# zlanhb.f - Man Page

## Synopsis

### Functions/Subroutines

double precision function **zlanhb** (NORM, UPLO, **N**, K, AB, LDAB, WORK)**ZLANHB** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

## Function/Subroutine Documentation

### double precision function zlanhb (character NORM, character UPLO, integer N, integer K, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK)

**ZLANHB** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

**Purpose:**

ZLANHB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals.

**Returns:**ZLANHB

ZLANHB = ( 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 ZLANHB as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular

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

*K*K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.

*AB*AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the hermitian band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.

*LDAB*LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1.

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; 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 134 of file zlanhb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK