slansb(3F)

NAME
     SLANSB - return 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

SYNOPSIS
     REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

         CHARACTER NORM, UPLO

         INTEGER   K, LDAB, N

         REAL      AB( LDAB, * ), WORK( * )

PURPOSE
     SLANSB  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.


DESCRIPTION
     SLANSB returns the value

        SLANSB = ( 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 SLANSB as described above.

     UPLO    (input) 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) INTEGER
             The order of the matrix A.  N >= 0.  When N = 0, SLANSB is set to
             zero.
     K       (input) INTEGER
             The number of super-diagonals or sub-diagonals of the band matrix
             A.  K >= 0.

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

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