slanhs (l) - Linux Manuals

slanhs: 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

NAME

SLANHS - 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

SYNOPSIS

REAL FUNCTION

SLANHS( NORM, N, A, LDA, WORK )

    

CHARACTER NORM

    

INTEGER LDA, N

    

REAL A( LDA, * ), WORK( * )

PURPOSE

SLANHS 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

SLANHS returns the value

SLANHS = ( 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 SLANHS as described above.

N (input) INTEGER

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

A (input) REAL 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) REAL array, dimension (MAX(1,LWORK)),

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