.TH DLANTR 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLANTR - the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A .SH SYNOPSIS .TP 17 DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK ) .TP 17 .ti +4 CHARACTER DIAG, NORM, UPLO .TP 17 .ti +4 INTEGER LDA, M, N .TP 17 .ti +4 DOUBLE PRECISION A( LDA, * ), WORK( * ) .SH PURPOSE DLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. .SH DESCRIPTION DLANTR returns the value .br DLANTR = ( 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 DLANTR as described above. .TP 8 UPLO (input) CHARACTER*1 Specifies whether the matrix A is upper or lower trapezoidal. = \(aqU\(aq: Upper trapezoidal .br = \(aqL\(aq: Lower trapezoidal Note that A is triangular instead of trapezoidal if M = N. .TP 8 DIAG (input) CHARACTER*1 Specifies whether or not the matrix A has unit diagonal. = \(aqN\(aq: Non-unit diagonal .br = \(aqU\(aq: Unit diagonal .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0, and if UPLO = \(aqU\(aq, M <= N. When M = 0, DLANTR is set to zero. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0, and if UPLO = \(aqL\(aq, N <= M. When N = 0, DLANTR is set to zero. .TP 8 A (input) DOUBLE PRECISION array, dimension (LDA,N) The trapezoidal matrix A (A is triangular if M = N). If UPLO = \(aqU\(aq, the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced. If UPLO = \(aqL\(aq, the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = \(aqU\(aq, the diagonal elements of A are not referenced and are assumed to be one. .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.