```      SUBROUTINE SLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          SIDE
INTEGER            LDC, M, N
REAL               TAU
*     ..
*     .. Array Arguments ..
REAL               C( LDC, * ), V( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  SLARFX applies a real elementary reflector H to a real m by n
*  matrix C, from either the left or the right. H is represented in the
*  form
*
*        H = I - tau * v * v'
*
*  where tau is a real scalar and v is a real vector.
*
*  If tau = 0, then H is taken to be the unit matrix
*
*  This version uses inline code if H has order < 11.
*
*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': form  H * C
*          = 'R': form  C * H
*
*  M       (input) INTEGER
*          The number of rows of the matrix C.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C.
*
*  V       (input) REAL array, dimension (M) if SIDE = 'L'
*                                     or (N) if SIDE = 'R'
*          The vector v in the representation of H.
*
*  TAU     (input) REAL
*          The value tau in the representation of H.
*
*  C       (input/output) REAL array, dimension (LDC,N)
*          On entry, the m by n matrix C.
*          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
*          or C * H if SIDE = 'R'.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDA >= (1,M).
*
*  WORK    (workspace) REAL array, dimension
*                      (N) if SIDE = 'L'
*                      or (M) if SIDE = 'R'
*          WORK is not referenced if H has order < 11.
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
*     ..
*     .. Local Scalars ..
INTEGER            J
REAL               SUM, T1, T10, T2, T3, T4, T5, T6, T7, T8, T9,
\$                   V1, V10, V2, V3, V4, V5, V6, V7, V8, V9
*     ..
*     .. External Functions ..
LOGICAL            LSAME
EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL           SGEMV, SGER
*     ..
*     .. Executable Statements ..
*
IF( TAU.EQ.ZERO )
\$   RETURN
IF( LSAME( SIDE, 'L' ) ) THEN
*
*        Form  H * C, where H has order m.
*
GO TO ( 10, 30, 50, 70, 90, 110, 130, 150,
\$           170, 190 )M
*
*        Code for general M
*
*        w := C'*v
*
CALL SGEMV( 'Transpose', M, N, ONE, C, LDC, V, 1, ZERO, WORK,
\$               1 )
*
*        C := C - tau * v * w'
*
CALL SGER( M, N, -TAU, V, 1, WORK, 1, C, LDC )
GO TO 410
10    CONTINUE
*
*        Special code for 1 x 1 Householder
*
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
*
*        Special code for 2 x 2 Householder
*
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
*
*        Special code for 3 x 3 Householder
*
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
*
*        Special code for 4 x 4 Householder
*
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
*
*        Special code for 5 x 5 Householder
*
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
*
*        Special code for 6 x 6 Householder
*
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
*
*        Special code for 7 x 7 Householder
*
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
*
*        Special code for 8 x 8 Householder
*
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
*
*        Special code for 9 x 9 Householder
*
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
C( 8, J ) = C( 8, J ) - SUM*T8
C( 9, J ) = C( 9, J ) - SUM*T9
180    CONTINUE
GO TO 410
190    CONTINUE
*
*        Special code for 10 x 10 Householder
*
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
V10 = V( 10 )
T10 = TAU*V10
DO 200 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 ) +
\$            V10*C( 10, 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
C( 9, J ) = C( 9, J ) - SUM*T9
C( 10, J ) = C( 10, J ) - SUM*T10
200    CONTINUE
GO TO 410
ELSE
*
*        Form  C * H, where H has order n.
*
GO TO ( 210, 230, 250, 270, 290, 310, 330, 350,
\$           370, 390 )N
*
*        Code for general N
*
*        w := C * v
*
CALL SGEMV( 'No transpose', M, N, ONE, C, LDC, V, 1, ZERO,
\$               WORK, 1 )
*
*        C := C - tau * w * v'
*
CALL SGER( M, N, -TAU, WORK, 1, V, 1, C, LDC )
GO TO 410
210    CONTINUE
*
*        Special code for 1 x 1 Householder
*
T1 = ONE - TAU*V( 1 )*V( 1 )
DO 220 J = 1, M
C( J, 1 ) = T1*C( J, 1 )
220    CONTINUE
GO TO 410
230    CONTINUE
*
*        Special code for 2 x 2 Householder
*
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
DO 240 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
240    CONTINUE
GO TO 410
250    CONTINUE
*
*        Special code for 3 x 3 Householder
*
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
DO 260 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
260    CONTINUE
GO TO 410
270    CONTINUE
*
*        Special code for 4 x 4 Householder
*
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 280 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
280    CONTINUE
GO TO 410
290    CONTINUE
*
*        Special code for 5 x 5 Householder
*
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 300 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
300    CONTINUE
GO TO 410
310    CONTINUE
*
*        Special code for 6 x 6 Householder
*
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 320 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 ) + V6*C( J, 6 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
C( J, 6 ) = C( J, 6 ) - SUM*T6
320    CONTINUE
GO TO 410
330    CONTINUE
*
*        Special code for 7 x 7 Householder
*
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 340 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 ) + V6*C( J, 6 ) +
\$            V7*C( J, 7 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
C( J, 6 ) = C( J, 6 ) - SUM*T6
C( J, 7 ) = C( J, 7 ) - SUM*T7
340    CONTINUE
GO TO 410
350    CONTINUE
*
*        Special code for 8 x 8 Householder
*
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 360 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 ) + V6*C( J, 6 ) +
\$            V7*C( J, 7 ) + V8*C( J, 8 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
C( J, 6 ) = C( J, 6 ) - SUM*T6
C( J, 7 ) = C( J, 7 ) - SUM*T7
C( J, 8 ) = C( J, 8 ) - SUM*T8
360    CONTINUE
GO TO 410
370    CONTINUE
*
*        Special code for 9 x 9 Householder
*
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 380 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 ) + V6*C( J, 6 ) +
\$            V7*C( J, 7 ) + V8*C( J, 8 ) + V9*C( J, 9 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
C( J, 6 ) = C( J, 6 ) - SUM*T6
C( J, 7 ) = C( J, 7 ) - SUM*T7
C( J, 8 ) = C( J, 8 ) - SUM*T8
C( J, 9 ) = C( J, 9 ) - SUM*T9
380    CONTINUE
GO TO 410
390    CONTINUE
*
*        Special code for 10 x 10 Householder
*
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
V10 = V( 10 )
T10 = TAU*V10
DO 400 J = 1, M
SUM = V1*C( J, 1 ) + V2*C( J, 2 ) + V3*C( J, 3 ) +
\$            V4*C( J, 4 ) + V5*C( J, 5 ) + V6*C( J, 6 ) +
\$            V7*C( J, 7 ) + V8*C( J, 8 ) + V9*C( J, 9 ) +
\$            V10*C( J, 10 )
C( J, 1 ) = C( J, 1 ) - SUM*T1
C( J, 2 ) = C( J, 2 ) - SUM*T2
C( J, 3 ) = C( J, 3 ) - SUM*T3
C( J, 4 ) = C( J, 4 ) - SUM*T4
C( J, 5 ) = C( J, 5 ) - SUM*T5
C( J, 6 ) = C( J, 6 ) - SUM*T6
C( J, 7 ) = C( J, 7 ) - SUM*T7
C( J, 8 ) = C( J, 8 ) - SUM*T8
C( J, 9 ) = C( J, 9 ) - SUM*T9
C( J, 10 ) = C( J, 10 ) - SUM*T10
400    CONTINUE
GO TO 410
END IF
410 RETURN
*
*     End of SLARFX
*
END

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