zlanhe(3P)

NAME

zlanhe - return 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

SYNOPSIS

DOUBLE PRECISION
FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )

double zlanhe(char norm, char uplo, long int n, doublecomplex ∗za, long int lda)

CHARACTER NORM, UPLO

INTEGER LDA, N

DOUBLE PRECISION WORK( ∗ )

COMPLEX∗16 A( LDA, ∗ )

PURPOSE

ZLANHE 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.

DESCRIPTION

ZLANHE returns the value

   ZLANHE = ( 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 ZLANHE 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, ZLANHE is set to zero.

A (input) COMPLEX∗16 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) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = ’I’ or ’1’ or ’O’; otherwise, WORK is not referenced.