zlantr (l) - Linux Manuals

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

Command to display zlantr manual in Linux: $ man l zlantr

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.