NAME

       zlangb.f -

SYNOPSIS

   Functions/Subroutines
       double precision function zlangb (NORM, N, KL, KU, AB, LDAB, WORK)
           ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest
           absolute value of any element of general band matrix.

Function/Subroutine Documentation

   double precision function zlangb (characterNORM, integerN, integerKL, integerKU, complex*16,
       dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)
       ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest
       absolute value of any element of general band matrix.

       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.

       Returns:
           ZLANGB

               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 consistent matrix norm.

       Parameters:
           NORM

                     NORM is CHARACTER*1
                     Specifies the value to be returned in ZLANGB as described
                     above.

           N

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

           KL

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

           KU

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

           AB

                     AB is 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

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

           WORK

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 125 of file zlangb.f.

Author

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