CLANTR(3)      LAPACK routine of NEC Numeric Library Collection      CLANTR(3)



NAME
       CLANTR

SYNOPSIS
       REAL FUNCTION CLANTR (NORM, UPLO, DIAG, M, N, A, LDA, WORK)



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.


       Returns:
           CLANTR

               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 consistent matrix norm.




ARGUMENTS
           NORM      (input)
                     NORM is CHARACTER*1
                     Specifies the value to be returned in CLANTR as described
                     above.

           UPLO      (input)
                     UPLO is 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)
                     DIAG is CHARACTER*1
                     Specifies whether or not the matrix A has unit diagonal.
                     = 'N':  Non-unit diagonal
                     = 'U':  Unit diagonal

           M         (input)
                     M is 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)
                     N is 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)
                     A is 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(M,1).

           WORK      (output)
                     WORK is REAL array, dimension (MAX(1,LWORK)),
                     where LWORK >= M when NORM = 'I'; otherwise, WORK is not
                     referenced.



LAPACK routine                  31 October 2017                      CLANTR(3)