clantr(3)

NAME

CLANTR - return the value of the one norm, or the Frobe

nius norm, or the infinity norm, or the element of largest abso

lute value of a trapezoidal or triangular matrix A

SYNOPSIS

REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK
)
    CHARACTER DIAG, NORM, UPLO
    INTEGER   LDA, M, N
    REAL      WORK( * )
    COMPLEX   A( LDA, * )

PURPOSE

CLANTR 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

CLANTR returns the value

CLANTR = ( 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 ma

trix (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 CLANTR 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 triangu

lar instead of trapezoidal if M = N.

DIAG (input) CHARACTER*1

Specifies whether or not the matrix A has unit di

agonal. = '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, CLANTR 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, CLANTR is set to zero.

A (input) COMPLEX 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 as

sumed to be one.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(M,1).

WORK (workspace) REAL array, dimension (LWORK),

where LWORK >= M when NORM = 'I'; otherwise, WORK

is not referenced.

LAPACK version 3.0 15 June 2000

CLANTR(3)