# ?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 )

## 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 vaule to be returned by the routine:

  = 'M' or 'm': `val = max(abs(Aij))`, 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

  COMPLEX*16 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: Auxiliary Routines