LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dlarf.f
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1 *> \brief \b DLARF applies an elementary reflector to a general rectangular matrix.
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 December 2016
121 *
122 *> \ingroup doubleOTHERauxiliary
123 *
124 * =====================================================================
125  SUBROUTINE dlarf( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
126 *
127 * -- LAPACK auxiliary routine (version 3.7.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * December 2016
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
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:158
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:126
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:132