?lansb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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

valslansb ( norm , uplo , n , k , ab , ldab , work )

valdlansb ( norm , uplo , n , k , ab , ldab , work )

valclansb ( norm , uplo , n , k , ab , ldab , work )

valzlansb ( norm , uplo , n , k , ab , ldab , work )

Include Files

mkl.fi

Description

slansb dlansb clansb zlansb

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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lansb

Syntax

Include Files

Description

Input Parameters

Output Parameters