANHE = ( 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.
CLANHE = ( 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 CLANHE as described
above. |
| UPLO |
(input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced |
| N |
(input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANHE is
set to zero. |
| A |
(input) COMPLEX array, dimension (LDA,N)
The hermitian matrix A. If UPLO = 'U', the leading n by n
upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. |
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
|
| WORK |
(workspace) REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced. |