?lantb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?lantb

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

Syntax

valslantb ( norm , uplo , diag , n , k , ab , ldab , work )

valdlantb ( norm , uplo , diag , n , k , ab , ldab , work )

valclantb ( norm , uplo , diag , n , k , ab , ldab , work )

valzlantb ( norm , uplo , diag , n , k , ab , ldab , work )

Include Files

mkl.fi

Description

slantb dlantb clantb zlantb

The function ?lantb 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 triangular band matrix A , with ( k + 1 ) 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 matrix A is upper or lower triangular. = ‘U’ : Upper triangular = ‘L’ : Lower triangular.
diag: CHARACTER*1 . Specifies whether or not the matrix A is unit triangular. = ‘N’ : Non-unit triangular = ‘U’ : Unit triangular.
n: INTEGER . The order of the matrix A . n≥ 0 . When n = 0 , ?lantb is set to zero.
k: INTEGER . The number of super-diagonals of the matrix A if uplo = 'U' , or the number of sub-diagonals of the matrix A if uplo = 'L' . k ≥ 0.
ab: REAL for slantb DOUBLE PRECISION for dlantb COMPLEX for clantb DOUBLE COMPLEX for zlantb Array, DIMENSION ( ldab , n ). The upper or lower triangular 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 when diag = 'U' , the elements of the array ab corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.
ldab: INTEGER . The leading dimension of the array ab . ldab≥k+1 .
work: REAL for slantb and clantb . DOUBLE PRECISION for dlantb and zlantb . Workspace array, DIMENSION (max(1,lwork)) , where lwork≥n when norm = 'I' ; otherwise, work is not referenced.

Output Parameters

val: REAL for slantb / clantb . DOUBLE PRECISION for dlantb / zlantb . Value returned by the function.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lantb

Syntax

Include Files

Description

Input Parameters

Output Parameters