DLANTB  -  return the value of the one norm, or the Frobe­
       nius norm, or the infinity norm, or the element of largest
       absolute value of an n by n triangular band matrix A, with
       ( k + 1 ) diagonals


SYNOPSIS

       DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N,  K,
                        AB, LDAB, WORK )

           CHARACTER    DIAG, NORM, UPLO

           INTEGER      K, LDAB, N

           DOUBLE       PRECISION AB( LDAB, * ), WORK( * )


PURPOSE

       DLANTB returns the value of the one norm, or the Frobenius
       norm, or the infinity norm,  or  the  element  of  largest
       absolute value of an n by n triangular band matrix A, with
       ( k + 1 ) diagonals.


DESCRIPTION

       DLANTB returns the value

          DLANTB = ( 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  Frobe­
       nius 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 DLANTB as
               described above.

       UPLO    (input) CHARACTER*1
               Specifies whether the matrix A is upper  or  lower
               triangular.  = 'U':  Upper triangular
               = 'L':  Lower triangular

       DIAG    (input) CHARACTER*1
               Specifies whether or not the matrix A is unit tri­
               angular.  = 'N':  Non-unit triangular


       N       (input) INTEGER
               The order of the matrix A.  N >= 0.  When N  =  0,
               DLANTB is set to zero.

       K       (input) INTEGER
               The  number  of super-diagonals of the matrix A if
               UPLO = 'U', or the number of sub-diagonals of  the
               matrix A if UPLO = 'L'.  K >= 0.

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
               The upper  or  lower  triangular  band  matrix  A,
               stored in the first k+1 rows of AB.  The j-th col­
               umn of A is stored in the j-th column of the array
               AB  as  follows:  if  UPLO  = 'U', AB(k+1+i-j,j) =
               A(i,j)  for  max(1,j-k)<=i<=j;  if  UPLO  =   'L',
               AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).  Note
               that when DIAG = 'U', the elements of the array AB
               corresponding  to  the  diagonal  elements  of the
               matrix A are not referenced, but are assumed to be
               one.

       LDAB    (input) INTEGER
               The  leading  dimension  of the array AB.  LDAB >=
               K+1.

       WORK    (workspace) DOUBLE PRECISION array, dimension
               (LWORK),
               where  LWORK >= N when NORM = 'I'; otherwise, WORK
               is not referenced.


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