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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?langb

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

Syntax

val = slangb( norm, n, kl, ku, ab, ldab, work )

val = dlangb( norm, n, kl, ku, ab, ldab, work )

val = clangb( norm, n, kl, ku, ab, ldab, work )

val = zlangb( norm, n, kl, ku, ab, ldab, work )

Include Files

mkl.fi

Description

The function 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 band matrix A, with kl sub-diagonals and ku 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).

n

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

kl

INTEGER. The number of sub-diagonals of the matrix A. kl≥ 0.

ku

INTEGER. The number of super-diagonals of the matrix A. ku≥ 0.

ab

REAL for slangb

DOUBLE PRECISION for dlangb

COMPLEX for clangb

DOUBLE COMPLEX for zlangb

Array, DIMENSION (ldab,n).

The band matrix A, stored in rows 1 to kl+ku+1. The j-th column of A is stored in the j-th column of the array ab as follows:

ab(ku+1+i-j,j) = a(i,j)

for max(1,j-ku) ≤ i ≤ min(n,j+kl).

ldab

INTEGER. The leading dimension of the array ab.

ldab≥kl+ku+1.

work

REAL for slangb/clangb

DOUBLE PRECISION for dlangb/zlangb

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

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

Output Parameters

val

REAL for slangb/clangb

DOUBLE PRECISION for dlangb/zlangb

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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