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    1: *> \brief \b DLANHS
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DLANHS + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanhs.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanhs.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanhs.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          NORM
   25: *       INTEGER            LDA, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DLANHS  returns the value of the one norm,  or the Frobenius norm, or
   38: *> the  infinity norm,  or the  element of  largest absolute value  of a
   39: *> Hessenberg matrix A.
   40: *> \endverbatim
   41: *>
   42: *> \return DLANHS
   43: *> \verbatim
   44: *>
   45: *>    DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   46: *>             (
   47: *>             ( norm1(A),         NORM = '1', 'O' or 'o'
   48: *>             (
   49: *>             ( normI(A),         NORM = 'I' or 'i'
   50: *>             (
   51: *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   52: *>
   53: *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
   54: *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   55: *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
   56: *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   57: *> \endverbatim
   58: *
   59: *  Arguments:
   60: *  ==========
   61: *
   62: *> \param[in] NORM
   63: *> \verbatim
   64: *>          NORM is CHARACTER*1
   65: *>          Specifies the value to be returned in DLANHS as described
   66: *>          above.
   67: *> \endverbatim
   68: *>
   69: *> \param[in] N
   70: *> \verbatim
   71: *>          N is INTEGER
   72: *>          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
   73: *>          set to zero.
   74: *> \endverbatim
   75: *>
   76: *> \param[in] A
   77: *> \verbatim
   78: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   79: *>          The n by n upper Hessenberg matrix A; the part of A below the
   80: *>          first sub-diagonal is not referenced.
   81: *> \endverbatim
   82: *>
   83: *> \param[in] LDA
   84: *> \verbatim
   85: *>          LDA is INTEGER
   86: *>          The leading dimension of the array A.  LDA >= max(N,1).
   87: *> \endverbatim
   88: *>
   89: *> \param[out] WORK
   90: *> \verbatim
   91: *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
   92: *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
   93: *>          referenced.
   94: *> \endverbatim
   95: *
   96: *  Authors:
   97: *  ========
   98: *
   99: *> \author Univ. of Tennessee 
  100: *> \author Univ. of California Berkeley 
  101: *> \author Univ. of Colorado Denver 
  102: *> \author NAG Ltd. 
  103: *
  104: *> \date November 2011
  105: *
  106: *> \ingroup doubleOTHERauxiliary
  107: *
  108: *  =====================================================================
  109:       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
  110: *
  111: *  -- LAPACK auxiliary routine (version 3.4.0) --
  112: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  113: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  114: *     November 2011
  115: *
  116: *     .. Scalar Arguments ..
  117:       CHARACTER          NORM
  118:       INTEGER            LDA, N
  119: *     ..
  120: *     .. Array Arguments ..
  121:       DOUBLE PRECISION   A( LDA, * ), WORK( * )
  122: *     ..
  123: *
  124: * =====================================================================
  125: *
  126: *     .. Parameters ..
  127:       DOUBLE PRECISION   ONE, ZERO
  128:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  129: *     ..
  130: *     .. Local Scalars ..
  131:       INTEGER            I, J
  132:       DOUBLE PRECISION   SCALE, SUM, VALUE
  133: *     ..
  134: *     .. External Subroutines ..
  135:       EXTERNAL           DLASSQ
  136: *     ..
  137: *     .. External Functions ..
  138:       LOGICAL            LSAME
  139:       EXTERNAL           LSAME
  140: *     ..
  141: *     .. Intrinsic Functions ..
  142:       INTRINSIC          ABS, MAX, MIN, SQRT
  143: *     ..
  144: *     .. Executable Statements ..
  145: *
  146:       IF( N.EQ.0 ) THEN
  147:          VALUE = ZERO
  148:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
  149: *
  150: *        Find max(abs(A(i,j))).
  151: *
  152:          VALUE = ZERO
  153:          DO 20 J = 1, N
  154:             DO 10 I = 1, MIN( N, J+1 )
  155:                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
  156:    10       CONTINUE
  157:    20    CONTINUE
  158:       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
  159: *
  160: *        Find norm1(A).
  161: *
  162:          VALUE = ZERO
  163:          DO 40 J = 1, N
  164:             SUM = ZERO
  165:             DO 30 I = 1, MIN( N, J+1 )
  166:                SUM = SUM + ABS( A( I, J ) )
  167:    30       CONTINUE
  168:             VALUE = MAX( VALUE, SUM )
  169:    40    CONTINUE
  170:       ELSE IF( LSAME( NORM, 'I' ) ) THEN
  171: *
  172: *        Find normI(A).
  173: *
  174:          DO 50 I = 1, N
  175:             WORK( I ) = ZERO
  176:    50    CONTINUE
  177:          DO 70 J = 1, N
  178:             DO 60 I = 1, MIN( N, J+1 )
  179:                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  180:    60       CONTINUE
  181:    70    CONTINUE
  182:          VALUE = ZERO
  183:          DO 80 I = 1, N
  184:             VALUE = MAX( VALUE, WORK( I ) )
  185:    80    CONTINUE
  186:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  187: *
  188: *        Find normF(A).
  189: *
  190:          SCALE = ZERO
  191:          SUM = ONE
  192:          DO 90 J = 1, N
  193:             CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
  194:    90    CONTINUE
  195:          VALUE = SCALE*SQRT( SUM )
  196:       END IF
  197: *
  198:       DLANHS = VALUE
  199:       RETURN
  200: *
  201: *     End of DLANHS
  202: *
  203:       END