zlangb(3F)

NAME
     ZLANGB - 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 band
     matrix A, with kl sub-diagonals and ku super-diagonals

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

         CHARACTER    NORM

         INTEGER      KL, KU, LDAB, N

         DOUBLE       PRECISION WORK( * )

         COMPLEX*16   AB( LDAB, * )

PURPOSE
     ZLANGB  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.


DESCRIPTION
     ZLANGB returns the value

        ZLANGB = ( 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 ZLANGB as described above.

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

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

     AB      (input) COMPLEX*16 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) INTEGER
             The leading dimension of the array AB.  LDAB >= KL+KU+1.

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