clarf.f revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba 
1*> \brief \b CLARF
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          SIDE
25*       INTEGER            INCV, LDC, M, N
26*       COMPLEX            TAU
27*       ..
28*       .. Array Arguments ..
29*       COMPLEX            C( LDC, * ), V( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> CLARF applies a complex elementary reflector H to a complex M-by-N
39*> matrix C, from either the left or the right. H is represented in the
40*> form
41*>
42*>       H = I - tau * v * v**H
43*>
44*> where tau is a complex scalar and v is a complex vector.
45*>
46*> If tau = 0, then H is taken to be the unit matrix.
47*>
48*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
49*> tau.
50*> \endverbatim
51*
52*  Arguments:
53*  ==========
54*
55*> \param[in] SIDE
56*> \verbatim
57*>          SIDE is CHARACTER*1
58*>          = 'L': form  H * C
59*>          = 'R': form  C * H
60*> \endverbatim
61*>
62*> \param[in] M
63*> \verbatim
64*>          M is INTEGER
65*>          The number of rows of the matrix C.
66*> \endverbatim
67*>
68*> \param[in] N
69*> \verbatim
70*>          N is INTEGER
71*>          The number of columns of the matrix C.
72*> \endverbatim
73*>
74*> \param[in] V
75*> \verbatim
76*>          V is COMPLEX array, dimension
77*>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
78*>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
79*>          The vector v in the representation of H. V is not used if
80*>          TAU = 0.
81*> \endverbatim
82*>
83*> \param[in] INCV
84*> \verbatim
85*>          INCV is INTEGER
86*>          The increment between elements of v. INCV <> 0.
87*> \endverbatim
88*>
89*> \param[in] TAU
90*> \verbatim
91*>          TAU is COMPLEX
92*>          The value tau in the representation of H.
93*> \endverbatim
94*>
95*> \param[in,out] C
96*> \verbatim
97*>          C is COMPLEX array, dimension (LDC,N)
98*>          On entry, the M-by-N matrix C.
99*>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
100*>          or C * H if SIDE = 'R'.
101*> \endverbatim
102*>
103*> \param[in] LDC
104*> \verbatim
105*>          LDC is INTEGER
106*>          The leading dimension of the array C. LDC >= max(1,M).
107*> \endverbatim
108*>
109*> \param[out] WORK
110*> \verbatim
111*>          WORK is COMPLEX array, dimension
112*>                         (N) if SIDE = 'L'
113*>                      or (M) if SIDE = 'R'
114*> \endverbatim
115*
116*  Authors:
117*  ========
118*
119*> \author Univ. of Tennessee
120*> \author Univ. of California Berkeley
121*> \author Univ. of Colorado Denver
122*> \author NAG Ltd.
123*
124*> \date November 2011
125*
126*> \ingroup complexOTHERauxiliary
127*
128*  =====================================================================
129      SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
130*
131*  -- LAPACK auxiliary routine (version 3.4.0) --
132*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
133*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*     November 2011
135*
136*     .. Scalar Arguments ..
137      CHARACTER          SIDE
138      INTEGER            INCV, LDC, M, N
139      COMPLEX            TAU
140*     ..
141*     .. Array Arguments ..
142      COMPLEX            C( LDC, * ), V( * ), WORK( * )
143*     ..
144*
145*  =====================================================================
146*
147*     .. Parameters ..
148      COMPLEX            ONE, ZERO
149      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
150     $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
151*     ..
152*     .. Local Scalars ..
153      LOGICAL            APPLYLEFT
154      INTEGER            I, LASTV, LASTC
155*     ..
156*     .. External Subroutines ..
157      EXTERNAL           CGEMV, CGERC
158*     ..
159*     .. External Functions ..
160      LOGICAL            LSAME
161      INTEGER            ILACLR, ILACLC
162      EXTERNAL           LSAME, ILACLR, ILACLC
163*     ..
164*     .. Executable Statements ..
165*
166      APPLYLEFT = LSAME( SIDE, 'L' )
167      LASTV = 0
168      LASTC = 0
169      IF( TAU.NE.ZERO ) THEN
170!     Set up variables for scanning V.  LASTV begins pointing to the end
171!     of V.
172         IF( APPLYLEFT ) THEN
173            LASTV = M
174         ELSE
175            LASTV = N
176         END IF
177         IF( INCV.GT.0 ) THEN
178            I = 1 + (LASTV-1) * INCV
179         ELSE
180            I = 1
181         END IF
182!     Look for the last non-zero row in V.
183         DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
184            LASTV = LASTV - 1
185            I = I - INCV
186         END DO
187         IF( APPLYLEFT ) THEN
188!     Scan for the last non-zero column in C(1:lastv,:).
189            LASTC = ILACLC(LASTV, N, C, LDC)
190         ELSE
191!     Scan for the last non-zero row in C(:,1:lastv).
192            LASTC = ILACLR(M, LASTV, C, LDC)
193         END IF
194      END IF
195!     Note that lastc.eq.0 renders the BLAS operations null; no special
196!     case is needed at this level.
197      IF( APPLYLEFT ) THEN
198*
199*        Form  H * C
200*
201         IF( LASTV.GT.0 ) THEN
202*
203*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
204*
205            CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
206     $           C, LDC, V, INCV, ZERO, WORK, 1 )
207*
208*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
209*
210            CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
211         END IF
212      ELSE
213*
214*        Form  C * H
215*
216         IF( LASTV.GT.0 ) THEN
217*
218*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
219*
220            CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
221     $           V, INCV, ZERO, WORK, 1 )
222*
223*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
224*
225            CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
226         END IF
227      END IF
228      RETURN
229*
230*     End of CLARF
231*
232      END
233