?lansp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lansp

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 matrix supplied in packed form.

Syntax

val = slansp( norm, uplo, n, ap, work )

val = dlansp( norm, uplo, n, ap, work )

val = clansp( norm, uplo, n, ap, work )

val = zlansp( norm, uplo, n, ap, work )

Include Files

mkl.fi

Description

The function ?lansp 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, supplied in packed form.

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 symmetric matrix A is supplied.

If uplo = 'U': Upper triangular part of A is supplied

If uplo = 'L': Lower triangular part of A is supplied.

n

INTEGER. The order of the matrix A. n≥ 0. When

n = 0, ?lansp is set to zero.

ap

REAL for slansp

DOUBLE PRECISION for dlansp

COMPLEX for clansp

DOUBLE COMPLEX for zlansp

Array, DIMENSION (n(n+1)/2).

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array ap as follows:

if uplo = 'U', ap(i + (j-1)j/2) = A(i,j) for 1 ≤ i ≤ j;

if uplo = 'L', ap(i + (j-1)(2n-j)/2) = A(i,j) for j ≤ i ≤ n.

work

REAL for slansp and clansp.

DOUBLE PRECISION for dlansp and zlansp.

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 slansp/clansp

DOUBLE PRECISION for dlansp/zlansp

Value returned by the function.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lansp