NAME¶

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

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 consistent 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 (MAX(1,LWORK)),

where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.