


SLANHS(3f)    LAPACK auxiliary routine (version 3.1)   SLANHS(3f)


NAME
       SLANHS  -  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 = '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  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).




 LAPACK auxiliary routine November 2006                         1





SLANHS(3f)    LAPACK auxiliary routine (version 3.1)   SLANHS(3f)


       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer-
               enced.






















































 LAPACK auxiliary routine November 2006                         2


