zlantb(3F)

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

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

         CHARACTER    DIAG, NORM, UPLO

         INTEGER      K, LDAB, N

         DOUBLE       PRECISION WORK( * )

         COMPLEX*16   AB( LDAB, * )

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.


DESCRIPTION
     ZLANTB returns the value

        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  matrix norm.


ARGUMENTS
     NORM    (input) CHARACTER*1
             Specifies the value to be returned in ZLANTB as described above.

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

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

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

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

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