LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zlarzb.f
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1 *> \brief \b ZLARZB applies a block reflector or its conjugate-transpose to a general matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
22 * LDV, T, LDT, C, LDC, WORK, LDWORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIRECT, SIDE, STOREV, TRANS
26 * INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
30 * \$ WORK( LDWORK, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZLARZB applies a complex block reflector H or its transpose H**H
40 *> to a complex distributed M-by-N C from the left or the right.
41 *>
42 *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] SIDE
49 *> \verbatim
50 *> SIDE is CHARACTER*1
51 *> = 'L': apply H or H**H from the Left
52 *> = 'R': apply H or H**H from the Right
53 *> \endverbatim
54 *>
55 *> \param[in] TRANS
56 *> \verbatim
57 *> TRANS is CHARACTER*1
58 *> = 'N': apply H (No transpose)
59 *> = 'C': apply H**H (Conjugate transpose)
60 *> \endverbatim
61 *>
62 *> \param[in] DIRECT
63 *> \verbatim
64 *> DIRECT is CHARACTER*1
65 *> Indicates how H is formed from a product of elementary
66 *> reflectors
67 *> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
68 *> = 'B': H = H(k) . . . H(2) H(1) (Backward)
69 *> \endverbatim
70 *>
71 *> \param[in] STOREV
72 *> \verbatim
73 *> STOREV is CHARACTER*1
74 *> Indicates how the vectors which define the elementary
75 *> reflectors are stored:
76 *> = 'C': Columnwise (not supported yet)
77 *> = 'R': Rowwise
78 *> \endverbatim
79 *>
80 *> \param[in] M
81 *> \verbatim
82 *> M is INTEGER
83 *> The number of rows of the matrix C.
84 *> \endverbatim
85 *>
86 *> \param[in] N
87 *> \verbatim
88 *> N is INTEGER
89 *> The number of columns of the matrix C.
90 *> \endverbatim
91 *>
92 *> \param[in] K
93 *> \verbatim
94 *> K is INTEGER
95 *> The order of the matrix T (= the number of elementary
96 *> reflectors whose product defines the block reflector).
97 *> \endverbatim
98 *>
99 *> \param[in] L
100 *> \verbatim
101 *> L is INTEGER
102 *> The number of columns of the matrix V containing the
103 *> meaningful part of the Householder reflectors.
104 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
105 *> \endverbatim
106 *>
107 *> \param[in] V
108 *> \verbatim
109 *> V is COMPLEX*16 array, dimension (LDV,NV).
110 *> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
111 *> \endverbatim
112 *>
113 *> \param[in] LDV
114 *> \verbatim
115 *> LDV is INTEGER
116 *> The leading dimension of the array V.
117 *> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
118 *> \endverbatim
119 *>
120 *> \param[in] T
121 *> \verbatim
122 *> T is COMPLEX*16 array, dimension (LDT,K)
123 *> The triangular K-by-K matrix T in the representation of the
124 *> block reflector.
125 *> \endverbatim
126 *>
127 *> \param[in] LDT
128 *> \verbatim
129 *> LDT is INTEGER
130 *> The leading dimension of the array T. LDT >= K.
131 *> \endverbatim
132 *>
133 *> \param[in,out] C
134 *> \verbatim
135 *> C is COMPLEX*16 array, dimension (LDC,N)
136 *> On entry, the M-by-N matrix C.
137 *> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
138 *> \endverbatim
139 *>
140 *> \param[in] LDC
141 *> \verbatim
142 *> LDC is INTEGER
143 *> The leading dimension of the array C. LDC >= max(1,M).
144 *> \endverbatim
145 *>
146 *> \param[out] WORK
147 *> \verbatim
148 *> WORK is COMPLEX*16 array, dimension (LDWORK,K)
149 *> \endverbatim
150 *>
151 *> \param[in] LDWORK
152 *> \verbatim
153 *> LDWORK is INTEGER
154 *> The leading dimension of the array WORK.
155 *> If SIDE = 'L', LDWORK >= max(1,N);
156 *> if SIDE = 'R', LDWORK >= max(1,M).
157 *> \endverbatim
158 *
159 * Authors:
160 * ========
161 *
162 *> \author Univ. of Tennessee
163 *> \author Univ. of California Berkeley
164 *> \author Univ. of Colorado Denver
165 *> \author NAG Ltd.
166 *
167 *> \date September 2012
168 *
169 *> \ingroup complex16OTHERcomputational
170 *
171 *> \par Contributors:
172 * ==================
173 *>
174 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
175 *
176 *> \par Further Details:
177 * =====================
178 *>
179 *> \verbatim
180 *> \endverbatim
181 *>
182 * =====================================================================
183  SUBROUTINE zlarzb( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
184  \$ ldv, t, ldt, c, ldc, work, ldwork )
185 *
186 * -- LAPACK computational routine (version 3.4.2) --
187 * -- LAPACK is a software package provided by Univ. of Tennessee, --
188 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189 * September 2012
190 *
191 * .. Scalar Arguments ..
