LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zlarf.f
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1 *> \brief \b ZLARF 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/
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER SIDE
25 * INTEGER INCV, LDC, M, N
26 * COMPLEX*16 TAU
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZLARF 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, 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*16 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*16
92 *> The value tau in the representation of H.
93 *> \endverbatim
94 *>
95 *> \param[in,out] C
96 *> \verbatim
97 *> C is COMPLEX*16 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*16 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 December 2016
125 *
126 *> \ingroup complex16OTHERauxiliary
127 *
128 * =====================================================================
129  SUBROUTINE zlarf( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
130 *
131 * -- LAPACK auxiliary routine (version 3.7.0) --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 * December 2016
135 *
136 * .. Scalar Arguments ..
137  CHARACTER SIDE
138  INTEGER INCV, LDC, M, N
139  COMPLEX*16 TAU
140 * ..
141 * .. Array Arguments ..
142  COMPLEX*16 C( ldc, * ), V( * ), WORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  COMPLEX*16 ONE, ZERO
149  parameter( one = ( 1.0d+0, 0.0d+0 ),
150  $ zero = ( 0.0d+0, 0.0d+0 ) )
151 * ..
152 * .. Local Scalars ..
153  LOGICAL APPLYLEFT
154  INTEGER I, LASTV, LASTC
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL zgemv, zgerc
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  INTEGER ILAZLR, ILAZLC
162  EXTERNAL lsame, ilazlr, ilazlc
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 = ilazlc(lastv, n, c, ldc)
190  ELSE
191 * Scan for the last non-zero row in C(:,1:lastv).
192  lastc = ilazlr(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 zgemv( '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 zgerc( 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 zgemv( '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 zgerc( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
226  END IF
227  END IF
228  RETURN
229 *
230 * End of ZLARF
231 *
232  END
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:130
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:132