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      SUBROUTINE <a name="DLARFX.1"></a><a href="dlarfx.f.html#DLARFX.1">DLARFX</a>( SIDE, M, N, V, TAU, C, LDC, WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          SIDE
      INTEGER            LDC, M, N
      DOUBLE PRECISION   TAU
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLARFX.19"></a><a href="dlarfx.f.html#DLARFX.1">DLARFX</a> applies a real elementary reflector H to a real m by n
</span><span class="comment">*</span><span class="comment">  matrix C, from either the left or the right. H is represented in the
</span><span class="comment">*</span><span class="comment">  form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        H = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where tau is a real scalar and v is a real vector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If tau = 0, then H is taken to be the unit matrix
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This version uses inline code if H has order &lt; 11.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SIDE    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'L': form  H * C
</span><span class="comment">*</span><span class="comment">          = 'R': form  C * H
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  V       (input) DOUBLE PRECISION array, dimension (M) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment">                                     or (N) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">          The vector v in the representation of H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The value tau in the representation of H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment">          On entry, the m by n matrix C.
</span><span class="comment">*</span><span class="comment">          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
</span><span class="comment">*</span><span class="comment">          or C * H if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array C. LDA &gt;= (1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment">                      (N) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment">                      or (M) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">          WORK is not referenced if H has order &lt; 11.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            J
      DOUBLE PRECISION   SUM, T1, T10, T2, T3, T4, T5, T6, T7, T8, T9,
     $                   V1, V10, V2, V3, V4, V5, V6, V7, V8, V9
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.76"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.77"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DGEMV, DGER
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( TAU.EQ.ZERO )
     $   RETURN
      IF( <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Form  H * C, where H has order m.
</span><span class="comment">*</span><span class="comment">
</span>         GO TO ( 10, 30, 50, 70, 90, 110, 130, 150,
     $           170, 190 )M
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Code for general M
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        w := C'*v
</span><span class="comment">*</span><span class="comment">
</span>         CALL DGEMV( <span class="string">'Transpose'</span>, M, N, ONE, C, LDC, V, 1, ZERO, WORK,
     $               1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        C := C - tau * v * w'
</span><span class="comment">*</span><span class="comment">
</span>         CALL DGER( M, N, -TAU, V, 1, WORK, 1, C, LDC )
         GO TO 410
   10    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 1 x 1 Householder
</span><span class="comment">*</span><span class="comment">
</span>         T1 = ONE - TAU*V( 1 )*V( 1 )
         DO 20 J = 1, N
            C( 1, J ) = T1*C( 1, J )
   20    CONTINUE
         GO TO 410
   30    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 2 x 2 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         DO 40 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
   40    CONTINUE
         GO TO 410
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 3 x 3 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         DO 60 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
   60    CONTINUE
         GO TO 410
   70    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 4 x 4 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         DO 80 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
   80    CONTINUE
         GO TO 410
   90    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 5 x 5 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         V5 = V( 5 )
         T5 = TAU*V5
         DO 100 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J ) + V5*C( 5, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
            C( 5, J ) = C( 5, J ) - SUM*T5
  100    CONTINUE
         GO TO 410
  110    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 6 x 6 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         V5 = V( 5 )
         T5 = TAU*V5
         V6 = V( 6 )
         T6 = TAU*V6
         DO 120 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J ) + V5*C( 5, J ) + V6*C( 6, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
            C( 5, J ) = C( 5, J ) - SUM*T5
            C( 6, J ) = C( 6, J ) - SUM*T6
  120    CONTINUE
         GO TO 410
  130    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 7 x 7 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         V5 = V( 5 )
         T5 = TAU*V5
         V6 = V( 6 )
         T6 = TAU*V6
         V7 = V( 7 )
         T7 = TAU*V7
         DO 140 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J ) + V5*C( 5, J ) + V6*C( 6, J ) +
     $            V7*C( 7, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
            C( 5, J ) = C( 5, J ) - SUM*T5
            C( 6, J ) = C( 6, J ) - SUM*T6
            C( 7, J ) = C( 7, J ) - SUM*T7
  140    CONTINUE
         GO TO 410
  150    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 8 x 8 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         V5 = V( 5 )
         T5 = TAU*V5
         V6 = V( 6 )
         T6 = TAU*V6
         V7 = V( 7 )
         T7 = TAU*V7
         V8 = V( 8 )
         T8 = TAU*V8
         DO 160 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J ) + V5*C( 5, J ) + V6*C( 6, J ) +
     $            V7*C( 7, J ) + V8*C( 8, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
            C( 5, J ) = C( 5, J ) - SUM*T5
            C( 6, J ) = C( 6, J ) - SUM*T6
            C( 7, J ) = C( 7, J ) - SUM*T7
            C( 8, J ) = C( 8, J ) - SUM*T8
  160    CONTINUE
         GO TO 410
  170    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Special code for 9 x 9 Householder
</span><span class="comment">*</span><span class="comment">
</span>         V1 = V( 1 )
         T1 = TAU*V1
         V2 = V( 2 )
         T2 = TAU*V2
         V3 = V( 3 )
         T3 = TAU*V3
         V4 = V( 4 )
         T4 = TAU*V4
         V5 = V( 5 )
         T5 = TAU*V5
         V6 = V( 6 )
         T6 = TAU*V6
         V7 = V( 7 )
         T7 = TAU*V7
         V8 = V( 8 )
         T8 = TAU*V8
         V9 = V( 9 )
         T9 = TAU*V9
         DO 180 J = 1, N
            SUM = V1*C( 1, J ) + V2*C( 2, J ) + V3*C( 3, J ) +
     $            V4*C( 4, J ) + V5*C( 5, J ) + V6*C( 6, J ) +
     $            V7*C( 7, J ) + V8*C( 8, J ) + V9*C( 9, J )
            C( 1, J ) = C( 1, J ) - SUM*T1
            C( 2, J ) = C( 2, J ) - SUM*T2
            C( 3, J ) = C( 3, J ) - SUM*T3
            C( 4, J ) = C( 4, J ) - SUM*T4
            C( 5, J ) = C( 5, J ) - SUM*T5
            C( 6, J ) = C( 6, J ) - SUM*T6
            C( 7, J ) = C( 7, J ) - SUM*T7
12

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