.TH DLANGE 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLANGE - 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 .SH SYNOPSIS .TP 17 DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) .TP 17 .ti +4 CHARACTER NORM .TP 17 .ti +4 INTEGER LDA, M, N .TP 17 .ti +4 DOUBLE PRECISION A( LDA, * ), WORK( * ) .SH 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. .SH DESCRIPTION DLANGE returns the value .br DLANGE = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq .br ( .br ( norm1(A), NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq .br ( .br ( normI(A), NORM = \(aqI\(aq or \(aqi\(aq .br ( .br ( normF(A), NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq 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. .SH ARGUMENTS .TP 8 NORM (input) CHARACTER*1 Specifies the value to be returned in DLANGE as described above. .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0. When M = 0, DLANGE is set to zero. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0. When N = 0, DLANGE is set to zero. .TP 8 A (input) DOUBLE PRECISION array, dimension (LDA,N) The m by n matrix A. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(M,1). .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = \(aqI\(aq; otherwise, WORK is not referenced.