.TH CLANHP 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLANHP - 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, supplied in packed form .SH SYNOPSIS .TP 14 REAL FUNCTION CLANHP( NORM, UPLO, N, AP, WORK ) .TP 14 .ti +4 CHARACTER NORM, UPLO .TP 14 .ti +4 INTEGER N .TP 14 .ti +4 REAL WORK( * ) .TP 14 .ti +4 COMPLEX AP( * ) .SH PURPOSE CLANHP 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, supplied in packed form. .SH DESCRIPTION CLANHP returns the value .br CLANHP = ( 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 CLANHP as described above. .TP 8 UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian matrix A is supplied. = \(aqU\(aq: Upper triangular part of A is supplied .br = \(aqL\(aq: Lower triangular part of A is supplied .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHP is set to zero. .TP 8 AP (input) COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangle of the hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. .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.