.TH ZLANTR 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
ZLANTR - 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 ZLANTR( 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 WORK( * )
.TP 17
.ti +4
COMPLEX*16
A( LDA, * )
.SH PURPOSE
ZLANTR 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
ZLANTR returns the value
.br
ZLANTR = ( 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 ZLANTR 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, ZLANTR 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, ZLANTR is set to zero.
.TP 8
A (input) COMPLEX*16 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.