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    1: *> \brief \b DLARFY
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *  Definition:
    9: *  ===========
   10: *
   11: *       SUBROUTINE DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
   12: *
   13: *       .. Scalar Arguments ..
   14: *       CHARACTER          UPLO
   15: *       INTEGER            INCV, LDC, N
   16: *       DOUBLE PRECISION   TAU
   17: *       ..
   18: *       .. Array Arguments ..
   19: *       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
   20: *       ..
   21: *
   22: *
   23: *> \par Purpose:
   24: *  =============
   25: *>
   26: *> \verbatim
   27: *>
   28: *> DLARFY applies an elementary reflector, or Householder matrix, H,
   29: *> to an n x n symmetric matrix C, from both the left and the right.
   30: *>
   31: *> H is represented in the form
   32: *>
   33: *>    H = I - tau * v * v'
   34: *>
   35: *> where  tau  is a scalar and  v  is a vector.
   36: *>
   37: *> If  tau  is  zero, then  H  is taken to be the unit matrix.
   38: *> \endverbatim
   39: *
   40: *  Arguments:
   41: *  ==========
   42: *
   43: *> \param[in] UPLO
   44: *> \verbatim
   45: *>          UPLO is CHARACTER*1
   46: *>          Specifies whether the upper or lower triangular part of the
   47: *>          symmetric matrix C is stored.
   48: *>          = 'U':  Upper triangle
   49: *>          = 'L':  Lower triangle
   50: *> \endverbatim
   51: *>
   52: *> \param[in] N
   53: *> \verbatim
   54: *>          N is INTEGER
   55: *>          The number of rows and columns of the matrix C.  N >= 0.
   56: *> \endverbatim
   57: *>
   58: *> \param[in] V
   59: *> \verbatim
   60: *>          V is DOUBLE PRECISION array, dimension
   61: *>                  (1 + (N-1)*abs(INCV))
   62: *>          The vector v as described above.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] INCV
   66: *> \verbatim
   67: *>          INCV is INTEGER
   68: *>          The increment between successive elements of v.  INCV must
   69: *>          not be zero.
   70: *> \endverbatim
   71: *>
   72: *> \param[in] TAU
   73: *> \verbatim
   74: *>          TAU is DOUBLE PRECISION
   75: *>          The value tau as described above.
   76: *> \endverbatim
   77: *>
   78: *> \param[in,out] C
   79: *> \verbatim
   80: *>          C is DOUBLE PRECISION array, dimension (LDC, N)
   81: *>          On entry, the matrix C.
   82: *>          On exit, C is overwritten by H * C * H'.
   83: *> \endverbatim
   84: *>
   85: *> \param[in] LDC
   86: *> \verbatim
   87: *>          LDC is INTEGER
   88: *>          The leading dimension of the array C.  LDC >= max( 1, N ).
   89: *> \endverbatim
   90: *>
   91: *> \param[out] WORK
   92: *> \verbatim
   93: *>          WORK is DOUBLE PRECISION array, dimension (N)
   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: *> \ingroup doubleOTHERauxiliary
  105: *
  106: *  =====================================================================
  107:       SUBROUTINE DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
  108: *
  109: *  -- LAPACK test routine --
  110: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  111: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  112: *
  113: *     .. Scalar Arguments ..
  114:       CHARACTER          UPLO
  115:       INTEGER            INCV, LDC, N
  116:       DOUBLE PRECISION   TAU
  117: *     ..
  118: *     .. Array Arguments ..
  119:       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
  120: *     ..
  121: *
  122: *  =====================================================================
  123: *
  124: *     .. Parameters ..
  125:       DOUBLE PRECISION   ONE, ZERO, HALF
  126:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0, HALF = 0.5D+0 )
  127: *     ..
  128: *     .. Local Scalars ..
  129:       DOUBLE PRECISION   ALPHA
  130: *     ..
  131: *     .. External Subroutines ..
  132:       EXTERNAL           DAXPY, DSYMV, DSYR2
  133: *     ..
  134: *     .. External Functions ..
  135:       DOUBLE PRECISION   DDOT
  136:       EXTERNAL           DDOT
  137: *     ..
  138: *     .. Executable Statements ..
  139: *
  140:       IF( TAU.EQ.ZERO )
  141:      $   RETURN
  142: *
  143: *     Form  w:= C * v
  144: *
  145:       CALL DSYMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
  146: *
  147:       ALPHA = -HALF*TAU*DDOT( N, WORK, 1, V, INCV )
  148:       CALL DAXPY( N, ALPHA, V, INCV, WORK, 1 )
  149: *
  150: *     C := C - v * w' - w * v'
  151: *
  152:       CALL DSYR2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
  153: *
  154:       RETURN
  155: *
  156: *     End of DLARFY
  157: *
  158:       END