.TH CLANHE 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
CLANHE - 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
.SH SYNOPSIS
.TP 14
REAL FUNCTION
CLANHE( NORM, UPLO, N, A, LDA, WORK )
.TP 14
.ti +4
CHARACTER
NORM, UPLO
.TP 14
.ti +4
INTEGER
LDA, N
.TP 14
.ti +4
REAL
WORK( * )
.TP 14
.ti +4
COMPLEX
A( LDA, * )
.SH 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.
.SH DESCRIPTION
CLANHE returns the value
.br
CLANHE = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq
.br
(
.br
( norm1(A), NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq
.br
(
.br
( normI(A), NORM = \(aqI\(aq or \(aqi\(aq
.br
(
.br
( normF(A), NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq
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.
.SH ARGUMENTS
.TP 8
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANHE as described
above.
.TP 8
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is to be referenced.
= \(aqU\(aq: Upper triangular part of A is referenced
.br
= \(aqL\(aq: Lower triangular part of A is referenced
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANHE is
set to zero.
.TP 8
A (input) COMPLEX array, dimension (LDA,N)
The hermitian matrix A. If UPLO = \(aqU\(aq, 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 = \(aqL\(aq, 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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
.TP 8
WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = \(aqI\(aq or \(aq1\(aq or \(aqO\(aq; otherwise,
WORK is not referenced.