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dlantb

 NAME
      DLANTB - return the value of the one norm, or the Frobenius
      norm, or the infinity norm, or the element of largest abso-
      lute 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  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 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
              = 'U':  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 column of A
              is stored in the j-th column of the array AB as fol-
              lows: 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 refer-
              enced, 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.