192  CHARACTER DIRECT, SIDE, STOREV, TRANS
193  INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
194 * ..
195 * .. Array Arguments ..
196  COMPLEX*16 C( ldc, * ), T( ldt, * ), V( ldv, * ),
197  \$ work( ldwork, * )
198 * ..
199 *
200 * =====================================================================
201 *
202 * .. Parameters ..
203  COMPLEX*16 ONE
204  parameter ( one = ( 1.0d+0, 0.0d+0 ) )
205 * ..
206 * .. Local Scalars ..
207  CHARACTER TRANST
208  INTEGER I, INFO, J
209 * ..
210 * .. External Functions ..
211  LOGICAL LSAME
212  EXTERNAL lsame
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL xerbla, zcopy, zgemm, zlacgv, ztrmm
216 * ..
217 * .. Executable Statements ..
218 *
219 * Quick return if possible
220 *
221  IF( m.LE.0 .OR. n.LE.0 )
222  \$ RETURN
223 *
224 * Check for currently supported options
225 *
226  info = 0
227  IF( .NOT.lsame( direct, 'B' ) ) THEN
228  info = -3
229  ELSE IF( .NOT.lsame( storev, 'R' ) ) THEN
230  info = -4
231  END IF
232  IF( info.NE.0 ) THEN
233  CALL xerbla( 'ZLARZB', -info )
234  RETURN
235  END IF
236 *
237  IF( lsame( trans, 'N' ) ) THEN
238  transt = 'C'
239  ELSE
240  transt = 'N'
241  END IF
242 *
243  IF( lsame( side, 'L' ) ) THEN
244 *
245 * Form H * C or H**H * C
246 *
247 * W( 1:n, 1:k ) = C( 1:k, 1:n )**H
248 *
249  DO 10 j = 1, k
250  CALL zcopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
251  10 CONTINUE
252 *
253 * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
254 * C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T
255 *
256  IF( l.GT.0 )
257  \$ CALL zgemm( 'Transpose', 'Conjugate transpose', n, k, l,
258  \$ one, c( m-l+1, 1 ), ldc, v, ldv, one, work,
259  \$ ldwork )
260 *
261 * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
262 *
263  CALL ztrmm( 'Right', 'Lower', transt, 'Non-unit', n, k, one, t,
264  \$ ldt, work, ldwork )
265 *
266 * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
267 *
268  DO 30 j = 1, n
269  DO 20 i = 1, k
270  c( i, j ) = c( i, j ) - work( j, i )
271  20 CONTINUE
272  30 CONTINUE
273 *
274 * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
275 * V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
276 *
277  IF( l.GT.0 )
278  \$ CALL zgemm( 'Transpose', 'Transpose', l, n, k, -one, v, ldv,
279  \$ work, ldwork, one, c( m-l+1, 1 ), ldc )
280 *
281  ELSE IF( lsame( side, 'R' ) ) THEN
282 *
283 * Form C * H or C * H**H
284 *
285 * W( 1:m, 1:k ) = C( 1:m, 1:k )
286 *
287  DO 40 j = 1, k
288  CALL zcopy( m, c( 1, j ), 1, work( 1, j ), 1 )
289  40 CONTINUE
290 *
291 * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
292 * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
293 *
294  IF( l.GT.0 )
295  \$ CALL zgemm( 'No transpose', 'Transpose', m, k, l, one,
296  \$ c( 1, n-l+1 ), ldc, v, ldv, one, work, ldwork )
297 *
298 * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
299 * W( 1:m, 1:k ) * T**H
300 *
301  DO 50 j = 1, k
302  CALL zlacgv( k-j+1, t( j, j ), 1 )
303  50 CONTINUE
304  CALL ztrmm( 'Right', 'Lower', trans, 'Non-unit', m, k, one, t,
305  \$ ldt, work, ldwork )
306  DO 60 j = 1, k
307  CALL zlacgv( k-j+1, t( j, j ), 1 )
308  60 CONTINUE
309 *
310 * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
311 *
312  DO 80 j = 1, k
313  DO 70 i = 1, m
314  c( i, j ) = c( i, j ) - work( i, j )
315  70 CONTINUE
316  80 CONTINUE
317 *
318 * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
319 * W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
320 *
321  DO 90 j = 1, l
322  CALL zlacgv( k, v( 1, j ), 1 )
323  90 CONTINUE
324  IF( l.GT.0 )
325  \$ CALL zgemm( 'No transpose', 'No transpose', m, l, k, -one,
326  \$ work, ldwork, v, ldv, one, c( 1, n-l+1 ), ldc )
327  DO 100 j = 1, l
328  CALL zlacgv( k, v( 1, j ), 1 )
329  100 CONTINUE
330 *
331  END IF
332 *
333  RETURN
334 *
335 * End of ZLARZB
336 *
337  END
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:179
subroutine zlarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARZB applies a block reflector or its conjugate-transpose to a general matrix.
Definition: zlarzb.f:185
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76