zlanhs(l) — SunSoft Performance Library

NAME

zlanhs - return 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

SYNOPSIS

DOUBLE PRECISION
FUNCTION ZLANHS( NORM, N, A, LDA, WORK )

CHARACTER NORM

INTEGER LDA, N

DOUBLE PRECISION WORK( ∗ )

COMPLEX∗16 A( LDA, ∗ )

PURPOSE

ZLANHS 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.

DESCRIPTION

ZLANHS returns the value

   ZLANHS = ( 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 matrix norm.

ARGUMENTS

NORM (input) CHARACTER∗1
Specifies the value to be returned in ZLANHS as described above.

N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHS is set to zero.

A (input) COMPLEX∗16 array, dimension (LDA,N)
The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).

WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = ’I’; otherwise, WORK is not referenced.