# ?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 )

## 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

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 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

  COMPLEX*16 for zlansy

  Array, DIMENSION (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: Auxiliary Routines