?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 )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

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 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).

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

DOUBLE COMPLEX 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.