LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zlarz.f
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1 *> \brief \b ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER SIDE
25 * INTEGER INCV, L, 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 *> ZLARZ applies a complex elementary reflector H to a complex
39 *> M-by-N matrix C, from either the left or the right. H is represented
40 *> in the 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 *>
51 *> H is a product of k elementary reflectors as returned by ZTZRZF.
52 *> \endverbatim
53 *
54 * Arguments:
55 * ==========
56 *
57 *> \param[in] SIDE
58 *> \verbatim
59 *> SIDE is CHARACTER*1
60 *> = 'L': form H * C
61 *> = 'R': form C * H
62 *> \endverbatim
63 *>
64 *> \param[in] M
65 *> \verbatim
66 *> M is INTEGER
67 *> The number of rows of the matrix C.
68 *> \endverbatim
69 *>
70 *> \param[in] N
71 *> \verbatim
72 *> N is INTEGER
73 *> The number of columns of the matrix C.
74 *> \endverbatim
75 *>
76 *> \param[in] L
77 *> \verbatim
78 *> L is INTEGER
79 *> The number of entries of the vector V containing
80 *> the meaningful part of the Householder vectors.
81 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
82 *> \endverbatim
83 *>
84 *> \param[in] V
85 *> \verbatim
86 *> V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
87 *> The vector v in the representation of H as returned by
88 *> ZTZRZF. V is not used if TAU = 0.
89 *> \endverbatim
90 *>
91 *> \param[in] INCV
92 *> \verbatim
93 *> INCV is INTEGER
94 *> The increment between elements of v. INCV <> 0.
95 *> \endverbatim
96 *>
97 *> \param[in] TAU
98 *> \verbatim
99 *> TAU is COMPLEX*16
100 *> The value tau in the representation of H.
101 *> \endverbatim
102 *>
103 *> \param[in,out] C
104 *> \verbatim
105 *> C is COMPLEX*16 array, dimension (LDC,N)
106 *> On entry, the M-by-N matrix C.
107 *> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
108 *> or C * H if SIDE = 'R'.
109 *> \endverbatim
110 *>
111 *> \param[in] LDC
112 *> \verbatim
113 *> LDC is INTEGER
114 *> The leading dimension of the array C. LDC >= max(1,M).
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is COMPLEX*16 array, dimension
120 *> (N) if SIDE = 'L'
121 *> or (M) if SIDE = 'R'
122 *> \endverbatim
123 *
124 * Authors:
125 * ========
126 *
127 *> \author Univ. of Tennessee
128 *> \author Univ. of California Berkeley
129 *> \author Univ. of Colorado Denver
130 *> \author NAG Ltd.
131 *
132 *> \date September 2012
133 *
134 *> \ingroup complex16OTHERcomputational
135 *
136 *> \par Contributors:
137 * ==================
138 *>
139 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
140 *
141 *> \par Further Details:
142 * =====================
143 *>
144 *> \verbatim
145 *> \endverbatim
146 *>
147 * =====================================================================
148  SUBROUTINE zlarz( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
149 *
150 * -- LAPACK computational routine (version 3.4.2) --
151 * -- LAPACK is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 * September 2012
154 *
155 * .. Scalar Arguments ..
156  CHARACTER SIDE
157  INTEGER INCV, L, LDC, M, N
158  COMPLEX*16 TAU
159 * ..
160 * .. Array Arguments ..
161  COMPLEX*16 C( ldc, * ), V( * ), WORK( * )
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  COMPLEX*16 ONE, ZERO
168  parameter ( one = ( 1.0d+0, 0.0d+0 ),
169  \$ zero = ( 0.0d+0, 0.0d+0 ) )
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL zaxpy, zcopy, zgemv, zgerc, zgeru, zlacgv
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. Executable Statements ..
179 *
180  IF( lsame( side, 'L' ) ) THEN
181 *
182 * Form H * C
183 *
184  IF( tau.NE.zero ) THEN
185 *
186 * w( 1:n ) = conjg( C( 1, 1:n ) )
187 *
188  CALL zcopy( n, c, ldc, work, 1 )
189  CALL zlacgv( n, work, 1 )
190 *
191 * w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
192 *
193  CALL zgemv( 'Conjugate transpose', l, n, one, c( m-l+1, 1 ),
194  \$ ldc, v, incv, one, work, 1 )
195  CALL zlacgv( n, work, 1 )
196 *
197 * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
198 *
199  CALL zaxpy( n, -tau, work, 1, c, ldc )
200 *
201 * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
202 * tau * v( 1:l ) * w( 1:n )**H
203 *
204  CALL zgeru( l, n, -tau, v, incv, work, 1, c( m-l+1, 1 ),
205  \$ ldc )
206  END IF
207 *
208  ELSE
209 *
210 * Form C * H
211 *
212  IF( tau.NE.zero ) THEN
213 *
214 * w( 1:m ) = C( 1:m, 1 )
215 *
216  CALL zcopy( m, c, 1, work, 1 )
217 *
218 * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
219 *
220  CALL zgemv( 'No transpose', m, l, one, c( 1, n-l+1 ), ldc,
221  \$ v, incv, one, work, 1 )
222 *
223 * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
224 *
225  CALL zaxpy( m, -tau, work, 1, c, 1 )
226 *
227 * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
228 * tau * w( 1:m ) * v( 1:l )**H
229 *
230  CALL zgerc( m, l, -tau, work, 1, v, incv, c( 1, n-l+1 ),
231  \$ ldc )
232 *
233  END IF
234 *
235  END IF
236 *
237  RETURN
238 *
239 * End of ZLARZ
240 *
241  END
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:132
subroutine zlarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: zlarz.f:149
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:132
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:53
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76