?lansy

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2025

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?lansy

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

Syntax

val = slansy( norm, uplo, n, a, lda, work )

val = dlansy( norm, uplo, n, a, lda, work )

val = clansy( norm, uplo, n, a, lda, work )

val = zlansy( norm, uplo, n, a, lda, work )

Include Files

mkl.fi

Description

The function ?lansy returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real/complex symmetric matrix A.

Input Parameters

The data types are given for the Fortran interface.

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 symmetric matrix A is to be referenced.

= 'U': Upper triangular part of A is referenced.

= 'L': Lower triangular part of A is referenced

n

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

a

REAL for slansy

DOUBLE PRECISION for dlansy

COMPLEX for clansy

DOUBLE COMPLEX for zlansy

Array, size (lda,n). The symmetric matrix A.

If uplo = 'U', the leading n-by-n upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.

lda

INTEGER. The leading dimension of the array a.

lda≥ max(n,1).

work

REAL for slansy and clansy.

DOUBLE PRECISION for dlansy and zlansy.

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 slansy/clansy

DOUBLE PRECISION for dlansy/zlansy

Value returned by the function.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lansy

Syntax

Include Files

Description

Input Parameters

Output Parameters