# ?lanhb

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.

## Syntax

val = clanhb( norm, uplo, n, k, ab, ldab, work )

val = zlanhb( norm, uplo, n, k, ab, ldab, work )

## Description

The routine returns the value of the 1-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.

## Input Parameters

norm

  CHARACTER*1. Specifies the vaule to be returned by the routine:

  = 'M' or 'm': val = max(abs(Ai j)), largest absolute value of the matrix A.

  = '1' or 'O' or 'o': val = norm1(A), 1-norm of the matrix A (maximum column sum),

  = 'I' or 'i': val = normI(A), infinity norm of the matrix A (maximum row sum),

  = 'F', 'f', 'E' or 'e': val = normF(A), Frobenius norm of the matrix A (square root of sum of squares).

uplo

  CHARACTER*1.

  Specifies whether the upper or lower triangular part of the band matrix A is supplied.

  If `uplo = 'U'`: upper triangular part is supplied;

  If `uplo = 'L'`: lower triangular part is supplied.

n

  INTEGER. The order of the matrix A. `n ≥ 0`. When `n = 0`, ?lanhb is set to zero.

k

  INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A.

  `k ≥ 0`.

ab

  COMPLEX for clanhb.

  COMPLEX*16 for zlanhb.

  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

  INTEGER. The leading dimension of the array ab. ldab ≥ k+1.

work

  REAL for clanhb.

  DOUBLE PRECISION for zlanhb.

  Workspace array, DIMENSION `max(1, lwork)`, where

  `lwork ≥ n` when `norm = 'I'` or '1' or 'O'; otherwise, work is not referenced.

## Output Parameters

val

  REAL for slanhb/clanhb

  DOUBLE PRECISION for dlanhb/zlanhb

  Value returned by the function.

Parent topic: Auxiliary Routines