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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

```NAME
LAPACK-3 - 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
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 consistent 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 (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```