clantr(3F)

NAME
     CLANTR - 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
     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 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 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 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, 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 assumed 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.