?lansb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lansb

Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Syntax

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

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

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

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

Include Files

mkl.fi

Description

The function ?lansb 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 real/complex symmetric 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, ?lansb is set to zero.

k

INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. k≥ 0.

ab

REAL for slansb

DOUBLE PRECISION for dlansb

COMPLEX for clansb

DOUBLE COMPLEX for zlansb

Array, DIMENSION (ldab,n).

The upper or lower triangle of the symmetric 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).

ldab

INTEGER. The leading dimension of the array ab.

ldab≥k+1.

work

REAL for slansb and clansb.

DOUBLE PRECISION for dlansb and zlansb.

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 slansb/clansb

DOUBLE PRECISION for dlansb/zlansb

Value returned by the function.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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