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



NAME
       ZLANSB

SYNOPSIS
       DOUBLE PRECISION FUNCTION ZLANSB (NORM, UPLO, N, K, AB, LDAB, WORK)



PURPOSE
            ZLANSB  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 symmetric band matrix A,  with k super-diagonals.


       Returns:
           ZLANSB

               ZLANSB = ( 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 ZLANSB as described
                     above.

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

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

           K         (input)
                     K is INTEGER
                     The number of super-diagonals or sub-diagonals of the
                     band matrix A.  K >= 0.

           AB        (input)
                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     The upper or lower triangle of the symmetric 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 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).

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

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



LAPACK routine                  31 October 2017                      ZLANSB(3)