LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
clarf.f
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1 *> \brief \b CLARF applies an elementary reflector to a general rectangular matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \ingroup complexOTHERauxiliary
125 *
126 * =====================================================================
127  SUBROUTINE clarf( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
128 *
129 * -- LAPACK auxiliary routine --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 *
133 * .. Scalar Arguments ..
134  CHARACTER SIDE
135  INTEGER INCV, LDC, M, N
136  COMPLEX TAU
137 * ..
138 * .. Array Arguments ..
139  COMPLEX C( LDC, * ), V( * ), WORK( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  COMPLEX ONE, ZERO
146  parameter( one = ( 1.0e+0, 0.0e+0 ),
147  \$ zero = ( 0.0e+0, 0.0e+0 ) )
148 * ..
149 * .. Local Scalars ..
150  LOGICAL APPLYLEFT
151  INTEGER I, LASTV, LASTC
152 * ..
153 * .. External Subroutines ..
154  EXTERNAL cgemv, cgerc
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  INTEGER ILACLR, ILACLC
159  EXTERNAL lsame, ilaclr, ilaclc
160 * ..
161 * .. Executable Statements ..
162 *
163  applyleft = lsame( side, 'L' )
164  lastv = 0
165  lastc = 0
166  IF( tau.NE.zero ) THEN
167 ! Set up variables for scanning V. LASTV begins pointing to the end
168 ! of V.
169  IF( applyleft ) THEN
170  lastv = m
171  ELSE
172  lastv = n
173  END IF
174  IF( incv.GT.0 ) THEN
175  i = 1 + (lastv-1) * incv
176  ELSE
177  i = 1
178  END IF
179 ! Look for the last non-zero row in V.
180  DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
181  lastv = lastv - 1
182  i = i - incv
183  END DO
184  IF( applyleft ) THEN
185 ! Scan for the last non-zero column in C(1:lastv,:).
186  lastc = ilaclc(lastv, n, c, ldc)
187  ELSE
188 ! Scan for the last non-zero row in C(:,1:lastv).
189  lastc = ilaclr(m, lastv, c, ldc)
190  END IF
191  END IF
192 ! Note that lastc.eq.0 renders the BLAS operations null; no special
193 ! case is needed at this level.
194  IF( applyleft ) THEN
195 *
196 * Form H * C
197 *
198  IF( lastv.GT.0 ) THEN
199 *
200 * w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
201 *
202  CALL cgemv( 'Conjugate transpose', lastv, lastc, one,
203  \$ c, ldc, v, incv, zero, work, 1 )
204 *
205 * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
206 *
207  CALL cgerc( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
208  END IF
209  ELSE
210 *
211 * Form C * H
212 *
213  IF( lastv.GT.0 ) THEN
214 *
215 * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
216 *
217  CALL cgemv( 'No transpose', lastc, lastv, one, c, ldc,
218  \$ v, incv, zero, work, 1 )
219 *
220 * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
221 *
222  CALL cgerc( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
223  END IF
224  END IF
225  RETURN
226 *
227 * End of CLARF
228 *
229  END
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine cgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERC
Definition: cgerc.f:130
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128