clanhe (l) - Linux Manuals

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

NAME

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

SYNOPSIS

REAL FUNCTION

CLANHE( NORM, UPLO, N, A, LDA, WORK )

    

CHARACTER NORM, UPLO

    

INTEGER LDA, N

    

REAL WORK( * )

    

COMPLEX A( LDA, * )

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.

DESCRIPTION

CLANHE returns the value

CLANHE = ( max(abs(A(i,j))), NORM = aqMaq or aqmaq

      (

      ( norm1(A),         NORM = aq1aq, aqOaq or aqoaq

      (

      ( normI(A),         NORM = aqIaq or aqiaq

      (

      ( normF(A),         NORM = aqFaq, aqfaq, aqEaq or aqeaq 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.

ARGUMENTS

NORM (input) CHARACTER*1

Specifies the value to be returned in CLANHE as described above.

UPLO (input) CHARACTER*1

Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced. = aqUaq: Upper triangular part of A is referenced
= aqLaq: Lower triangular part of A is referenced

N (input) INTEGER

The order of the matrix A. N >= 0. When N = 0, CLANHE is set to zero.

A (input) COMPLEX array, dimension (LDA,N)

The hermitian matrix A. If UPLO = aqUaq, 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 = aqLaq, 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) REAL array, dimension (MAX(1,LWORK)),

where LWORK >= N when NORM = aqIaq or aq1aq or aqOaq; otherwise, WORK is not referenced.