# dlanhs.f - Man Page

## Synopsis

### Functions/Subroutines

double precision function **dlanhs** (NORM, **N**, A, **LDA**, WORK)**DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

## Function/Subroutine Documentation

### double precision function dlanhs (character NORM, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WORK)

**DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

DLANHS 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.

**Returns:**DLANHS

DLANHS = ( 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.

**Parameters:***NORM*NORM is CHARACTER*1 Specifies the value to be returned in DLANHS as described above.

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

*A*A is DOUBLE PRECISION 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 110 of file dlanhs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlanhs(3) is an alias of dlanhs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK