DLANGE(l) — LAPACK auxiliary routine (version 2.0)

NAME

DLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A

SYNOPSIS

DOUBLE PRECISION
FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )

CHARACTER NORM

INTEGER LDA, M, N

DOUBLE PRECISION A( LDA, ∗ ), WORK( ∗ )

PURPOSE

DLANGE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A.

DESCRIPTION

DLANGE returns the value

   DLANGE = ( max(abs(A(i,j))), NORM = ’M’ or ’m’
            (
            ( norm1(A),         NORM = ’1’, ’O’ or ’o’
            (
            ( normI(A),         NORM = ’I’ or ’i’
            (
            ( normF(A),         NORM = ’F’, ’f’, ’E’ or ’e’

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a matrix norm.

ARGUMENTS

NORM (input) CHARACTER∗1
Specifies the value to be returned in DLANGE as described above.

M (input) INTEGER
The number of rows of the matrix A. M >= 0. When M = 0, DLANGE is set to zero.

N (input) INTEGER
The number of columns of the matrix A. N >= 0. When N = 0, DLANGE is set to zero.

A (input) DOUBLE PRECISION array, dimension (LDA,N)
The m by n matrix A.

LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).

WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= M when NORM = ’I’; otherwise, WORK is not referenced.