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    1:       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
    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            LDA, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   A( LDA, * ), WORK( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DLANHS  returns the value of the one norm,  or the Frobenius norm, or
   20: *  the  infinity norm,  or the  element of  largest absolute value  of a
   21: *  Hessenberg matrix A.
   22: *
   23: *  Description
   24: *  ===========
   25: *
   26: *  DLANHS returns the value
   27: *
   28: *     DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   29: *              (
   30: *              ( norm1(A),         NORM = '1', 'O' or 'o'
   31: *              (
   32: *              ( normI(A),         NORM = 'I' or 'i'
   33: *              (
   34: *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   35: *
   36: *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
   37: *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   38: *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
   39: *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   40: *
   41: *  Arguments
   42: *  =========
   43: *
   44: *  NORM    (input) CHARACTER*1
   45: *          Specifies the value to be returned in DLANHS as described
   46: *          above.
   47: *
   48: *  N       (input) INTEGER
   49: *          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
   50: *          set to zero.
   51: *
   52: *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
   53: *          The n by n upper Hessenberg matrix A; the part of A below the
   54: *          first sub-diagonal is not referenced.
   55: *
   56: *  LDA     (input) INTEGER
   57: *          The leading dimension of the array A.  LDA >= max(N,1).
   58: *
   59: *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
   60: *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
   61: *          referenced.
   62: *
   63: * =====================================================================
   64: *
   65: *     .. Parameters ..
   66:       DOUBLE PRECISION   ONE, ZERO
   67:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   68: *     ..
   69: *     .. Local Scalars ..
   70:       INTEGER            I, J
   71:       DOUBLE PRECISION   SCALE, SUM, VALUE
   72: *     ..
   73: *     .. External Subroutines ..
   74:       EXTERNAL           DLASSQ
   75: *     ..
   76: *     .. External Functions ..
   77:       LOGICAL            LSAME
   78:       EXTERNAL           LSAME
   79: *     ..
   80: *     .. Intrinsic Functions ..
   81:       INTRINSIC          ABS, MAX, MIN, SQRT
   82: *     ..
   83: *     .. Executable Statements ..
   84: *
   85:       IF( N.EQ.0 ) THEN
   86:          VALUE = ZERO
   87:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
   88: *
   89: *        Find max(abs(A(i,j))).
   90: *
   91:          VALUE = ZERO
   92:          DO 20 J = 1, N
   93:             DO 10 I = 1, MIN( N, J+1 )
   94:                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
   95:    10       CONTINUE
   96:    20    CONTINUE
   97:       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
   98: *
   99: *        Find norm1(A).
  100: *
  101:          VALUE = ZERO
  102:          DO 40 J = 1, N
  103:             SUM = ZERO
  104:             DO 30 I = 1, MIN( N, J+1 )
  105:                SUM = SUM + ABS( A( I, J ) )
  106:    30       CONTINUE
  107:             VALUE = MAX( VALUE, SUM )
  108:    40    CONTINUE
  109:       ELSE IF( LSAME( NORM, 'I' ) ) THEN
  110: *
  111: *        Find normI(A).
  112: *
  113:          DO 50 I = 1, N
  114:             WORK( I ) = ZERO
  115:    50    CONTINUE
  116:          DO 70 J = 1, N
  117:             DO 60 I = 1, MIN( N, J+1 )
  118:                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  119:    60       CONTINUE
  120:    70    CONTINUE
  121:          VALUE = ZERO
  122:          DO 80 I = 1, N
  123:             VALUE = MAX( VALUE, WORK( I ) )
  124:    80    CONTINUE
  125:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  126: *
  127: *        Find normF(A).
  128: *
  129:          SCALE = ZERO
  130:          SUM = ONE
  131:          DO 90 J = 1, N
  132:             CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
  133:    90    CONTINUE
  134:          VALUE = SCALE*SQRT( SUM )
  135:       END IF
  136: *
  137:       DLANHS = VALUE
  138:       RETURN
  139: *
  140: *     End of DLANHS
  141: *
  142:       END