```      REAL             FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB,
\$                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          NORM, UPLO
INTEGER            K, LDAB, N
*     ..
*     .. Array Arguments ..
REAL               WORK( * )
COMPLEX            AB( LDAB, * )
*     ..
*
*  Purpose
*  =======
*
*  CLANHB  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 hermitian band matrix A,  with k super-diagonals.
*
*  Description
*  ===========
*
*  CLANHB returns the value
*
*     CLANHB = ( 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.
*
*  Arguments
*  =========
*
*  NORM    (input) CHARACTER*1
*          Specifies the value to be returned in CLANHB 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
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.  When N = 0, CLANHB is
*          set to zero.
*
*  K       (input) INTEGER
*          The number of super-diagonals or sub-diagonals of the
*          band matrix A.  K >= 0.
*
*  AB      (input) COMPLEX array, dimension (LDAB,N)
*          The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
*          not be set and are assumed to be zero.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= K+1.
*
*  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
*          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*          WORK is not referenced.
*
* =====================================================================
*
*     .. Parameters ..
REAL               ONE, ZERO
PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
INTEGER            I, J, L
REAL               ABSA, SCALE, SUM, VALUE
*     ..
*     .. External Functions ..
LOGICAL            LSAME
EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL           CLASSQ
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, MAX, MIN, REAL, SQRT
*     ..
*     .. Executable Statements ..
*
IF( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = MAX( K+2-J, 1 ), K
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
10          CONTINUE
VALUE = MAX( VALUE, ABS( REAL( AB( K+1, J ) ) ) )
20       CONTINUE
ELSE
DO 40 J = 1, N
VALUE = MAX( VALUE, ABS( REAL( AB( 1, J ) ) ) )
DO 30 I = 2, MIN( N+1-J, K+1 )
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
30          CONTINUE
40       CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
\$         ( NORM.EQ.'1' ) ) THEN
*
*        Find normI(A) ( = norm1(A), since A is hermitian).
*
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
SUM = ZERO
L = K + 1 - J
DO 50 I = MAX( 1, J-K ), J - 1
ABSA = ABS( AB( L+I, J ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
50          CONTINUE
WORK( J ) = SUM + ABS( REAL( AB( K+1, J ) ) )
60       CONTINUE
DO 70 I = 1, N
VALUE = MAX( VALUE, WORK( I ) )
70       CONTINUE
ELSE
DO 80 I = 1, N
WORK( I ) = ZERO
80       CONTINUE
DO 100 J = 1, N
SUM = WORK( J ) + ABS( REAL( AB( 1, J ) ) )
L = 1 - J
DO 90 I = J + 1, MIN( N, J+K )
ABSA = ABS( AB( L+I, J ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
90          CONTINUE
VALUE = MAX( VALUE, SUM )
100       CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
*        Find normF(A).
*
SCALE = ZERO
SUM = ONE
IF( K.GT.0 ) THEN
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
CALL CLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
\$                         1, SCALE, SUM )
110          CONTINUE
L = K + 1
ELSE
DO 120 J = 1, N - 1
CALL CLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
\$                         SUM )
120          CONTINUE
L = 1
END IF
SUM = 2*SUM
ELSE
L = 1
END IF
DO 130 J = 1, N
IF( REAL( AB( L, J ) ).NE.ZERO ) THEN
ABSA = ABS( REAL( AB( L, J ) ) )
IF( SCALE.LT.ABSA ) THEN
SUM = ONE + SUM*( SCALE / ABSA )**2
SCALE = ABSA
ELSE
SUM = SUM + ( ABSA / SCALE )**2
END IF
END IF
130    CONTINUE
VALUE = SCALE*SQRT( SUM )
END IF
*
CLANHB = VALUE
RETURN
*
*     End of CLANHB
*
END

```