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



NAME
       SLANGB

SYNOPSIS
       REAL FUNCTION SLANGB (NORM, N, KL, KU, AB, LDAB, WORK)



PURPOSE
            SLANGB  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:
           SLANGB

               SLANGB = ( 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 SLANGB as described
                     above.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.  When N = 0, SLANGB 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 REAL 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 REAL array, dimension (MAX(1,LWORK)),
                     where LWORK >= N when NORM = 'I'; otherwise, WORK is not
                     referenced.



LAPACK routine                  31 October 2017                      SLANGB(3)