# zlantr (l) - Linux Manuals

## NAME

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

## SYNOPSIS

DOUBLE PRECISION
FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

CHARACTER DIAG, NORM, UPLO

INTEGER LDA, M, N

DOUBLE PRECISION WORK( * )

COMPLEX*16 A( LDA, * )

## 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.

## DESCRIPTION

ZLANTR returns the value

ZLANTR max(abs(A(i,j))), NORM aqMaq or aqmaq

(

norm1(A),         NORM aq1aq, aqOaq or aqoaq

(

normI(A),         NORM aqIaq or aqiaq

(

normF(A),         NORM aqFaq, aqfaq, aqEaq or aqeaq 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 ZLANTR as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower trapezoidal. = aqUaq: Upper trapezoidal
= aqLaq: Lower trapezoidal Note that A is triangular instead of trapezoidal if M = N.
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A has unit diagonal. = aqNaq: Non-unit diagonal
= aqUaq: Unit diagonal
M (input) INTEGER
The number of rows of the matrix A. M >= 0, and if UPLO = aqUaq, M <= N. When M = 0, ZLANTR is set to zero.
N (input) INTEGER
The number of columns of the matrix A. N >= 0, and if UPLO = aqLaq, N <= M. When N = 0, ZLANTR is set to zero.
A (input) COMPLEX*16 array, dimension (LDA,N)
The trapezoidal matrix A (A is triangular if M = N). If UPLO = aqUaq, 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 = aqLaq, 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 = aqUaq, the diagonal elements of A are not referenced and are assumed to be one.
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 = aqIaq; otherwise, WORK is not referenced.