# ?lange

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

## Syntax

val = slange( norm, m, n, a, lda, work )

val = dlange( norm, m, n, a, lda, work )

val = clange( norm, m, n, a, lda, work )

val = zlange( norm, m, n, a, lda, work )

## Description

The function ?lange 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 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).

m

  INTEGER. The number of rows of the matrix A.

  `m ≥ 0`. When `m = 0`, ?lange is set to zero.

n

  INTEGER. The number of columns of the matrix A.

  `n ≥ 0`. When `n = 0`, ?lange is set to zero.

a

  REAL for slange

  DOUBLE PRECISION for dlange

  COMPLEX for clange

  COMPLEX*16 for zlange

  Array, DIMENSION (lda,n).

  The m-by-n matrix A.

lda

  INTEGER. The leading dimension of the array a.

  `lda ≥ max(m,1)`.

work

  REAL for slange and clange.

  DOUBLE PRECISION for dlange and zlange.

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

## Output Parameters

val

  REAL for slange/clange

  DOUBLE PRECISION for dlange/zlange

  Value returned by the function.

Parent topic: Auxiliary Routines