# ?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 )

## 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 vaule to be returned by the routine:

  = 'M' or 'm': val = max(abs(Ai j)), 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

  COMPLEX*16 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: Auxiliary Routines