ZLANTR(l) — LAPACK auxiliary routine (version 2.0)

NAME

ZLANTR - return 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 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 (LWORK),
where LWORK >= M when NORM = ’I’; otherwise, WORK is not referenced.