?lantp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lantp

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 matrix supplied in packed form.

Syntax

val = slantp( norm, uplo, diag, n, ap, work )

val = dlantp( norm, uplo, diag, n, ap, work )

val = clantp( norm, uplo, diag, n, ap, work )

val = zlantp( norm, uplo, diag, n, ap, work )

Include Files

mkl.fi

Description

The function ?lantp 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 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 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, ?lantp is set to zero.

ap

REAL for slantp

DOUBLE PRECISION for dlantp

COMPLEX for clantp

DOUBLE COMPLEX for zlantp

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

The upper or lower triangular 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.

Note that when diag = 'U', the elements of the array ap corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

work

REAL for slantp and clantp.

DOUBLE PRECISION for dlantp and zlantp.

Workspace array, DIMENSION(max(1,lwork)), where lwork≥n when norm = 'I' ; otherwise, work is not referenced.

Output Parameters

val

REAL for slantp/clantp.

DOUBLE PRECISION for dlantp/zlantp.

Value returned by the function.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lantp