NAME

       zlantb.f -

SYNOPSIS

   Functions/Subroutines
       double precision function zlantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
           ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
           or the element of largest absolute value of a triangular band matrix.

Function/Subroutine Documentation

   double precision function zlantb (character NORM, character UPLO, character DIAG, integer N,
       integer K, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension(
       * ) WORK)
       ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a triangular band matrix.

       Purpose:

            ZLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.

       Returns:
           ZLANTB

               ZLANTB = ( 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 ZLANTB as described
                     above.

           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the matrix A is upper or lower triangular.
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           DIAG

                     DIAG is CHARACTER*1
                     Specifies whether or not the matrix A is unit triangular.
                     = 'N':  Non-unit triangular
                     = 'U':  Unit triangular

           N

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

           K

                     K is INTEGER
                     The number of super-diagonals of the matrix A if UPLO = 'U',
                     or the number of sub-diagonals of the matrix A if UPLO = 'L'.
                     K >= 0.

           AB

                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     The upper or lower triangular 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).
                     Note that when DIAG = 'U', the elements of the array AB
                     corresponding to the diagonal elements of the matrix A are
                     not referenced, but are assumed to be one.

           LDAB

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= K+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

Author

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