.TH CLANHS 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLANHS - the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A .SH SYNOPSIS .TP 14 REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK ) .TP 14 .ti +4 CHARACTER NORM .TP 14 .ti +4 INTEGER LDA, N .TP 14 .ti +4 REAL WORK( * ) .TP 14 .ti +4 COMPLEX A( LDA, * ) .SH PURPOSE CLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A. .SH DESCRIPTION CLANHS returns the value .br CLANHS = ( 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 CLANHS as described above. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero. .TP 8 A (input) COMPLEX array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced. .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; otherwise, WORK is not referenced.