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