?lanhb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?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 )

Include Files

mkl.fi

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 value to be returned by the routine:

= 'M' or 'm': val = max(abs(A_ij)), 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.

DOUBLE COMPLEX 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, DIMENSIONmax(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: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lanhb