ZLANTR(3f)

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

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 = 'M' or 'm'
            (
            ( norm1(A), NORM = '1', 'O' or 'o'
            (
            ( normI(A), NORM = 'I' or 'i'
            (
            ( normF(A), NORM = 'F', 'f', 'E' or 'e' 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. = 'U': Upper trapezoidal
    = 'L': 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. = 'N': Non-unit diagonal
    = 'U': Unit diagonal

M       (input) INTEGER
    The number of rows of the matrix A. M >= 0, and if UPLO = 'U', 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 = 'L', 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 = 'U', 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 = 'L', 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 = 'U', 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 = 'I'; otherwise, WORK is not referenced.