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    1:       DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
    2: *
    3: *  -- LAPACK auxiliary routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          NORM
   10:       INTEGER            N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   D( * )
   14:       COMPLEX*16         E( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  ZLANHT  returns the value of the one norm,  or the Frobenius norm, or
   21: *  the  infinity norm,  or the  element of  largest absolute value  of a
   22: *  complex Hermitian tridiagonal matrix A.
   23: *
   24: *  Description
   25: *  ===========
   26: *
   27: *  ZLANHT returns the value
   28: *
   29: *     ZLANHT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   30: *              (
   31: *              ( norm1(A),         NORM = '1', 'O' or 'o'
   32: *              (
   33: *              ( normI(A),         NORM = 'I' or 'i'
   34: *              (
   35: *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   36: *
   37: *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
   38: *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   39: *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
   40: *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   41: *
   42: *  Arguments
   43: *  =========
   44: *
   45: *  NORM    (input) CHARACTER*1
   46: *          Specifies the value to be returned in ZLANHT as described
   47: *          above.
   48: *
   49: *  N       (input) INTEGER
   50: *          The order of the matrix A.  N >= 0.  When N = 0, ZLANHT is
   51: *          set to zero.
   52: *
   53: *  D       (input) DOUBLE PRECISION array, dimension (N)
   54: *          The diagonal elements of A.
   55: *
   56: *  E       (input) COMPLEX*16 array, dimension (N-1)
   57: *          The (n-1) sub-diagonal or super-diagonal elements of A.
   58: *
   59: *  =====================================================================
   60: *
   61: *     .. Parameters ..
   62:       DOUBLE PRECISION   ONE, ZERO
   63:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   64: *     ..
   65: *     .. Local Scalars ..
   66:       INTEGER            I
   67:       DOUBLE PRECISION   ANORM, SCALE, SUM
   68: *     ..
   69: *     .. External Functions ..
   70:       LOGICAL            LSAME
   71:       EXTERNAL           LSAME
   72: *     ..
   73: *     .. External Subroutines ..
   74:       EXTERNAL           DLASSQ, ZLASSQ
   75: *     ..
   76: *     .. Intrinsic Functions ..
   77:       INTRINSIC          ABS, MAX, SQRT
   78: *     ..
   79: *     .. Executable Statements ..
   80: *
   81:       IF( N.LE.0 ) THEN
   82:          ANORM = ZERO
   83:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
   84: *
   85: *        Find max(abs(A(i,j))).
   86: *
   87:          ANORM = ABS( D( N ) )
   88:          DO 10 I = 1, N - 1
   89:             ANORM = MAX( ANORM, ABS( D( I ) ) )
   90:             ANORM = MAX( ANORM, ABS( E( I ) ) )
   91:    10    CONTINUE
   92:       ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
   93:      $         LSAME( NORM, 'I' ) ) THEN
   94: *
   95: *        Find norm1(A).
   96: *
   97:          IF( N.EQ.1 ) THEN
   98:             ANORM = ABS( D( 1 ) )
   99:          ELSE
  100:             ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
  101:      $              ABS( E( N-1 ) )+ABS( D( N ) ) )
  102:             DO 20 I = 2, N - 1
  103:                ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
  104:      $                 ABS( E( I-1 ) ) )
  105:    20       CONTINUE
  106:          END IF
  107:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  108: *
  109: *        Find normF(A).
  110: *
  111:          SCALE = ZERO
  112:          SUM = ONE
  113:          IF( N.GT.1 ) THEN
  114:             CALL ZLASSQ( N-1, E, 1, SCALE, SUM )
  115:             SUM = 2*SUM
  116:          END IF
  117:          CALL DLASSQ( N, D, 1, SCALE, SUM )
  118:          ANORM = SCALE*SQRT( SUM )
  119:       END IF
  120: *
  121:       ZLANHT = ANORM
  122:       RETURN
  123: *
  124: *     End of ZLANHT
  125: *
  126:       END