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



NAME
       DLANGB

SYNOPSIS
       DOUBLE PRECISION FUNCTION DLANGB (NORM, N, KL, KU, AB, LDAB, WORK)



PURPOSE
            DLANGB  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 band matrix  A,  with kl sub-diagonals and ku super-diagonals.


       Returns:
           DLANGB

               DLANGB = ( 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 DLANGB as described
                     above.

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

           KL        (input)
                     KL is INTEGER
                     The number of sub-diagonals of the matrix A.  KL >= 0.

           KU        (input)
                     KU is INTEGER
                     The number of super-diagonals of the matrix A.  KU >= 0.

           AB        (input)
                     AB is DOUBLE PRECISION array, dimension (LDAB,N)
                     The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
                     column of A is stored in the j-th column of the array AB as
                     follows:
                     AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

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

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



LAPACK routine                  31 October 2017                      DLANGB(3)