---
name: "clanhs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/clanhs/3lapack"
---

# clanhs(3lapack)

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

CLANHS - 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

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

- CHARACTER

  NORM

- INTEGER

  LDA, N

- REAL

  WORK( \* )

- COMPLEX

  A( LDA, \* )

## PURPOSE

CLANHS  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

CLANHS returns the value\
\
    CLANHS = ( 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 CLANHS as described above.

- N (input) INTEGER

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

- A (input) COMPLEX 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 = 'I'; otherwise, WORK is not referenced.